Investigation of hectometric and kilometric radio emissions from Jupiter and Neptune

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Title:
Investigation of hectometric and kilometric radio emissions from Jupiter and Neptune
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viii, 209 leaves : ill. ; 29 cm.
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Wang, Liyun, 1960-
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Thesis:
Thesis (Ph. D.)--University of Florida, 1994.
Bibliography:
Includes bibliographical references (leaves 199-208).
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by Liyun Wang.
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Typescript.
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Vita.

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INVESTIGATION OF
HECTOMETRIC AND KILOMETRIC RADIO EMISSIONS FROM
JUPITER AND NEPTUNE












By

LIYUN WANG


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENT IS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


1994


















To my mother, wife, and lovely daughter
for their love, encouragement and endless support

.. -^^}am















ACKNOWLEDGEMENTS


First of all, I would like to express my deepest gratitude to Dr. Thomas D. Carr,

chairman of my supervisory committee, for his guidance and support during my years

at the University of Florida. He suggested this topic and was a major influence in its

development.

I would wish to thank Dr. Alex G. Smith, Dr. John P. Oliver, Dr. George R.

Lebo, and Dr. Henri A. Van Rinsvelt, members of my supervisory committee, for

their advice and many helpful suggestions. I also wish to acknowledge valuable help

from Dr. Kwan-yu Chen.

Further, I would like to thank the entire Department of Astronomy for the en-

couragement, support and friendships they have provided.

My deepest love and gratitude go to my family, especially to my mother and wife,

for their tremendous encouragement, understanding, patience, support, and sacrifice

during all these years of my study. I should also express my appreciation to my lovely

daughter, Christine, for filling my family with all the joy and happiness.

This research project has been supported primarily by grants from the National

Aeronautics and Space Administration, and has been benefited from the support of

low frequency planetary radio astronomy research by the National Science Foundation

at the University of Florida.















TABLE OF CONTENTS



Page


ACKNOWLEDGEMENTS ............................ iii

ABSTRACT .................................... vii

CHAPTERS

1 INTRODUCTION ............................... 1


2 THE VOYAGER PRA EXPERIMENT AND ITS ANTENNA CALIBRA-
T IO N . . . . 6

2.1 Description of the Voyager PRA Experiment ............. 8
2.2 Calibration of the PRA Antenna for Polarization Sense Measurement 9
2.2.1 Polarization Response of the PRA Antenna ......... 9
2.2.2 Antenna E-plane Calibration for Sources in a Particular Az-
im uth Region ........................... 16
2.2.3 Full Calibration Based on all Usable Events ......... 24
2.2.4 Discussion .... ... .. .. .... ... .. .. .. .. 28
2.3 The PRA Data Base at the University of Florida .......... 29

3 A BRIEF REVIEW OF JUPITER'S RADIO EMISSIONS ........ 33

3.1 The Synchrotron Radiation (DIM) .................. 35
3.2 Decametric Radiation .......................... 36
3.3 Hectometric Radiation ......................... 39
3.4 Kilometric Radiation .......................... 40
3.5 Power Spectrum .............................. 41

4 JUPITER'S HECTOMETRIC RADIO EMISSIONS . .... 43

4.1 Characteristics of the HOM Emission . . ... 43
4.1.1 Frequency Coverage . . . 44
4.1.2 Intensity Profile in CML .................... 46








4.1.3 Magnetic Latitudinal Beaming . . .
4.1.4 Polarization . . . .
4.1.5 Solar W ind Control ........................
4.1.6 Propagation Effect from the lo Plasma Torus . .
4.2 Emission Mechanisms . . . ..
4.2.1 The CMI Theory ........................
4.2.2 Indirect Emission Mechanisms . . .
4.3 M odeling . . . . .
4.3.1 Equatorial Beaming Models . . .
4.3.2 Model Assumptions ........................
4.3.3 The Beaming Geometry . . .
4.3.4 Modeling Procedures and Results . .
4.3.5 Discussion . . . .

5 STUDY OF THE HOM EMISSIONS VIA RAYTRACING ........

5.1 The Necessity of Raytracing Studies of the Jovian HOM Emission
5.2 Early Raytracing Studies on the HOM Emissions . .
5.3 Formulation of Ray Equations . . .
5.4 Procedures of Solving the Ray Equations . .
5.5 Magnetic Field Model and Magnetospheric Plasma Model .
5.6 Two-dimensional Raytracing Result . . .
5.6.1 R-X M ode .. .. ... .. .. .. .. ... .. .. .. .. ..
5.6.2 L-O M ode .. .. ... .. .. .... ... .. .. .. .
5.7 Three-dimensional Raytracing Result . . .
5.8 HOM Source Localization via Raytracing . .

6 A MODEL OF NEPTUNE'S SMOOTH RADIO COMPONENT ......


Introduction ...............
The Neptunian Magnetic Field Models
Plasmasphere Model . .
M odeling .................
Discussion ................


7 SUMMARY AND CONCLUSIONS . . .


APPENDICES

A REFRACTIVE INDEX AND RAY EQUATIONS ...............

A.1 Refractive Index and the Appleton-Hartree Formula .........
A.2 Ray Equations and Relevant Terms ................ ..








B THE JOVIAN AND NEPTUNIAN MAGNETIC FIELD MODELS .... 181

B.1 Models Without External Terms .................... 182
B.2 Models With External Terms ..................... 187

C TRANSFORMATION OF SPACECRAFT COORDINATE SYSTEMS 191

C.1 Transformation at a Given Catalog Time ............... 192
C.2 Transformation at any Given Time .................. 195

REFERENCES ................................... 199

BIOGRAPHICAL SKETCH ............................ 209















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment
of the Requirements for the Degree of
Doctor of Philosophy

INVESTIGATION OF
HECTOMETRIC AND KILOMETRIC RADIO EMISSIONS FROM
JUPITER AND NEPTUNE

By

LIYUN WANG

August 1994

Chairman: Thomas D. Carr
Major department: Astronomy

This dissertation concerns radio emissions at hectometric and kilometric wave

lengths from the planets Jupiter and Neptune, as observed with the Planetary Radio

Astronomy (PRA) experiment on board the two Voyager spacecraft.

The PRA antenna system is found to be incorrectly calibrated in early work, and

the system is recalibrated for polarization sense determination. It is concluded that

the PRA antenna E-surface is not a plane as had previously been supposed that

its tilt can be significantly different at different azimuths. It is suggested that a tilt

of 270 and 450 of the "E-plane" be used when the observed radiation arrives from the

front and back sides of the antenna system, respectively.

New observational results of the Jovian hectometric (HOM) emission are pre-

sented. Characteristics of the HOM emission are thoroughly discussed. It is found

that the HOM emission at different frequencies is beamed into different magnetic lat-

itudes. The beaming profile is shown to contradict the generally accepted belief that








refraction of rays passing through the Io plasma torus is solely responsible for the

beaming. A beaming model of the HOM emission is established that can account for

the major characteristics of the HOM observation. Raytracing (both two-dimension

and three-dimension) is performed over the entire frequency range of the HOM emis-

sion, and it is concluded that the presence of the lo plasma torus can affect only to

a certain extent the propagation of the HOM emission, but it is not responsible for

the magnetic equatorial beaming and for the shadowing of the emission. A special

spacecraft maneuver event is used in searching for the HOM source location with help

of the raytracing technique; the result is found to be consistent with those predicted

by our beaming model.

Finally, the Voyager 2 observation of the Neptune kilometric radiation (NKR) is

reviewed. A similar modeling process is applied to the NKR modeling, but a more

realistic magnetic field model is used in the modeling process. Results that fit the

observation of the NKR smooth component are presented. A plasmaspheric model

based on the source location as determined in the beaming model is also presented.















CHAPTER 1
INTRODUCTION



Among the nine known planets of the solar system, Jupiter, Saturn, Uranus, and

Neptune are classified as the giant or Jovian planets. They are strikingly similar,

and are very much different from the terrestrial planets (Mercury, Venus, Earth and

Mars). Next to the Sun, Jupiter is by far the most massive object in the solar system,

and the combined mass of all the Jovian planets is over 200 times that of terrestrial

planets. In contrast to the terrestrial planets, which are relatively small and light

and are composed mainly of rock, the Jovian planets are huge and massive, yet their

average mass densities are surprisingly low (in the range of 0.7 to 1.8 g/cm3). Their

chemical compositions are mainly hydrogen and helium, mixed with much smaller

amounts of methane (CH4), ammonia (NH3), water (H1120) and other compounds.

Each of the Jovian planets probably has a relatively small rocky core and a mantle

composed of either liquid metallic hydrogen or liquid water, ammonia, and methane,

but does not have a solid surface. Although the Jovian planets are much larger

and more massive than Earth, they all rotate faster than Earth and in the same

direction, with the exception of Uranus (due to some ancient impact that tilted its

rotation axis past 900). An outstanding feature of the Jovian planets is their powerful
global magnetic moments (among the terrestrial planets only Earth has an appreciable

magnetic field). The main type of markings on the visible disks of the Jovian planets

are the bands of clouds that run parallel to the equator. As a result of complex and

variable patterns of atmospheric winds, the cloud bands at different latitudes indicate








slightly different planetary rotation periods (which is approximately 10 hours in the

case of Jupiter). Before the discovery of the Jovian radio emissions and through

them the Jovian magnetic field, it was customary to specify the central meridian

longitudes of Jupiter's visible markings in terms of one or the other of two standard

longitude systems based on assumed rotation periods differing by about 5 minutes

(although the visible features never remained stationary in longitude in either system

for long at a time). Radio astronomy, however, made possible the measurement of the

highly stable rotation period of the Jovian interior, because it is believed that episodic

radio emissions are locked in phase with the rotation of Jupiter's magnetic field and

therefore the electrically conducting deep interior of the planet. It is the magnetic

fields the Jovian planets possess that are responsible for most of the phenomena with

which this dissertation is concerned.

The accidental discovery in 1955 of non-thermal radio emissions from Jupiter in

the decametric wavelength band (nominally 3 to 30 MHz) [Burke and Franklin, 1955;

Franklin and Burke, 1956] marked the beginning of planetary radio astronomy. Since

this discovery, the Jovian decametric radiation has been studied intensively from

ground based radio observatories and from spacecraft. No emission in the decametric

band has been observed from any other planets, except for the so-called Saturn Elec-

trostatic Discharges or SEDs (presumably lightning transients) that were observed

by the Voyager spacecraft. Radiation from the Jovian planets at lower frequencies,

in the hectometer and kilometer wavelength bands, is blocked out by the Earth's

ionosphere and was not detected until observations from Earth orbiting satellites and

other spacecraft became available. These lower frequency emissions from all four of

the Jovian planets were first investigated by the two Voyager spacecraft.

Soon after the 1955 discovery of the Jovian decametric emission (DAM), several

investigators found that the probability of detecting Jovian activity was dependent








upon the central meridian longitude (CML) of the observer. It was found that his-

tograms of Jovian activity as a function of CML remain relatively stationary in lon-

gitude over a time span of a decade or more if a rotation period about 0.5 minutes

longer than the so-called System II period (based on an early estimate of the mean

rotation period of visible features outside the equatorial zone) is invoked. The System

III longitude (Aml) rotation period, 9h55m29!71, is based in part on such decametric

observations. This is the period of rotation of the Jovian magnetic field. The DAM

source longitude regions were named A, B, and C, according to their relative strengths

at an intermediate decametric frequency. The two main sources, A and B, have now

been recognized to be due to the two edges of a hollow cone beam originating from a

common location.

Bigg [1964] discovered that the orbital phase of the Galilean satellite Io (Io),

measured from the superior geocentric conjunction, also had a profound effect on the

occurrence of the Jovian DAM emission: A very large enhancement in the detection

probability for lo phase angles of 900 and 2400 was found. In the two-dimensional

picture of dynamic interaction between the planet and the satellite Io, the regions

of (AIII,
named Sources Io-A, Io-B, Io-C and Io-D; those regions showing no Io dependence

become non-lo-A, non-lo-B, non-Io-C, etc. [Carr et al., 1983]. Also from long term

ground-based observations, it was learned that the occurrence of DAM varies with

the 12-year periodicity of the observer's Jovicentric declination or DE [Carr et al.,

1970].

The first detection of radio emission from Jupiter at frequencies higher than those

of the DAM bursts was in the centimeter-wavelength band, at about 9500 MHz [Mayer

et al., 1958]; this continuous emission was later shown to be thermal radiation from

the Jovian atmosphere. Subsequently, a non-thermal component of continuous emis-

sion was discovered in the decimetric-wavelength band at frequencies considerably








higher than the 40 MHz upper limit of the DAM bursts (see Berge and Gulkis [1976]

and references therein). As a result of extensive observational and theoretical inves-

tigations, it was shown that this non-thermal component was synchrotron emission

from high energy electrons trapped in Jovian Van Allen belts, located between 1.6

and 3 Rj (1Rj = 71,372 km) at equatorial latitudes. This was the first positive proof

that any planet other than Earth has a magnetic field, although it had been suggested

earlier that a Jovian field is involved in the emission of the DAM bursts [Carr, 1959].

Before the spacecraft age, Jupiter's magnetic field could be studied only remotely,

from groundbased observations of the radio emissions. Other Jovian planets' magnetic

fields were not known until the in situ measurements from spacecraft were made. The

first in situ measurements of Jupiter's (and Saturn's) magnetic fields were made by

four spacecraft: Pioneer 10 in 1973, Pioneer 11 in 1974, Voyager 1, and Voyager 2

(both in 1979). The first indication that Uranus and Neptune also possess magnetic

fields was from the Voyager 2 observation of the non-thermal radio emission, and then

from the in situ measurements during Voyager 2's flyby of these two planets in early

1986 and 1989, respectively.

In this dissertation I will present results from my research on the radio emis-

sions from Jupiter in the hectometric and the adjacent part of the kilometric bands,

and those from Neptune in the kilometric band, observed mainly from the Voyager

spacecraft. I will first present in Chapter 2 the result of our Voyager PRA antenna

calibration which will be used in later chapters to correctly interpret the polarization

sense of the observed radiation and to locate the Jovian radio sources at hectometric

wavelengths. An overview of various components of Jupiter's radio emissions will

be made in Chapter 3 before I discuss in great details the Jovian hectometric radia-

tion. Chapter 4 will be devoted solely to the study of the Jovian hectometric radio

emission. Various characteristics of this emission component will be discussed; many

data analysis results that have never been seen in the literature will be presented.





5


Theoretical models that account for many, if not all, observational characteristics of

this emission component will be then presented. In Chapter 5, I will continue to in-

vestigate in detail the propagation of Jupiter's hectometric radio waves in the Jovian

magnetosphere by using a raytracing program that I developed. Results of source

localizations via the raytracing technique will be presented and compared with those

obtained in Chapter 4. In Chapter 6, results of observation and modeling of the Nep-

tune smooth kilometric emission will be presented. I will conclude this dissertation

in Chapter 7 with some discussions and a summary.















CHAPTER 2
THE VOYAGER PRA EXPERIMENT AND ITS ANTENNA CALIBRATION



The passage of Voyager 2 by Neptune in late August 1989 marked the end of

an amazingly successful program of exploration of the outer planets. During the

missions of the two Voyagers, the Planetary Radio Astronomy (PRA) measurement

system recorded spectral intensity distributions of low frequency radio emissions from

Jupiter, Saturn, Uranus, and Neptune. The PRA observations yielded a huge amount

of data which has been and will long continue to be of great importance in developing

an understanding of source locations and beaming geometry, emission mechanisms,

and relationships of the radio sources to their magnetospheric environments. The

PRA data bank is an invaluable scientific resource. It may remain the only such data

we have for decades to come, particularly in the case of Uranus and Neptune.

The PRA experiment on board both Voyagers is identical and is designed to re-

ceive whatever decametric, hectometric, or kilometric radio signals might be observed

from the vicinity of each of the radio planets Jupiter, Saturn, Uranus, and Neptune.

Its primary goals were of course to locate the radio sources, to determine their emis-

sion beaming patterns, and to ascertain the magnetoionic mode of the radiation.

Unfortunately, the PRA antenna was not designed for direction finding. Since the

spacecraft was three-axis stabilized, the antenna beam could not execute the repeated

scans across the source that might have provided direction information. However, in

the vicinity of each planet the spacecraft was occasionally made to execute a complete

or partial rotation in a relatively short time, usually causing the antenna beam to








be scanned once across the source direction. Although the moving antenna beam in

such cases was much too broad to produce a sufficiently sharp pattern of intensity

modulation of the received radiation from which useful source directional information

could be derived, the sweeping of the electric plane1 of the antenna system across

a source direction sometimes produced a relatively abrupt reversal of the indicated

sense of elliptical polarization. Measurements have previously been made of the an-

tenna E-plane orientation relative to the spacecraft as deduced from the observed

times of occurrence of polarization reversals during spacecraft maneuvers, using an

assumed location of the calibration source (which was at Saturn in some cases and at

Uranus in others) [Ortega-Molina and Daigne, 1984; Lecacheux and Ortega-Molina,

1987; Ortega-Molina and Lecacheux, 1990; Sawyer et al., 1991]. In this chapter I will

demonstrate that when the best of these previous E-plane orientation calibrations

are used to obtain directional information from other sources, impossible results can

be obtained. From previously unused spacecraft-maneuver observations of a Jovian

source made under particularly favorable conditions, I will derive a corrected value of

the relative orientation of the antenna E-plane which is much different from the cur-

rently accepted value. I will make other determinations from observations obtained

during other spacecraft rotation-maneuvers that suggest that the tilt of an assumed

antenna E-plane is different when the source is to the rear of the plane formed by the

PRA orthogonal monopole pair than it is when the source is forward of this plane.

Calibration data will be provided in the form of the tilt angles of the effective E-plane

as a function of the azimuth of the source (in the antenna monopole coordinate sys-

tem). I believe that the new calibration data can make possible correction of previous


1The electric plane, or "E-plane", of an antenna is that plane upon which is pro-
jected the component of the incident-wave electric field vector that is effective in
exciting the antenna. In the present case it is also the plane dividing the directions
of incident rays for which the indicated elliptical polarization sense is correct from
those for which it is reversed.








erroneous conclusions regarding the true polarization sense of a significant amount of

the radiation received by the Voyagers from Jupiter, Saturn, Uranus, and Neptune,

from direction angles greater than 450 with respect to the normal to the monopole

antenna plane. The result of this newly calibrated data will be applied in Chapter 5

to locate the Jovian HOM emission source.


2.1 Description of the Voyager PRA Experiment


The Voyager PRA Experiment consists of a pair of 10-m orthogonal monopoles

connected to a high sensitivity broadband stepped-frequency receiver covering the

range 1.2 kHz to 40.2 MHz. The signals from the two antennas are added in phase

quadrature by two switchable quarter wave hybrids in order to send alternately the

apparent right hand (RH) and left hand (LH) circularly polarized components of

the observed emission to the receiver. There were actually two receivers on each

spacecraft, for the lower and higher frequency ranges, respectively. The low-frequency

(LF) band receiver had 70 channels of 1.0 kHz bandwidth each, with center frequencies

spaced at 19.2 kHz intervals from 1.2 kHz to 1326 kHz. The high-frequency (HF) band

receiver consisted of 128 channels of 200 kHz bandwidth each, with center frequencies

spaced at 307.2 kHz intervals from 1.2 MHz to 40.4 MHz. The HF band receiver was

designed especially for the observation of Jovian decametric radio emissions.

The PRA experiment can be operated in six modes but only three of them were

operated to a large extent in the mission during each of its encounters with a planet.

One of the basic routine modes is called the POLLO sweeping mode, in which the

receiver sweeps and samples all its 198 frequency channels in 6 seconds, dwelling at

each frequency channel for a total of 30 msec and measuring alternately flux densities

of RH and LH circular polarizations. (There are additional 2 channels being used

to store "housekeeping" data describing the experiment's status.) From one step to








the next during the channel switching sequence, the antenna polarization sense is

reversed, i.e., it is changed from RH to LH or vice versa. At a given frequency the

left and right circular components are not observed simultaneously but alternately at

consecutive (6-sec interval) frequency sweeps; in other words, measurements of both

polarizations can be obtained in opposite polarizations at two adjacent frequencies

in 30 msec or at the same frequency in 6 seconds. The time required for making a

measurement of both the RH and LH intensity components at both senses of elliptical

polarization at a given frequency was therefore 12 sec. The PRA experiment can

be also operated in other special high-rate modes. For example, in FIXLO mode,

the receiver performs over an integer number of telemetry frames (48 sec), with a

high time resolution (30 ms), on selected groups of three channels, each frequency

being sampled consecutively with alternated polarization state during 6 seconds. In

so-called PHIEX mode, which is designed for high time resolution, fixed-frequency

observations and is operated only at selected times, the instrument simultaneously

observes signals in two adjacent channels. The resolution of the data obtained in this

mode is 140 ps. Much more detailed descriptions of the PRA experiment are given

by Warwick et al. [1977] and by Lang and Peltzer [1977].


2.2 Calibration of the PRA Antenna for Polarization Sense Measurement


2.2.1 Polarization Response of the PRA Antenna


Since the Voyager spacecraft was three-axis stabilized, and the only signals ob-

tained from the PRA experiment were the intensity outputs from the receiver, the

PRA experiment was not able to completely determine the polarization status (the

four Stokes parameters) of the incoming radio waves. Ideally, however, if the two

monopoles together with the spacecraft body were equivalent to a pair of orthogo-

nal dipoles in free space and if a source being observed were located in the positive








direction of the axis perpendicular to the two dipoles, the indicated RH and LH re-

ceiver outputs (background-subtracted) would actually be the RH and LH circularly

polarized intensity components of the radiation, and the apparent polarization ratio

(defined as [IL-IR]/[IL+IR], where IL and IR are the indicated LH and RH intensity

outputs of the receiver) would be the true degree of circular polarization. The sources

that were actually observed, however, were almost always considerably offset from

the axis perpendicular to the equivalent dipoles. Furthermore, unwanted coupling

between the two monopoles due to other structures projecting from the spacecraft

had resulted in a certain amount of contamination of both the RH and LH outputs.

Thus the measured Voyager RH and LH elliptically polarized intensity components

uniquely define neither the polarization ellipse of the incident radiation nor its true

RH and LH circularly polarized intensity components. The only Voyager polarization

measurement that can be made unambiguously is the sense of elliptical or circular

polarization, and only if it is known on which side of the E-plane the source lies.

The indicated sense becomes incorrect when a source direction crosses the E-plane

in passing to the lower side. That is, the sign of the apparent polarization ratio is

opposite from that of the true degree of circular polarization on the lower side of the

antenna E-plane, but is correct on the upper side.

The two orthogonal 10-meter monopoles are insulated from the spacecraft body.

As previously indicated, each monopole together with the spacecraft body, includ-

ing its projecting structures, acts as a dipole. Since each monopole resonates as a

quarter-wave element at about 7.5 MHz, and the spacecraft body together behave

more or less like a free-space half-wave dipole in the vicinity of this frequency. Thus

for all frequency channels of the low-band receiver, i.e., at 1326 kHz and below,

the equivalent dipole corresponding to each monopole has approximately the "short

dipole" frequency-independent directional E-field pattern (for which the field strength

of a transmitted signal at a fixed distance is proportional to the sine of the direction










Spacecraft Symmetry Plane Plane of Telemetry Dish


z Z
I I

*-- X ---------------------
400 ----.
S ..............








-:Electric Plane
-- (Front

Electric Plane
(B a -. -







Magnetometer Boom /. X. Monopole Plane




Figure 2.1. Coordinate systems used in the PRA experiment on board the Voyager
spacecraft. The Xm and Ym axes correspond to the directions of two monopoles,
and the negative direction of the Zm axis is that of the magnetometer boom.



angle with respect to the dipole). The longest of the projecting structural features

of the spacecraft body is the 13-meter magnetometer boom, which is perpendicular

to both monopoles. The spacecraft is approximately bilaterally symmetrical about

the plane that contains the magnetometer boom and bisects the 900 angle between

the two monopoles. The aperture plane of the paraboloidal telemetry dish (3.7 m in

diameter) is perpendicular to the symmetry plane.

To make our description easier, we establish some relevant coordinate systems

which are shown in Figure 2.1. The Voyager structural geometry is also illustrated in

figures in papers by Warwick et al. [1977] and by Ortega-Molina and Daigne [1984].








In the spacecraft coordinate system, [X, Y, Z], the Y axis lies along the intersection

of the spacecraft symmetry plane and the telemetry dish plane, its positive direction

being the one which is farther from the magnetometer boom2. The Z axis is perpen-

dicular to the dish aperture plane, its positive direction being the farther one from the

magnetometer boom. This coordinate system is used in the Voyager SEDR (Supple-

mentary Experimental Data Record) ephemeris files for expressing spacecraft-centered

positions and directions. In the PRA antenna coordinate system, [Xm, Ym, Zm], the

Xm and Ym axes are defined by the directions of the two monopoles, and the negative

direction of the Zm axis is that of the magnetometer boom.

Unfortunately, it was not feasible to measure the directional and polarization char-

acteristics of the PRA antenna system prior to the Voyager launching. However,

while the system was under development, Sayre [1976] approximated its directional

characteristics at frequencies of 0.25, 0.5, and 2.5 MHz by numerical modeling and

simulating the shape of the spacecraft body and its projecting structures. Sayre's

report, which was not published, contains PRA antenna directional patterns that

are relevant to our investigation. These plots have apparently not been used in re-

lated investigations, except for being briefly mentioned by Ortega-Molina and Daigne

[1984]. We reproduce in Figure 2.2 Sayre's unpublished Voyager PRA antenna di-

rectional E-field patterns at 0.5 MHz for the Xm monopole (in combination with the

spacecraft body) in the XmZm and YmZm planes, and also for the Ym monopole in

these two planes. The sharply defined diametrically opposite minima in each of these

patterns are in the directions closest to the line along which the equivalent dipole

lies. The following information can be deduced from the plots of Figure 2.2: (1) Each

monopole pattern is approximately that of a short dipole which is tilted from the


2The boom supporting the instrumentation platform extends about 4.5 m approx-
imately in the positive Y-axis direction, and the nuclear-electric power supply boom
extends about the same distance in the opposite direction; these features are not
indicated in Figure 2.1.








Cross-Polarized Gain () = 90, 270 Plane)
"


a) PRA X-Directed Monopole



Cross-Polarized Gain ( = 0', 1800 Plane) Cross-Polarized Gain ( = 90*, 270 Plane)













Is b) PRA Y-Directed Monopole iW


Figure 2.2. The PRA antenna directional patterns at 0.5 MHz for the Xm
monopole in the XmZm and YmZm planes (a), and for the Ym monopole in these
two planes (b), reproduced from a numerical simulation modeling by Sayre [1976].



monopole direction, the dipole centers being approximately at the intersection of the

two monopoles. (2) The two equivalent dipoles are not perpendicular, but intersect

in the present case at an angle of about 1370; this intersection angle is bisected by the

spacecraft symmetry plane. (3) The normal to the plane (on its "front" or positive

side) that is defined by the two equivalent dipoles lies within a degree of the spacecraft

symmetry plane, and is tilted 550 from the normal to the monopoles, in the direction

away from the telemetry dish aperture plane.








In Figure 2.1, the orientation of the [x, y, z] coordinate system is determined by

that of the assumed equivalent crossed free space dipoles, which are not necessarily

orthogonal. These dipoles, the positive half of each of which is indicated by a dotted

line in the figure, determine the xy plane. The dipole nearest the x axis will be re-

ferred to as the x equivalent dipole, and that nearest the y axis as the y dipole. They

correspond, respectively, to the Xm and Ym monopoles. The x and y axes are sym-

metrical about the spacecraft symmetry plane, as are the x and y equivalent dipoles.

The angle of intersection of the E-plane (xy) with the monopole plane (XmYm) is /3,

as is the intersection angle of the z axis with the Zm axis. The direction of a radio

source can be expressed by the colatitude and azimuth with respect to either the

[Xm, Ym, Zm] system or the [x, y, z] system. Transformation from the [Xm, Ym, Zm]

system to the [x, y, z] system can be done through the matrix M:

M = R3(-45) R2(-fl) R3(450)

where R2 and R3, which are rotation matrices about the y and z axes, are expressed

as:

cos a 0 sin a cos a sin a 0
R2(a)= 0 1 0 R3(a)= -sina cosa 0 .
sin a 0 cos a 0 0 1

Ortega-Molina and Daigne [1984] developed an analytical model of the Voyager

PRA antenna system, based on equivalent tilted and not necessarily orthogonal

crossed dipoles. Leblanc and Daigne [1984], Lecacheux and Ortega-Molina [1987],

and Leblanc et al. [1987] identified a number of instances of purely instrumental

polarization reversals that occurred during spacecraft maneuvers when radiation was
being received from Jupiter, Saturn, and Uranus. Although it had long been known

that a reversal of the indicated sense of polarization would occur if the antenna E-

plane swept across an elliptically or circularly polarized source, the first quantitative

demonstration of such instrumental reversals (and the first actual measurement of








the relative orientation of the E-plane) was provided by Lecacheux and Ortega-Molina

[1987]. They found from the analysis of a set of such events, that had been observed

with the low-band receiver channels during the Saturn and Uranus encounters, that

regardless of the initial state of polarization of the radiation, the instrument has a

null-polarization response for a set of source directions that lie approximately within

a plane. In each case the polarization sense became reversed from its initial sense as

the plane was crossed by the source direction vector. They interpreted this plane as

the E-plane of the equivalent crossed short dipoles. Assuming the Saturnian source

to be located as proposed by Kaiser and Desch [1982], which was later confirmed

by Lecacheux and Genova [1983], and the Uranian source to be located at the cen-

ter of the planet, they calculated the approximate orientation of the E-plane in the

coordinate system of the spacecraft. They found the E-plane tilt angle / in Figure

2.2 to be about 23?3 and the equivalent dipole intersection angle to be 900100. We

note that this value of I is less than half that found by Sayre, but that our initial

and most accurately determined value, to be presented below, is in general agreement

with Sayre's.

Ortega-Molina and Lecacheux [1990] deduced from a combined analytical study

and statistical investigation of a considerable amount of kilometric radiation data

from Saturn that the equivalent dipole intersection angle is 82?61?8. Their method

required the assumption that the Saturnian kilometric radiation is always 100 percent

circularly polarized, in opposite senses for two assumed polar sources. They presented

evidence that this assumption is correct. In their analysis, the E-plane tilt angle #

could not be measured. There is a large difference in the Ortega-Molina and Sayre

values of the equivalent dipole intersection angle.

Ortega-Molina and Lecacheux [1991] and Pedersen et al. [1992] have subsequently

attempted to use the foregoing E-plane orientation calibration data to deduce source

location information from spacecraft-maneuver polarization-reversal events occurring








during the Jupiter and Neptune encounters. As I have stated previously, however, I

will demonstrate that the directional calibration used by these investigators can lead

to improbable results. It is attributed to their use of spacecraft-maneuver polarization

reversal (referred to as SMPR hereafter) events for the E-plane calibration that did

not meet the selection criteria that are outlined below.


2.2.2 Antenna E-plane Calibration for Sources in a Particular Azimuth Region


Choosing optimum spacecraft-maneuver polarization reversal events I have ini-

tially attempted to recalibrate the relative orientation of the PRA antenna E-plane

using particularly favorable and previously unused SMPR events that occurred near

Jupiter. For these events I was able to derive enough independent information about

the magnetospheric location of the sources so that their offset from the center of the

planet could be estimated with the required accuracy. (The SEDR ephemeris tape

provided precise locations of the center of the planet at regular intervals.) In choosing

suitable SMPR events with which to make the calibration, the following conditions

were favored: (a) the ratio of the intensity of the received radiation to the spacecraft

background noise level must be relatively high; (b) the received radiation must have a

relatively high degree of circular polarization; (c) the geometry must be such that the

spacecraft maneuver produces large changes in the angle between the radius vector to

the planet and the antenna E-plane both before and after this angle passes through

zero; (d) the radiation must have been emitted from only one source, as indicated

by the uniqueness and sharpness of the transition from the initial apparent polariza-

tion sense to the opposite one, and the uniformity of this reversal over a wide range

of frequencies. During the Voyager flybys of Jupiter, Saturn, Uranus, and Neptune

many spacecraft maneuvers were made, but only a few of them that satisfy the above

criteria were found. The three best events for E-plane calibration took place during










BG: 26.5 dB
3 q" .r"


2.5 3.0 3.5
SCET (HOURS ON DAY 65, 1979)


Figure 2.3. A spacecraft-maneuver polarization reversal (SMPR) event recorded
by the Voyager 1 PRA experiment in the low-frequency-band channels on March
6 (day 65), 1979. Panel (a) is the total flux density as a function of time and
frequency, with darker shades of gray indicating higher intensities. Panel (b)
indicates the apparent sense of elliptical or circular polarization as a function of
time and frequency, with the LH sense represented by black and the RH by white;
gray regions are for other cases.



the encounter with Jupiter; they are the ones upon which our initial calculations are

based.

Initial E-Plane Calibration from Three Selected Events The best of the three

above-mentioned SMPR events was a near-perfect one that occurred between about

02:54 and 03:19 SCET (spacecraft event time) on March 6 (day 65), 1979, when

Voyager 1 was about 15 Rj from Jupiter's center. This is illustrated in Figure 2.3.

Panel (a) shows the total intensity as a function of time and frequency (darker shades

of gray indicate higher intensities). Panel (b) indicates the apparent sense of elliptical


VOYAGER 1
310.


4682
I723600

2700

1800


S0.4

0
z
0.8
u-

1.2




N 0.4


12
0 0.8
U .


1.2


4.0


-100


. . .









a) b) _-- 'b)
S= 8-23.3= 0 3 .00
150' 50*


100o t 03: 12
-- - - -
U -- -- -


S 2.5 3 3.5 4 160" 180 200" 22* 240" 260" 280"
SCET (HOURS ON DAY 65, 1979) AZIMUTH


Figure 2.4. (a) Colatitude of the center of Jupiter with respect to the positive
normal to each of three planes associated with the PRA antenna, as a function
of Spacecraft Event Time (SCET) during the SMPR event of Figure 2.3. The
indicated values of 3 are the tilt angles of the three planes from the monopole
plane, for which /3 = 00 (see Figure 2.1). (b) The above colatitudes have been
replotted as functions of the azimuths about the respective positive normals to
the above three planes; the symmetry plane lies at 450 azimuth in each case.


polarization as a function of time and frequency. In this panel the polarization sense as

indicated by the PRA receiver is left-handed in the black regions and right-handed in

the white regions. Gray regions can indicate linearly polarized radiation, unpolarized

radiation (not believed to occur in the Voyager data), no radiation at all, or radiation

having two components (from separate sources) of approximately equal intensities

and axial ratios but opposite senses of elliptical or circular polarization. During the

spacecraft maneuver, Jupiter's direction angle in the monopole coordinate system

[XmYmZm] changed more than 700 in colatitude and more than 1000 in longitude.

Figure 2.4a shows the time variation of the colatitude of Jupiter's center as expressed

in the equivalent-dipole coordinate system [xyz] for each of three assumed values of

the tilt angle /3 of the xy plane (E-plane) with respect to the XmYm plane monopolee

plane). The upper curve, for 3 = 00, is the one that would apply if the E-plane

coincided with the monopole plane. The middle curve should be used if /3 = 23?3 as

found by Lecacheux and Ortega-Molina [1987]. The lower curve is applicable if a value

of /3 calculated below, 450, is the correct one. It is apparent that before the spacecraft

maneuver began, Jupiter's center and also all possible positions of the radio source








were far south of the assumed E-plane for each of the curves. Thus at every frequency

in Figure 2.3b the indicated polarization sense was opposite to the true sense before

the maneuver began, but was correct after the maneuver. We can rule out the # = 00

curve without consideration of the actual source location relative to Jupiter's center.

For any reasonable assumed offset of the source from the center of the planet the

polarization sense reversal as indicated in Figure 2.4a for / = 00 would have been

marginal if it had occurred at all, whereas the actual reversal shown in the figure is

not at all marginal. The three curves in Figure 2.4b are plots of colatitude (from the

z axis) as a function of azimuth (in the xy plane) for the 0 values 0, 23?3, and 450. It

is apparent that for the f values 23?3 and 450 the azimuths at which the polarization

reversals take place (i.e., at which the curves cross 0 = 900) differ by only 100, and

the times of the reversals differ by slightly more than a minute.

The event displayed in Figure 2.3 clearly demonstrates that the lower limit of

Jupiter's predominantly hectometric component can be as low as 100 kHz, extending

deep into the kilometric band. It also shows that there is an actual reversal of po-

larization sense at a frequency near 500 kHz. The true polarization sense was LH for

frequencies above a somewhat variable boundary in the vicinity of 500 kHz and was

RH for frequencies below this boundary. The spacecraft was in the southern Jovian

magnetic hemisphere at the time of the event. If we make the usual assumption that

the radiation is emitted in the X mode simultaneously from magnetically conjugate

sources in opposite auroral zones, and we assume that in this case the contribution

of the nearer southern hemisphere source to the received radiation was greater than

that of the northern source, then the observed polarization sense at frequencies above

about 500 kHz is correctly explained. Two possible explanations of the reversed po-

larization sense below 500 kHz are that (a) although the emission from the conjugate

sources is still in the X mode, the frequency dependence of their emission beams has

caused the intensity contribution from the northern source to exceed that from the








southern one despite the latter being the closer, or (b) the lower-frequency emission

from the two conjugate sources was predominantly in the 0 mode. We are not con-

cerned here with the true polarization sense of radiation at frequencies less than 500

kHz.

Figure 2.3 clearly shows that the reversal of the apparent polarization sense at

most frequencies between 100 and 1300 kHz occurred simultaneously to within one

48-sec pixel width. The reversal time was 03:06 SCET. If the source were located at

the position of the center of the planet, the polarization reversal times for assumed

E-plane tilts of 23?3 and 450 would be the times at which the corresponding curves

cross the 900 colatitude line in Figure 2.4. Although the fact that the f3 = 23?3

curve crosses this line considerably after 03:06 SCET suggests that this value of the

E-plane tilt angle is unrealistic, such a conclusion is not yet justified because the

effect of the offset of the true source position from the center of the planet has not

been taken into consideration. However, Figure 2.5 shows clearly that this is indeed

the case. The four oval-shaped curves in Figure 2.5 represent the colatitude of the

radio horizon as a function of azimuth (in the monopole coordinate system) at a

frequency of 1 MHz as seen from the spacecraft at the SCETs of 03:03, 03:06, 03:09,

and 03:12, respectively. By radio horizon we mean the set of directions of the locus

of the points of tangency of the straight lines3 from the spacecraft to the surface at

which the electron cyclotron frequency fc equals the frequency of observation. The

OTD magnetic field model was used in the horizon calculations. At a given time

the points representing the directions of the radio source at 1 MHz must lie on or

inside the corresponding horizon oval. The dotted curves intersecting the ovals are

plots of colatitude versus azimuth for assumed E-planes having tilt angles # (from


3The ray tracing investigations presented in Chapter 5 indicate that refraction of
rays penetrating the lo plasma torus can be neglected at the relatively high frequency
of 1 MHz; straight-line propagation can be assumed in this case.








DOY = 65. f = 1000.0 kHz Voyager 1, Jupiter Encounter
I I I I I I I I I I I I I I I I I I
1600 700
t = 03:03 ..............
( t .......... ...................---... --- -6--

r 1400 ............
t....-. ....... 5 -
.....0... -.- --6-- .... -.... -- ........ .... -- 4 --

S 120
-. .... .. ..............3 .

120 F ......". ....... .......... **.. -_...... ............. .. ............... .... ...... ..0...

1 0 0 .



1500 1600 1700 1800 190 2000 2100
Azimuth

Figure 2.5. Colatitude versus azimuth (in the monopole antenna coordinate sys-
tem) for the radio horizons at 1 MHz as seen from the spacecraft (zero refraction
assumed) at SCETs of 03:03, 03:06, 03:09 and 03:12, respectively, on day 65 of
1979. The finely dotted curves indicate the possible directions of arrival of rays
lying within assumed antenna E-planes having the indicated tilt angles, in 5 in-
crements. The two thick solid-line curves near the top and bottom of the radio
horizon at the time of the apparent polarization reversal (03:06 SCET) represent
the directions of all points along two possible conjugate source regions at the
northern (upper) and southern (lower) intersections of the L = 20 magnetic shell
with the fc = 1 MHz surface.


the monopole plane) in 50 increments. The thin solid curve at / = 23?3 represents the

E-plane as determined by Lecacheux and Ortega-Molina [1987]; I shall hereafter refer

to it as the L-OM E-plane. It is obvious that at the time of the apparent polarization

reversal (03:06 SCET), all possible source regions intersected by the extended L-OM

E-plane were beyond the radio horizon. At this time the lower edge of the horizon

oval was still 200 below the L-OM E-plane. If this had been the true E-plane, it would

have taken another 2 to 4 minutes for the reversal to occur. (Our mean timing error

is less than 24 sec, i.e., half the interval between the Voyager data points.) Figure

2.5 indicates that the true E-plane was tilted at least 430 from the monopole plane.








It is generally believed that the Jovian HOM sources are located within magneti-

cally conjugate regions in the two auroral zones having L-shell values of approximately

10 to 20, at altitudes at which the electron cyclotron frequency (fe) is nearly equal to

the wave frequency [Carr and Wang, 1989, 1990; Ladreiter and Leblanc, 1989, 1990;

Barrow, 1991]. The extent to which these sources are distributed in magnetic longi-

tude is still in question; they may extend around the full 3600 or they may be limited

to a sector of longitude. I have plotted in Figure 2.5 for the time of the apparent

polarization reversal (03:06 SCET) two closed (thick) solid-line curves representing

the directions of all points in the two possible source regions along the northern and

southern intersections of the L = 20 magnetic shell with the fc = 1 MHz surface. On

the basis of the oval-like curves in Figure 2.5 alone it can be stated that (a) the 9/

value for the true E-plane is between 420 and 480 if the source was in the southern

hemisphere, (b) the true /3 is between 620 and 67 if the source was in the northern

hemisphere, and (c) the L-OM / value 23?3 defines a plane that passes no closer than

230 from the southern hemisphere source (the nearer one). From the solid curves

superimposed on the oval for 03:06 SCET one can decide in which hemisphere the

source was located. Since the true polarization sense was LH at the time of the re-
versal of the apparent polarization, the predominant source region must have been

the southern-hemisphere one (lower curve). Thus, on the basis of this best SMPR

event alone, one would have concluded that the E-plane tilt, /3, was 450-3. This is

twice the L-OM value, but agrees more closely with the value deduced from Sayre's

numerical modeling results shown in Figure 2.2.

Next, similar calculations of #f were made from each of the other two of the three

best SMPR events, for which the planet-to-spacecraft distances were 35 Rj and 60 Rj,
respectively. Figure 2.6 shows three ovals representing the radio horizon directions at

the time (t = 18:50) of the 35 Rj event and also at times one minute earlier and one

minute later. Superimposed on the t = 18:50 oval are the possible source points along









I' J I I I I' I '


50 0 60 6.............70
0 ......................

... ............... .. ..... / .. / .

S 00 .-T "I \l I *.- ..I. / / / /
1700 110 .. 115. 120 1250 1300









Figure 2.6. Three ovals representing colatitude versus azimuth (in the monopoly
antenna coordinate system) for the radio horizons at 1 MHz for SCETs of 18:49,
18:50, and 18:51 on day 62 of 1979. The two solid-line curves near the top and




bottom of the middle oval (at t= 18:50, the time nearest the SMPR event) repre-/
100 105 110 115a 120 125 130
Azimuwith the f1 MHz surfaceth

Figure 2.6. Three ovals representing colatitude versus azimuth (in the monopole
antenna coordinate system) for the radio horizons at 1 MHz for SCETs of 18:49,
18:50, and 18:51 on day 62 of 1979. The two solid-line curves near the top and
bottom of the middle oval (at t = 18:50, the time nearest the SMPR event) repre-
sent the directions of all points along two possible conjugate source regions at the
northern (lower) and southern (upper) intersections of the L = 20 magnetic shell
with the fc = 1 MHz surface.


the northern (lower) and southern (upper) intersections of the L = 20 magnetic shell

with the fc = 1 MHz surface. Since the true polarization sense for this event was LH,

the source must have been on the upper curve. The corresponding 3 value is 272.

Corresponding plots for the 60 Rj event are very similar in appearance to those for 35

R3, and also give 271 for 0. I believe that the apparent large discrepancy between

this /3 value and the previous value of 450 is not due to measurement error, but instead

is an indication that the assumption of a single E-plane for source directions at all

azimuths about the antenna is an oversimplification. This is borne out by the results

presented in the next section.









3140


1200 3


S 1000


I 800






00 600 1200 1800 2400 3000 3600
Azimuth, p


Figure 2.7. Estimated source colatitude and azimuth (in the monopole antenna
coordinate system) for all usable SMPR events listed in Table 2.1. The three
highest-quality events are indicated by arrows, with the longest arrow at the near-
perfect event. The point marked "N" is for Neptune; all the rest of the points
with error bars are for Jupiter. A family of quasi-sinusoidal curves representing
colatitude versus azimuth for incident rays lying within assumed E-planes having
the indicated tilt angles are also plotted. The small triangular points without
error bars represent the measurements by Lecacheux and Ortega-Molina [1987].


2.2.3 Full Calibration Based on all Usable Events


There were a number of SMPR events that occurred at greater distances from

Jupiter from which some information is obtainable despite the fact that they were of

poorer quality than the three above. For these poorer-quality events the measurement

error had become so large due to the increased distance from the planet that the

source could be assumed to be located at the center of the planet without appreciably

increasing the error. (This was the case for all the measurements made for the L O-M

paper.) The measurements for all usable SMPR events used in this study are displayed

in Figure 2.7, with the three high-quality events that were considered in the previous

section being indicated by arrows (the longest arrow for the near-perfect event). Each








event provides one measurement of the antenna E-plane tilt, /0, together with the

colatitude and azimuth (in the XmYmZm coordinate system) the source point would

have if it lay within this E-plane. The family of quasi-sinusoidal curves give colatitude

versus azimuth for assumed E-planes having the indicated tilt angles (at 5 intervals).

The vertical and horizontal error bar lengths represent mean errors due to the fact that

measurements were made only at 48-sec intervals, rather than continuously. There

are probably other sources of appreciable error that cannot be represented here. All

of the points having error bars are for Jupiter except the one labeled "N", which is

measured from an SMPR event during the Neptune encounter. The small triangles

without error bars indicate the L O-M results, obtained from SMPR events at Saturn

and Uranus. Unfortunately, insufficient information was provided in the L O-M paper

for the determination of error bars for their measurements.

The data associated with all SMPR events, from which the measured points in

Figure 2.7 were derived, are summarized in Table 2.1. In this table, V1 and V2

indicate Voyagers 1 or 2; HOM is hectometric or combined hectometric-kilometric

radiation from Jupiter; NKR represents kilometric radiation from Neptune; SCET is

spacecraft event time (i.e., UT at the spacecraft); r is distance from the center of

the planet to the spacecraft in planetary radii (Rj and RN for Jupiter and Neptune,

respectively); W5 and 0 are the azimuth and colatitude in the monopole coordinate

system [Xm, Ym, Zm]; and 0 is the tilt angle of the equivalent E-plane with respect to

the monopole plane.

If the Voyager PRA antenna had been an isolated orthogonal pair of short dipoles,

it would have possessed an E-plane with a tilt angle that would be independent of

the direction of the radiation source used to measure it. It is clear from Figure

2.7, however, that the Voyager PRA antenna does not have such a unique E-plane.

Significantly different values of #f can occur for different azimuths of the source. We

attribute this to the effect of the highly irregular conducting surface of the spacecraft










Table 2.1. The SMPR events used in the
measurement based on source location.


S/C Source Year/Day SCET
(hh:mm)
V1 HOM 1979/062 18:49.8
18:49.8t
V1 HOM 1979/065 03:06.2
03:06.2t
V1 HOM 1979/067 18:00.0
18:00.Ot
18:36.6
V1 HOM 1979/069 15:23.4
12:55.2
03:49.2
V1 HOM 1979/096 03:06.6
V2 HOM 1979/195 23:18.6
V2 NKR 1989/237 10:03.0


r (Rp)

35.3
35.3
15.5
15.5
60.3
60.3
60.7
89.3
131.7
140.7
456.3
72.5
16.8


study. Entries marked with t are


117.75.0
113.01.5
172.71.0
173.02.5
104.95.0
103.01.0
152.53.0
152.33.0
149.04.0
151.52.5
295.32.0
181.54.0
2763.0


0()

77.14.0
79.01.0
130.22.0
121.71.0
73.14.0
75.02.0
107.13.0
101.84.0
101.93.0
98.64.0
91.92.0
116.57.0
1265.0


)3(0)

36.02.0
27.02.0
56.02.5
45.02.5
30.51.5
27.01.0
45.010.0
35.011.0
41.012.0
28.012.0
7.013.0
34.57.0
48.05.0


and its various projecting members. In Figure 2.7, the two nodal points in the family

of quasi-sinusoidal curves are located at the (0, p) points (900, 1350) and (900, 3150),

i.e., in the two directions of sources lying in the plane of the orthogonal monopoles.

The front side of the antenna system, which is the side for which both Zm and Z in

Figure 2.1 are positive, lies between the nodal points in the region for which 0 < 900

in Figure 2.7; the back side is the 0 > 900 region. In Figure 2.8, I have plotted the

same # values that appear in Figure 2.7 as a function of azimuth, W. Here again,

the three points calculated from the three relatively high-quality SMPR events are

indicated by arrows, with the longest arrow indicating the near-perfect event. The

point marked "N" is for data obtained during the Neptune encounter, the only one

that is not for Jupiter. Point "N" is ranked as the fourth-highest in quality. Our

conclusions are drawn almost entirely from these four points.








-60 Front Side 1 | Back Side --
600 f





23.30
40 -












Azimuth, p


Figure 2.8. Measured E-plane tilt angle plotted as a function of source azimuth for
the SMPR events of the previous figure. The composite E-surface is approximated
here by two half-planes, one with tilt angle of 270 for sources on the front side
of the monopole plane, and the other with a 450 tilt for sources to the rear, as
indicated by the two horizontal heavy lines.


One can now assume that the antenna does not have an E-surface that is a single

tilted plane. This E-surface can be best approximated by two half-planes of different

tilt angles intersecting along the X axis, one for sources on the front side of the

monopole plane and the other for sources to the rear, as depicted in Figure 2.1 (the

front and rear half-planes are indicated by solid rather than dashed lines). The two

horizontal heavy lines in Figure 2.8 represent this best estimate of the tilt angle of

the E-surface as a function of azimuth, 'p. The two tilt angles obtained in this way

are f = 270 and b = 450 for sources on the front and back sides of the antenna,

respectively. The L O-M value of the tilt angle for all azimuths is 23?3; it is indicated

by the horizontal dotted line. Our value /f for the front side is in reasonable agreement

with the L O-M value but our /3b for the back side differs from the L O-M value by

210. Our #b agrees more closely with the value calculated from Sayre's numerical








model of the antenna-spacecraft system than with the L O-M value; however, the

Sayre E-plane tilt, unlike ours, appeared to be about the same at all azimuths. I have

to point out that this bent E-plane model is at best a very rough approximation. The

actual E-surface dividing the arrival directions, for which the indicated polarization

sense is correct from those for which it is reversed, probably has a more complex

shape than the bent E-plane.


2.2.4 Discussion


We conclude that the PRA antenna E-surface is not a single plane its tilt can

be significantly different at different azimuths. Our results indicate that there are

certain azimuths at which the L O-M (Lecacheux Ortega-Molina) E-plane tilt angle

of 23?3 is in error by as much as 200, although at other azimuths the L O-M tilt

value appears reasonable. We believe that the error bars associated with our four

best points in Figure 2.8 (i.e., the three with arrows and the one marked "N") are

realistic. We are less sure that our two horizontal solid lines in the figure indicate

the correct tilt angles at all azimuths, but they represent the best approximation

we can make from the presently available data. It is our opinion that a significant

amount of Voyager data exists for which the use of the L O-M E-plane tilt angle

would lead to an incorrect interpretation of the polarization sense of the received

radiation. There is also the possibility that when observed times of the reversal of

the indicated polarization sense (as the true E-surface sweeps across a source) are

employed to obtain information related to source direction, the assumption of the L

O-M tilt value can sometimes lead to a grossly inaccurate result. In order to minimize

the possibility of such errors it is advised that the L O-M tilt of 230 (or our value of

270) be used when the observed radiation is incident on the front of the monopole








antenna plane, and that tilt of 450 be used when the radiation arrives from the back

side of this plane.

It is unfortunate that the quantity of suitable data was insufficient to yield more

conclusive results on the variation of 0 with


48-sec-average Voyager data from Jupiter and Neptune in locating the usable SMPR

events, and found no other events in these two data sets that meet the requirements

(as listed in Section 2.2.2 on page 16). However, some of the Jovian events which I

was forced to reject because the 48-sec sampling rate did not provide sufficient time

resolution could perhaps be salvaged if the same data sampled at 12 sec intervals

(in both senses of apparent polarization) were available. Other sources of additional

unused data are the Saturn PRA data sets obtained by the two Voyagers and the

Uranus data set of Voyager 2. If additional points obtained from these unused data

sets could be added to the plot of Figure 2.8, the variation of E-surface tilt as a

function of azimuth might be much better defined.


2.3 The PRA Data Base at the University of Florida


The Voyager PRA data of the Jupiter observations archived at the University of

Florida are processed POLLO data (12-sec averages nominally) obtained directly from

the Goddard Space Flight Center in the original, unedited, and unsmoothed form.

The data set was later edited and cleaned with the removal of the recognizable solar

interference and abnormal noise, and was smoothed by taking averages over a 48-sec

interval. Data in a few channels have been also removed due to heavy contamination

by interference. The overall coverage of the PRA data for the Jupiter observation

available at the University of Florida is shown in Figure 2.9, in terms of channel

number and the day number in the year 1979. On a specific day, if a channel contains

usable data points, it is considered to be a "good" one and is represented by a dot in








Voyager 1
200 r---------------------
a) I I I '



) -150



100 -
Q)-


C 50 -



0 I I I I I i I I I II
0 50 100 150
Day Number of Year 1979



Voyager 2
b) 200 p- | I I I I -I I I I I I I I F ,r
b) soo I



150 -


I -
100



g -50



0 li l i l l l l l I I
0 50 100 150 200 250
Day Number of Year 1979


Figure 2.9. A map of availability of the Voyager PRA data base for Jupiter
encounters at the University of Florida. Channels which contain usable data
points on a specific day are represented with dots. Upper and lower panels are
for Voyager 1 and Voyager 2 data respectively.








the figure. Notice that the data for Voyager 2 after encounter from day 199 to day

238 are not available in our data base. Also note that the LF band observations were

made for a much longer period than the HF band observations. Meaningful HF band

data were only obtained during a period of about one and a half months before and

after Jupiter encounter. This is due to an extremely high level of noise in the HF

band related to Voyager spacecraft high-speed switching logic which greatly reduces

its effective sensitivity. The excellent spacecraft noise rejection design employed in

the LF band permitted detection of Jupiter's HOM emission almost immediately after

launch.

The PRA data from the Neptune observation was also processed POLLO-mode

data obtained directly from the Goddard Space Flight Center. It covers data collected

by Voyager 2 during its Neptune encounter period, from Day 219 (August 7) to Day

248 (September 5) of the year 1989. Like the data from Jupiter, the data from

Neptune are also subject to intermittent spacecraft-generated interference and other

instrumental abnormalities, and contamination to the data sets is far more severe

than for the Jupiter case. Cleaning by the removal of all recognizable interference

and effects of receiver channel malfunctioning while preserving the good data points

becomes very necessary before analyzing and drawing conclusions from the PRA

Neptune data. Procedures and methods employed for the data cleaning and editing

are described in detail by Wang et al. [1991]. To maintain the maximum time

resolution, no smoothing process is performed, which means that the time resolution

is 12 sec for both LH and RH intensity outputs. My PRA data analyzing and modeling

are based on cleaned data sets.

The importance and advantage of using edited, cleaned data set are obvious.

Both Voyagers were very noisy spacecraft. The background noise generated within

the spacecraft itself greatly exceeds the galactic background and internally generated

receiver noise, which can limit the sensitivity of the system for detecting weak radio








signals. Intermittent episodes of greatly increased and sometimes violently fluctuating

background noise often occur. Removing this kind of noise along with other types of

interference (such as solar wind interference) can maximize the information potential

of the data set by minimizing the probability of misidentification. As will be seen

in later chapters, the main component of the Jovian HOM emission and the smooth

component of the Neptunian kilometric emission are rather stable and persistent,

having almost the same appearance from one rotation to the other. Time averaged

quantities such as flux density and occurrence probability are suitable to describe

some aspects of the HOM emission characteristics. This requires an interference-free

data sets to avoid misleading results.















CHAPTER 3
A BRIEF REVIEW OF JUPITER'S RADIO EMISSIONS



Jupiter, by far the largest and most massive planet in our solar system, possesses a

complex magnetosphere which would appear from Earth, if it emitted visible light, to

be larger than the full moon. This magnetosphere is driven by the rotational energy

of the planet, coupled through an intense magnetic field which deflects the solar wind

incident upon it. The Galilean satellite lo with its volcanic activity provides perhaps

the most prodigious plasma source in the solar system short of the Sun. Each of these

is a factor in generating intense and multifaceted radio emissions.

It was by accident that Burke and Franklin [1955] discovered Jupiter to be emit-

ting sporadic, strongly polarized decametric radio emission. This discovery was the

first observational evidence of any kind that indicated that Jupiter possesses a strong

magnetic field. Although the fact was not recognized until several years later, the dis-

covery proved to be a landmark in solar system exploration, preceding such historical

events as the discovery of Earth's radiation belts, the determination of the nature of

the solar wind, and the discovery of magnetospheres around the magnetized planets.

Prior to the great increase in our knowledge of the Jovian planets made possible

by observations from spacecraft, a considerable amount of information on the Jovian

magnetic field and magnetosphere had been deduced from groundbased radio observa-

tions in the decametric and decimetric wavelength bands. It was known, for example,

(a) that Jupiter has a very strong, predominantly dipolar, magnetic field oppositely

oriented, relative to the rotational angular velocity vector, from that of Earth, (b)








that there is an extensive Van Allen belt composed of trapped particles with rela-

tivistic energies, (c) that contrary to the indications of optical observations, Jupiter's

rotation period is constant to a high degree, (d) that a unique electrodynamic in-

teraction between the Galilean satellite Io and the Jovian magnetospheric plasma

plays an important role in the physics of this magnetosphere, and (e) that there are

strongly localized wave-particle interactions taking place at the northern foot of the

tube of magnetic flux passing through lo. Observations of Jupiter's radio spectrum

from Earth are restricted at low frequencies by effects of the terrestrial ionosphere.

The lowest frequency at which such observations are feasible from Earth ranges from

about 25 MHz down to 5 MHz, depending on the state of the ionosphere. Jupiter's

hectometric component (nominally at frequencies from 3 MHz down to 300 kHz) and

kilometric component (300 to 30 kHz) were not discovered until the 1970's, when

Earth-orbiting satellites from which radio observations could be made well above the

densest part of the ionosphere became available. Although Jovian radio emissions

down to 1 MHz had been detected from the satellites RAE-1, IMP-6, and ISEE-3,

most of our knowledge of the hectometric and kilometric components has come from

the data provided by the Planetary Radio Astronomy (PRA) on board Voyagers 1

and 2, and more recently by the Unified Radio and Plasma Wave (URAP) experiment

on board Ulysses. Now, Jupiter's radio emissions have been observed over the entire

spectral region from the lowest frequency which can propagate through the interplan-

etary medium (20 kHz more or less) up to frequencies of about 300 GHz, where the

radio and infrared spectral regions merge. Thermal emission from the Jovian cloud-

tops dominates the radio spectrum above about 5000 MHz, and it peaks well inside

the infrared region. Jupiter's three low-frequency radio emission components (occur-

ring below 40 MHz), that will be discussed briefly in the remainder of this chapter,

are the decametric (abbreviated DAM), hectometric (HOM), and kilometric (KOM)

components; the latter is subdivided into the broad-band kilometric (bKOM) and the








narrow-band kilometric (nKOM) components. For the sake of completeness, I will

also briefly discuss the much higher frequency Jovian decimetric radio component

(DIM), even though it is not directly related to my research.


3.1 The Synchrotron Radiation (DIM)


The Jovian synchrotron radiation, referred to as the decimetric radiation in the

early literature, was first detected at wavelengths of 10 cm and longer in 1958 [Mc-

Clain, 1959]. Distinguishing characteristics of this radiation component are its non-

thermal spectrum, the relatively large extent and distinctive shape of the emitting

region, the relatively high degree of linear polarization, the very small degree of

circular polarization, and the beaming effect. This radiation is due to synchrotron

emission by high energy electrons trapped in the Jovian Van Allen belt between 1.6~3

Rj. Such emission consists of extremely high and closely-spaced integral harmonics

of fc/ sin a, where fc is the electron cyclotron frequency and a is the pitch angle

of the magnetically trapped relativistic electrons. Although the early observations

of the Jovian synchrotron radiation were in the decimetric wavelength band (hence

the abbreviation DIM), it has since been observed over the entire frequency range

from 80 MHz to 300 GHz. Its spectrum has a broad maximum centered at about

800 MHz. At about 4000 MHz the synchrotron and thermal radiation components

are equal, and above that frequency the latter increases in intensity while the former

decreases. Because of the beaming of the radiation together with the fact that the

Jovian magnetic dipole axis is tilted about 100 with respect to the rotation axis, the

flux density observed at Earth varies periodically as the planet rotates, generally with

two maxima and two minima during each rotation. A related effect is the rocking of

the polarization plane of the linearly polarized component back and forth by 100

relative to the rotational equatorial plane as the planet rotates. Because the Jovian








synchrotron radiation was relatively well understood from the Earth-based observa-

tions (together with the fact that the frequency coverage of the receivers would have

had to be greatly extended), the Voyager PRA instrumentation was not designed for

observing the synchrotron component as well as the lower frequency components.


3.2 Decametric Radiation


The Jovian decametric radiation (DAM) is the first component of radio emissions

from Jupiter discovered in 1955 from ground-based observatories. It has been observed

from the ground and from space ever since its discovery (see, for example, Carr and

Desch [1976],Carr et al. [1983], and references therein). This radiation is by far the

most powerful radio emission from planets. Both ground and space borne observations

of DAM emission show that there is a high frequency cut-off at about 39.5 MHz which

is known as the magnetic cut-off because it represents the maximum electron cyclotron

frequency occurring in the emission region. The lower end of this emission component

is at about 2 MHz. A typical DAM storm can last several hours and the emission

shows drifting features in a frequency-time spectrogram.

Soon after the 1955 discovery of the DAM emission, several investigators found

that the probability of detecting Jovian activity was dependent upon the central

meridian longitude (CML), AIII, and the Jovicentric declination of the observer. His-

tograms of Jovian activity, as a function of CML, appear similar from apparition to

apparition when a planetary rotation rate of 9h55m29!71 is invoked. This period is

approximately 5 minutes longer than that obtained from the visible features at the

equator and is believed to represent the intrinsic rotation rate of the planet (Jupiter's

magnetic field is believed to be generated by the so-called dynamo effect). The DAM








sources were named A, B, and C, according to their relative strengths at an inter-

mediate decametric frequency. Those sources have now been recognized to be due to

multiple beams originating from a common location.

Bigg [1964] reported that the orbital phase of the Galilean satellite lo, !Io, mea-

sured from the superior geocentric conjunction, had a profound effect on the oc-

currence of the Jovian DAM emission: A very large enhancement in the detection

probability for lo phase angles of 900 and 2400 was found. In the two dimensional

picture of dynamic interaction between the planet and the satellite lo, the regions

of (Aml,, SIo) configuration space which showed dependence on both parameters were

named Sources lo-A, lo-B, lo-C and lo-D; those regions showing no lo dependence

become non-lo-A, non-lo-B, non-lo-C, etc [Carr et al., 1983]. Also from long term

ground-based observations, it was learned that the occurrence of DAM varies not only

with the CML and lo-phase of the observer, but also with the observer's Jovicentric

declination. This was first pointed out by Carr et al. [1970] as the well known "DE"

effect.

Frequency-time dynamic spectra of Jupiter's emissions display a high degree of

complexity, exhibiting intricate structure on several widely different time scales. It

also shows at least two distinct types of emission: the "greater arcs" extending from

as low as 1 MHz up to the 39.5 MHz cutoff, and the "less arcs" limited in frequency

extent. The dynamic spectra of DAM are often organized into individual storms

which can last up to several hours separated by long periods of complete radio silence.

The L-bursts, with durations usually between 1 and 10 sec, are the most common

type observable from Earth. It has long been known that the modulation envelope

characterizing individual L-bursts is impressed upon Jovian bursts of much longer

intrinsic durations by scintillation due to the rapidly drifting inhomogeneities in the

interplanetary plasma along the ray path [Douglas and Smith, 1961; 1967]. This








modulation pattern is disordered, and its frequency dependence is hardly apparent in

relatively narrow band dynamic spectra [Genova et al., 1981].

There is an additional modulation component known as the modulation lanes,

which were discovered by Riihimaa [1968; 1970]. The characteristic spectral pattern

of this modulation, in contrast to those of L-bursts, is relatively well ordered and is

strongly frequency dependent, even when relatively narrow bandwidths are observed.

Imai et al. [1992] showed that the major component of the Jovian modulation lane

structure is probably impressed upon escaping Jovian radiation by constructive and

destructive interference due to some type of regular striational structure in the part

of the lo plasma torus through which the radiation passes, and that the frequency

drifts of the modulation lanes are due to the relative inclination and motion of this

interfering structure with respect to the radio-emitting part of the active flux tube.

The DAM radiation from Sources A and B is predominantly right hand (RH) but

more left hand (LH) polarization becomes apparent outside the A-B longitude region

when the frequency is below about 20 MHz. Most RH polarization occurs within the

900 CML range while most LH occurs in the other 1800 CML range.

The emission is generally believed to be produced by a mechanism related to the

cyclotron maser plasma instability [ Wu and Lee, 1979] that is apparently responsible

for the terrestrial kilometric radiation. There is considerable evidence indicating

that the Jovian radiation originates in the northern auroral zone (and perhaps to a

much lesser extent in the southern zone) at altitudes above the cloud tops at which

the electron cyclotron frequencies are only slightly less than the frequencies being

emitted.

It is generally accepted that Io related emissions are emanating from sources

located within the lo flux tube at magnetospheric altitudes where the local electron

gyrofrequency is slightly less than the observed wave frequency. The emission is

beamed in a hollow cone with the cone symmetry axis being tangent to the magnetic








field at the source. The non-Io DAM is believed to be generated elsewhere, possibly

at higher magnetic latitudes near the tail field auroral zones or the north and south

polar cusps.

It has long been supposed that the DAM radiation patterns are due to the rotation

with the planetary magnetic field of a complex set of emission beams. Dulk [1967]

and Goldreich and Lynden-Bell [1969] first proposed that lo-B and Io-C sources result

from the two sides of a bilobed beam: the DAM radiation is beamed within a thin

conical sheet where the flux tube passing through lo meets the top of the ionosphere.

Source B is seen when this sheet first crosses the direction of the Earth, and Source

C when the other side of the cone sweeps past. Carr [1972] showed that both the

longitude oscillations and the variations in overall occurrence probability of lo-A

source are consistent with a rotating beam having a leading edge parallel to the spin

axis and a wedge-shaped trailing edge.


3.3 Hectometric Radiation


The Jovian hectometric (HOM) radio emission was not discovered until observa-

tions from spacecraft became available. The first observations of Jovian radiation at

frequencies below the ionospheric critical frequency were made by Desch and Carr

[1974] using data from the RAE-1 satellite, and by Brown [1974a] using IMP-6 data.

Most of our knowledge on the HOM emission has come from the observations by

the Planetary Radio Astronomy (PRA) experiment on board Voyager 1 and 2 [War-

wick et al., 1979a, 1979b], and only recently by the Unified Radio and Plasma Wave

(URAP) experiment on board Ulysses [Stone et al., 1992].

The hectometric radio band nominally extends from about 100 to 1000 meters,

corresponding to frequencies from 3 MHz down to 300 kHz. Emission in this waveband

from Jupiter fairly well delimits a rather distinctive region of Jupiter's radio spectrum








that lies between the well known decametric radiation above 3 MHz and the kilometric

radiation, most of which is below 300 kHz.

The activity of the HOM emission was observed mainly in the frequency range

between 400 kHz and about 2 or 3 MHz, with a broad spectral peak centered at about

800 kHz, but sometimes it can be observed down to about 40 kHz, especially near

the Voyager encounters. Its upper frequency limit was somewhat unclear, but it can

be as high as 8 MHz, as will be shown in the next chapter. The appearance of the

HOM emission in a dynamic spectrum plot always shows up as a "block" of emission

with a well defined gap centered near 2000 CML; another gap can appear near 25

CML, depending on the observer's latitude. In later chapters, various characteristics

of the HOM emission will be discussed in details, and models that best fit those

observational characteristics will be established.


3.4 Kilometric Radiation


Two kilometric (KOM) components were detected for the first time by the Voy-

ager PRA experiment: a broad-band emission (bKOM) and a narrow-band emission

(nKOM). The bKOM recurs favorably when the Jovian north magnetic pole points

toward the observer. The emission is RH dominated when seen in the northern mag-

netic hemisphere and LH dominated when seen in the southern hemisphere. The

bKOM is generally observed between about 20 and 400 kHz, and occasionally events

may occur up to some 1 MHz. It is believed that sources of the bKOM are probably

located at the edge of the Io plasma torus near the magnetic equator. The nKOM,

on the other hand, is very narrow in bandwidth (around 20~60 kHz), and confined to

a narrow band of frequencies between about 60 and 140 kHz. The nKOM is a quite

smooth emission in contrast to the bKOM. The sources of nKOM are believed also






41

N -181



S-22 ARTH




-24 URANUS
NEPTUNE

-26

0 200 400 600 800 1000 1200
FREQUENCY (kHz)


Figure 3.1. Peak flux density of the four giant planets (Jupiter, Saturn, Uranus,
and Neptune) and Earth, all normalized to a standard distance of 4 AU.


to lie near the lo plasma torus but distinct from the bKOM sources. It is believed

that the same CMI mechanism is responsible for the KOM emissions.


3.5 Power Spectrum


Having briefly reviewed Jupiter's radio emission components, we are now ready

to take a look at them in a bigger picture. Taking the PRA data from Voyager 1

recorded from February 9 to February 11, 1979, I calculated the peak flux density

spectrum for the Jovian radio emission, normalized to a standard distance of 4 AU

(1 AU= 1.496x108 km). The result is shown in Figure 3.1. To make comparisons with

other radio planets, I also plotted in the figure the peak flux density spectrum curves

for Earth, Saturn, Uranus and Neptune, all normalized to the distance of 4 AU. They

are all calculated from the Voyager PRA observations, except that for Earth. The

curves for Earth, Saturn, and Uranus are from Gurnett [1974], Carr et al. [1981], and








Gulkis and Carr [1987], respectively; and that for Neptune was calculated recently

by me from the Voyager 2 data. As can be seen, radio emissions from Earth, Saturn,

Uranus and Neptune do not reach 1 MHz, and curves for these planets are similar,

suggesting that they may share a common emission mechanism. Jupiter, on the other
hand, emits up to nearly 40 MHz (not shown in Figure 3.1), much higher than other

planets. Brown [1974b] and Desch and Carr [1974] reported from the observations

of the RAE-1 spacecraft a power spectral peak of the HOM emission near 1 MHz.

The Voyager observation, however, shows a broader peak centered somewhat lower

than 1 MHz, at about 800 kHz. The power spectrum curve displays no well-defined

peak in the KOM and HOM frequency range. This, however, does not necessarily

mean that different types of emission mechanisms are involved. Jupiter's magnetic

field is at least ten times stronger than those of other planets so that plausible Jovian

magnetospheric source locations could be found having electron cyclotron frequencies

from a few tens of kilohertz to nearly 40 MHz. Thus, generally speaking, Jupiter's

entire spectrum, as well as those of other magnetized planets, could possibly result

predominately from a single type of emission mechanism. One of most probable

mechanism candidates might be the cyclotron maser instability (CMI), which is well

established as the source of Earth's auroral kilometric radiation (AKR) [ Wu and Lee,

1979].















CHAPTER 4
JUPITER'S HECTOMETRIC RADIO EMISSIONS



The successful Voyager mission enabled the exploration of the magnetospheres of

the outer planets: Jupiter, Saturn, Uranus, and Neptune. The mission has become

one of the most exciting and successful explorations in the history of space flights.

One of many exciting results made by Voyager 1 and 2 in their missions to Jupiter

was the detection of the intense Jovian radio emission at hectometric wavelengths by

the Planetary Radio Astronomy (PRA) experiment [Warwick et al., 1979a, 1979b] on

board the spacecraft. My investigation of the Jovian hectometric (HOM) emission is

mainly based on observations from the PRA experiment. Detailed discussion of the

PRA experiment and the PRA data has been given in Chapter 2. In this chapter, I will

first discuss various properties of the Jovian HOM emission, followed by a presentation

of a model that accounts for most of the observational phenomena. Comparison of

this model with others being proposed in the literature will be discussed.


4.1 Characteristics of the HOM Emission


Before the Voyager observations are discussed, it is helpful to get an idea about the
Voyager trajectories during their encounters with Jupiter. Both Voyager spacecraft

were launched in 1977 and flew over Jupiter in 1979. The closest approaches to Jupiter

occurred on March 5 (Day 64) and July 9 (Day 190) for Voyager 1 and Voyager 2,

respectively. The trajectories during the encounter period for both Voyagers are

shown in Figure 4.1. The two Voyagers approached Jupiter at different Jovigraphic
























,. 5'--
V 1 V2

50

400 300 200 100 0 100 200 300 400
Before Encounter DISTANCE (Pj) After Encounter


Figure 4.1. Trajectory of both Voyagers during their mission to Jupiter. The local
time is defined as the angle of observer-Jupiter-Sun.



latitudes (at about 3?2 and 70 for Voyager 1 and 2, respectively) and at different local

times (at about 10:30 and 9:40 for Voyager 1 and 2, respectively). They flew away

from Jupiter at almost the same Jovigraphic latitude (about 5) but at different local

times (about 04:15 and 03:00 for Voyager 1 and 2, respectively).



4.1.1 Frequency Coverage



Let us begin our discussion of the characteristics of the HOM emission with a

typical dynamic spectrum plot, shown in Figure 4.2, of Jupiter's radio emissions

observed with both low- and high-frequency band receivers of the PRA experiment of

Voyager 1 after the encounter on March 21 (Day 80), 1979. The dynamic spectrum is

a plot of received total intensity as a function of frequency (or channel number) and

spacecraft event time (SCET). This plot is made such that the darkness in the plot









VOYAGER 1
q" "? ,. ( ,'


jff w
:A 99* 27O' O*


V4
4>j A


BG: 26.5 dB
IqV 27 ---

V -


IU114I.K.6


I


0 4 8 12 16 20 24
SCET (HOURS ON DAY 80, 1979)


Figure 4.2. A typical dynamic spectrum plot of the Jovian radio emissions in
the low- and high-frequency bands recorded by Voyager 1 on March 21 (Day 80),
1979. The CML of the spacecraft, Am, is plotted on the top of the figure.



is proportional to the logarithmic intensity of the signal above a selected background

(labeled as BG in the figure) as shown in the scale bar with numerical labels in units

of millibels (the number on the top of the scale bar for each panel is the maximum

intensity reading in the panel). The System III (1965) central meridian longitude

(CML) of the spacecraft, Am, is also plotted on the top of the figure. The presence

of the horizontal streaks is due to the problem of spacecraft interference which made

some of the channels permanently unusable. White blanked regions correspond to

bad data points being removed.

The HOM emissions were observed when the CML of the spacecraft was between

about 2800 and 1200. Radiation occurring elsewhere in the LF panel (mainly in low

frequency regions) is the kilometric emission. Clearly, this figure shows that the HOM


" 0.4
>-
Z
D 0.8
w
L.
u_
1.2


3234
1800


1200


600


0


3933
1800


1200


600








emission occurs mainly from a lower frequency of about 350 kHz and extends to the

high-frequency band receiver up to about 8 MHz. Radiation at frequencies as low as

40 kHz was observed in the same CML range when Voyager was very close to Jupiter.

The decrease in the power spectrum near 400 kHz shown in Figure 3.1, as well as

occurrence probabilities (to be discussed next), indicate that 400 kHz is an average

of the lower frequency limit of the HOM emission. The upper frequency limit is not

as clear as the lower frequency limit, because the HOM emission merges into the

decametric emission (DAM). Barrow and Desch [1989] suggested it to be as high as

7 MHz. Our dynamic spectrum (Figure 4.2) shows clearly that the HOM emissions

can reach the frequency as high as 8 MHz.


4.1.2 Intensity Profile in CML


From Figure 4.2 and other dynamic spectrum plots similar to it, one can see that

the HOM emission appears to be strongly modulated as Jupiter rotates. Radiation at

about 1 MHz reaches its peak in every rotation when the observer is near 3300 and 90

CML. Such emission peaks shift as the frequency decreases. For example, at 500 kHz,

the main emission peak has shifted from 3300 to 3500. It is a persistent feature that

is unique to the HOM emission. When fixed-frequency-channel plots of the emission

intensity as a function of time from a single channel in the vicinity of 1 MHz are made,

there is a strong tendency for a characteristic signature, which is either bilobed or

monolobed, to occur with each rotation of the planet as is shown in Figure 4.3. In

this figure, the observed right-hand (RH) and left-hand (LH) intensity outputs1 at 1

MHz, taken over four successive Jovian rotations for each Voyager, are plotted against

the SCET, and are compared before encounters when the Jovigraphic latitudes of


1The corresponding plot of the apparent polarization ratio in the same periods will
be shown in Figure 4.11 on page 66.










0a 16 2 1SF V a 18' 0 1B9W

V1, BEFORE ENCOUNTER











21.5 2175 22 2225 22'5 22.75
SCET (DOY IN 1979)


187.75 188 168-25 188.5 188.75 169 168925
SCET (DOY IN 1979)


0. 182' V IW' W' 0).
I I I I I I


0' IT


Vi, AFTER ENCOUNTER










I s l I I ,I I I
81.75 82 82.25 82.6 82.75 83
SCET (DOY IN 1979)
2 18In a' ,i r isr W r


V2, AFTER ENCOUNTER


LH








RH 187 18775 198.26 leas ~7


Figure 4.3. Intensity plots for both the LH and RH components at 1 MHz as a
function of spacecraft event time (SCET) in units of Day of Year (DOY) in 1979
for data from Voyager 1 and 2 before and after encounters, for four consecutive
rotations each. Plotted on the top of each panel is the CML (Am,,) of the spacecraft.




Voyager 1 and Voyager 2 were 3?2 and 7?1, respectively, and after encounters when

the Jovigraphic latitudes of Voyager 1 and Voyager 2 were 5?2 and 4?2, respectively.

In preparation of the intensity-time plots, the intensity is normalized by a factor

that is proportional to the square of the distance. The ordinate in Figure 4.3 is the

logarithm of the normalized intensity.

The most conspicuous feature of the apparent corotating emission pattern shown

in Figure 4.3 is a deep and relatively wide null centered around 2000 CML, which is the

approximate longitude of the northern magnetic pole (when a tilted dipole magnetic

field model is assumed). Furthermore, the emission gap of pre-encounter data is wider

for Voyager 2, which was at higher latitudes, than for Voyager 1, which approached


, ,. t ,. . i i i i i i i ]








Jupiter at lower latitudes. The monolobed response for Voyager 2 before encounter

differs from the bilobed response for the three other cases due to the difference in

spacecraft's Jovigraphic latitude. There is also a narrow gap centered around 300

CML between the leading and trailing maxima in a bilobed feature, and this gap in

each cycle is more widely separated for the RH data than for the LH data. Such

a repeating structure appears to be quite stable except during the period of close

encounter. The apparent activity of the HOM emission varies with the latitude of the

observer; it is very similar to the behavior of the Jovian decametric radio emission

(DAM), known as the "DE effect" [Carr et al., 1970; Carr and Desch, 1976]. Plots

similar to Figure 4.3 at all frequencies from about 0.7 to 1.3 MHz show the same

characteristics, but the repeating structure is best displayed at about 1 MHz.

It has been argued that the wide gap around 2000 CML and the narrow gap around

300 CML, where low or no HOM emission was detected by the PRA receiver, is due

to the drop-out of emission intensities near these longitudes below the threshold that

the receiver can detect. It was suggested that the HOM source is still active but its

emission is just too weak to be detected by the PRA receiver [Ladreiter and Leblanc,

1989]. However, it is important to note that the intensity readings recorded near

900 and 330 CML (where the HOM emission reaches its peak) are at least 15 dB

higher than those recorded near 2000 CML (the center of the wide gap). This means

that the peak intensity of the HOM emission is at least 30 times stronger than the

intensity that could have been detected in the wide gap. Recent observations from the

Unified Radio and Plasma Wave (URAP) experiment, which is at least one order of

magnitude more sensitive than the PRA experiment, on board the spacecraft Ulysses

also showed a gap near 2000 CML when Ulysses was at about 1?5 Jovigraphic latitude

[Lecacheux et al., 1992b]. All these facts indicate that the gap near 2000, and probably

that near 300 CML, are true gaps. A successful HOM model should be able to produce

such gap(s). I will come to this point later in Section 4.3 regarding modeling.








As can be seen from Figures 4.2 and 4.3, the HOM emission is strongly modulated

by the rotation of Jupiter. The emission appearance as a function of CML of the

observer is quite stable, although rapid changing of HOM activity on a time scale of

minutes is also obvious. Such a stable character is best described by the averaged total

flux density or the occurrence probability as a function of CML and frequency for data

over many rotational cycles. The occurrence probability is calculated by dividing

the number of activity counts by the total number of observing counts. Only the

activity that exceeds a certain threshold above the background level is counted. The

appearance of stronger emissions can be best described by using a larger threshold

value when the occurrence probability is calculated. Weaker emissions are emphasized

by plotting flux density values in a logarithmic scale above the background level. The

averaged total flux density as a function of CML of the spacecraft and emission

frequency before and after encounters is presented in Figure 4.4 for each of the two

Voyagers. Data for over 70 rotational cycles were used for the calculation except for

the Voyager 2 after-encounter case, where only 12 rotational cycle data were used.

The observed intensity for both RH and LH components was normalized to a distance

of 200 Rj before it was added and its average was taken. The HOM emission appears

clearly as two maxima concentrated near the 3300 and 90 CML for Voyager 1 pre-

and post-encounters and for Voyager 2 post encounter. For Voyager 2 pre-encounter,

the emission is seen near 350 as a single broad maximum. It is worth noting that

the intensity peak near 3300 became more intensive after encounter, a sign of local

time effect. This is most obvious for the case of Voyager 1 after encounter. Figure 4.5

shows the occurrence probability from Voyager 1 and 2 observations over 70 rotational

cycles (except for Voyager 2 after encounter, in which 12 cycles are considered) before

and after encounter with Jupiter with a threshold value of 10 dB. As can be seen in

the figure, the HOM emission occurs in every rotation of the planet with almost

100% occurrence probability when the spacecraft is near 90 and 3300 CML, and the


















































0 0 0
0 0 0N

(ZHw) A3N3nO3aJ






m *0


0 0
a 0o
(ZH*O A3N3flO~ai


(ZHI) AON3nO38A


0 0 0



0 0 0
? 10 0

(ZHol) A3N3nf3lj


o0




o
uu





o0 0 4,


00
!-


o<- ---
40,
0 "0





b 0 u0










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0 >
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oo 4

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oo
10)










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-II


0 0
(ZHM) kON3no38j


0 0
(ZHi) AON3nO3aW


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0 0 N


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in
0 c

0





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Table 4.1. Measurements of longitude associated with the midpoints of the wide
and narrow gaps.

Wide gap Narrow gap
CML N SSL CML N SSL

Voyager 1 before encounter 203?81?9 47 180 31?02?0 32 70
Voyager 1 after encounter 203?014 74 870 30?41?8 59 2750
Voyager 2 before encounter 199?11?7 48 1660 30?54?1 12 10
Voyager 2 after encounter 201?62?8 11 560 32?217 8 2490
Weighted mean 202?00?9 31?61?0


occurrence probability near 2000 CML is almost zero. There is a trend that emissions

at higher frequencies occurs a little earlier than those at lower frequencies, causing the

shift in CML of the emission peaks. Part of such shifting is a stable spectral feature

which appears as lanes of decreasing intensity within the otherwise persistent HOM

emission. Such lane features have been studied by Green et al. [1992] and by Higgins

et al. [1993], who suggest that the lane phenomenon may be intrinsic to the source

of the HOM emission and is unlikely to originate from the propagation effect. The

lane feature is most obvious for the peak near 3300 CML. It is important to note that

the HOM emission in its broad frequency range (from about 450 kHz to 1.3 MHz)

has almost the same occurrence probability distribution. It means that the HOM

emission in its frequency range is observed almost simultaneously. This implies that

the HOM emission at different frequencies experiences the same propagation effect

from the Jovian magnetosphere on its way out. Of course, the averaged flux density

or occurrence probability only describes the stable part of the HOM emission.

A close examination of the overall stability of the HOM emission appearance has

been made as a function of CML from observations obtained by both Voyagers. The

midpoint longitudes of the wide and narrow gaps are measured, and the results are

given in Table 4.1. In this table, CML is the average central meridian longitude








(System III) of the midpoint of the gap; N is the number of values averaged; SSL is

the average of the subsolar longitudes occurring when the gap midpoints were on the

central meridian. The CML indicated error is the standard deviation of the mean.

The standard deviation of a single measurement ranged from 50 to 140. The mean

of the mid-longitude of the wide gap centered near 2000 CML was measured for 180

rotational cycles, and the result (202?20?9) turned out to be quite close to the mean

of the north magnetic pole longitudes for the four tilted dipole models discussed by

Acuna et al. [1983]. The mean of the mid-longitudes of the narrow gap was found

to be 31?61?0, which differs by 9?1 from the longitude (22?2) diametrically opposite

the wide gap midpoint. The fact that the midpoint longitude of the wide gap can be

accurately measured makes it an extremely good candidate as a fiducial point for the

precise measurement of the mean Jovian magnetospheric rotation period. Carr and

Wang [1990] first proposed that the long-term monitoring of the Jovian HOM emission

at a frequency of about 1 MHz from a high-orbit satellite or from the surface of the

moon would eventually provide a record of rotation period changes revealing secular

variations in the Jovian magnetic field, with a sensitivity and accuracy higher than

could be achieved from terrestrial observatories. The Jovian hectometric observations

will be made by the spacecraft Galileo in 1995, and when such observations are used

in conjunction with those of the Voyagers obtained in 1979, a mean rotation period

measurement with an accuracy of 0.01 sec can be achieved [Wang and Carr, 1990].

The HOM emission profiles shown in Figures 4.3, 4.4, and 4.5 indicate that there

are some differences for data recorded by both Voyagers before and after their Jupiter

encounters. This can be due to (1) difference of the spacecraft's Jovigraphic latitude

and (2) difference in local time (i.e., the observer-Jupiter-Sun angle) during which

the observation was made. As shown in Figure 4.1, Voyager 1 and Voyager 2 ap-

proached Jupiter at local times of 10:30 and 9:40 on the day side, and after encounter

they traveled away at local times of 4:20 and 3:00 on the night side, respectively.








When on the day side (before encounter), radiation received at about 3300 CML was

on the average weaker than that received at 900 CML; after encounter, the opposite

result became dominant. Previous study by Alexander et al. [1979] from combined

observations of the two Voyager spacecraft and two other spacecraft (PRE-1 and

IMP-6) provided a strong evidence that the HOM profile changes with the observer's

latitude, an effect similar to that long observed DAM emission, known as the "DE"

effect [Carr et al., 1970]. However, the difference shown in Figures 4.4 and 4.5 of

pre- and post-encounter observations does show a local time effect. From those fig-

ures it is clear that the HOM emission undergoes some changes in intensity level

and occurrence probability between the pre- and post-encounter observing intervals.

Apparently, the leading beam (Am < 3600) becomes more intense and more common

after encounter for both Voyagers. Such variation cannot be explained by the change

of the spacecraft's latitude, because the Voyager 1 observation was made at a lower

latitude before encounter and at a higher latitude after encounter, while the Voyager

2 observation was made at a higher latitude before encounter and at a lower latitude

after encounter. Both observations lead to the same change in intensity level and

occurrence probability. We conclude that the difference in the HOM emission profiles

before and after encounter is mainly due to the local time effect.

It is interesting to note that Figures 4.5 and 4.2 clearly show an anti-correlation

between the broad kilometric (bKOM) and the HOM occurrences in CML.


4.1.3 Magnetic Latitudinal Beaming


Figures 4.3, 4.4 and 4.5 show that the HOM emission occurrence varies with the
latitude of the observer. Based on their study, Alexander et al. [1979] suggest that the

HOM emission is beamed to a constant magnetic latitude, 30 north of the magnetic

equator with a beam width of about 10.








We notice that the magnetic latitude of a "stationary" observer consistently

changes as the planet rotates, due to the tilt of the Jovian magnetic field. The

HOM emission occurs just before and after the observer reaches its minimum mag-

netic latitude. To see how the HOM emission at all frequencies occurs as a function of

the magnetic latitude, it is best to calculate the occurrence probability or average flux

density in terms of frequency and magnetic latitude of the observer. As the planet

rotates, an observer experiences increasing and decreasing changes in his magnetic

latitude, depending on the CML position of the observer. Figure 4.6 shows the av-

eraged total flux density of the HOM emission calculated from both Voyagers before

and after their encounters with Jupiter for over 70 rotational cycles, except for the

Voyager 2 observation of 12 rotational cycles taken after the encounter. This calcula-

tion indicates that the HOM emission as a whole occurs when the observer is near the

magnetic equator, a strong evidence of magnetic latitudinal beaming. However, the

HOM emission at different frequencies is not beamed to a constant magnetic latitude,

as Alexander et al. [1979] suggested; beaming widths are also different for emissions

at different frequencies, depending on the observer's Jovigraphic latitude. For exam-

ple (see Figure 4.6), at 800 kHz the emission is beamed to about 3 with about 5

width for Voyager 1 before encounter (6 w 3?2), but is to about -1 with 7 width

after encounter (6 f 5?2). Another important feature to note is that the emission at

lower frequencies (< 600 kHz) is actually beamed to a lower magnetic latitude after

encounter than before encounter. As will be seen next, after encounter with Jupiter,

each Voyager was oriented in the position such that the PRA antenna behaved like an

almost perfect circular polarimeter, and the outputs of the PRA polarization channels
are nearly proportional to the true left and right circular components of the sources)

[see Equation (4.6) on page 64]. It is therefore possible to determine how the LH

and RH circularly polarized emissions are beamed to the magnetic latitude from the
















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30nilYli OI.3NODV


Ui











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post-encounter observations. I made similar calculations, shown in Figure 4.7, of oc-

currence probabilities for the LH and RH components from after encounter data of

Voyager 1 (left panels) and Voyager 2 (right panels). These calculations once again

show that radiation at different frequencies is beamed in different magnetic latitudes.

The most obvious feature shown in such calculations is that for RH (LH) components,

radiation is beamed toward lower (higher) magnetic latitudes as the frequency goes

down. Such a shifting feature is not caused by the lane feature as described by Green

et al. [1992]. This is quite a surprising feature that has never been investigated or

reported before, quite contrary to what would be expected by the traditional source

modelings, especially when the role of the lo plasma torus for reshaping the beaming

of the HOM emission is considered to be appreciable. It is generally believed that

the HOM emission originates from high magnetic latitude regions in both (magnetic)

hemispheres, propagating in the R-X mode [Carr and Wang, 1989; Ladreiter and

Leblanc, 1989; Ladreiter, 1990]. It was suggested that the propagation path of the

HOM emission is altered heavily due to the presence of the lo plasma torus [Ladreiter

and Leblanc, 1989, 1990a, 1990b; Barrow, 1991]. However, if this were true, one would

expect that RH (LH) polarized component from the northern (southern) hemisphere

would be refracted by the Io torus, and the result of this would be that the HOM

beaming would be shifted to a higher (lower) magnetic latitude for lower frequencies.

To investigate the magnetic latitudinal beaming of the HOM emission further,

I calculated the occurrence probability, as a function of magnetic latitude and fre-

quency, for both RH and LH components of the HOM emission by using only the

data taken while the spacecraft's magnetic latitude was increasing and decreasing,

respectively. In other words, I investigated the magnetic latitudinal beaming in two

longitudinal regions separately in which the spacecraft's magnetic latitude is mono-

tonically increasing or decreasing. I refer to these two longitudinal regions as region














0 0 0 0


3afLIUvI 3t3NO"
U;.*


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C-,



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"I" (for increasing magnetic latitude) and region "D" (for decreasing magnetic lati-

tude), respectively. The CML range for the "I" region is 220*202*, and is 2020220

for the "D" region. The results are shown in Figure 4.8 for the "I" region and in

Figure 4.9 for the "D" region. Figures 4.8 and 4.9 reveal several features of the

HOM emission. The occurrence probability of HOM emission is higher for the "D"

region than for the "I" region. The LH component of the HOM emission is beamed

roughly at a constant magnetic latitude in the "I" region, although the shifting fea-

ture still is obvious. The beam shifting is most obvious for the "D" region, in which

the RH (LH) beam is shifted toward lower (higher) magnetic latitude. The beaming

width is wider for Voyager 2 than for Voyager 1. The lanes that "interrupt" the HOM

beam appear to have a steeper slope for the "D" region than for the "I" region. It is

also obvious, especially for emission at lower frequencies, that the RH component is

beamed considerably to a lower latitude in the "D" region than in the "I" region. For

example, the RH component at 500 kHz is beamed to a magnetic latitude as low as

-6, while that at 1 MHz is beamed to 00. For the LH component, emission at 1 MHz

is beamed to about -20, while that at 700 kHz is beamed to about 10. Different mag-

netic beamings at different frequencies in different regions may be an indication of a

distorted beam pattern or a curved magnetic equator. The existence of the Io plasma

torus usually leads to an anticipation that the HOM emission would be affected dif-

ferently at different frequencies (such effect is greater the lower the frequency). The

fact that the presumed R-X mode emission from the northern (southern) hemisphere

is beamed more southward (northward) seems to contradict the role of the Io plasma

torus on altering paths of the HOM emission. There are two possible ways for this to

happen: (1) the HOM emission does not go through the dense part of the torus on its

way out; or (2) the plasma torus is not as dense as has been reported, so that it does

not have too much refraction effect on the HOM emission. No evidence was found in

the Voyager and Ulysses observations to support the idea that the Io torus would be




















o o 0 0
C C C. 0


30niliVl 3113NO"


































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so dense. The only plausible explanation is therefore that the HOM emission does

not propagate deep inside the lo torus.


4.1.4 Polarization


The polarization status of radio emissions is of great importance in revealing phys-

ical processes involved in wave generation and propagation. The only polarization

measurements of Jupiter's radiation below 2 MHz are those of the Voyager PRA ex-

periment and the recent Ulysses URAP experiment. As has been described in Chapter

2, the Voyager receiver was designed only to provide two intensity measurements on

each frequency channel, which would be the RH and LH circularly polarized intensity

components if the source lay on the antenna axis.

The only unambiguous polarization information provided by the Voyager PRA

receiver is the polarization sense (i.e., whether the RH or LH circular component is

the larger one) because the RH and LH outputs were contaminated by the unwanted

coupling between the two monopoles due to the interference effect of the spacecraft

structures. In addition, Jupiter was never in a direction perpendicular to the antenna

plane during the whole encounter period. Polarization of the HOM emission observed

by Voyager was investigated previously by Warwick et al. [1979a, 1979b], Alexander

et al. [1981], and Ladreiter and Leblanc [1989]. Their work was all based on the

apparent polarization calculated from the LH and RH outputs without taking actual

antenna response into account. Lecacheux and Ortega-Molina [1987] and Ortega-

Molina and Lecacheux [1990, 1991] studied, based on an early calibration results of

Ortega-Molina and Daigne [1984], the polarization properties of the Jovian HOM

emission observed by the PRA experiment. They showed that the apparent degree

of circular polarization measured by the PRA instrument is the result of fluctuations

in the relative intensities of the two HOM circular components, and therefore they








concluded that the complex morphology of the HOM emission can be explained by

simultaneous radiation from two independent, oppositely circularly polarized sources

with 100% polarization degree. Linear polarization in HOM was found to be extremely

rare; the maximum percentage of linear polarization was less than 10%. Observations

from the Ulysses URAP experiment, which is capable of measuring all four Stokes

parameters, also confirmed that the linear polarization component is insignificant in

the HOM emission [Reiner et al., 1993a].

In this section, I will make a new determination of average polarization sense,

taking into account the newly calibrated antenna response (see Chapter 2). For

each set of the PRA data taken at a given time, Jupiter's directions with respect

to the spacecraft at that moment will be calculated. According to Ortega-Molina

and Lecacheux [1990, 1991], once the direction angle of Jupiter (and hence the HOM

source) relative to the E-plane (front side or back side) is calculated, the normalized

Stokes parameters of the antenna system, q, u, v, can be deduced:

q. + a v.b v(c
q u -- v = --, (4.1)
1 + q1a 1 +qa 1 + q.a

sin2 0 2cos 0
where q. 2 u. = 0 v 2 cos 0 (4.2)
1 + cos2 1 + cOS2

are the Stokes parameters of an orthogonal dipole antenna system, and


a = cos a sin 20 b = cos a cos 20 c = sin a, (4.3)

a is the opening angle of the equivalent dipole. The apparent total intensity Sapp and

degree of circular polarization Vapp can be obtained:


Sapp = IL + IR = sS(1 + qQ + uU) (4.4)

IL IR vV (4.5)
p IL + IR 1+qQ+uU'










VOYAGE 1 '
30 -


0' --- -

-M- --------


64



VOYAGER 2
80* -


i '- ---- -
-0-- ---- ----
---------------- -- -- -- -------


10 20 30 40 5O 6s 70 s0 0o t20 40 180 180 200 200 2 40
SCET (Days n 1979) SCET (Days In 1979)


Figure 4.10. Jupiter's latitudinal angles as a function of spacecraft event time
(SCET), seen from the Voyager spacecraft with respect to the monopole plane
(solid line), front-side E-plane (dotted curve), and back-side E-plane (dashed
curve). Left panel and right panel are for Voyager 1 and Voyager 2, respectively.



where (S, SQ, SU, SV) are the Stokes parameters of the incoming wave. Conse-

quently, two incoherent circular components and their relative intensities can be

separated:


A = (v + 1)IL + (v 1)IR
2sv (4.6)

S= (v 1)IL + (v + 1)I
SB == -- ---
2sv

where SA and SB are the true intensities of the two incoherent circularly polarized

sources; IL and IR are the apparent left- and right-circular intensity components of

the receiver, and s = v/q2 + u2 + v2. When the antenna-source geometry is such that

|vI|1, the apparent left and right intensity levels (IL and IR) will be proportional

to the true intensities of two left- and right-handed circularly polarized sources (SA

and SB). Formulation of calculating the 0 value of a radio source or planet center

at any given time based on the Supplementary Experimental Data Record (SEDR) is

presented in Appendix C. Shown in Figure 4.10 are the latitudinal angles of Jupiter's

center, measured from the E-plane (see Chapter 2) tilted 00, 270 and 450 from the

monopole plane, as a function of Spacecraft Event Time (SCET). Short-time varia-

tions of the spacecraft's position and orientation were not included in the figure. The








solid curves (for 00) are therefore Jupiter's latitude relative to the monopole plane,

dotted (for 27) and dashed (for 450) curves are Jupiter's latitude relative to the

E-plane when Jupiter is seen from the spacecraft in the front side and in the back

side, respectively. Before their encounters with Jupiter, both Voyagers saw Jupiter to

be on their front side (with azimuthal angles of about 250 and 270 respectively) and

they were oriented such that Jupiter (and therefore all radio sources) was actually

quite close to the direction of null-polarization response, which led to a poor PRA

sensitivity to the circular polarization (v ~0 and therefore ISAI |5 ISBI). Calculations

of polarization ratio (referred to as PR hereafter) for pre-encounter data would be

very questionable. After encounter with Jupiter, both Voyagers were in an orientation

which led to a very good PRA sensitivity (jvj|l). Thus only calculations of PR for

the post encounter period are meaningful. Also note that after its encounter with

Jupiter, Voyager 2 was oriented such that Jupiter was seen below the E-plane (i.e.,

v < 0), which means that the polarization sense detected after encounter was false

and opposite to the true polarization sense. Taking into account the PRA antenna's

actual response to circularly polarized incoming radio waves, I plotted in Figure 4.11

the apparent PR for both Voyagers before and after encounters with Jupiter for the

same periods as those shown in Figure 4.3 (on page 47) for the total intensity plots.

The apparent PR (i.e., the apparent degree of circular polarization) is defined by

(IL-IR)/(IL+IR). Since the LH and RH intensity measurements made by the PRA
instrument were recorded in a logarithmic scale, uncertainties can be introduced when

calculating the PR for weak intensity readings. To minimize such uncertainty, only

data points that exceed a certain threshold level (5 dB for plots shown in Figure

4.11) above the background are used in the PR calculation. Clearly, the PR is poorly

determined before encounter because during such time Jupiter was quite close to (the

front side of) the E-plane, and both intensity components are almost the same. It






66

W 1I M W 1c) 1W r W 1 Lwr o- foWr rW Io I 1W

1 _1, BEFORE ENCOUNTER 1 31, AFTER ENCOUNTER




o 0





21.5 21.75 22 22.25 22.5 22.755 82 8Z25 825 82.75 83
SCET (DOY IN 1979) SCET (DOY IN 1979)
W 0" ..r .r. m w r I" o r 111 VW.

_V2, BEFORE ENCOUNTER 1 V2, AFTER ENCOUNTER








-1 1- -1 -
167.75 188 16m25 1088 188.75 188 189.5 197.5 197.75 198 19825 198.5 198.75
SCET (DOY IN 1979) SCET (DOY IN 1979)


Figure 4.11. Plots of apparent polarization ratio at 1 MHz as a function of space-
craft event time (SCET) in units of day of year (DOY) for data from Voyager 1
and 2 before and after encounter, for four consecutive rotations each.



is evident, however, that the LH polarized radiation (with positive PR) was domi-

nant when Voyager was at its lowest magnetic latitude (close to 220 CML), and the

RH polarized radiation (with negative PR) became dominant when Voyager got into

the northern magnetic hemisphere. After encounters, both Voyagers were in favorite

orientations for the PR measurement (jvj;1). It is evident (see Figures 4.3 and

4.11) that intensities of the two polarization components have a similar global profile

and occurrence appearance. However, any correlation of the detailed structures of

the spectral patterns are not apparent. This is an indication of the presence of two

independent, oppositely polarized sources.









APPARENT POLARIZATION SENSE
VOYAGER 1 BG: 26.5 dB, A 2 dB
,q' 27p' 0o 9" Iq. 27 .

100
0.4 50

0
: 0.8
U"r "-50
U.
1.2 -100

0 4 8 12 16 20 24
SCET (HOURS ON DAY 80, 1979)


Figure 4.12. Polarization sense as a function of frequency and SCET during the
same period of time for Figure 4.2. Black, white and grey features correspond
respectively to the left-handed, right handed and unpolarized (or no) emissions.



To see the polarization pattern for all frequency channels of the low-frequency

band receivers, I present in Figure 4.12 the calculation of the polarization sense (sign

of PR) as functions of frequency and SCET for Voyager 1 during the same period of

time as in Figure 4.2 of the dynamic spectral plot. Black, white and grey features

correspond to RH polarized, LH polarized and unpolarized (or no) emissions, respec-

tively. This figure shows a great complexity with alternating left and right circular

polarizations at a time scale of hours. Apparently, as has been shown in Figure 4.11,

the polarization is, in the entire HOM frequency range, predominantly right hand

at the beginning and end of a HOM storm and predominantly left hand when the

spacecraft is near 300 CML, i.e., when the spacecraft reaches its lowest magnetic lati-

tude. There is often an abrupt reversal of the observed circular polarization when the

spacecraft crosses the magnetic equator. From the intensity profiles of both LH and

RH components (Figure 4.3) it is clearly seen that the polarization pattern depends

on the relative strengths of the RH and LH emissions. It can be expected that when

the spacecraft is in the northern magnetic hemisphere it receives stronger emission








originating from the northern hemisphere; likewise, it receives stronger emission origi-

nating from the southern hemisphere when it is in the southern magnetic hemisphere.

The polarization profile of the HOM emission suggests that the majority of the HOM

emission is in the R-X mode originating from both hemispheres.


4.1.5 Solar Wind Control


It is well known that the solar wind strongly affects planetary radio emissions,

such as the auroral kilometric radiation (AKR) from Earth [Gallagher and D'Angleo,

19811, the Saturnian kilometric radiation (SKR) [Desch, 1982; Desch and Rucker,

19831, and the DAM and HOM from Jupiter [Desch and Barrow, 1984; Rabl et al.,

1990]. In the case of HOM, it was found that the arrival of high density solar wind

streams at Jupiter can enhance the HOM energy output, activate low frequency HOM

sources located at 6~7 Rj, and widen the HOM beam to higher magnetic northern

latitudes and possibly to higher magnetic southern latitudes.

The linear cross correlation between the HOM energy and the fluctuations of

the solar wind density and velocity at Jupiter was investigated by Desch and Barrow

[19841. They found significant correlation only between variations in the HOM energy
and the solar wind density; the solar wind velocity did not seem to correlate with the

HOM energy output. The solar wind influence on the HOM emission indicates that

the solar wind particles must have direct or indirect access to the HOM source region.

There are two ways that the solar wind particles can enter the Jovian magnetosphere,

one is from the tail region, and the other from the two cusp regions near the magnetic

poles. When modeling the HOM emissions, the solar wind influence must be taken

into consideration.








4.1.6 Propagation Effect from the Io Plasma Torus


It is well known that the Jovian satellite lo has a tremendous influence on Jupiter's

DAM emissions, whose sources have been identified as Io-A, lo-B, and Io-C, etc. (see,

e.g., Carr et al. [1983]). No evidence was found for Io itself to control Jupiter's

activity below 1300 kHz from the RAE-1 observation [Desch and Carr, 1978] nor from

the Voyager PRA observation [Kaiser et al., 1979]. One aspect of the uniqueness

of the Jovian magnetosphere is the existence of the Io plasma torus in which the

(electron) plasma frequency was reported to be as high as 500 kHz from the Voyager

1 observation [Bagenal et al., 1980; Divine and Garrett, 1983; Bagenal et al., 1985].

This plasma torus could undoubtedly affect the observed radiation by refracting those

rays that must pass through it. The amount of this refraction is greater the lower the

frequency. In the case of the Voyager HOM observations, if the HOM sources are in a

high Jovigraphic latitude auroral region, some of the rays can indeed pass through a

part of the torus, although not through the densest central part, before they reach the

observer. If the HOM sources are in a low Jovigraphic latitude region (for example

close to the magnetic equator), radiation from those sources would definitely have

to pass through the torus to reach the distant observer near the equator. In this

case, radio waves would be subject to strong refraction or reflection by the torus,

depending on the actual electron density distribution in the torus. Ray paths at a

given frequency can be modeled by using a ray-tracing computer program if a source

location and an electron density distribution are assumed. One of the objectives of

this study is to determine, using the raytracing techniques, the lowest HOM frequency

at which we can neglect refraction altogether. At frequencies lower than this, an HOM

emission model should include raytracing calculations to account for the HOM source

locations and radiation beaming patterns. The propagation of the HOM emission








as a whole may be affected by the lo torus (see page 52). The detailed modeling

including the lo torus effect will be investigated in Chapter 5.


4.2 Emission Mechanisms


The purpose of studying radio emissions from the magnetospheres of planets is to

understand the relevant physical emission processes and conditions at these planets.

Radiative energy is produced in plasma by the action of any of several types of emis-

sion mechanisms. If this radiation can propagate to reach the observer, information

about the physical processes, energy exchange, and plasma environment can be ob-

tained in a coded way. The high intensities, limited bandwidths, short time scales,

and sporadic nature of the low-frequency radio emissions indicate that they are due

to stimulated emission from plasma micro-instabilities. The remarkable repeatabil-

ity of many of the decameter, hectometer, and kilometer wavelength spectra implies

a long term stability of at least some of the plasma parameters. The variations in

intensity and frequency band reflect the changes of the propagation characteristics

of the medium and/or physical processes that are involved in generating the free

energy. The repeatability of the DAM, HOM and KOM spectra suggests that the

wave frequencies are related to the characteristic frequencies of the plasma. Among

all characteristic frequencies, only the electron cyclotron frequency and the upper-

hybrid frequency appear to be directly related to the observed spectra. This leads to

the expectation that the maximum frequency of the lo controlled DAM (39.5 MHz)

corresponds to the maximum magnetic field at the foot of the lo flux tube. The

strength of that magnetic field was inferred from the Pioneer 11 observations [Smith

et al., 1976; Acunia and Ness, 1976] to be approximately 14 gauss in the northern

hemisphere. All radio waves observed so far are of the high frequency type in the








sense that they appear at frequencies higher than the local electron cyclotron fre-

quency at the source. According to Stix [1962], there are two high frequency normal

modes in a magnetized plasma: the ordinary (0) mode and the extraordinary (X)

mode. The X mode consists of two branches separated by a stop band where the elec-

tromagnetic wave becomes evanescent and cannot propagate. In the low frequency

side of the stop band is the slow mode for which the phase velocity is less than the

velocity of light; in the high frequency side, on the other hand, is the fast mode for

which the phase velocity is greater than the velocity of light. Far from a planet that

emits radio radiation, the observed radiation must be in either the fast X mode or the

O mode. Observations from Jupiter, Uranus, and Neptune indicate that most radio

emissions are in the X mode. Theories of radio emission mechanisms address how

the plasma distribution is modified so that its free energy is converted with adequate

efficiency into the electromagnetic waves near the local electron cyclotron frequency,

and how this radiation propagates through the intervening plasma to a distant ob-

server. Such theories are distinguished by whether they depend on direct or indirect

emission processes.


4.2.1 The CMI Theory


Since the discovery of radio emissions from planets with magnetic fields, many the-

ories have been proposed and developed to explain possible mechanisms and processes

involved in the generation of the planetary radio emissions. Among those theories,

the cyclotron maser instability (CMI) theory proposed by Wu and Lee [1979] has

gained significant popularity and proved to be the most promising one. The CMI

theory was developed to explain the generation mechanism of the auroral kilometric

radiation (AKR, also called the terrestrial kilometric radiation or TKR) from Earth,

and has been applied to the generation mechanism of radio emissions from other








planets. According to the theory, the emission mechanism of the AKR is attributed

to a maser effect associated with the trapped energetic electrons which originate in

the plasma sheet during a substorm. The free energy of the electrons is transferred

to electromagnetic waves via a relativistic normal Doppler resonance process. Specif-

ically, it is assumed that the energetic electron distribution function contains more

free energy in velocity components perpendicular to the magnetic field than in those

parallel to the magnetic field. Wu and Lee [1979] showed that a kinetic instability

exists when the population of suprathermal electrons possess a loss-cone distribution

function; such an instability can lead to the direct amplification of the extraordinary

and ordinary mode radiation. The loss-cone distribution function results from the

fact that injected electrons (from the plasma sheet) travel downward along the con-

vergent magnetic field lines, those with sufficiently small pitch angles can precipitate

into the upper atmosphere and therefore are lost (by collision with atmospheric par-

ticles); those with pitch angles outside the atmospheric loss cone will be reflected at

their mirror points. It is found that those ascending electrons (due to the reflection

at mirror points) play a decisive role in the amplification of electromagnetic waves

which can propagate (or escape) from Earth. Although radiation in both the X and 0

modes can be generated, the CMI theory predicts that the X-mode radiation prevails

over the 0-mode radiation [Lee and Wu, 1980]. The growth rate of the emission is

found to be related with the angle 9 of the wave normal with respect to the magnetic

field direction; it reaches a maximum when 0 is at some large value, leading to a

hollow cone of emission and the radiation is confined to the edges. Later work on

CMI theory [Wong et al., 1982; Wu et al., 1982] shows that the angle 9 at the source
is a strong function of both the ratio of the electron plasma frequency (fp) to the

cyclotron frequency (fe), and the ratio of the energetic electron density (ne) to the

background electron density (nb). Radiation triggered by the loss-cone distribution

will propagate upward and escape into free space. However, Le Queau et al. [1984a,








1984b] showed that such initially propagating waves would be heavily damped when

penetrating regions of decreasing magnetic field, while initially downward propagating

waves, on the other hand, can be amplified till they are reflected as a consequence of

the increasing magnetic field, eventually travelling upward and escaping the magneto-

sphere. Beside the loss-cone instability, there can be other types of instabilities which

also lead to freely escaping emissions. The hole-like electron distribution function is

an example of such instability; it is caused by the accelerated down-going electrons

and trapped electrons, which are suggested to be trapped throughout a time-varying

(or space-varying) parallel electric field [Luoarn et al., 1989], near the vj axis in the

(vil, v) space. The AKR is believed to be excited by the loss-cone and hole-like

feature instabilities.


4.2.2 Indirect Emission Mechanisms


The CMI mechanism described above is a type of direct emission mechanism, i.e.,
the electromagnetic waves are generated directly by the interaction of particles with

the magnetosphere.

It has been suggested, however, that the Jovian decametric radiation can arise
from indirect processes where the energetic electrons first excite electrostatic waves,

which then combine to produce the observed electromagnetic radiation. The indirect
emission mechanisms start with an assumption that the distribution function of en-

ergetic electrons is essentially that of a beam; the excess free energy is parallel to the

magnetic field. Roux and Pellat [1979] suggested that both upper- and lower-hybrid
waves can be excited by beam driven instabilities, which in turn could couple to pro-

duce the electromagnetic radiation. In the Jovian magnetosphere, where fp/fc < 1,

the coupling f "C fLHR+fUHR can produce radiation above fR=o, the right hand cut-off
frequency, thus giving a freely escaping electromagnetic wave with a frequency close








to the local gyrofrequency. It is not yet clear which of these somewhat contradictory

mechanisms produces the observed low frequency magnetospheric emissions. At the

present time, however, the Wu and Lee [1979] theory is the most popular.


4.3 Modeling


I have described characteristics of the Jovian HOM emission, mostly based on the

Voyager PRA observations. The fact that the HOM emission is strongly modulated

as the planet rotates suggests that the radiation is beamed in a way that only when

such beam is aligned with the observer can the radiation be received. This is usually

depicted as a rotating lighthouse or searchlight beam. Depending on the Jovigraphic

latitude of the observer, the HOM emission can be received twice (or once) during

each rotation of Jupiter. In this section, I will first briefly discuss some equatorial

beaming models that were proposed in the literature and show the difficulties that

those models face. I will describe in detail a beaming model that can account for

the beaming effects. The key point for a successful model is that it should be able

to simulate the intensity variations observed by the two Voyagers, namely the two

radiation peaks near the CML of 3300 and 900, and a true wide gap around 2000

CML, and a narrow gap around 300 CML.


4.3.1 Equatorial Beaming Models


By comparing observations from four spacecraft (RAE-1, IMP-6, Voyager 1 and

Voyager 2), which covered Jovigraphic latitudes from -3?2 to 6?5, Alexander et al.

[1979] first pointed out that a magnetic latitudinal beaming pattern could very well

account for HOM emission behavior. Although they did not provide any proposal or

hypothesis regarding the HOM source location and mechanism of generation of the

HOM emission that can form such a beaming pattern, they concluded that the HOM








emission is confined in a curved thin sheet with a thickness of about 100 centered at

a constant magnetic latitude of 2,4 north of the magnetic equator at about 2Rj.

One of the attempts to model such an equatorial beaming pattern was made

by Ladreiter and Leblanc [1989, 1990b] who used the raytracing technique to locate

the HOM sources) and tried to simulate the HOM beam. According to them, the

equatorial beam of the HOM emission was formed by the HOM sources distributed

all over the longitudinal region around an auroral zone, each of the source points

emits radiation in the hollow cone fashion. By adjusting the source location and the

beaming cone angle, they argued that the combination of all such beaming cones

would produce an equatorial beam with about 10 thickness and centered at about

+3 magnetic latitude, as proposed by Alexander et al. [1979]. If one closely studies

the latitudinal profile produced in such manner, one can indeed see at least one

maximum close to the magnetic equator that is formed by the contribution from

equatorial edges of all beaming cones. What is ignored in both the Ladreiter and

Leblanc model (referred to as the LL model hereafter) and a more qualitative model

by Barrow [1991] is the contribution from overlaps of side edges of all beaming cones.

It will be shown following that side edges of beaming cones of all sources can make

up to 50% of contribution to the received radiation. Such a side-edge contribution

was subtracted as a background noise in the LL model, for which they did not give

any justification. To demonstrate how significant the side-edge contribution can be,

let us assume, as the LL model suggests, that the HOM sources are distributed on

a certain L-shell (~ 20) along all (magnetic) longitudes around the auroral zone

(in either the northern or the southern hemisphere, depending on the polarization
component being concerned). The continuously distributed source can be replaced

by an arbitrary number of point sources (or sub-sources). Each subsource emits

radiation and the radiation is beamed into a hollow cone with a half-angle of /o and

thickness of A0. The normalized beam pattern is given by Equation (4.7). Radiation








from all subsources received by an observer at a given magnetic latitude are incoherent

and are summed together to yield the final intensity for each latitude position of the

observer. Once the received intensity for an observer at a broad range of latitudes

is calculated, an intensity profile as a function of magnetic latitude is obtained and

normalized to the peak intensity values. The latitudinal intensity profile so calculated

is shown in Figure 4.13 for the emission at 1 MHz located at L = 20. The cone half

angles (flo) for each subsource are assumed to be identical and are adjusted so that

a maximum is formed near 30 magnetic latitude. In panels (a) and (b), the HOM

source is approximated by 360 point sources distributed uniformly on the L = 20 shell

along the magnetic longitude all over the auroral zone and the beam thickness, A#3,

is assumed to be 50 and 1, respectively; while in panels (c) and (d) the number of

subsources are reduced to 25 for emissions at f = 1 MHz and f = 500 kHz for the

same beam thickness. In order to make an intensity profile with a maximum near

the magnetic equator which is independent of observer's longitude, the number of

subsources must be large enough. Only 9 subsources were used in the LL model used

to simulate the assumed continuously distributed HOM sources. One can see clearly

from Figure 4.13 that contributions from side edges of emission cones of subsources

can be 50% that of the equatorial edges and therefore cannot be ignored in the

equatorial beaming model suggested by Ladreiter and Leblanc.

Even when the wall of the emission cone is very thin (1 shown in Figure 4.13b), the

side edge contribution is still more than 20% that of the peak value of the equatorial

beam (however, the resultant beam width of 50 is too narrow to account for the

HOM beam). One of the strong arguments made by Ladreiter and Leblanc [1989,

1990b] with regard to the HOM source locations is that the HOM emission was also

detected near the CML region of 2000 where the wide gap usually occurs, when

Voyager was very close to Jupiter and was at lower Jovigraphic latitudes. The wide

gap occurred, as suggested in the LL model, when the observer was too far away











































HafnILLV'7 OlJ3NDVN


0 0 0 0 0


~U~HLWI D113'NDVJ'l


' aanulIV I. iNDVAo


0 0 0 0


* aaniJiLV DII3ND vA


8




v 0
o




bOQ



'e-0










0 Q)




bMO
&4 ce
cQ (J



0
0








*
u0 0








o d


.-4-
~044








10 0 0
o-










&.40
- CI)
.a0 --

-i




















bO ce
0 L <
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from the source such that the intensity of the radiation arrived at the receiver had

dropped below the detectable limit of the receiver. There is no doubt that very weak

emissions could not be detected by the Voyager PRA experiment until the spacecraft

was very close to Jupiter. However, the peak intensity values obtained near 3300

and 900 CML just four or five rotations before and after the closest approach are at

least 15 dB above the background level, while the intensity readings near the wide

gap region centered at 2000 CML are virtually the same as that of the background

level. In other words, the intensity values near the two peaks are at least 30 times

stronger than that which would have been detected near 2000 CML. If the equatorial

beaming model of Ladreiter and Leblanc were correct, the intensity readings of the

Voyager PRA receiver near 2000 CML would have been much higher than that of the

background level due to contributions from side edges of subsources. Furthermore,

recent observations made by the URAP experiment on board Ulysses also indicate a

true gap near 2000 CML [Lecacheux et al., 1992b]. The fact that the URAP receiver is

at least one order of magnitude more sensitive than that of PRA's strongly suggests

that the gap at 2000 is a true one.

Another strong argument which does not favor the LL equatorial model is that

there is no clear mechanism that would make the HOM emission at all frequencies

(from 300 kHz up to 7 or 8 MHz) from high latitude region to be all beamed parallel

to the magnetic equator. Since the HOM emission is believed to originate from the

place close to the local electron cyclotron frequency, the source radial distances and

the magnetic field directions at the sources are very different for different frequencies.

It is hard to imagine that the beaming geometry is set so coincidentally that radiation

at different frequencies would eventually be in the same latitudinal direction. It will

be demonstrated with the raytracing technique in the next chapter that the presence

of the lo plasma torus does not play this magic role either.








I have demonstrated above that the proposed equatorial beaming pattern cannot

be constructed by simply overlaying emission hollow cones from subsources located in

not-so-large L-shells (L < 30~50) distributed along a broad range of longitudes. It is

possible, however, to construct such equatorial beams from sources at other locations

with different beaming properties. For example, if the HOM sources are located

on the R = 0 cutoff frequency surface (or fc surface) at the places where the local

magnetic field direction is nearly parallel (or anti-parallel) to the magnetic equator,

then filled-cone beaming would provide a true equatorial beaming pattern. In this

case, an observer near the equator would indeed detect a lack of radiation near 2000

CML. For this model to work, it is required that radiation at different frequencies

originates from different L-shells (the higher f is, the smaller L value will be) and

source (magnetic) latitude for all frequencies would be roughly the same value close

to 530 (if an OTD magnetic field model is assumed). The problem is that there has

been no physical mechanism supporting such a filled-cone beaming model.

The other possible model that can produce the proposed equatorial beaming pat-
tern can be that radiation beamed in a single, wide-open hollow cone comes from a

very high latitude (cusp) region. If the HOM emission does originate in a small region

at very high latitude (i.e., very large L-shell) in the cusps in both hemispheres and

beamed into a large angle hollow cone, one can expect that the resultant beaming

would be close to the magnetic equator. Figure 4.14 shows the intensity profile sim-

ilar to those shown in Figure 4.13 as a function of magnetic latitude of an observer,

produced by a single source located on the L = 100 shell with radiation beamed into

a hollow cone of half-angle of /o = 850. The emission beam is correctly produced near

the magnetic latitude of 30 with width of about 100. This is the kind of beaming

pattern that Alexander et al. [1979] had proposed. The cusp region is one that the

solar wind particles have the direct and the easiest access along the opened magnetic

field lines, giving rise to particles that could trigger the HOM emission. In this region,









f = 1000.0 kHz, L = 100.0


10




S 6

40




0o

0 .2 .4 .6 .8 1
NORMALIZED POWER


Figure 4.14. Intensity profile created with a single source located near the north-
ern cusp region with radiation beamed into a 850 half-angle emission cone. A
latitudinal beam near the magnetic equator is correctly produced.



the plasma density might be low enough that would make the CMI mechanism easy

to work [Dulk et al., 1992; Lecacheux et al., 1992a; Zarka, 1992].



4.3.2 Model Assumptions


Hollow cone beaming models have been previously proposed to explain the DAM

emissions from Jupiter (see, e.g., Goldstein et al. [1979] and Thieman and Smith

[1979]), and kilometric emissions from Uranus (e.g., Gulkis and Carr [1987], Carr and

Gulkis [1987]). The similarity of the power spectrum of the Jovian HOM and KOM

emissions to those of other giant planets suggests that they may share a common

emission mechanism. Based on the exceptional intensity profile and other charac-

teristics of the HOM emission observed by both Voyagers, a hollow cone beaming








originating from a confined source region is chosen for the model to explain the HOM

emission's bilobed and monolobed pattern.

The following assumptions will be made in my HOM emission modeling process.

(1) The emission mechanism is similar to that of the auroral kilometric radiation
(AKR) from Earth, namely the cyclotron maser instability (CMI) [ Wu and Lee, 1979;

Omidi et al., 1984; Lyons and Williams, 1984]. The AKR spectrum is characterized

by lower and upper cutoff frequencies at about 50 and 500 kHz, respectively [Lyons

and Williams, 1984]. If it is assumed that the Jovian kilometric, hectometric, and

decametric components are distinct (Io control is observed only in the case of the

DAM emission), then the hectometric cutoff frequencies appear to be about 300 and

2000 kHz [Carr et al., 1983]. If it is further assumed that the Jovian hectometric

radiation is emitted within regions having the same range of values of the ratio fp/fc,

(fp and fc are the plasma and cyclotron frequencies, respectively) as does the AKR
[Lyons and Williams, 1984], it follows that fp as well as f, are about 4 times higher in

the Jovian than in the terrestrial source regions. The indicated values of the electron

number density of Jupiter would thus be from approximately 0.3 to 30 cm-3. These

values are in good agreement with those predicted by the Jovian ionosphere modeled

by Divine and Garrett [1983]. (2) The radiation is generated from a pair of conju-

gate cyclotron resonant sources on the same magnetic field line in both (magnetic)

hemispheres, and is in the R-X mode at frequencies which is determined by the rel-

ativistic Doppler-shifted cyclotron resonance condition. Consequently it is near the

local electron cyclotron frequency, fc. This implies that the northern and southern
conjugate sources will emit right and left elliptically or circularly polarized radiation,
respectively. This assumption is supported by the fact that the HOM emission is RH

polarization dominated when it is observed from the northern magnetic hemisphere
and LH polarization dominated when it is observed from the southern magnetic hemi-

sphere. It is also supported by the fact shown in Figure 4.3 that intensities from the








two polarization channels have a similar global profile and occurrence appearance.
Ortega-Molina and Lecacheux [1991] provided the evidence that the two HOM com-
ponents are emitted in different source regions and very likely from the conjugated
source regions with similar beaming properties. (3) The radiation is beamed into a
hollow cone whose axis is tangent to the local magnetic field at the source and whose
vertex is located at the source. Such a beaming cone or cones is fixed to the magnetic
field and rotating with the planet. (4) The emitted power from each point in the
source region is gyrotropic, i.e., it is azimuthally symmetrical about the tangent of
the magnetic field at the source point. The normalized power pattern at a constant
azimuth is specified by


S+ I cos [k (f-/)], if lk(0 o-/) 5 1800; (47)
10, for other # values ,

where 3o0 is the half opening angle of the hollow cone defined by the azimuthal direc-
tions for which p(/) = 1 (its maximum), #/ is the angle between the magnetic field at
the source and the observer, k is a parameter that determines the beam thickness. An
equivalent term, the half-power beamwidth A/3, where A3 = 180/k, is also used to
measure the beam thickness. The second condition (I k (f3o-fl) I > 1800) in Equation
(4.7), approximately, is a necessary one. It simply indicates that no radiation would
propagate toward and pass through the stop zone surface. The stop zone surface is
determined by f = fR=o (and therefore f a fc) and is normal to VB (and therefore
approximately normal to B at high latitude regions); inside this surface no radio
wave in the R-X mode is allowed to propagate. (5) The local magnetic field vector of
the magnetic field line that connects the pair of conjugate cyclotron resonant sources
is pointed toward the longitude of the narrow gap (w 30 CML). The narrow gap
occurs, therefore, as the radial vector from the source to the spacecraft comes closest
to the axis of the hollow cone beam (when the spacecraft is traversing the inside of
the hollow emission cone); while the wide gap occurs when the hollow cone beam is






83



4^ 250 kH



S-..Hz7----------------
/.-----_-----:
1i250kHz








5 10 15 20 25
L-SHELL

Figure 4.15. Distance of sources to the magnetic equator at indicated frequencies
as a function of the L-shell value.


turning away from the spacecraft. The longitude of this field line connecting both the

northern and southern sources is an adjustable parameter of the model. (6) The initial

wave refraction, if any, occurs only in a small localized region near the source and the

final directions of wave propagation is confined in the hollow beaming cone. Refrac-

tion by other sources such as the lo plasma torus will be neglected. This is not totally

true, because the presence of the lo plasma torus will certainly alter propagation di-

rection of waves that pass through the central, dense region of the torus. However,

since all the HOM sources are at least 1.5 Rj above the cloud-tops of Jupiter, and

they have relatively large distance from the magnetic equator, radiation received by

a distant observer would barely go through the lo plasma torus and therefore would

not be affected by the torus. To demonstrate this, I calculated, as is shown in Figure

4.15, distances to the magnetic equator of many different potential source positions

at frequencies of 250 kHz, 500 kHz, 750 kHz, 1000 kHz and 1250 kHz as a function

of the L-shell values. This figure clearly shows that if the HOM radiation is from








the fc = f surface on L-shells with L > 5, the source will be at least 2 Rj from the

magnetic equator. Even if the lo plasma torus extends 1 Rj above and below the

(centrifugal) equator, radiation from given source locations can reach an observer at

a magnetic latitude as low as -11 without passing through the lo torus. Refraction

from the lo plasma torus can be therefore, to the first approximation, ignored. This

assumption will be justified in Chapter 5 where raytracing calculations indicate that

radiation from high magnetic latitude region can reach a distant spacecraft near the

magnetic equator without being affected by the lo torus.


4.3.3 The Beaming Geometry


Figure 4.16 shows the geometry of our corotating hollow cone beaming model and

how the model could produce the observed results. In panel (a), (X, Y, Z) are the

axes of the Jovicentric equatorial system (not to be confused with the XYZ system

in Chapter 2), and the source (southern source not shown) is located at the point

P(r, 0, A) at which the magnetic field vector is B. The longitudes of the spacecraft

and the sun are indicated in each of four diagrams in panel (b). The leading-lobe and

trailing-lobe maxima of the intensity-time plot occur in the diagrams for which the

Jovigraphic longitudes of the spacecraft are assumed to be 323 and 830, respectively.

The CML locations of the apparent sources corresponding to these edges can be found

with this model. The midpoint of the narrow gap occurs when spacecraft's longitude

is midway between these values, at 230. The wide gap occurs when the longitude

of the spacecraft is 203 (i.e., 180 opposite) which is actually the observed mean

midpoint of the wide gap for the Voyager 1 data after encounter (see Table 4.1). It is

also the longitude of the north magnetic pole for the tilted dipole field. If the emission

cone is inclined such that only the equatorial edge of the cone reaches the observer,

then only one radiation event will occur, resulting in monolobed intensity profile.































b) Sun





sc


Sun




I
... ........ S


(. r S. .


Figure 4.16. (a) Geometry of the hollow cone beaming model. Only one "sub-
source" point is shown. Source(s) in the southern hemisphere are not shown. (b)
A sequence of rotation seen from top of the north pole during the post-encounter
period. The "V" shape beaming pattern is the intersection of the beaming cone
defined by the beam-maximum directions with the plane containing the observer
and the vertex of the cone. The angle between the leading edge and the trailing
edge is about 1200, which is the angular separation of the two HOM emission
peaks.



When the axis of the emission cone is inclined by an angle t to the plane passing

through the cone vertex and the spacecraft, then the emission cone will intersect this

plane along a curve whose asymptotes are two straight lines intersecting at an angle

2a, where a has a relationship with t and the cone opening angle f/o:



cos os0 (0 < o0 < 90, 0 < t < 90), (4.8)
COS t


Sun




.. ....... S








or equivalently,

tan2 a = tan230o cos2 t sin2 t.

This formula was actually used first by Goldreich and Lynden-Bell [1969] and later by

Goldstein et al. [1979] and Thieman and Smith [1979] in their modeling of Jupiter's

decametric radio emissions. Equation (4.8) immediately leads to the following impor-

tant implications. First, the minimum cone opening angle will be flomin = a when

the tilting angle t is 0 (i.e., when the cone axis is parallel to the plane on which the

spacecraft lies). Also, in order for the emission cone to reach the observer (a > 00), the

tilt angle t has to be smaller than the cone opening angle fo. Since the tilting angle

t is measured from the magnetic field direction at the source, it can be expressed in

terms of the magnetic colatitude of the source (Om) and the magnetic latitude of the

spacecraft (6m):

3 sin 20m
cos(t + Sm) = 2 /1 +cos2 m (4.9)
2Vf1 + 3 cos2 Orm

From the second assumption of the model (on page 81), the radio source is located

on the surface of cyclotron frequency fc which is only slightly smaller than the radio

wave frequency. The magnetic field intensity at the source is thus determined by

B = 2rmefc/e, which at the magnetic colatitude 0m on a specified L-shell is expressed

as

M.V1 + 3 cos2 Om
LB sin6Om m

where M is the dipole moment. On the fe-surface, the L-shell value and the magnetic

colatitude Om are therefore related such that


3 eM_ v1 + 3 cos2 Om
L = mefc sin6 m (4.10)


Equations (4.8), (4.9) and (4.10) provide a guideline for us to set the adjustable

parameters of our model. The most important parameters that would affect fitting








quality are the L-shell values of the source and the opening half-angle of the emission

cone, /0. The Voyager observations after Jupiter encounters show that the HOM

emission reaches two peaks when the spacecraft is at about 3300 and 900 CML. This

means that the angular separation of the two peaks is about 1200. This leads to

a c 600. Equation (4.10) indicates that sources at larger L-shells will be at higher

magnetic latitude (smaller 0m), and therefore the cone axes will be tilted further away

(t increases) from the spacecraft. This naturally will require a larger cone opening

angle to maintain the angle a unchanged.


4.3.4 Modeling Procedures and Results


Based on the model assumptions and the geometry considerations, I simulated the

Jovian HOM emission as detected by the Voyager spacecraft with a pair of modeled

conjugate source regions which are located in the northern and southern hemispheres,

respectively. The following adjustable model parameters for each considered radio

wave frequency are used: (1) central longitude of the source region, Ac; (2) longitudi-

nal width of source region, AA; (3) L-shell value, L, of the magnetic field line passing

through both source regions; (4) half-angle of the hollow beaming emission cone, 0o;

(5) thickness of the emission cone, A/3; and (6) intensity scaling factor, S. The actual

source is continuously distributed within the specified region just outside the stop

zone, and is located above one, or each, auroral zone. The distributed source can

be approximated by a group of equally incoherently-emitting point sources, or "sub-

sources". Locations of each of the subsources are determined by radiation frequency,

L-shell value, and longitude of the field line.

In the modeling process, models that best fit to the observed curves of the radiation

intensity at 1 MHz, and at other frequencies, were made as a function of time. The

criteria to measure the goodness of fitting are: (1) positions of the emission peaks








in terms of CML or SCET; (2) duration of each emission peak; (3) relative strength
of the emission peak. These criteria are mainly used for visual examination of the

modeling process. In addition to the criteria, the standard deviation of the modeled

intensity curve from the observed, smoothed intensity curve is used for a quantitative

measurement along with the visual examination. The fitting was first done separately

for each of several groups of subsources equally spaced at 1 interval along the lines

of constant L-shell value. The magnetic field assumed was the 04 model [Acunia and

Ness, 1976] plus a contribution due to the current sheet [Connerney, 1981]. For each

of assumed sets of positions of the subsources, initial values were assumed for the cone

angle (/%0) and the beam thickness parameter (k). Then a normalized power p(/),

as defined by Equation (4.7), for each subsource was multiplied by the subsource-

to-spacecraft distance squared, and the intensity contributions were summed. After

adding a constant background value to the summed intensity and finding the most

suitable scale factor, the computed curve was visually compared with the observed

intensity curve. The process was repeated, systematically varying the adjustable

parameters /0, k, and scale factor S, until a best fit was obtained. Then the process

was again repeated for new sets of positions of the subsources until the latitude and

longitude range within which acceptable fits of modeled-to-observed intensity curves

could be obtained were determined. This was done for assumed source regions in

the northern and southern auroral zones separately, and also for conjugate pairs

of simultaneously emitting sources located in the two hemispheres. In the latter

case, models were investigated for which the adjustable parameters f0o and k were

identical for the two conjugate sources, and others were investigated for which they
were different.

The cone parameters, the source location, and the source width in longitude (in
each hemisphere) that would best fit to the observed data were determined for a series

of groups of subsources, with each group at a constant L-shell value. The RH and










Table 4.2. Model parameters that result in best fit to the observational emissions
at 1 MHz, 0.75 MHz and 0.5 MHz for a pair of conjugate sources in the northern
and southern hemispheres.


Northern source


Southern source


L Ac

f = 1 MHz 4 350
6 300
10 250
15 350
20 350
30 400
50 300

f =750 kHz 4 370
6 370
10 370
15 370
20 370
30 400

f =500 kHz 4 400
6 400
10 400
15 400
20 400
30 400


AA #o AO3

100 640 260
100 680 200
100 730 110
9 760 130
100 780 100
100 800 70
100 830 80

100 600 290
100 650 220
100 700 160
100 730 120
100 750 90
100 780 70

100 600 420
100 660 320
100 680 200
100 700 130
100 730 110
100 760 80


LH intensity components (from assumed conjugate source locations of the same set of

field lines) were modeled independently. For radiation at 500, 750, and 1000 kHz, the

parameters leading to a good fit to after encounter observational RH and LH intensity

curves are listed in Table 4.2. Seven locations of the sources were considered for 1

MHz, and six locations each for 750 kHz and 500 kHz. If the sources are in lower

latitudinal regions (smaller L-shell values), the magnetic field direction at the source

is more toward the observer, as has been predicted. In this case the inclination angle

of the emission cone relative to the observer would be smaller, which would lead to a


L Ac

4 300
6 300
10 300
15 300
20 300
30 300
50 300

4 250
6 250
10 250
15 200
20 200
30 200

4 300
6 300
10 300
15 300
20 300
30 300


AA #o

9 600
100 650
100 700
9 730
100 750
100 780
100 800


590
630
690
730
750
78

580
640
700
730
760
800


A#

480
400
310
260
230
200
160

480
380
300
260
230
200

540
430
340
280
260
240








smaller cone opening angle (/0o). Calculations shown in Table 4.2 also show that for

sources at high latitudes (and therefore larger L-shell value and greater emission cone

opening angle f3o), the cone thickness becomes narrower (smaller AO3). Examples of

comparison of the modeling results and the observed ones are shown in Figures 4.17

for radiation of both LH and RH components at 1 MHz and 750 kHz. These results

indicate that our model correctly simulated the occurrence of the HOM emission,

with a wide gap near 200 CML and a narrow gap near 300. The wider separation of

the leading and trailing maxima for each rotation cycle for the RH data than for the

LH data was also correctly simulated.

We have already seen, from the calculation of the averaged flux density and the

occurrence probability shown in Figures 4.4 and 4.5, that radiation received near 3300

CML are usually stronger in intensity or have higher occurrence probability than those

received near 900 CML. An additional parameter, ratio of the peak intensity of the

trailing lobe to that of the leading lobe, could be introduced to account for such

intensity variation. The best value of this ratio was usually about 0.5. This intensity

reduction might be attributed to the loss of energy of the group of radiating trapped

particles between the times the leading and trailing lobes were observed, as will be

discussed below. The other reason for this uneven intensity profile is probably that

the gradients in magnetic field strength B are asymmetric about the emission cone

axis, the amount of radiation beamed into the emission cone can be different on the

two sides.


4.3.5 Discussion


We have modeled the HOM emission at different frequencies originating on the

magnetic field lines with various L-shell values. Computation results with a variety

of parameter sets fit the observation almost equally well, and predict a wide range of
















































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L-shells for possible locations of the source. The question as to whether the HOM

sources are located on lower or higher L-shell magnetic field lines has been controver-

sial in the literature. One consideration in this regard is that the reported solar wind

control of the HOM favors large L-shell values, which would permit easier access of

solar wind electrons than would the small L-shell locations. Recent observations from

a new spacecraft, however, suggest otherwise.

In early 1992, the spacecraft Ulysses encountered Jupiter from a high latitude
orbit. The URAP experiment on board Ulysses is the first radiometer that has the

capability of direction finding. Preliminary results [Reiner et al., 1993a, 1993b] indi-

cate that the HOM sources are located in a low L-shell region with L w 4 ~ 8, assuming

that radiation is emitted near the fc = f surface and propagates along straight lines

without being affected by the lo plasma torus. This result appears to be in direct

support of the low L-shell source origin, but it cannot be relied upon because the

assumption of straight line propagation is almost surely incorrect. A better model

is needed to locate the source region by raytracing the observed radio waves back to

the source region.

If the HOM sources really are located on the low (4~7) L-shells, the natural

electron source would be the trapped electrons that cross the magnetic equator within

the cold plasma torus. The cold torus is about 5 to 5.8 Rj from the center of the

planet, located in the inner part of the toroidal distribution of relatively dense plasma

surrounding Jupiter near the orbit of Io. The distribution of the cold torus is highly

asymmetrical in longitude with the highest densities occurring approximately within

the range of 2500900 and the lowest at diametrically opposite longitudes. Trafton

[1980] found that the ratio of the highest to lowest plasma densities can be as large as

5, and other observers found longitudinal variations almost as high. According to our

results, the HOM emission originates at a magnetically conjugate pair of sources close

to the Jovigraphic longitude of the south magnetic pole. The reason for the absence of