Observations of Jupiter's decametric radiation with a very-long-baseline interferometer


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Observations of Jupiter's decametric radiation with a very-long-baseline interferometer
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xii, 156 leaves. : illus. ; 28 cm.
Lynch, Michel Allan, 1939-
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Jupiter (Planet)   ( lcsh )
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Thesis--University of Florida.
Bibliography: 152-154.
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Observations of Jupiter's Decametric Radiation

with a Very-Long-Baseline Interferometer






The author wishes to express his appreciation for direction and aid

furnished by his research advisor, Dr. Thomas D. Carr. The very-long-

baseline interferometer studies have been a continuing interest of

Dr. Carr's, and it has been the author's privilege to have served

under him in this project. It has been an instructive experience to

have studied under Drs. A. G. Smith, K. R. Allen, G. R. Lebo and

K-Y. Chen. Each contributed time and thought in the form of consulta-

tion, reading of the manuscript of the dissertation and encouragement.

While the author wrote most of the programs used in the research

reported in this dissertation, several programmers supplied specific

programs to help the project. The work of Mr. Jamie Stone, Jr., in

writing the digitization programs, was vital to the data processing

and is greatly appreciated. Miss Carol Vilece contributed the early

versions of the data handling programs for the IBM 1800 and operated

the machine during digitization. The author is in debt to both

Mr. Stone and Miss Vilece for expediting his work under the difficult

scheduling conditions that obtain on the IBM 1800 at the University of

Florida Medical Center. Mrs. Mary Coates Lynch wrote the program to

convert the column-binary card code to a useable form for the

IBM 360/65 at the University of Florida Computing Center. Both her aid

as a programmer and her encouragement as a wife determined, in no

little way, the success of this research.

The author wishes to acknowledge the aid of Mr. W. W. Richar,

and Mr. H. W. Schrader in the preparation of the drawings and pho

graphs. He wishes to thank Mrs. Terrie Campbell for her care in

typing the original draft of the dissertation.

This investigation was supported in part by the National Sci4

Foundation and the Office of Naval Research.























. vi
. vi

. xi

. 1

. 16

. 34

. 50

. 83

. 110

. 128



IV.1 . . . ... 52

IV.2 ............. ......... ....... 61

IV.3 .... ...... . ... ......... 66

IV.4 .. . .. . .76

V.1 . . . 89

V.2 . . . .. 99

V.3 ... .. . 101

V.4 ... ... ...... ............. 102

VII.1 . . .. . .. 128




-- Geometrical Relationship of Jupiter, Io and the
Earth for Io-Related Storms . .

-- (a) Diagram of the Classical Interferometer,
(b) Graph of the Output SO Versus Beam Angle @0

-- (a) Diagram of the Multiplying Interferometer,
(b) Graph of the Output S, as It Depends on y
(solid line) and on @0 (dashed line) .




-- (a) Diagram of the Brown and Twiss Post-Detection-
Correlation Interferometer, (b) a Sample Record 27

-- Graph of V,(s ) Versus Baseline Length for a Gaussian
Source of Various Angular Widths . .. 33

III.1 -- Diagram of 1969 Receiving System .... .35

111.2 -- Diagram of 1970 Receiving System . .. 38

111.3 -- Diagram Showing Frequency Conversion Scheme Used
in 1970 Receiving System . ... ... 40

111.4 -- Diagram of Details of 1970 Receiving System ... 41

III.5 -- (a) Computer Plotted Data of Entire Burst as
Received at MAIPU, (b) Portion of Time Channel
Digitized Simultaneously with Data in (a), (c)
Computer Plotted Expanded Portion of the Center
of the Burst in (a) . .

IV.1 -- Western Hemisphere Map Showing the Locations of
the Receiving Stations and WWV. MAIPU Is near
Santiago, Chile . .

. 44









IV.2 -- (a) View of Earth, Jupiter and the Sun from Above
the North Pole on 2 January 1969, (b) DNS and DEW
Projected on the Plane Perpendicular to the
Line-of-Sight to Jupiter . .. 53

IV.3 -- Actual Chart Records of the Heterodyned Data
from WKU (a), FPC (b), UFRO (c) and MAIPU (d)
for the L-Burst of 2 January 1969. Alternate
Lines Are the Timing Channels for the
Corresponding Stations . 56

IV.4 -- Plot of Heterodyned Data from WKU (a) and MAIPU
(b). Plot of Cross Correlation Function (c) and
Normalization (d) Versus Time for L-Burst of 2
January 1969 ... . 58

IV.5 -- Plot of Heterodyned Data from WKU (a) and FPC
(b). Plot of Cross Correlation Function (c)
and Normalization (d) Versus Time for L-Burst of
2 January 1969 . .. .59

IV.6 -- Plot of Heterodyned Data from FPC (a) and MAIPU
(b). Plot of Cross Correlation Function (c) and
Normalization (d) Versus Time for L-Burst of
2 January 1969 . ... 60

IV.7 -- Plot of Data After Receiving the One-Bit Treatment
from WKU (a) and MAIBU (b). Plot of Cross
Correlation Function (c) and Normalization (d)
for This Data . .... .64

IV.8 -- Plot of Detected Data from WKU (a) and MAIPU (b).
Plot of Cross Correlation Function (c) and
Normalization (d) Versus Time for L-Burst of
2 January 1969 . .. .67

IV.9 -- Plot of Detected Data from WKU (a) and FPC (b).
Plot of Cross Correlation Function (c) and
Normalization (d) Versus Time for L-Burst of
2 January 1969 . .... 68

IV.10 -- Plot of Detected Data from FPC (a) and MAIPU (b).
Plot of Cross Correlation Function (c) and
Normalization (d) Versus Time for L-Burst of
2 January 1969 . .... .69



IV.11 -- Actual Chart Records of the Detected Data from WKU
(a), FPC (b) and MAIPU (c) for the L-Burst of
2 January 1969. Records Are Laterally Adjusted
Such as to Be Aligned in Real Time .... 71

IV.12 -- Plot of the Amplitude of a Constant Intensity
Signal as Received at Two Stations as the Beam
of Radiation Sweeps from Station 1 to Station 2.
Frequency Modulation Features Are Visible Under
the Envelopes .. . 73

IV.13 -- Plot of Heterodyned Data near Data Point 840 for
WKU (a) and MAIPU (b). Plot of Cross Correlation
Function (c) and Normalization (d) for Relative Shift
= 38 Data Points. Plot of Cross Correlation
Function for Relative Shift = 37 (e), 39 (f) and
40 (g) Data Points . . 75

IV.14 -- Plot of Detected Data near Data Point 840 for
WKU (a) and MAIPU (b). Plot of Cross Correlation
Function (c) and Normalization (d) for Relative
Shift = 38 Data Points. Plot of Cross Correlation
Function for Relative Shift = 37 (e), 39 (f) and
40 (g) Data Points . .... 77

IV.15 -- Cross Correlation Measures Plotted as Function of
Relative Shift for the WKU-MAIPU Baseline. (a) C2
for Detected Data with N = 112 Milliseconds. (b)
and (d) C2 for Detected Data in the Vicinity of
Data Points 840 and 1240, Respectively, with N = 15
Milliseconds. (c) and (e) Amplitude of the Cross
Correlation Function Near the Same Two Locations
with N = 2.1 Milliseconds . .... .78

V.1 -- (a) View of Earth, Jupiter and the Sun from Above
the North Pole on 30 April 1970, (b) DNS and DEW
Projected on the Plane Perpendicular to the Line-
of-Sight to Jupiter . .... .84

V.2 -- Chart Records Showing Detected Data from MAIPU (a),
UFRO Channel A (b) and UFRO Channel B (c) Beginning
at 9h35m5195 U.T. on 30 April 1970. Bursts 1, 2 and 3
Are Labelled. The Tallest Marks Visible in the Time
Channels Are Second Ticks . .. .. 87




V.3 -- Chart Records Showing Detected Data from MAIPU (a),
UFRO Channel A (b) and UFRO Channel B (c) Beginning
at 9h35m54s82 U.T. on 30 April 1970. Bursts 4, 5,
6, 7, 8, 9, 10 and 11 Are Labelled. The Tallest
Marks Visible in the Time Channels Are Second Ticks 88

V.4 -- Computer Plots of S-Burst Number 5 from MAIPU (a)
and UFRO (c). Chart Records for the Same Burst
from MAIPU (b) and UFRO (d). The Features Marked by
A Are Aligned for the Best Relative Time Shift 91

V.5 -- (a) C2 Versus Relative Shift for Burst Number 1.

(b) /C + C Versus Relative Shift for Burst
Number 1 . .. .94

V.6 -- (a) C2 Versus Relative Shift for Burst Number 3.
(b) /C2 + C2 Versus Relative Shift for Burst
Number 3 . . .. ... 95

V.7 -- (a) C2 Versus Relative Shift for Burst Number 4.
(b) /C2 + C2 Versus Relative Shift for Burst
Number 4 . .. .96

V.8 -- (a) C2 Versus Relative Shift for Burst Number 9.
(b) /CA + C2 Versus Relative Shift for Burst
Number 9 . . 97

V.9 -- VC2 + C2 Versus Relative Shift for (a) Burst
Number 2, (b) Burst Number 5 and (c) Burst
Number 6 . .... .. ... .. .103

V.O0 -- /C2 + C2 Versus Relative Shift for (a) Burst
Number 7, (b) Burst Number 10 and (c) Burst
Number 11 . . ... 104

V.11 -- Cross Correlation Function (C) Versus Time for
all S-Bursts in Series. Connected Data Points
Are Taken from the Same Burst Number ... .107



VI.1 -- (a) View of Earth, Jupiter and the Sun from Above
the North Pole on 12 April 1971,(b) DNS and DEW
Projected on the Plane Perpendicular to the Line-
of-Sight to Jupiter . .. 112

VI.2 -- Actual Chart Records of Detected Data from
MAIPU (a) and UFRO (b). Data Starts at 8h51m23sU.T.. 115

VI.3 -- Computer Plot of Data from MAIPU (a) and UFRO (b)
Showing a Region Located 716 Milliseconds After
the Beginning of the Burst. Features Marked A
Are Aligned for the Best Relative Time Shift ... 117

VI.4 -- (a) C2 Versus Relative Shift and (b) /C2 + C2
Versus Relative Shift for Segment Number 14 of
L-Burst . . .. 119

VI.5 -- Actual Chart Records of Detected Data Running for
4 Seconds Starting at 8h51m23s4 Are Shown at (a).
Cross Correlation Function (b) and Normalization
(c) Plotted Versus Time . ... 121

VI.6 -- Time of the + to Transition of the Fringe Versus
the Number of the Fringe for the L-Burst Recorded
on 12 April 1971 . . 124

VI.7 -- Fringe Period Versus Fringe Number for the L-Burst
of 12 April 1971. . .. 126

VII.1 -- Graph of Vo(sX) Versus Baseline Length for a
Gaussian Source of Various Angular Widths.
Circled Data Points Are the Averaged Fringe
Amplitudes for the 1969 Data. A Triangle Indicates
the Averaged Fringe Amplitude for the 1970 Data,
and a Square Indicates the Same for the 1971 Data 130

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



Michel Allan Lynch

June, 1972

Chairman: Dr. Thomas D. Carr
Major Department: Astronomy

This dissertation presents the results of several types of

measurements made on the decametric electromagnetic radiation from

the planet Jupiter using a very-long-baseline interferometer. Jovian

signals were received at stations located at Old Town, Florida,

St. Petersburg, Florida, Maipu, Chile, and Bowling Green, Kentucky.

The interferometer baselines ranged from 11,150 to 456,000 wavelengths

of the 18 MHz receiving frequency. Interference of the signals was

accomplished by using the cross correlation function with digitized

data in a program for the IBM 360/65 at the University of Florida

Computing Center.

By interpreting the amplitude of the cross correlation function

as the fringe visibility, an upper limit on the angular size of the

source of the radiation was determined to be 0.1 seconds of arc, if it

were assumed that the source was incoherent and had a Gaussian brightness

distribution. The high correlation of the envelopes of the two L-Bursts

studied using the very long baseline (over 7,000 km) indicated that the

time dependence of the strength of the burst was probably intrinsic to

the source. The stability of the fringes formed by interference of

the L-Burst data indicates that the source did not "jump about" more

than 85 km for the 2.2 seconds'duration of the 1971 burst. The

"jumping about" motion is superimposed upon a constant drift of the

source with respect to the interferometer power pattern. The analysis

of a series of S-Bursts received in 1970 indicates that, if the radia-

tion from Jupiter is beamed and the beams rotate with respect to the

Earth-Jupiter line, then the minimum sweep rate of the beams must be

greater than 100/second in the north-south direction and greater than

04/second in the east-west direction. The method of sweep-rate

measurement involved comparing the time of arrival of an identifiable

phase point on the heterodyned Jupiter signal with that of a similarly

identifiable amplitude point on the envelope of the detected signal

at various pairs of stations.

While the use of the interferometer for the determination of source

size is restricted to a source that is an incoherent radiator, the

remaining analyses place new limits on any type of source.



I-1. Jupiter's Electromagnetic Radiation and the Wavelength

Dependence of Its Characteristics

The electromagnetic radiation received from Jupiter is the main

key available for man to use in determining the nature of the giant

planet. The visible spectrum from the planet is that of sunlight

reflected off the tops of clouds. The presence of absorption lines

due to gases above the reflecting level serves to modify the solar

spectrum. In the infrared a disk temperature of about 1300K was measured

by D. H. Menzel and others as early as 1926. This measurement is thought

to represent the temperature at the cloud tops, or even somewhat higher,

if the radiation is considered to be due to a source obeying the black

body radiation laws. It was reported by Mayer, McCullough and

Sloanaker (1958) that radiometer measurements at a wavelength of 3 cm

gave a disk temperature of about 1400K. The value is in approximate

agreement with the infrared value, and it is thought to indicate that

the radiation at this wavelength is still thermally generated. A

measurement at 10 cm by Sloanaker (1959) was quite different. If the

source of the radiation received at this wavelength is considered to be

a black body, then its temperature must have been about 6000K.

Succeeding measurements at the longer wavelengths of 21 cm and 31 cm

seemed to confirm the trend with disk temperatures of 20000K and 50000K,

respectively. Radhakrishnan and Roberts (1961) reported that the source

region for this wavelength was about three times the diameter of the

visible planet in the plane of the equator and that the radiation had

a moderate amount of linear polarization. A model of the source of the

radiation at this wavelength was proposed. The model accounts for the

linear polarization by having relativistic electrons emit synchrotron

radiation as they spiral in a magnetic field.

While radiation between the frequencies of 400 MHz and 40 MHz has

yet to be detected with certainty, Jupiter is very active in the decameter

wavelength region. The decameter region contains frequencies from 40 MHz

downward to about 5 MHz where the earth's ionosphere becomes opaque. The

flux density reported by Carr, et al. (1964) increases very rapidly with

wavelength, seemingly with a spectral index on the order of + 8. Radiation

in the decameter region was first reported by Burke and Franklin (1955)

and confirmed by Shain, who used old records dating back to 1950. Shain

(1955 and 1956) reported that the source of the radiation did not emit

isotropically but seemed to radiate into preferred directions in a

coordinate system attached to the planet. System II coordinates, with

a rotation period of 9h55m40N6 (based on the temperate zone visual

markings), provided a rotating frame in which the radio sources appeared

to be at rest. This later was modified, due to the sources drifting in

System II, to a longitude coordinate frame with a rotation period of

9h55m29s37 based on the work of Shain (1956), Carr, Smith, Bollhagen, Six and

Chatterton (1961) and other groups.

1-2. The Nature of the Decametric Radiation

The most noticeable feature of Jupiter's decametric radiation is its

extreme intensity variation with time. Radiation at this wavelength comes

in the form of noise storms that last on the order of a few minutes to

a few hours. Gallet (1961) further breaks down the noise storms into

burst groups (with durations on the order of minutes) and into two types

of pulses that make up the burst groups. The L-pulse is characterized

by having a length of from 0.1 to 5 seconds while the S-pulse is shorter

with a length of from less than 10 to about 100 milliseconds. Flagg and

Carr (1967) reported that bursts substantially shorter than this have

been detected. Theories for the formation of the two types of pulses are

given later in this chapter.

Due to the extreme time variability of the radiation, it is usually

more convenient to use the probability of occurrence of an event as the

dependent variable. The location of the sources with respect to System

III was accomplished by plotting the probability of occurrence of Jupiter

radiation versus the central meridian longitude (that longitude in

System III that is directly below the earth as viewed from Jupiter). Source

A is located at approximately 2500, Source B at about 1600 and Source C

at about 3200 in System III. The source regions are each about 600 wide.

Bigg (1964) found a correlation between the superior geocentric longitude

of lo, the innermost Galilean satellite, and the probability of

occurrence of radiation from the previously described sources. Prediction

of lo-Source events can now be made. The events described in this

dissertation occurred during lo-B predicted storms. The lo-B storms

occur when Io is about 900 from superior geocentric conjunction and

Source B is crossing the central meridian.

Jupiter radiation is generally of relatively wide bandwidth. Work

by Carr, et al. (1964), Riihimaa (1964) and Dulk (1965) characterizes

the bursts as having bandwidths on the order of a MHz with center

frequencies that move in time. Some interesting features in the form of

modulation lanes visible in the amplitude-frequency domain have been

reported by Riihimaa (1970). Since the receivers in the experiments

described here have bandwidths on the order of a few kHz, the inter-

action of a frequency-drifting band of noise with the narrow-band,

fixed-frequency receivers must be borne in mind.

Decametric radiation from Jupiter exhibits strong circular

polarization. Emission from Source B is almost always polarized in the

right hand sense at the commonly studied frequencies in the decametric

part of the spectrum.

I-3. A Brief History of Jovian Decametric Measurements

Using Long-Baseline-Interferometry.

It was indicated early in the investigation of Jovian radiation

that the source was in the vicinity of the planet and was probably

rather small. It was therefore necessary to resort to interferometric

methods to measure the size of the source. Gardner and Shain (1958)

found no burst-for-burst correlation between signals received at the

ends of a 20 km baseline. Douglas and Smith (1961) reported a few bursts,

especially of the S-type, that were correlated over a baseline of 100 km.

Slee and Higgins (1963) used a radio-linked phrse sensitive interferometer

with a baseline of 32 km and frequency of 19.7 MHz. They found that the

fringe visibility was not reduced, hence the source was not resolved,

with this baseline.

The University of Florida group used a Brown and Twiss Post-

Detection-Correlation Interferometer before 1965 with a baseline of

55 km, as reported by Carr, et al. (1965). May (1965) employed data

from this interferometer to determine a maximum source size of 50 seconds

of arc. A phase interferometer was also used by this group that employed

the cross correlation of the heterodyned radio frequency noise. Brown,

et al. (1969) used this system with a baseline of 880 km to reduce the

maximum possible source size to less than one second of arc. The phase

interferometer of the University of Florida group used tape recorders

for the storage of data before cross correlation was done.

Meanwhile Dulk, Rayhrer, and Lawrence (1967) used detected, tape-

recorded receiver output to form an interferometer of the Brown and

Twiss type with a baseline of 175 km at 34 MHz. They obtained an upper

limit of 3 seconds of arc on the size of the sources of both L- and

S-bursts. Dulk (1970) and Stannard, et al. (1970) extended the baseline

to 487,000 wavelengths at the operating frequency of 34 MHz. By using

the instrument in the phase interferometer mode, they were able to

explore the phase stability of the source. If the source were assumed

to be incoherent, they found that its maximum size was less than 0.1

second of arc.

A preliminary report of part of the work detailed in this disser-

tation was made by Carr, et al. (1970) in the form of a history of the

University of Florida 18 MHz interferometry experiment. At that time a

456,000 wavelength baseline was in use, but only small samples of the

data had been hand reduced.

1-4.1. Early Theories Concerning the Production of Jovian Noise Storms

The earliest suggestions as to the origin of the Jovian decametric

radiation included Jovian lightning storms and dynamo effects created

by slippage of the cloud bands relative to one another. These early

proposals ran into energetic problems in accounting for the high

intensity of the bursts.

Warwick (1963) proposed Cerenkov radiation of relativistic

electrons as a source. This was followed by Zhelesznyakov (1965) with

a theory involving plasma waves in Jupiter's ionosphere. Ellis (1965)

is the first to have published a model that involved cyclotron radiation

from electron streams. This model stands as the direct ancestor to most

of the seriously considered theories in use today. The discovery of

the Io effect by Bigg in 1964 required the inclusion of an interaction

mechanism between the satellite and the emitting region. Gledhill

(1967) proposed that Io interacted with an implausibly dense plasma

discus about the planet by producing waves in it. Piddington and Drake

(1968) had Io disturbing the plasma as a result of its having a high

degree of conductivity or, alternatively, a permanent magnetic moment.

References to these papers are contained in Schatten and Ness (1971).

Goldreich and Lynden-Bell's theory (1969), which is discussed in the

next section, requires that Io be about 100 times as conductive as the

earth's moon. This problem is alleviated in two more recent theories.

One, by Schmahl (1970), treats Io as the source of Alfvenic waves that

travel down the magnetic field lines to the ionosphere of the planet.

The waves become shockfronts that cause radiation from coherent electron

groups. The theory is still not finished in that it does not develop

the interaction mechanism between the Alfvenic waves and the electromagnetic

waves. Another more recent theory by Schatten and Ness (1971) does

not require the high conductivity for Io that the theory of Goldreich and

Lynden-Bell does. They propose that Io is Moon-like and that Jupiter's

magnetic field lines slide through Io relatively unaffected. It causes

local perturbations in the pitch angle of the electrons spiralling in

the field near it, however, thus causing them to emit radiation when

they reach the top of the Jovian ionosphere. Schatten and Ness propose

that radiation is emitted into a plane perpendicular to the flux line

that passes through Io. Their paper presents a computer solution to the

geometry problem involving the orientation of the magnetic dipole of

Jupiter and the Earth-Jupiter line. The solutions agree with the

locations of the three commonly observed sources, and also the rarely

seen fourth source. The geometry of the theory shows promise, but as

in Schmahl's theory, the mechanism for the production of radiation is

not fully explored.

1-4.2. The Theory of Goldreich and Lynden-Bell

A possible explanation of the effect of Io on the Jovian radiation

is given by P. Goldreich and D. Lynden-Bell (1969). They propose that

the satellite acts as a unipolar inductor which generates currents along

a magnetic flux tube connecting it with Jupiter's ionosphere. The

electron currents are thought to undergo cooperation instabilities near

the planet, where they radiate by a form of MASER action into preferred

directions at frequencies just above the local gyrofrequency.

From the mapping of the source of the decimeter radiation and the

investigation of its linearly polarized component, it has been found that

a magnetic field having an approximately dipolar geometry can be assigned

to the planet. The N magnetic pole is located in the northern hemisphere

and is tilted 100 from the planet's rotation axis toward the System III

longitude of 2000. Figure I.la illustrates the geometrical relations

during Io-related storms.

Goldreich and Lynden-Bell, by assuming the conductivity of Io to

be about that of silicates, 10-5mho/cm, show that the Jovian magnetic

field would diffuse into Io in about one day. The field lines passing

through Io would rotate about the planet at Io's orbital speed. If Io

has a finite resistance, the flux tube will not be entirely trapped but

will slowly drift through it. The slippage time must be long compared

with the time for adjustments to be made in the rest of the "circuit."

The adjustments are propagated as Alfven waves. Hence, the slippage of

a flux line through Io must take longer than the time for an Alfven wave

to travel along the flux tube to the planet and return. Since, in Io's

reference frame, the parallel component of the electric field must vanish,

an electron current flows toward the planet along the outside of the flux

tube and returns to Io along the inside (the side nearest Jupiter). In

Jupiter's frame, there is an electric field in the ionosphere at the

feet of the flux tube which is directed toward the north for the one in

the northern hemisphere. The feet of the flux tube slip relative to the

rotation of the planet since the tube rotates about Jupiter at Io's

orbital rate (1.77 days). In the ionosphere the flux tube has an

elliptical cross section. When the ionization of the ionosphere is high

the feet of the flux tube will be pulled ahead of the satellite by

the rotation of the planet. The authors of the theory calculate that the

feet will lead Io by 120 under these conditions. When the ionization is

low, e.g.,night time at the foot of the flux tube, there will be no

Io-A lo-B lo-C

Pole Pole Pole


2700 A 200 1800. 1000 3500 3000 to

Io o
to to to
Earth Earth Earth



Tube Earth for l
180 1000

to (b)

Figure 1.1 -- Geometrical Relationship of Jupiter, Io and
the Earth for lo-Related Storms.

dragging, and the flux tube will terminate on the same Jovian longitude

for which lo is on the Meridian. During the transition from night to

day, the foot of the flux tube will be swept from its night position to

a point some 120 ahead in about 20 minutes (i.e., at Jupiter's rotation

rate of about 360/hour).

The weakly relativistic electrons spiralling in the flux tube can

serve as negative absorbers if their momentum distribution is sufficiently

inverted. The greatest amplification occurs in the extraordinary mode

for propagation at right angles to the magnetic field as seen in the

coordinate system in which the average electron streaming velocity is

zero. The linear Doppler effect causes the frequency of the radiation

to be raised above the local electron gyrofrequency as seen in the Jovian

frame. It also causes the radiation to be directed at large angles with

respect to the electron stream velocity.

The radiation from 10 keV electrons spiralling up from the planet

along the flux tube will be directed into a conical surface with a

half-angle of 790 that opens symmetrically about the flux tube outward

from Jupiter. The apex of the cone is located at the foot of the flux

tube in Jupiter's ionosphere. Electrons spiralling toward the planet

will also emit radiation into a similar cone which, upon reflection

of the radiation by the ionosphere, will open outward from the planet.

Such a cone will intersect Jupiter's equatorial plane in a pair of

diverging lines whose half-angle is between 65 and 75, depending on

the tilt of the magnetic axis with respect to the Jupiter-Io line. The

authors of the theory further require that the radiation be beamed only

into selected regions of the conical surface. The actual degree of

beaming anisotropy cannot he predicted; however, for reasons which seem

plausible, the assumption is made that the preferred beaming angle is

at 130 with respect to the east-west direction on Jupiter. The assumed

parameters give a model for the Source B emission geometry as shown in

Figure I.lb.

Observations show that the sources appear to be narrower at higher

monitoring frequencies. In the theory, the local gyrofrequency increases

nearer the planet such that the source of the higher frequency radiation

must be closer to Jupiter. The axis of the radiation cone is tilted

farther from the equatorial plane since the flux tube is more nearly

parallel to the magnetic dipole at lower altitudes. The greater the

tilt of the cone axis the smaller the angle is between the lines of inter-

section between the cone and the equatorial plane. This makes the source

seem narrower when viewed from Earth since radiation reaching the earth

can travel only along the lines of intersection.

The theory gives a model for the formation of the S-Burst. It

proposes that a column of electrons spiralling on the surface of the flux

tube emits coherently for a period of time. The time duration of the

S-Burst is determined by the coherence time of the column of electrons.

The bandwidth of the radiation is determined by the altitude range, hence

the range of local gyrofrequencies, spanned by the column. S-Bursts may

be formed by electrons moving in either direction with respect to the

planet during the time for emission of radiation.

The source of the radiation energy is the transverse kinetic energy

of the keV electrons spiralling in the magnetic field. The electrons have

undergone acceleration from an energy of about 4 eV to the keV region

by the electric field generated by lo moving in Jupiter's magnetic field.

The ultimate source of energy for the radiation resides in the orbital

energy of lo. Using plausible values for the number density of

radiating electrons, etc., the authors show that the doubling of lo's

angular momentum is comfortably long compared with the lifetime of the

solar system.

A serious weakness in the theory occurs in the assumed value for

the conductivity of Io. It was necessary to assume a conductivity of

about two orders of magnitude greater than that of the moon, an assumption

which may not be realistic.

We wish to consider the theory of Goldreich and Lynden-Bell in this

dissertation since it predicts the beaming of the decametric radiation.

If the beams sweep across Earth, they should arrive at one station of an

interferometer, such as ours, before they arrive at another station. We

will report on the measurements of arrival times in a later chapter.

1-4.3. The Theory of Douglas and Smith for the Formation of L-Bursts

by the Solar Wind

J. N. Douglas and H. J. Smith (1967) proposed a theory to account

for the L-burst structure in the Jovian radiation. Two types of

experiments, both involving spaced receivers, led to their conclusion.

Gardner and Shain (1958) had found that the burst envelope correlation

was often, but not always, poor over baselines of only a few tens of

kilometers. Carr, et al. (1964) obtained a similar result over a base-

line of 7000 km. The cases of positive correlation indicated that the

cause of the amplitude variation in the burst must be more distant than

the Earth's ionosphere, since such local variations should not influence

the signals at both receivers. Douglas and Smith (1961) started a

continuing program of monitoring Jovian radiation for the purpose of

trying to detect differences in arrival times of a given burst at

several stations. Results of this work (Douglas and Smith, 1967)

indicated that there is a marked dependence of the delay time and the

order of arrival at receivers in the east-west orientation on the

number of days before (or after) opposition of Jupiter.

In their paper (1967), they argue for a random distribution of

phase-changing irregularities in the solar wind located in the space

between Jupiter and the earth. They further require that these

irregularities be remote from both the earth and Jupiter. The

irregularities are stable in structure. Their motion causes an

isophotal pattern to drift past the earth-based receivers at a rate of

several hundred kilometers per second. Mariner II data concerning the

solar wind indicated that the velocity of the wind did not change

appreciably with distance from the sun. Douglas and Smith proposed that

an inhomogeneity in the solar wind would cause phase changes in the

radiation, creating a drifting isophotal pattern as seen at the earth.

According to their calculations, using data extrapolated to the region

of the Earth-Jupiter line-of-sight, they were able to account for the

drift rate of the isophotal pattern. Furthermore, their theory

predicted that before Jovian opposition the isophotal pattern should

drift eastward, and after opposition the pattern would drift westward.

The drift direction is determined by the sense of the solar wind velocity

vector projected on a plane perpendicular to the line-of-sight from the

barth to Jupiter. It is clear that the vector will switch directions

at opposition if the solar wind is assumed to move in a radial direction

from the sun. The predicted drift direction was shown to agree with

experimental data.

I-5. The Purpose of the Experiments Described in

This Dissertation

Theories are the intellectual creations of mankind in the same

sense as are the more conventional arts. In the natural sciences,

however, man has added the constraint that his theories must represent

the way in which a class of natural phenomena may be caused. There is

thus the requirement that any prediction concerning a natural phenomenon

made by a theory must agree with the measurements made on that natural

phenomenon. In case of disagreement, difficulties may lie both in the

theory and in the interpretation of the measurements. It is generally

not possible to make THE measurement that will unequivocably make the

choice between two or more theories obvious.

In astronomy, man is faced with taking data from phenomena

that are secondarily related to the information he is seeking. It is

therefore necessary to examine not only the performance of the theory in

question, but also to be aware of possible failures of theories concerning

the way the information is transmitted. A case in point is the deter-

mination of the features of Jupiter's magnetic field. The radio

astronomer received electromagnetic radiation that, according to

Maxwell's equations and the theory of electrical measurements, could be

shown to be partially linearly polarized. The synchrotron process had

been shown to be a source of linearly polarized radiation having the

spectral characteristics observed by the astronomer. Since this demon-

stration had been made on Earth, one had to make the assumption that such

a process could be carried on elsewhere given similar conditions. This

assumption is part of a set summarized by Newton in the Principia as a

list of Rules of Reasoning. One condition for the occurrence of the

synchrotron process was the presence of a magnetic field. Jupiter, then,

must have a magnetic field. Further measurements of the distribution

of the source of radiation led to the current understanding of the

geometry of the field.

At the same time that an inquiry is being made into the origin of

one natural phenomenon, i.e., the radiation from Jupiter in the

previous example, many other phenomena are being investigated. There

is, for example, exploration of many other features of Jupiter taking

place, such as: experimental studies of the atmospheric features of the

planet, of the red spot and theoretical studies of the interior of the

planet. The aim of man's inquiry seems, in this case, to be that he

is hoping to have at some future time a complete picture of Jupiter

which can be added to the rest of the pictures he has made of the

universe. By that time, if he is successful, he will feel at home in a

familiar world, a world of his own intellectual creation.

The experiments in this dissertation are proposed to give man a

little more insight into the natural phenomena that he is hoping to


List of Experiments

1. The angular size of the source of Jupiter's decametric radiation

will be determined using both a phase and an intensity interferometer.

2. The stability of the position of the source will be examined

using the fringe pattern generated by the interferometer.

3. The arrival times of S- and L-Bursts at several stations will be

examined to provide experimental information in connection with the theories

of Goldreich and Lynden-Bell and of Douglas and Smith. A new method for

eliminating the residual timing errors will be used.



The theoretical structure for the understanding of the phase and

intensity interferometer is developed in the first two sections of this

chapter. Since the interference pattern of the received signals from

Jupiter is actually obtained from the computer, the last section of

this chapter is devoted to establishing the connection between the

classical forms of the interferometer and the experimental technique

used here.

II-1. The Phase Interferometer

Classically, the phase interferometer adds the signal voltages from

two spaced antennas at some central point. The fluctuation in the

combined signal power is dependent on the size and location of the source

with respect to the interferometer power pattern. Consider an inter-

ferometer formed by placing mixers between each antenna and the signal

adding point. A system of this nature allows the signals to be stored

on magnetic tape and the interference to be accomplished under more

convenient conditions.

Figure II.la shows a block diagram of the system to be considered.

The left half of the system is called receiver one and has an input






Figure II.1 -- (a)

Diagram of the Classical Interferometer,
Graph of the Output S0 Versus Beam Angle 40.

frequency wi, a local oscillator frequency WLo, and a low-passed output

frequency wo. The right side, receiver two, has similar variables that

are given by wi, mLo, w'. For a single frequency the input voltage to

receiver one is E = E (g) cos (m.t + T), where T is the phase lag
i 10 i

introduced by the extra path length yl with respect to the point halfway

between the antennas. Its value is T = v (s+a) sin 9 The input voltage

to receiver two is E! = E'c(C) cos (!'t Y), where P has the same value.
1 01
The amplitude factors, E and E', are angle dependent since each antenna
10 10
has a power pattern appropriate to its design. The angle variable, 9 = Q0-,

denotes a direction in the far field pattern of the interferometer

measured from the center of the main lobe. The local oscillator injection

voltages take the form: E = E cos (L t) and E' = E' cos (' t + ),
Lo Lo Lo Lo Lo Lo

where n is the phase at time = zero. Before low-pass filtering the outputs

of the mixers are E = E1 (C) cos (wit + 7) ELo cos ( Lot) and
0 10 1 Lo Lo

E' = E' (() cos (m!t V) E' cos (w' t + n). Each of these voltages
0 10 1 Lo Lo

contains terms that oscillate with frequencies w. i and w' .
i Lo i Lo
The summing point will receive only the difference frequencies due to the

low-pass filters in each mixer.

Some restrictions are now placed on the variables that are

multiplied in the mixers. Let m. = w'. If the source emits over a wide
1 i
frequency range, these equations apply to each frequency in the bandwidth

of the low-pass filters. Specifying w' = W + y provides a means of
Lo Lo
distinguishing the fringes from scintillations in the interplanetary

medium. It has been shown, Dulk (1970), that these scintillations have

a power spectrum that contains very little power above a frequency of a

few Hz. If y is greater than this amount, then several fringes will

pass during one phase fluctuation due to the interplanetary medium. It

is convenient to let E = E' = E and,since the individual antennas
Lo Lo 1

are steered, E (0) = E' (0) = 1.
10 10
The voltage at the summing point is given by E = E +E =
0 0

E {cos (wit + V) cos (Lot)+ os (WLot + t + n) cos (W.t V)}. Upon

using a trigonometric identity and the condition that (w. W >> Y,
1 Lo Lo
the summing point voltage becomes E = E1i{cos [(i iLo)t ]

cos (' + it + )}. The power pattern, after smoothing on a 2w/(w. L )
2 2 i Lo
time scale and normalizing, is P (Ct,n) = cos2 (' + It + 4). The power
n 2 2
pattern can be written as Pn(C,t) = 1 + cos (0 + yt), where 8 = 2' is

the total phase difference due to path length caused by the separation of

the antennas. The y term gives temporal fringes if 6 is held constant.

The phase, n, does not depend on the source and can be chosen to be zero

for convenience.

The observed flux density from a source is given by So(#o,t) =

I B(>) Pn(#o d) d4, where B() is the true source brightness distri-

bution, *0 is the hour angle of the main lobe of the interferometer power

pattern, and is the hour angle of a point in the source. Using the

previously calculated normalized power pattern, P (g,t), the observed
a ^a
flux density becomes S0(00,t) = fy B(O) d# + j2 B(() cos (0 + yt) d4 where
a a
2 -7t

the angular width of the source is a and 0 = <0 *. The integral

S = J B(O) d> is the total flux density from the source. If a is

small compared with the lobe spacing, the values of 0 for which the

second integral has any appreciable size are limited to the region

) 0 I < w. Under this condition 6 becomes 0 = 2r sA (00 ').

The second integral takes the form f2 B(O) cos [2r (s *0 + Vt)]

cos (2w s. A) de + f B(4) sin [2w (sA 0 + vt)] sin (2w sA 0) di, where

S= 2 and s = If SO (o',s,t) is written as S0 (o,s ,t) =
A = 2 and sO = A(
So [1 + V (40,s ,t)], the visibility function can be identified as

V(oosAt) = (-) {cos [2w (s 0 + Vt)] f2 B(4) cos (27 s 4) do +
sin [2r (s, 0 + vt)] f2 B(4) sin (2w s 4) do}. Let V(C ,sx,t) be

written as V(40,s ,t) = V0 (s ) cos [27 (sA *0 s A A0) + yt]. 1)

Figure II.lb is a graph of S (4P,s ,t) plotted against 0Q in which the

local oscillator offset, y, is made to be zero.

It will be useful for later derivations to identify the following

terms in an expansion of V (3o,s ,t) above (eq. 1):

V (s ) cos (2w sX A 4) = 1 f2 B(O) cos (2w s )d) d4
00 --

F B(4) 2)
0 cos

V (s ) sin (2 s A = () 2 B(O) sin (2w s 0) dO
0 0 s o a

S ) F B() 3)
0 sin

where F and F are the Fourier cosine and sine transforms of the
cos sin
brightness distribution B(O). In order to make the identification of

the transforms it is necessary to require that there are no other

sources of appreciable strength in the antenna pattern.

If Equation 3) is multiplied by i and added to Equation 2), and

the Fourier transform is taken, the following equation results:

B(0) = S0 f V0 (s ) e-i2rs x (-A 0) ds If the visibility

function's amplitude, V0 (sX), can be determined for all baseline lengths,

the brightness distribution of the source can be reconstructed by an

integration over the baseline. In the classical interferometer this

S S *
quantity is determined by evaluating the equation V (s ) = max min
Smax + Smin
for many different baselines. A practical limitation on this method's

use is that many measurements are required with increasingly longer

baselines. In the case of a small source emitting at long wavelengths,

as for Jupiter, the earth's diameter may form the limit on the integral.

An added requirement was made when the Fourier transform took place. The

source was required to be the only one in the antenna pattern. This is

reasonably true of Jupiter. Subject to these conditions, the brightness

distribution of the source can be determined from a knowledge of the

visibility function, V (~0,sx,t).

It is possible to calculate V (0,s ,t) by a method that is more

easily realized on a digital computer. The technique uses the cross

correlation function which is defined as

E0 (t) E' (t + T)
C (s ,,t) = 0
S[E 2 (t)] [E'2 (t + T)]

where E0 (t) is the voltage output, after low-pass filtering, of the

first mixer and E0 (t + T) is that of the second mixer at time, T, later

(see Figure II.2a). The voltages are given by

E0 (t) = a fa ar (C) cos [{ir (C) WLo t + nr () + r ()] d5 and

E; (t + T) =b J E a, (5') cos [{Wl (') wLo}t + T)

+ n (W') d (l')] de',

where a (C') and a (5) are the amplitudes of the frequencies w and r .

The same restrictions as for the classical interferometer are added, i.e.,

E = E' and w' = w + y. The phases of each component frequency
Lo Lo0 Lo Lo

of the source are nr (5) and n (5'), and the initial relative phase of

the local oscillators is ignored. It should be noticed that the amplitudes

and phases of the a and r components depend on positions in a random way.

It is further required that B (5) a E ar (5) a (0). The summation on
A and r is carried only over the frequencies passed by the low-pass

filters to the multiplier. The filters are assumed to have a flat

response inside their passband with no response outside, and the band-

width of each is much less than the center frequency.

The numerator of C (s,,S,t) becomes E (t) E' (t + T) =

t r ro r r

f E a, (C') cos [W ((' + Y)(t + T) + n ()') ] (')] do' dt

where wO (4) = w () wLo (4) and w0 ((') = W (4') Lo (0'). The
ro r Lo 0 A Lo
variable is defined as before, V = ir s (0o ), where the small

angle approximation has been made. The integration period T is taken

as being long with respect to 2r/wo and short compared to 2i/y and the
fringe rate due to the source moving across the interferometer pattern.

A diagram of the interferometer is given in Figure !I.2a. Such a system

is called a multiplying interferometer and has the varying part of the

observed flux density as its output. By rearrangement of the integration

the voltage product becomes E0 (t) E '(t + T) = f d t -a f t ar
0 0;-ft *' r,

cos [ w (0) t + rn (W) + V (0)] a (a') cos [(Wa + Y)(t + T) +
ro r r 0

n ((') 'V (4')] d0'dt. It is necessary to examine the behavior of the
amplitudes and phase factors under the integration over time and *. The

amplitudes and phases, a (0) and n (W), of the frequencies are random

functions of position. This requires that the integration over *' be zero

except where *' = *. Also if the integration over time at any point is




S 0

Figure 11.2 -- (a)



Diagram of the Multiplying Interferometer,
Graph of the Output S4 as It Depends on t
line) and on o0 (dashed line).



considered, the integral will be zero unless w < 2_. This
ro R T

is caused by the random relation of phases for two different frequencies

and the integration time. If this term serves as the integrand for

an integral over position, the result will be zero unless w = W ,
ro ,0
which is again due to the random nature of the phases and amplitudes

of different frequencies with position.

We are left with the product term having the form EO (t) E0'(t + T) =

ab a
a- J 2 a (4) a, (0) cos [Rt + 2T (4)] do, where the integration time

is short compared to 2i/Y and to the time for the source to pass through

one fringe. This is the same form as the varying component of the

observed flux density as derived for the voltage adding interferometer.

The denominator of C (sA,,,t) can be written as [E02 (t)]

{a-2 f ff ar (0) as (') cos [W rot + () + r] cos
T r,s sro r r
T r,s

( sot (+ s ( ') + T' (')] d' do] dt d where the product of the spatial

integrals has been replaced by the double integral over the position

variables. By the arguments used in the previous part, 0' = 1 and

Wro = "0 or the integral will be zero. Then [E02 (t)] =

{f d4 R-f E ar (4) a (0) cos2 [W t + n (0) + T (4)] dt}. After
Sr=s s ro r r
a 2
the time integration this becomes [E02 (t)] = { a- J ar (4) as (o) do},
2 r=s

where, upon substituting B (0) for the sum on frequency, we recognize

[E02 (t)] = {a2 B (.) dlh to be a S0 /r. A similar term for the rms

value of the second receiver's voltage is also demonstrable.

The cross correlation function can then be written as

E0 (t) E' (t + T) ab
0t E- V(s ,#0't)sO
C(sX,E,t) =- =-
[E 2 (t)] [E'2 (t + T)] a b
0 0 -S S
I/i. 0/2 0

SO V0 (s ) cos [yt + 2w s (s Ao)]


It is then seen that the cross correlation function is just the fringe

visibility. The amplitude of the fringes generated by plotting the

cross correlation function against time is just V0 (s.). The cross

correlation function lends itself to being calculated with digitized

data in the computer. Figure II.2b is a graph of the output of this

form of interferometer plotted against time. The envelope represents

fringes due to the motion of the source with respect to the interfero-

meter fringes and the solid curve is the cross correlation function.

The amplitude variations are due to the relative local oscillator offset

and source motion.

11-2. The Intensity Interferometer

A new form of interferometer was proposed by R. Hanbury Brown and

R. Q. Twiss (1954) that had the advantages of being operable over a

very long baseline and of being relatively insensitive to phase distortions

caused by electron density variations in the ionosphere. A diagram of

the system is given in Figure II.3a. The Michelson (phase) interfero-

meter is sensitive to phase shifts that occur to the signals before they


S2(t) S l2 jIs2t) I



Figure 11.3 -- (a) Diagram of the Brown and Twiss Post-
Detection-Correlation Interferometer, (b)
a Sample Record.



s1 S

reach the summing point. The system described here is not as sensitive

to this problem since the data sent from the remote station is square-

law detected and filtered. This data undergoes two types of treatment

at the time that interference is applied. Each signal is linearly

detected, filtered and plotted on a chart recorder. A third channel is

formed by multiplying the original signals, filtering and then plotting

the product. A delay network is incorporated into one leg to compensate

for the time delay, T, caused by the data transmission link. The

normalized correlator output c (k,t) is given by the equation,

s1 (t) S2 (t TO)
c (,t) = where the
{[S 2 (t)] p )}{[S2 (t r) p
1 Ni 2 0 N2

numerator is the filtered multiplier output signal at a given time, t,

and [S12]h and [S22]h are the values of the individual, linearly detected

channels at the same time. P and P are the average values of the
N1 N2
low-frequency filtered outputs observed when the source is outside the

antenna beam. C (a) is formed by averaging c (A,t) over a number of

passes of the source through the beam. The variable a is the separation

of the two antennas.

Brown and Twiss show, in the first part of their paper, that a term

they call the correlation coefficient,p (A), is given by

[F 2 (s) + F si2 (s )J]
cos sin for the Michelson interferometer.
F (O)

It is seen that the numerator can be formed by referring to the square

root of the sum of the squares of Equations 2) and 3) in the previous

section. The denominator is just Equation 2) evaluated for a baseline

length of zero; in other words, the antennas are adjacent. This shows

that the correlation coefficient of Brown and Twiss is just the

amplitude of the fringe visibility function derived in the first

section of this chapter. It was also shown at that time that the

amplitude of the fringes generated by the cross correlation function

was equal to the fringe amplitude of the visibility function.

They continue in their paper to show that c (A,t) is given by

F 2 (s +F 2 (s)
c (,t) = cos sin which is just the square of p (C).
F 2 (0)

We will use such a method in the computer to determine the best time

shift of the envelopes of bursts received at two different stations in

order to determine relative arrival times. The integration period used

in the averages of the functions is long compared with any time variation

in the arguments of the voltages sent to the square-law detectors.

Figure II.3b is a sample record of data taken as a source crosses the

antenna pattern of the individual antennas.

11-3. The Formation of an Interferometer Using the

Cross Correlation Function

A phase interferometer can be formed using data that is tape

recorded at the antenna locations. The receivers must heterodyne the

signal from the observing frequency, in this case 18 MHz, to a frequency

compatible with the tape recorder. The data must be digitized and is

then used in the equation for the cross correlation function

E (t) E '(t + r) I
C (sx,Et) = 0 0. The form actually employed
[ 2 Ct)]' [E02 (t + T)]

must, of course, perform the integration discretely. The cross

correlation function takes the form

Z E (t) E' (t + T)
C (s ,j,t) = 1=1 Oj Oj The variable T, is a
AN N 2
E (Ej2) E (E.2)]
=1 j=l 30J

time correction factor to account for any relative timing errors

generated by such things as transmission time for timing signals, timing

resolution, etc. The method involves the calculation of C (sA ,,t) for

many different values of T, and the selection of the value of T that

maximizes the amplitude of C (sx,E,t). Further description of the

procedure follows in the next chapter.

A post-detection-correlation interferometer as introduced by Brown

and Twiss is formed by first square-law detecting the heterodyned data

on the magnetic tape. After smoothing, the envelopes are cross

correlated. A value for the best relative shift of the envelopes is

determined by finding that value of T that maximizes the cross correlation

function for a given region of integration. A comparison of the best

shifts found for the two methods gives a means to detect the presence of

a sweeping beam of Jupiter decametric radiation.

Occasionally a combination of circumstances can occur in which a

segment of data that has been interfered is so short in time that the

fringe does not reach maximum value. This makes the determination of the

fringe amplitude difficult if not impossible. If the local oscillator

initial phase term had not been ignored in the development of the cross

correlation function, C (s ,S,t), a function of the form

C (s ,$,n,t) = V (s ,,,n,t), where n is the initial phase, would have resulted.

Equation 1) in section II-1 would have the form V (s ,g,n,t) = V0 (s )
cos [2i s (C0 A00) + n + yt]. If the receiver at one station were

arranged such that two equal local oscillator frequencies with phases

shifted 900 were injected into two mixers, the signals from another

station cross correlated with the first station would exhibit fringes

with a 90 phase shift. The fringe amplitude V0 (s ) could be obtained

by taking the square root of the sum of the squares of the cross

correlation function for each pair of signals. The derivation is

given below:

Vlst pair = V0 (s) cos [2n sX (0" "AO) + no+ yt]

V2nd pair = (s) cos [2w sX (0 AO0) + n + 90 + yt] =

V0 (s ) sin [2w s (C0 A ) + n + yt]

[V2 + V2nd p =ai V0 (s ) [cos2 {2w s (0 A0) + no +
1st pair 2nd pair 0 X A X

yt} + sin {2* sx (C0 AO0) + no + yt}J]


V = 2 (rin) + V2 (n + 900)]h
V0 (A [lst pair 0 2nd pair 0 +90

For a strip source with a Gaussian spatial distribution of

radiators, Equation 2)can be used to calculate a set of values for the

amplitude of the visibility function, V (s ), if the source is symmetrical.


Since it has been shown that the cross correlation function and the

fringe visibility function are equal, the experimental values of the

amplitude of C(s ,C,n,t) should lie on the curve representing the source.

Figure 11.4 is a graph of VCo(s) plotted versus baseline length for

sources with angular widths of 0'1, 0'25, and 0.'5 of arc. Values for

the amplitude of the cross correlation function determined in later

chapters will be compared with this graph to determine the size of the

source. This graph is adapted from Dulk (1970).








S .,4 ac
-^ 0



r 4e
Oyfl 11

a 1o a a
v, I
___ h

o ^ 0 0 o 0



III-1. The Signal Receiving Systems

In 1969 receiving systems as diagrammed in Figure III.1 were

located at Western Kentucky University, University of Florida Radio

Observatory, Florida Presbyterian College, and the Observatorio

Radioastronomico de Maipu in Chile. At each station a steerable,

linearly polarized Yagi antenna provided the Jupiter signal to a

Collins 75S-1 communications receiver. The receiver used crystal-

controlled local oscillators throughout and employed a mechanical

filter to establish the overall bandpass of the receiver. The

mechanical filter had a 455 kHz center frequency and a 2.1 kHz band-

width. A 50-ohm resistor serving as a dummy load could be switched

to the receiver input in place of the antenna. A WWV time standard

receiver was operated concurrently with the system to provide real

time synchronization of the composite time channel. A data channel

multiplexer received the audio signals from the Collins and WWV

receivers and placed them on one channel of a Magnecord stereo tape

recorder. The multiplexer placed the Jupiter signal on the tape most

of the time. WWV was keyed in for two seconds every minute for the

double tick and for 20 seconds every five minutes for the voice announcement.

18 MHz WWV
Linearly Polarized Antenna

Figure III.1 -- Diagram of 1969 Receiving System.

Before the voice announcement the dummy load was keyed into the receiver

input in place of the antenna for a few seconds at 5-minute intervals

to serve as a system check. A crystal oscillator was used as the source

of a stable frequency to drive a divider chain to provide the composite

time signal. All stations had the one pulse-per-second and 60 pulses-

per-second outputs. All but Western Kentucky University used the 960

pulses-per-second output. A 600 pulses-per-second output was used by

WKU. The composite timing signal was formed by pulse-height coding

the tick. The one-second pulse was tallest, followed by the 1/60th-

second pulse with the 1/960th-second (or 1/600th) pulse the shortest.

The pulses could be identified on a chart recording or oscilloscope by

this means. The composite time signal was recorded on the other

channel of the Magnecord tape recorder. Real time synchronization of

the composite time signal was accomplished by comparing the time marks

in one channel with the onset of the WWV tone or double ticks that

were keyed into the other channel.

The processing of data from this system revealed two shortcomings.

The local oscillators, although they were crystal controlled, were not

stable enough. One could not predict the fringe rate generated by the

local oscillator offset, y, since this offset was, in itself, not

predictable. The other shortcoming occurred when two stations were

interfered at a time when their fringe was passing through zero, or was

a value other than a maximum. If the fringe could not be reconstructed

for a long enough time to show the peak, then the amplitude of the

fringe could not be determined. The data processed for this disserta-

tion from 1969 fortunately had a duration longer than one fringe cycle.

A receiving system was designed for the 1970 Jupiter season to

overcome these shortcomings. Figure III.2 is a block diagram of the

system operated at the University of Florida Radio Observatory. A

very stable crystal in a double oven was used as the source of all

frequencies employed in the system. The composite time signal was

produced as in the 1969 system, except the frequencies were changed to

1 pulse per second, 50 pulses per second and 1000 pulses per second.

The time signal was recorded continuously on one channel of a four-

channel Viking tape recorder. The 1.8 MHz crystal standard also drove

a frequency synthesizer that provided the local oscillator injections

to the receiver. The first and second local oscillator frequencies

were produced by a combination of multiplying and dividing. The second

local oscillator frequency was switch selectable between 3.15 MHz and

4.05 MHz to provide a means of tuning the receiver off of an inter-

fering station. The product detector local oscillator input was

produced by dividing and phase shifting. Two product detectors were

sent the signal from the receiver I.F. stage. Their local oscillator

inputs were the same frequency, 450 kHz, but one was phase shifted 900

with respect to the other. The interference of both of the product

detector outputs with another station allows the reconstruction of the

fringe amplitude without having either combination actually reach a

fringe peak. The receiver was designed around a Collins mechanical filter

of the type used in the earlier system. Two different bandwidths were

used, 2.1 kHz and 6 kHz, at the center frequency of 455 kHz. The R.F.

preamp and mixers were made using dual-gate, metal-oxide-silicon-field-

effect transistors (MOSFET). They provide a much wider dynamic range

and superior resistance to cross modulation due to adjacent channel

interference. A frequency conversion scheme for two different I.F.

18 MHz

1.8 MHz


1 p/s
50 p/s
1000 p/s
Isooo P/5

21.6 MHz

3.15 MHz
4.05 MHz
450 kHz










3 3'



CH. 1

CH. 4
CH. 3


CH. 2


Figure III.2 -- Diagram of 1970 Receiving System.


L, |


bandwidths is shown in Figure III.3. A detailed block diagram of the

system is shown in Figure III.4. The receiver located at the other

station in the network (Maipu, Chile) had a single product detector;

otherwise the system was identical.

The real time synchronization for stations in the United States

used signals from WWV and LORAN-C. The data multiplexer keyed WWV

into the data channel every minute for the double tick and every five

minutes for the voice announcement. This was followed by LORAN-C for

two seconds to provide as accurate timing as possible. The VLF trans-

mission time from the station is very stable and predictable for ground

wave. Information concerning the transmission time delay for WWV time

signals came from Application Note 52 by the Hewlett-Packard Company

(1965). Information pertaining to the VLF network of LORAN-C came from

papers by L. D. Shapiro (1968a and 1968b). The inputs to the four-

channel Viking tape recorder consist of: channel 1 composite time

signal; channel 2 continuous WWV; channel 3 multiplexed data and

time signals; channel 4 data.

Since it is difficult to receive any of the LORAN-C networks in

Chile, they were provided with a rubidium frequency standard on loan

from NRAO. The 1 MHz output was divided down to 1 pulse per second and

compared with NBS time at the NASA satellite tracking station near

Santiago, Chile. The atomic standard was carried while still running

to the Jupiter observatory at Maipu, Chile, to calibrate the local

standard and to be keyed into the data channel every minute instead

of the WWV double tick. The WWV voice announcement was keyed in every

five minutes as at the University of Florida station.


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The antenna system at Chile consisted of a polarimeter that was

used near the meridian and a steerable Yagi for sources away from the

meridian. The 1970 data processed here uses the linearly-polarized

Yagi. The Florida antenna was a manually steerable polarimeter or,

on the night when the data was recorded, a linearly polarized Yagi.

The network has since been enlarged to include stations at Western

Kentucky University (a single product detector model) and San Antonio,

Texas. All recording in the network in 1971 was done using right hand

circular polarization except at WKU (linear).

III-2. The Treatment of the Data on the Computer

Interference fringes are formed for various pairs of stations by

calculating the cross correlation function for a given integration

period as a function of time. In order to use the computer to aid in

the calculations, it was necessary to present the data to it in a

digital form.

The data tapes were digitized using an analog-to-digital converter

as a data source for an IBM 1800 computer. Two forms of the digitiza-

tion program were used. The 1969 data was digitized by passing a burst,

that had been located earlier, to the digitizer using the original

magnetic tape. The operator, listening with ear phones to the time

channel, counted from a known starting time (usually the WWV minute mark)

to the second tick before the second tick that preceded the part to be

digitized. He pushed the START button on the computer, which searched

for the next second mark. Upon finding this mark, it waited for a

length of time given to it on a data card. After the wait, the computer

began digitizing until it filled a data array which was allotted 3520

words. The time channel was digitized by alternate samples with the

data channel and stored in a similar array. Both arrays were transferred

to a disk and plotted on an incremental plotter. Figure III.5 shows

a composite plot of the digitized data and time channels and an

expanded plot of the data channel for Chile. The time channel is

digitized to allow the exact time interval of digitization to be

determined. By careful comparison with the chart recordings of the

raw data the exact starting and ending times of the digitization

period can be determined.

The data from 1970 was handled a bit differently. The Computer

Sciences Division of the University of Florida Medical Center, where

the previous work had been done, had produced a general purpose

digitization program that would digitize up to 509,440 words of data

at speeds in excess of 7 000 data points per second per channel. After

the data was discovered, from the search of chart records, it was

slowed down by a factor of eight-to-one and presented to the machine.

Approximately six seconds of data were digitized, with points being

taken alternately from the data channel and time channel. The tape had

been started by the operator and digitization begun immediately. A

program called LOOK was provided that searched the data for the

addresses of the bursts and the second ticks. The interesting bursts,

which were previously seen on chart records, were then located and

transferred with a program called TRNFR to another disk for storage

and plotting on the incremental plotter. The method used was theoretically

easier than that used the previous year, but tape recorder instabilities

complicated the efforts.






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Data was transferred from the IBM 1800 on cards. The remainder

of the data processing was done on an IBM 360/65. The 1970 data

was transferred in a column binary format in order to require the

punching of fewer cards by the IBM 1800. An Assembler program was

written to convert the column binary information on the cards to

files on a tape that could be read by a FORTRAN program such as

CROCO, which is described later.

In order for interference to be achieved properly, the two tapes

from a pair of stations must present data to the multiplier at the

same rate in real time. Tape stretch and other inconsistencies made

some correction in the digitized data necessary. A program called

BADE was written by the author to adjust the number of data points

in a table to represent the same real time period and to move the

zero value of the data to the average value for the table. The

program also adjusted each data table to begin at the same point in

real time by correcting for time signal transmission time and errors in

the starting time of digitization. In 1969 a data table of 2240 data

points was prepared by BADE such that the first point in each table

occurred at the same time. This left an error due to the

geometrical path length differences for the Jupiter signal and some

residual timing errors, since WWV was the prime source of real time

that year.

Two programs were written by the author to prepare data for the

intensity interferometer mode and the envelope correlation experiment.

The program, BASQ, square-law detected the data in each of the data

tables prepared by BADE and integrated it over 20 data points. The inte-

gration period was sufficient to remove the audio and leave the slowly

time-varying envelope. A post-detection-correlation interferometer

of the Brown and Twiss type was formed with this data. The other

program, BABS, took the absolute value of the BADE data, integrated

over 20 data points, and adjusted the baseline of the data to the

average. It played the part of a full-wave, linear detector with

integrator, followed by a coupling capacitor. BABS provided the

data to examine the relative arrival times of the fine structure

in an L-Burst.

The program, called CROCO, was the main analysis tool used on

the data. Its purpose was to calculate the cross correlation function,

C(sx,S,,,t). It was written by the author to be very flexible in its

choice of integration times, number of values of C calculated for a

data table, and where (in a data table) it started and ended calcula-

tions of C. CROCO performs the calculation of the cross correlation


Z E E'
Ij=l 0 j 0 j+ITAU 4)
CITAU(s ,,n,t) =
E E 2 E E12
j=1 0 j j=1 0 j+ITAU

in two parts. The numerator is formed by summing the product E0 j

E over N values of j, where N is the selected integration time
0 j+ITAU

and ITAU is the initial shift of the two data tables with respect to

each other. The denominator is formed by computing the sum of the

square of E j and the sum of the square of E' .I The two sums
are multiplied together and the square root is taken. The cross
are multiplied together and the square root is taken. The cross

correlation function is formed and given the name PXC(J), an

element of an array. The denominator is saved and stored as PNM.

The program steps LDELT data points further into the data tables and

calculates another value for C and the denominator. After calculating

three values of C, a line of print is generated. The line of print

consists of the denominator (PNM), three values of C (XCOR1, XCOR2,

XCOR3) and the line number. In addition, the program assigns an

asterisk to one of the 100 remaining spaces in the line at a position

that is proportional to the value of the first C calculated. Since C

ranges from -1 to +1, each space represents a change in C of .02.

The process is repeated until the index for the selection of the data

points to be multiplied reaches NDPS, which is the number of data

points in each table. The program increments the relative shift

variable K by KDELT and repeats the calculation. When K has the

value JTAU, the program will repeat the cycle once more and stop.

Some essential quantities which must be provided by the user are

the following:

1. IDATE(1), IDATE(2), AND IDATE(3) are the numbers of the month,

day and year, respectively, e.g., 1, 2, 69, on which the burst occurred.

2. IFIL1 and IFIL2 are used to denote the portion of an input

array in which data from each station has been placed. The initial

array usually must be changed for different batches of data.

3. JHOUR and XSEC are the hour and second at which the burst of

interest occurred.

4. ITAU and JTAU are the beginning and ending relative shifts.

They are calculated by the formulas ITAU = (initial time shift) x

(digitization rate) and JTAU = (final time shift) x (digitization rate).

If the two shifts are on the same side of zero-relative-shift, ITAU

is given a negative sign.

5. N is the integration time in data points. N = (integration

time) x (digitization rate).

6. KDELT is the increment of shifting in data points.

7. LDELT is the increment of stepping through the data tables.

8. DPS is the digitization rate in data points per second.

9. NDPS is the number of data points in each data table. All

tables are assumed to contain the same number of data points.

The program is run on data from a pair of stations for a given

range of relative shifts. The best shift is selected by noting the

shift that makes the fringes have the greatest amplitude and have the

smoothest curve.

A modification of CROCO was made that incorporated statements

to control an incremental plotter. CROCOCAL produced the graphs of the

fringes shown in a number of the figures. It was hoped that it would

be inexpensive enough to use as an analytic tool in place of CROCO,

since the smoothness of the curves is much easier to see. Unfortunately,

it turned out to be anything but inexpensive. A listing of a combina-

tion version of BADE and BASQ is included in the Appendix,

followed by a listing of CROCO.

A refinement in the method of setting the digitization rate was

added during the processing of the 1970 data. An integrated circuit

phase-lock detector made by Signetics (NE 565) was used to lock an

oscillator to the 15 KHz tone that had been placed on the time channel.

Since the tone had been derived from the crystal-frequency standard,

it remained in phase with the timing marks on this channel. The analog-

to-digital converter in the IBM 1800 Data Acquisition System was driven

from the synchronized oscillator. The synchronization of the converter

eliminates any change in the effective digitization rate due to

changes in tape speed (caused either by differences in tape recorder

speeds or wow and flutter in a given tape recorder). The time channel

of the digitized data was printed by the IBM 1800 in such a form as

to make detection of any loss of coherence between the timing channel

and the phase-locked oscillator obvious. For further checking the

data channel was plotted on the incremental plotter. The data was

punched on cards in a column binary format for transportation to the

IBM 360 for use in CROCO.



IV-1. Spatial Orientation of the Receiving System

The Jovian decametric burst that is analyzed in this chapter was

received on the morning of 2 January 1969 at 08h22m14s UT by the four

stations that were members of the interferometer network that year.

The stations were located at Bowling Green, Kentucky (lat. 36057' N,

long. 86025' W), Old Town, Florida (lat. 29031'50" N, long, 8201'

55" W), St. Petersburg, Florida (lat. 27045'45" N, long. 82038' W),

and Maipu, Chile (lat. 33023'50" S, long. 60042'12" W). The primary

timing source was the National Bureau of Standards radio station WWV,

located in Boulder, Colorado (lat. 40040'48" N, long. 10502'25" W),

as shown in Figure IV.I. The local one-second ticks were delayed by

approximately one second from the one-second tick transmitted by WWV

due to the transmission time delay and the manual method used for

aligning the local tick with that from WWV. The total delays for the

stations were 1.0016 seconds for Bowling Green, 0.4202 seconds for

Old Town, 0.8917 seconds for St. Petersburg, and 0.2555 seconds for

Maipu. The actual transmission delay from WWV ranged from 6.1 milli-

seconds for Bowling Green to about 33 milliseconds for Maipu. The latter

Figure IV.1 -- Western Hemisphere Map Showing the Locations of the
Receiving Stations and WWV. MAIPU Is near Santiago,

time is uncertain by at least 2 milliseconds since it is not known, a

priori, how many hops were required for transmitting the timing signal

that was received at Maipu.

Figure IV.2a shows the arrangement of the earth, Jupiter, and

the sun on 2 January 1969 as seen from the North Pole of the ecliptic.

The right ascension of Jupiter was 12h22ml9s2 and its declination was

-059'28". The right ascension of the sun on that date was approximately

18h41m or 2800 east of the Vernal Equinox, The North Pole of the earth

is pointing to the right as the observer looks along the line-of-sight

from the earth to Jupiter, since this is the northern hemisphere winter.

The receiving stations will be referred to by the initials of the

university radio observatory that operated them. They were Western

Kentucky University (WKU) at Bowling Green, University of Florida Radio

Observatory (UFRO) at Old Town, Florida Presbyterian College (FPC) at

St. Petersburg, and Observatorio Radioastronomico de Maipu of the

Universidad de Chile (MAIPU) at Maipu, Chile. Table IV.1 gives the

baseline lengths of pairs of these stations for the baselines projected

Table IV.1

Station Pair DEW (km) DNS (km) D (km)

UFRO FPC 83.1 166 185.8

WKU UFRO 44.7 697 698

WKU FPC 89.6 896 905

FPC MAIPU 2000 6520 6820

UFRO MAIPU 1913 6690 6980

WKU MAIPU 1875 7380 7620

Vernal Equinox






/a DNS


%,. Equator

Figure IV.2 -- (a) View of Earth, Jupiter and the Sun from Above the
North Pole on 2 January 1969, (b) D and D Projected
on the Plane Perpendicular to the Line-of-Sight to



on a plane perpendicular to the line-of-sight to Jupiter from the earth.

The variable DEW is the length of the baseline projected on a line that

is parallel to the equatorial plane and is perpendicular to the line-

of-sight. The variable DNS is the length of the baseline projected on

a line parallel to the north-south axis of the earth and perpendicular

to the line-of-sight to Jupiter. The variable D is the total baseline

projected on a plane perpendicular to the line-of-sight to Jupiter.

The effective baseline lengths, measured in wavelengths of the 18 MHz

received signal of the various interferometers formed by all pairs of

stations, range from 11,150 to 456,000.

For the experiment involving the effect of the solar wind on the

envelope of the L-Burst (as proposed by Douglas and Smith), it is

necessary to know the effective length of the baseline as projected on

the plane of the ecliptic. It is the interaction of the solar wind

with the radiation travelling from Jupiter along the line-of-sight,

which lies in the ecliptic plane, that is proposed to be the cause of

the shape of the L-Burst envelope. Figure IV.2b shows the appearance

of the WKU MAIPU baseline components DNS and DEW as seen by an

observer at the center of the earth looking toward Jupiter. The direction

sense for east and west is that used by an observer at the location of

the stations, i.e., on the side of the earth toward Jupiter in Figure

IV.2a. The angle, a, is the projection of the polar angle of the earth

(230)-on the plane perpendicular to the line-of-sight to Jupiter. Its

value is given by tan a = tan 23 cos (RA -1800), where RAJ is the

right ascension of Jupiter in degrees. On 2 January 1969 the right

ascension of Jupiter was 1855. The value of a was then 234. The

east-west baseline, BEW, as projected on the plane of the ecliptic,

is given by BE = DNS sin a + DE cos a for the orientation shown

in Figure IV.2b.

IV-2. The Nature of the Received Signal

According to a classification of Jovian noise storm activity

given by Douglas and Smith (1967) and attributed to Gallet, a burst

with a duration of from 0.1 second to 5 seconds is an L-Burst.

Inspection of Figures IV.3 and IV.11 will reveal that the burst under

study here is about 0.130 seconds long; hence, by strict application

of the classification scheme, it is technically an L-Burst. Recall

that the largest time marks that are visible in the figures occur at

1/60th second intervals. This burst will henceforth be referred to

as an L-Burst, even though an added requirement for a burst to be so

classified will be shown as a result of the analysis in this chapter.

As can be seen in Figure IV.3, the signals, as received at the

several stations, were not all of the same strength. An important

requirement for the use of the signals in the interferometer is their

signal-to-noise ratio. This number is gotten by comparing the voltage

ratio of the peaks of the burst with the peaks of the noise outside of

the burst. Expressed in decibels, the (S+N)/N ratios are the following:

WKU 14 db, FPC 9.5 db, MAIPU 9 db, and UFRO 6 db. The signal-

to-noise ratio for UFRO is too low to make the fringes detectable.

Another factor in the form of the relative frequency effect of the

local oscillator at UFRO made the fringes almost indistinguishable

from other noise effects. This required the exclusion of the UFRO data

from the calculations of the cross correlation function.

.,M ,'-"_A.k ;= i, .. ,-I ..L.
... i ....,,Ti rT.,qq! .m] = qW'l v~l' I'I- I... ....lp

........, ....in ( ir "i f4ill(( ii tif Ii lmm jltHim.i s.. f.l, n iir,,, (i,,' f,. (, i.. i. tilt f:i t i, ..... I "it 'l n,, I n( i,, iii..i..i..i.. oI ii".j(b)i

-1-7 ,*1I. Pi .<1- 111F R",vR M1P


w- d

Figure IV.3 -- Actual Chart Records of the Heterodyned Data from WKU (a),
FPC (b), UFRO (c) and MAIPU (d) for the L-Burst of
2 January 1969. Alternate Lines Are the Timing Channels
for the Corresponding Stations.

IV-3. Measurement of the Size of the Source of

Jovian Decametric Radiation

It was shown in Chapter II that the brightness distribution of a

source could be calculated from the fringe visibility function V (s )

by the following equation: B(A0) = S f Vo(s )e i21rs(0"A(o0)ds .

In that chapter it was also shown that the visibility function was

equal to the amplitude of the cross correlation function, C(s ,S,t).

Therefore, in order to find the angular width (i.e., twice the value

of 0 for which B( 0) is just zero) of the source, one must calculate

the cross correlation function for the best relative shift of the data

from all pairs of stations. The best relative shift is determined by

the relative shift, T, in Equation 4) in Chapter III that maximizes the

amplitude of the curve of the cross correlation function plotted

against time. The reason T was introduced was to make allowance for

the relative inaccuracy of the knowledge of real time at each of the

stations (due to real time being received from WWV) and for the

difference in path length that the signal from Jupiter had to travel

to the various stations.

The program CROCO was used on the heterodyned data, which had

previously been adjusted in time and length by the program BADE, to

calculate and make a plot of the cross correlation function as a function

of time. The plot was in the form of a series of asterisks on the computer

printout, as is described in Chapter III. After the best shift was

discovered, the program CROCOCAL plotted the curves that are shown in

Figures IV.4, IV.5, and IV.6. The individual figures are composites

of three pages of plotting of the output of CROCOCAL done on a



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Calcomp plotter. The first two lines are a plot of the data as

received by the stations (the heterodyned signal), hence can be

compared directly with Figure IV.3. The third line in each figure is

the cross correlation function plotted against time, and the fourth

line is the denominator of C(s ,S,t) which serves as a normalizing
factor. The integration time, N, is 2.1 milliseconds. The peaks in

the normalization curve indicate where especially strong regions of

the burst are located. The time axis is calibrated in data points,

such that one data point is 0.07 milliseconds. Time is counted from

the beginning of the burst, or 08h22ml43 UT.

Figure IV.4 shows the data from WKU compared with that from

MAIPU. Figure IV.5 compares data from WKU and FPC, while Figure IV.6

compares data from FPC and MAIPU. Table IV.2 gives the amplitude of

the cross correlation function near the two selected regions of

high signal level and shows the fringe rate in this vicinity. As was

shown in Chapter II, the fringe rate is due to the relative motion

of the source with respect to the far field pattern of the inter-

ferometer, together with the relative local oscillator offset frequency.

The fringe rate due to the motion of the source through the inter-

ferometer pattern for the longest east-west baseline is on the order of 0.1

fringe/second. Most of the fringe rate in Table IV.2 can be attributed

Table IV.2

Stations ICI near D.P. 880 ICI near D.P. 1240 F.R.

WKU FPC 0.90 14% 0.92 14% 107 Hz

FPC MAIPU 0.80 20% 0.87 20% 216 Hz

WKU MAIPU 0.95 16% 0.80 16% 103 Hz

to the local oscillator offsets. It is encouraging to note that the

sum of two of the fringe rates (the first and the third) is very

nearly equal to the fringe rate of the other pair of stations (the

second) as is predicted by the theory of operation of the super-

heterodyne receivers used in this experiment.

It is clear from Table IV.2 that the amplitude of the cross

correlation function does not decrease with baseline length. The

variation in IC| is closely related to the signal-to-noise ratio of

the signals used to calculate it. This effect is also noticed in the

relative "fuzziness" of the curve for C(sx,,,t) in regions where the

signal is not strong, as is reflected by the normalization curve.

The immediate conclusion from this data is that the longest inter-

ferometer baseline did not resolve the source of this burst. There is

another interpretation of this result, however. If the source is

coherent, the assumptions made concerning the random nature of the

signal as a function of both time and position on the source are

invalid. The result is that the fringe visibility function, V0

cannot be used to reconstitute the brightness distribution. This

consequence will be considered in the concluding portion of the

dissertation. At this point, it can be concluded that the angular

width of the source is less than the width of one beam lobe, if the

source is incoherent. This angle, for the longest baseline, is given

by 0 = A radians. For the WKU MAIPU baseline, D is 7620 km,
making 8 have a value on the order of second of arc. The corresponding

linear distance on Jupiter is 1880 km.

A smaller upper limit on the size of the source can be found by

using the family of curves for the amplitude of the fringe visibility

function, V0(s ), that jis given in Figure 11.4. Using the inter-

pretation that low values of ICI are due to uncorrelated noise

contamination when the signal strength is weaker, it is seen that the

data points form a curve that lies above the curve for a 01' of arc

Gaussian strip source. This implies that, if the source is incoherent,

its size is less than 0'.'1 of arc or a linear distance of 490 km

on Jupiter.

An experiment was conducted using a one-bit correlation scheme to

compare the method with that already given. Weinreb (1963) and Cooper

(1970) have demonstrated the utility of various one- and two-bit

correlation techniques in the field of radio astronomy. The

sensitivity of the one-bit technique is 64% that of the continuous

multiplying correlator used above. The various two-bit correlation

methods have a sensitivity on the order of 85% compared with the

continuous multiplying correlator. It was felt that by converting the

data to the form in which plus one represents excursions of the data

voltage above the zero axis and minus one those below the axis, any

contribution of the envelope to the cross correlation function

would be eliminated. It should be recalled that there are many

physical modifications that can occur to the envelope of the Jovian

burst, e.g., solar wind interaction, interaction of a Faraday rotated

plane-polarized wave and an antenna polarized in another sense, etc.

Any frequency effect, having been introduced at the source, is useful

for the purpose of giving information about the source itself. Figure

IV.7 is a composite of the fringes generated by interfering signals

that have been treated in the one-bit method from the stations WKU

and MAIPU. The one-bit representations of the signals from WKU and



~- I1;

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MAIPU are shown on lines one and two, respectively. The third line is

the cross correlation function plotted against time, with N = 2.1

milliseconds, and the fourth line is the normalization. The normaliza-

tion has a constant value since the amplitude information in the

original signals has been removed. This is one of the attractive

features of the method from an instrumentation point of view. The

hardware for the correlator is relatively easy to implement with

digital logic integrated circuits. The time delay, T, can be handled

by shift registers, for example. The cross correlation function

plotted in Figure IV.7 shows the fringes that were seen in

Figure IV.4, which is a plot of the same data without the one-

bit representation. Some regions, corresponding to highly intense

radiation in Figure IV.4, show a fringe amplitude on the order of

0.9. It should be noticed in Figure IV.7 that the fringe amplitude

decreases away from the center of the burst. This artifact is caused

by the time scaling having some residual error which causes the data

at the beginning and end of the burst not to have exactly the same

best shift. This is removed in Figure IV.4 by plotting the first and

last thirds of the data at the proper best shift for that section of

the data. The one-bit correlator is seen to depend very sensitively

on relative shift of the data. This feature will be used in the

section of Chapter IV dealing with the beam-sweep experiment. The

principal shortcoming of the one-bit correlator is that it must integrate

over a longer period of time to overcome the loss of information due

to the one-bit representation. In normal radio astronomical appli-

cations there is no difficulty encountered with this shortcoming since

the sources that are studied do not change in intensity over times

that are long with respect to a typical integration period. The

Jovian burst envelope, however, changes with time and its shape is

not preserved from one burst to another. The S-burst, especially,

requires the use of the continuous multiplying correlator.

In Chapter II, it was shown that the Brown and Twiss post-detector-

correlation interferometer could be formed using the same form of the

cross correlation function as was used for the phase interferometer.

The data from the four stations was full-wave detected in the computer

by the program BABS. CROCO was run using this data in the same

manner as before. The best shift for each pair of stations was

found, and the cross correlation function was plotted by CROCOCAL.

Figures IV.8, IV.9, and IV.10 show the results of these calculations

for the three pairs of stations used in the phase interferometer.

In each figure, lines one and two are the detected data from the

stations. The full-wave detected data was filtered for an integra-

tion time of 1.4 milliseconds. The integration time, N, in the

cross correlation function calculation was 70 milliseconds, which is

approximately the length of the detail structure in the data. The

third line is the cross correlation function, which no longer

exhibits fringes. The fourth line is the normalization. Table IV.3

summarizes some values of the cross correlation function near

Table IV.3

Stations C2 near D.P. 880 C2 near D.P. 1240

WKU FPC 0.84 0.97

FPC MAIPU 0.64 0.95

WKU MAIPU 0.90 0.97




o r


o 0;

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u I




0 o
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'-1 0,

o^ -^
s_ ^ -^" ^ c*o '
^ ~ ~~~ ~ Q^^ *ic
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<-^-, ~~ ~~ r ( a -
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^ > k < 0'

regions of especially strong signal (the same regions as were shown

in Table IV.2). The symbol C2 means that this cross correlation

function is to be interpreted as the square of the C found using

the phase interferometer. It is seen that the values obtained by the

two methods are essentially the same. Since the cross correlation

function, C2, also does not decrease with increasing baseline length

it can be concluded that, if the source is incoherent, it is not

resolved. The beam lobe angle is the same as for the phase inter-

ferometer. If the source of this burst was incoherent, it must have

been less than O'.'1 of arc in angular width.

IV-4. Burst Arrival Time Experiment

Figure IV.11 is a composite of three chart records depicting

the envelope of the burst as it was received at WKU, FPC and MAIPU.

The envelopes have been aligned in real time, i.e., local tick

misadjustment and WWV time delay have been removed. It is clear that

this burst arrived at all of the stations at essentially the same time.

A much more accurate technique can be used than that given above.

The normal method to measure the burst arrival time consists of

providing stable local time marks on the data tape that have been

accurately calibrated in real time. The calibration procedure is very

difficult and has only recently become practicable for widely

separated stations. The method usually involves flying an atomic

oscillator by plane to the various stations or comparison with a

continuously calibrated time standard in an earth satellite. In the

novel technique for measuring burst arrival time given here, Jupiter's

signals themselves are used to calibrate the local clocks.


A Q i ". tu : J n n "' on n q i r .i. m
Ill ll Aliifll. H ,-. .A .


S* + ...... ...
th? .3. ** hi




HI:.~ .4I;I(

. I *
i .
, .

~~mmr~k~c~ymmWHC-'*1 iAII11' -*~dftfW m a ILl -L .L~~


i 1 ..i I i -.... ... --

Figure IV.11 -- Actual Chart Records of the Detected Data from WKU (a),
FPC (b) and MAIPU (c) for the L-Burst of 2 January 1969.
Records Are Laterally Adjusted Such as to Be Aligned
in Real Time.


IC 'r

; I



nrr~YY2*l*k~kA A ------------- 1- :mm~

II--- --

. . .

---------"-"'--'V ~'~"~~~~RM

1 1


The property of the Jovian signals that is used can be demon-

strated by considering a model consisting of a frequency modulated

transmitter driving a directive antenna that is located in the

vicinity of Jupiter (it is only necessary that the station be a long

distance away and in the line-of-sight). If two receiving stations

are located such that the beam of the antenna can sweep across them,

the output of the receivers will be as shown in Figure IV.12. It is

assumed that the station that is not in the center of the beam can

still receive some signal. The receivers are superheterodynes and

have product detectors, as do those in our interferometer. Figure

IV.12 has been drawn in such a way that the phase changes in the

frequency modulation are aligned in each of the signals, e.g., the

feature at time "7". The frequency modulation features are produced

at the transmitter and, except for random Doppler shifting, cannot be

altered during transmission after the signal leaves the transmitter.

The envelopes, on the other hand, are determined by the location of

the receiver with respect to the antenna beam of the transmitter. If

the beam sweeps from one station to the other, there will be a

noticeable difference in the time relationship of the frequency

modulated "carrier" and the envelope when the signals received at each

station are compared. The frequency modulation feature at time "7"

has a high amplitude at station two, while it is weaker at station

one. If the signal underneath the envelope from one station is cross

correlated with that from the other, the relative shift for the greatest

amplitude of the cross correlation function will be zero for this

example. If the envelopes are cross correlated, it is clear from

Figure IV.12 that the envelope of station two would have to be shifted


I a I i I I a I I
0 2 4 6 8 10

Figure IV.12 -- Plot of the Amplitude of a Constant Intensity Signal
as Received at Two Stations as the Beam of Radiation
Sweeps from Station 1 to Station 2. Frequency
Modulation Features Are Visible Under the Envelopes.

forward by approximately 3 time units to obtain the maximum cross

correlation function.

It is proposed by a number of investigators, including Goldreich

and Lynden-Bell (1969), that the decametric radiation from Jupiter

is highly beamed. A burst envelope received on earth, then, may be

shaped by the way that the beam sweeps across the receiving station,

if it sweeps rapidly enough. The frequency modulation of the Jovian

signal is due to the source being a producer of random noise of

moderate bandwidth. It is the interaction of this noise spectrum

with the I.F. filter in the receiver that produces the wave forms

shown in Figure IV.3. The filters in all of the receivers in the

interferometer are identical, hence their effect on the same noise

spectrum is the same. There is only one best shift for the heterodyned

data due to the random nature of the noise spectrum produced by the

Jovian decametric source. The local clocks can be calibrated with

each other by using the correction produced by finding the best shift

for each pair of stations. The envelopes of the signals can be

cross correlated to find the best shift for them. The best shifts for

the heterodyned data and the envelopes from a given pair of stations

can be compared to determine the rate and direction of motion of a

sweeping beam.

Figure IV.13 is a plot of a portion of the burst as received at

WKU and MAIPU. The signal is especially strong in this part of the

burst. Figure IV.13a shows the heterodyned signal from WKU and MAIPU

on lines one and two, respectively. Line three is the cross correla-

tion function plotted versus time for a shift of 38 data points, and

line four is the normalization. Figure IV.13b shows the cross




0 100
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correlation function plotted versus time for other shifts. The

shift is 37, 39, and 40 data points in lines one, two and three,

respectively. The integration time for calculating C was 2.1 milli-

seconds. It should be obvious from the two parts of Figure IV.13

that the cross correlation function is very sensitive to relative

shift. The value of best shift of 38 data points indicates that the

clock at MAIPU must be advanced by 2.65 milliseconds from the time

that was indicated by the corrections given to BADE. Figure IV.14

is an illustration of the full-wave detected data from WKU and MAIPU

arranged in the same way as for Figure IV.13. Figure IV.14b shows

the dependence of the cross correlation function on relative shift.

The deviation from the value for the best shift is not as rapid as

for the heterodyned data and is the chief error introduced in the

technique. Table IV.4 is a summary of the best relative shifts for

the data from the three pairs of stations.

Table IV.4

Stations Best Shift Data Pt.

Heterodyned Data Detected Data

WKU FPC 1.05 msec 1.05 msec 1200

FPC MAIPU 1.54 msec 1.68 msec 1200

WKU MAIPU 2.66 msec 2.66 msec 840

Figure IV.15a is a graph of the dependence of the cross correla-

tion function on the relative shift for the entire burst as received

at WKU and MAIPU. The integration time for calculating C2 was 112

milliseconds, which covers the entire burst in one summation. While the









co to

- r0
0 .

h IS






0 P

N E-


0 )

0 404
& .*4 *
-) 4J


0) *-4


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0 0
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o 0
s rt us

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cd .
o g

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S0 00
j0 ao
4.1 )O U)

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4O4 U I
U) U

4 0 40 1









.80 -


Figure IV.15 --

Cross Correlation Measures Plotted as Function of
Relative Shift for the WKU-MAIPU Baseline. (a) C2
for Detected Data with N=112 Milliseconds. (b) and
(d) C2 for Detected Data in the Vicinity of Data Points
840 and 1240, Respectively, with N=15 Milliseconds. (c)
and (e) Amplitude of the Cross Correlation Function
Near the Same Two Locations with N=2.1 Milliseconds.

curve is not sharply peaked, it is obvious that the best shift for the

entire burst is within 400 microseconds of the best shift for the

separate sections of the burst. Figures IV.15b and c are graphs of

C2 and |CI for the detected and heterodyned data, respectively, near

the data point 850. Parts d and e are for C2 and IC| near the data

point 1240 in the bursts received at WKU and MAIPU. The time axis is

calibrated in multiples of data points (1 dp is 0.07 milliseconds)

relative to the best shift for the heterodyned data (2.66 milliseconds).

All curves show a peak in the vicinity of a relative best shift of

zero. Since there is no consistent deviation between the best shift

for the heterodyned data and that for the detected data, it is

concluded that there is no measurable beam sweeping effect, and that

the observed slight deviation is experimental scatter due to contamina-

tion of the Jupiter signal by uncorrelated galactic noise. The

uncertainty in timing is on the order of 400 microseconds. If a beam

had swept past the two stations at a rate slower than this, its

presence would have been detected.

On 2 January 1969 the distance from the earth to Jupiter was

7.81 x 108 km. The north-south baseline in equatorial coordinates for

WKU MAIPU was 1.9 seconds of arc as seen from Jupiter. The east-west

baseline in the same coordinate system was 0.50 seconds of arc. The

maximum detectable beam sweep rate in the north-south direction was

2/second and was 0?5/second in the east-west direction. For a beam

sweeping parallel to the baseline, the maximum detectable sweep rate

was on the order of 2l/second.

The theory of Goldreich and Lynden-Bell contains four possible

mechanisms that might cause a beam of radiation to be swept across

the earth. Jupiter's ionosphere, where the lower terminus of a flux

tube is located, rotates with the planet. If the source, moving with

the ionosphere, swept the beam of radiation with it, the beam would

rotate with an angular velocity of 0?01 per second. The flux tube

passes through lo and, in this theory, moves with the satellite.

The orbital angular velocity of Io is 00023 per second, which would

be the sweep rate of a beam influenced by this satellite. The theory

proposes that as ionization conditions in the ionosphere change from

those at night to the daytime state, that the foot of the flux tube

advances from a position below Io to one approximately 150 ahead. If

the beam is swept by this mechanism, its angular velocity would be on

the order of 0004 per second. The advance is assumed to occur in

about 20 minutes. It is obvious that any of these beam sweep rates

would be easily detectable by the method proposed above. A group of

electrons spirals along a field line that lies between Io and the

ionosphere of Jupiter. If it is assumed that the radius of curvature

of the field line in this region is on the order of 5 times the radius

of the planet and that the electrons are moving with a velocity of

0.1 times the speed of light, a beam of radiation generated by them

would sweep at a rate on the order of 4?8 per second. This sweep rate

is just beyond the range of measurement by the data that has been

analyzed in this chapter. The three sweep mechanisms mentioned earlier

are definitely ruled out, however.

Douglas and Smith (1967) proposed a theory that accounts for the

structure of the L-Burst. They attribute the L-Burst to an isophotal

pattern, caused by inhomogeneities in the solar wind, drifting across

the receiving stations. They support their theory with convincing

evidence based upon the time of arrival of a given L-Burst at several

receiving stations. Their model predicts that the easternmost

station on a baseline parallel to the ecliptic will receive the burst

before any stations to the west if Jupiter is before opposition.

The westernmost station will receive the burst earliest if Jupiter is

after opposition. The L-Burst analyzed in this chapter was received

when Jupiter was 82 days before opposition. Their data shows that

for a baseline length of about 100 km that the signal will arrive at

the station to the east about 0.1 second before it arrives at the

western station for this time (82 days before opposition). The WKU -

MAIPU baseline, when projected on the ecliptic, BEW, has a length of

4580 km on a plane perpendicular to the line-of-sight from the earth

to Jupiter. By scaling the time delay in a linear fashion proportional

to the relative baseline lengths, it is seen that the expected delay

time should be on the order of 4.5 seconds. No such effect was

observed in this case. It is therefore concluded that the source itself

may exhibit intensity variations that are at least as long as the

burst that has been analyzed here. Although most L-Burst envelopes are

probably shaped by the solar wind, some must be intrinsic to the source


IV-5. The Stability of the Position of the Source

While the phase interferometer can give no information about the

size of the source that radiates coherently, the fringes are a good

source of information about the relative motion of the source during

the time of emission. Examination of Figure IV.4 will reveal no

consistent departure of the fringe rate or rapid changes of phase

from that shown at the beginning of the burst. There are numerous

apparent losses of coherence, but these can be correlated with

intervals of low signal level. The effect of these low levels is to

allow the uncorrelated noise of the galactic background to cause

temporary loss of coherence. When the signal increases again, the

fringe regains its coherence, with no shift in phase. The inter-

pretation of this effect is that the source remained in essentially the

same position in the interferometer antenna pattern during the

emission of the radiation. The spatial resolution is on the order

of 0.1 part of a fringe or about 0.05 seconds of arc. This corresponds

to the source remaining within 245 km of its original position during

the burst.



V-1. Instrumentation, Timing and Baseline Orientation

In 1970 the receivers that are diagrammed in Figures III.2, III.3,

and III.4 were put on the air at the University of Florida Radio

Observatory, Old Town, Florida, and at the Observatorio Radioastronomico

de Maipu of the Universidad de Chile near Maipu, Chile. The geographical

coordinates of these stations were given in Chapter IV. The great

circle distance between UFRO and MAIPU is 7384 km and the chordal

distance, D, is 6980 km (419,000 X); the angle between first nulls for

the interferometer is 0.49 seconds of arc. Figure V.la shows a view

of the earth as seen from the North Pole of the ecliptic on 30 April

1970 at the time the bursts that are analyzed in this chapter were

received. The celestial coordinates of Jupiter on that date were as

follows: right ascension = 13h53m54s and declination = -105'41".

The right ascension of the sun was 2h27m22s

The various baseline projections that will be used in the interpreta-

tion of the data are shown in Figure V.lb. The projections are drawn

in a plane that is perpendicular to the line-of-sight from the stations

to Jupiter. DNS is the component of D parallel to the polar axis of

the earth projected on the plane perpendicular to the line-of-sight

Autumnal Equinox

3 Sun


' Vernal


I N.P.



I Equator



Figure V.1 --

(a) View of Earth, Jupiter and the Sun from Above
the North Pole on 30 April 1970, (b) DNS and DEW
Projected on the Plane Perpendicular to the Line-
of-Sight to Jupiter.


Mag. Axis







to Jupiter. DEW is the component of D parallel to the earth's equatorial

plane projected on the same plane. Angle a lies between DNS and the

North Pole of the ecliptic in the same plane and had a value of 205

when the data was received. The various baseline components had the

following lengths: DNS = 6560 km and DNW = 205 km, with MAIPU east of

UFRO using the directions for the side of the earth toward Jupiter.

To insure the accurate calibration of the locally generated time

signal at MAIPU with respect to real time, a rubidium vapor clock was

provided on loan from the National Radio Astronomy Observatory. Without

interrupting its operation, the clock could be transported to the NASA

satellite tracking station near Santiago for calibration. This procedure

was performed at biweekly intervals during the observing season. The

data channel was multiplexed in such a way that the WWV voice announce-

ment was recorded for 20 seconds at 5-minute intervals and the rubidium

vapor clock signal was recorded for three seconds every minute on

the minute.

While it was hoped to use signals transmitted by the East Coast

LORAN-C chain to provide very accurate timing at UFRO, the audio

preamplifier in the LORAN-C receiver was found to be saturating, and

the station identifiers could not be decoded on chart recordings made

from slowed-down magnetic tapes. Local timing was determined as

accurately as possible by correcting the WWV time marks for transmission

time from Boulder, Colorado, which amounted to 8.3 milliseconds (Hewlett-

Packard Company, 1965).

The data format, as recorded on magnetic tape at UFRO and MAIPU,

was given in Chapter III. Just prior to the installation of the

receivers at both stations, a fourth timing signal was added to the

local time channel for the purpose of synchronizing an analog-to-

digital converter. The sync pulse had a frequency of 15 kHz and was

derived by a separate divide chain from the 1.8 MHz crystal at each

station. Synchronization of the A-to-D converter to this signal caused

the resulting digitization rate to be constant with respect to the

local time standard (hence constant in real time). Since this

effectively eliminated the variation in digitization rate caused by tape

stretch and speed instabilities in the magnetic tape drives, the most

complex part of the program, BADE, could be eliminated.

V-2. The Nature of the Received Data

Figures V.2 and V.3 reproduce chart recordings of the envelope

detected data as received at UFRO (both channels) and MAIPU beginning

at 9h35m515 U.T. on 30 April 1970. The time covered by the chart

records is about 4.5 seconds. The taller marks in the time channels,

which are shown on alternate lines just below the corresponding data

channels, occur at one-second intervals, and the shorter marks occur

at 20-millisecond intervals. The one-millisecond marks and the 15 kHz

sync tone are not distinguishable.

There were approximately 68 S-Bursts in the time period beginning

at 9h35m51s6 U.T. and ending six seconds later. Of these 68 bursts,

only 7% were present at one station and missing at the other. This

analysis will be restricted to the eleven bursts that are indicated

in Figures V.2 and V.3. Table V.1 gives the beginning times of the

intervals that were digitized in terms of the locally generated times

at each station and in terms of U.T. The indicated times are in


I *

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