Title Page
 Table of Contents
 List of Tables
 List of Figures
 Theoretical aspects of fissile...
 Experimental research apparatu...
 Experimental results
 Discussion/analysis of results
 Conclusions/design extension
 Biographical sketch

Title: On the effect of nuclear radiation on ARC discharges
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Permanent Link: http://ufdc.ufl.edu/UF00090921/00001
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Title: On the effect of nuclear radiation on ARC discharges
Series Title: On the effect of nuclear radiation on ARC discharges
Physical Description: Book
Creator: Vitali, Juan A.,
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Bibliographic ID: UF00090921
Volume ID: VID00001
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Table of Contents
    Title Page
        Page i
        Page ii
        Page iii
        Page iv
    Table of Contents
        Page v
        Page vi
    List of Tables
        Page vii
    List of Figures
        Page viii
        Page ix
        Page x
        Page xi
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
    Theoretical aspects of fissile arcs
        Page 12
        Page 13
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        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
    Experimental research apparatus
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
    Experimental results
        Page 51
        Page 52
        Page 53
        Page 54
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        Page 78
    Discussion/analysis of results
        Page 79
        Page 80
        Page 81
        Page 82
        Page 83
        Page 84
        Page 85
        Page 86
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        Page 97
        Page 98
        Page 99
        Page 100
        Page 101
        Page 102
        Page 103
    Conclusions/design extension
        Page 104
        Page 105
        Page 106
        Page 107
        Page 108
        Page 109
        Page 110
        Page 111
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        Page 122
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        Page 126
        Page 127
        Page 128
        Page 129
        Page 130
        Page 131
        Page 132
        Page 133
        Page 134
    Biographical sketch
        Page 135
        Page 136
        Page 137
        Page 138
Full Text








To my parents,
Bruno and Maria Vitali,
for their support and guidance.


The author would like to express his deepest

appreciation and gratitude to Dr. Richard T. Schneider, the

chairman of his supervisory committee, for his support and

guidance in this research, and for the faith and friendship

he showed toward the author throughout this academic

endeavor. The author is eternally grateful for the

opportunity to learn the arts and sciences Dr. Schneider has

taught him.

The author wishes to thank Dr. Yoichi Watanabe for his

assistance in collecting physical parameters, and for the

private insightful theoretical discussions which validated

the discoveries found in this dissertation. The author

acknowledges and thanks the technical assistance of Kevin

Carter, technician at RTS Laboratories, Inc. for his support

in the experimental phase of this dissertation.

The author also wishes to thank the Department of

Nuclear Engineering Sciences at the University of Florida

and INSPI for their financial support in the different

stages of this dissertation, especially to Dr. John D. Cox

for his financial support in the latter stages of this



Finally, special thanks go to the faculty members of

the supervisory committee, Dr. Alan Jacobs, Dr. Alex Green,

Dr. Edward Carroll, and Dr. William Lear, for their

technical suggestions throughout this dissertation. Very

special thanks are extended to Dr. John V. Lombardi for

taking time out of his busy schedule as president of the

University and to seve as outside member on the supervisory




ACKNOWLEDGEMENTS . . . . . . . . . iii

LIST OF TABLES . . . . . . . . . vii

LIST OF FIGURES . . . . . . . .... viii

ABSTRACT . . . . . . . . . . . . x


I INTRODUCTION . . . . . . . . 1

Scope of Research . . . . . . . . 3
Technical Objectives . . . . . ... .. 4
Literature Review and Contemporary Developments on Arc-
Based Systems and Arc Performance Enhancement
Phenomena . . . . . . . . . 7


Physics of Arc Discharges ... . . . .. .12
Electrode Phenomena . . . . . ... 13
Cathode Energy Balance . . . . ... .17
Emission Mechanism . . . . . . . 20
Analysis of the Arc Column . . . . . 22
Plasma Temperature . . . . . . .. 25
Anode Phenomena . . . . . . . . 26
Energy Deposition by Fission Fragments in a Gas . 28
Theory and Application of Plasma Diagnostic Techniques
for Temperature Measurements . . . 39
Local Thermodynamic Equilibrium (LTE) . . 39
Relative Line Intensity Method . . . . 42


Arc Column and Electrodes . . . . ... 44
Spectroscopic System Calibration . . . . . 47
Neutron Generator . . ... . . . .. 49
Data Acquisition . . . . . . . .... .50
Arc Ignition . . . . . . . . . . 50

IV EXPERIMENTAL RESULTS . . . . . . . . 51

Local Thermodynamic Equilibrium (LTE) ...... 51
Arc Spectra . . . . . . . 52
Irradiation Effects ............ .. 57
Plasma Temperature Measurements . . . . 57
IV Characteristics . ........ . 62
Benchmarking Results: Particle Density Measurements 70
Mass Transfer: Gravimetric Measurements . .. 70


Physics of Observed Phenomena .. .. . . 79
Mathematical Model . ......... . .. 83
Cathode Energy Balance . . . . . . 89
Work Function Reduction Calculation . ... . .. 93
Fast-Neutron-Induced Sputtering Considerations . 99
Enhancement of Arc Temperature As a Function of Fission
Product Enhanced Arc Current . . ... 100
Boron Arc . . ..... . .. . 100
Uranium Arc . . . . . . . 101
Direct Impact Heating From Secondary Ions Produced
by Nuclear Ionization ......... . .. 102


Uranium Arc Fission Reactor and Nuclear-Augmented
Thruster Concepts . . .. . . . . .. 106
Nuclear Augmented Thruster Concept ...... .110




REFERENCES . ........ ....... .. . 130


Table Page

4.1 Uranium Recirculation and Recovery Experiments 78

5.1 Data Used in Charge Generation Computation .91

5.2 Comparison of Experimental and Theoretically
Obtained Values . . . . . . 98


Figure Page

2.1 Cathode Processes Affecting Energy Balance . 16

3.1 Schematic Diagram of Vortex Stabilized Arc . 45

3.2 Spectrometer/Data Acquisition Arrangement . 48

4.1 Spectral Line Emission of Boron (249.7 nm) and
Carbon (247.9 nm) . . . . .. 53

4.2 Spectral Line Emission of Uranium (417.1 nm) 54

4.3 Spectral Line Emission of Uranium (365.3 nm and
365.9 nm) ... . . . .. . 55

4.4 Spectral Line Emission of Helium (388.8 nm and
400.9 nm) . . . . . . . . 56

4.5 Boron Doublet Line Intensity as a Function of
Neutron Irradiation . . . . ... .58

4.6 Boron Doublet Line Intensity as a Function of
Neutron Irradiation (Continued Sequence) 59

4.7 Carbon Line Intensity as a Function of
Irradiation. . . . . . ... 60

4.8 Carbon Line Intensity as a Function of Irradiation
(Continued Sequence) . . . . ... 61

4.9 Line Intensity Ratio of Selected Helium Lines 63

4.10 Boron Arc Temperature as a Function of Neutron
Irradiation . . . . . . . 64

4.11 Uranium Arc Temperature as a Function of Neutron
Irradiation . . . . . . .. 65

4.12 IV Characteristics of Boron Arc Under Neutron
Irradiation . . . . . . ... 66

4.13 IV Characteristics of Uranium Arc Under Neutron
Irradiation . . . . . . ... 67


4.14 Boron Arc Current as Function of Oscillating
Neutron Irradiation . . . . . 68

4.15 Uranium Arc Current as Function of Oscillating
Neutron Irradiation . . . . .. 69

4.16 Boron Arc Current vs. Power as a Function of
Neutron Irradiation . . . . .. 71

4.17 Uranium Arc Current vs. Power as a Function of
Neutron Irradiation . . . . .. 72

4.18 Tungsten Arc Current as a Function of Neutron
Irradiation . . . . . . . 73

4.19 Carbon Arc Current as a Function of Neutron
Irradiation . . . . . . .. 74

4.20 Uranium Equilibrium Particle Density Population.
Total Pressures: 0.1, 0.3 atm . . .. .75

4.21 Gravimetric Measurements of Uranium Loss vs.
Insertion Loss . . . . . . . 77

5.1 Schottky Enhancement Factor as Function of
Electric Field . . . . . . .. 82

5.2 Geometric Configuration of Disk Source Charge 84

5.3 Uranium Fission Product Energy Spectrum From Thick
Sources . . . . . . . . 87

5.4 Arc Current vs Cathode Temperature . . .. .94

5.5 Schottky Enhancement Factor vs Ionization Mean
Free Path . . . . . .. . 96

5.6 Schottky Enhancement Factor vs. Arc Plasma Number
Density . . . . . . . ... 97

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



Juan A. Vitali

December, 1992

Chairman: Dr. Richard T. Schneider
Major Department: Nuclear Engineering Sciences

The performance of fissile arc discharges under the

influence of neutrons was investigated. Helium vortex

stabilized arcs were studied and boron and depleted uranium

filled cathodes were used to study the effect of neutron

irradiation. Plasma temperature measurements indicated that

the boron arc temperature increased from 9,500 K to 11,500 K

when irradiated by neutrons from a moderated DT source with

a flux of 106 cm'2 sec'". The depleted uranium filled cathode

plasma temperature increased from 8,500 K to 9,100 K, for

the same pressure and electrode distance. The arc plasma

temperature was predicated by a similar increase in arc

current for both boron and uranium arcs. The observed arc

current increase was consonant with the increase in plasma

temperature within experimental error range.

The observed phenomenon can be explained by a decrease

in the work function of the cathode surface. This decrease

is caused by an increase in the local electric field, which

is caused by the presence of additional space charge

introduced by the fission products produced at the surface

of the cathode. The additional space charge creates an

image charge inside the cathode thus influencing the

existing electric field. This effect is similar to the one

produced in solid state physics by the Schottky mechanism.

Other competing effects that could be present at higher

neutron fluxes are the increase in ion bombardment due to

the added positive ion current created by the fission

products, sputtering/evaporation of the cathode surface-

especially in the presence of fast neutrons.



The advent of nuclear power has meant to energy

resource management what the computer has meant to today's

informational revolution. In a sense, both have been

catalysts for research into further advancements in science

and technology. Nuclear energy has been a prominent player

in today's energy-hungry world. Its usefulness and efficient

systems have provided much-needed independence of imported

oil, and it has been relatively inexpensive when compared to

some other forms of energy.

Nuclear energy is also a versatile form of energy,

since it is based on the fissioning of the nucleus of

fissile materials. Such fissioning releases energy in

multiple ways, most prevalently in the form of heat.

Another form of entropy creation which could be exploited is

ionization caused by the fissioning fuel. One of the major

differences between these forms of energy dissipation is the

nature of the exchange. Heat involves randomizing directed

kinetic energy through "molecular friction" caused by the

high kinetic energy of the fission fragments. Ionization,

on the other hand, involves collisions which transfer energy

from the fission fragments to the surrounding medium. This

versatility has the potential to make nuclear energy a

viable source for electricity generation, and propulsion.

Recently, the impact on the energy market of nuclear

power and the advent of the Strategic Defense Initiative

indicate a strong trend towards the development of nuclear

fission-based technology and, in particular, uranium-based

technologies. Government entities as well as private

enterprises have turned to nuclear energy to provide their

needs for space propulsion. In doing so, a voluminous body

of research has been developed over the years to look at

properties of uranium and to look at different concepts. In

the late '60s attention was focused on lower temperature

plasmas, as NASA discovered the potential usefulness of

gaseous uranium as a source of lasting power for long-lived

space missions, such as interplanetary travel, and for space

propulsion, e.g., through MPD electric propulsion as well as

electricity generation by MHD.

Therefore in many scenarios nuclear power in space

plays an important role, especially in its use as a power

source. It is then important to establish the effects

produced by the generation of nuclear radiation in space,

and how such radiation affects the performance of different

components. If nuclear reactors are to be used in space,

research must focus on the effects of neutron and gamma

radiation on electronic control components as well as on

thrusters and thrusters mechanisms. For instance, the

effects of neutron irradiation on transistors and silicon-

based electronics is important in the design of radiation

shielding and in estimating the duration of long missions.

However, another important aspect of space propulsion

is the effect of nuclear radiation on electric thrusters and

in particular on the change in performance of such

parameters as thrust and conversion efficiency.

This leads to the main focus of this dissertation which

is to evaluate a particular set of effects on the

performance of electrical arc discharges, in particular

fissile arcs, i.e., those whose created plasma is composed

of fissile materials, and how they perform in a neutron

environment. Key design parameters and a reactor concept

could emerge from the evaluation of such effects.

Scope of Research

Power and propulsion systems utilizing nuclear fission

energy possess many advantages over chemical propulsion

systems. These include:

o Higher achievable operating temperatures

o Much greater energy and power densities

o Efficient nonthermal ionization mechanisms

These advantages lead to significant mission performance

advantages over chemical systems. However, in spite of

these advantages, systems using nuclear reactors are still

performance limited by the constraints imposed by material

temperature limits and heat transfer via standard thermal

processes. In this dissertation, I seek to address these

limitations by proving that by exploiting the high quality

ionization of fission fragments it is possible to increase

efficiency by inducing an increase in electric current in

fissile arcs thus increasing arc temperature and therefore

overall thermal efficiency.

Technical Objectives

The research performed in this dissertation is directed

to the demonstration of the effects of nuclear radiation on

the key aspects of nonthermal mechanisms of energy transfer,

dissociation, and ionization in fissioning arcs.

The objectives of the experiments described here were

to demonstrate that fission energy can be coupled to the

ionization and radiative emission of the arc. Nuclear

effects caused by fission fragment and gamma irradiation

were both obtained directly by using uranium and simulated

by using the charged fission fragments from the

10B(n,4He)7Li nuclear reaction. The objectives were

achieved by making measurements of electric current,

voltage, and plasma temperature, and by assembling a

mathematical model that is able to predict the effect.

In a conventional arc, electrical energy is converted

into heat via ohmic heating and collision-dominated


mechanisms. A nuclear-augmented fissile arc derives most of

its power directly from the fission energy of the fuel and

requires little electrical energy input. Such a fissile arc

transfers its energy to the propellant or working fluid via

optical radiation, in addition to the conventional heat

conduction and convection. The result is similar to a

propulsion afterburner that can elevate fluid temperatures

to levels above the melting point of any material since

energy transfer occurs without crossing solid material

boundaries. This enables very high specific impulse

propulsion,1,2,3,4 ultrahigh temperature power conversion, or

more efficient thruster designs.

In a conventional electrical arc, most of the energy

provided by the power supply is used to ionize the

participating arc species. After this latent heat has been

provided, additional energy is then spent in heating the

plasma. Depending on the arc design, some energy is also

required to provide the latent heat necessary to evaporate

atoms from the solid interface of the electrodes. In this

report we explore an alternate method of providing

ionization to the arc. Ionization can be achieved by

exposing the arc to an external source, such as an electron

beam, or by using a fissile plasma in a neutron environment.

In the latter, fission events at or near the electrode

surface provide for latent heat, dissociation, and

ionization of plasma species via fission fragments and

ionizing radiation. This results in direct energy input

into the arc via electron collisions with the arc plasma.

An additional energy source is the fissioning that occurs

directly in the plasma column.

In the experiments described here a conventional

electrical arc is augmented with a fissile component. As

the fissile plasma is exposed to neutrons, fission occurs

and a new source of ionization is created. The electrical

power that was previously used to ionize is now available

for other purposes, provided that the electrical power input

is held constant, i.e., via a constant current power supply.

In such an arc, this newly available power provides

additional ohmic heating of the plasma, thereby increasing

its overall temperature and radiative emission. Most

important, however, is the microscopic effect in the work

function of the surface material produced by the nuclear-

induced space charge in the vicinity of the cathode surface.

An effect similar to the Schottky effect is caused by the

increase in the field strength at the cathode surface. This

increase produces a net decrease in the effective work

function, which in turn causes an increase in thermionic

emission. The theoretical basis is described in chapter II,

the experimental setup is discussed in chapter III.

Chapters IV and V describe the experimental results and

provide a mathematical representation of the nuclear effect.

Chapter VI provides a description of a potential use of the

discovered effect for space power and propulsion.


Literature Review and Contemporary Developments on Arc-Based
Systems and Arc Performance Enhancement Phenomena

Electric propulsion has been studied extensively and

devices have been put into operation using electric

thrusters for the past ten years. Research in electric

thrusters has become an important segment of space research.

A good review of up-to-date research on the field is given

in a paper by Wilbur, Jahn, and Curran.5 In it, they

outlined the use of plasmas in electric propulsion and

classified electric thrusters into three separate classes:

1) expanding and electrically heated plasma in a nozzle, 2)

accelerating a plasma through the application of an

electrostatic body force, or 3) accelerating ions in an

electric field.

Electrothermal thrusters involve electrical heating and

subsequent acceleration of a propellant through a nozzle to

induce a reaction force. The heating can be accomplished by

circulating the propellant over resistively heated elements,

but it will not be heated into the plasma state in such a

device. The device in which heating is accomplished by

passing the current directly through the propellant (an

arcjet) does generate the plasma. The major aspects of

scientific interest in these devices are the state of the

plasma and the interaction of the plasma with thruster

components, especially electrodes.

Research and development efforts on arcjet thrusters

began in the late 1950s and focused on engines that fell

into distinct power ranges near 1 and 30 Kw. In this

period, the arcjet was mainly considered as a candidate for

primary propulsive applications, and high specific impulse

was deemed necessary to compete with other propulsion

systems, both chemical and electric. As the physical

properties of hydrogen (principally low molecular weight)

make it well suited for operation in the 1000-1500 second

specific impulse range, hydrogen was considered almost

exclusively as a propellant. When the anticipated mission

scenarios and space-based power plants failed to

materialize, interest in the arcjet waned and research and

development efforts were discontinued in the early 1960s.

Early in the evolution of electric propulsion science

and technology, a wide range of designs for electromagnetic

acceleration of ionized propellants was explored

experimentally and theoretically, with only limited

practical success. A modest review of this era of

enterprise is available in a textbook by Jahn,6 which

describes in some detail the myriad of technical

permutations of geometries, flow classifications, circuit

characteristics, and physical processes that were actually

attempted during the late 1950s and early 1960s. Over the

ensuing three decades of research and development, only a

very few of these concepts have survived the gauntlet of

deep space propulsion criteria to retain technological

promise, and only one--the self-field magnetoplasmadynamic

(MPD) thruster--is sufficiently advanced to merit


The MPD genre of plasma accelerators is characterized

by a coaxial geometry constituted by a center body cathode,

an annular anode, and a suitable interelectrode insulator.

Gaseous propellant is introduced axially through the breech

insulator, whereupon it is ionized by its passage into an

intense, azimuthally uniform electric arc standing in the

interelectrode channel. The self-generated azimuthal

magnetic field associated with the radial and axial arc

current patterns exert both axial and radial body-force

components on the ionized propellant stream, directly

accelerating it downstream and compressing it toward the

centerline into an extremely hot plasma just beyond the

cathode tip.

It has long been known empirically that such self-field

MPD thrusters operate most effectively in the several

megawatts power range, which is commensurate with the

theoretical requirements for manned interplanetary flight.7

Beyond the needs of availability of power and in-space

heat rejection limitations, the upper bounds on MPD

operation will be set by tolerable electrode erosion rates

and plasma instabilities. Any current carrying plasma is

potentially unstable to oscillations dependent on the plasma

state, and the magnitude of the current driven through it.


These oscillations are manifested in local plasma densities,

electric fields, ionization, heat transfer, conductivity,

and other transport processes, and may be bounded in

amplitude or exponentially unstable, linear or nonlinear,

longitudinal or transverse. They may under various

circumstances precipitate full plasma turbulence,

macroscopic instabilities, enhanced internal dissipation,

and electrode erosion. Clearly, some understanding and

control of such oscillations is requisite to the enhancement

of MPD thruster performance, and substantial research

programs are in progress to study these phenomena.8

Considerable experimental studies of electrode and insulator

erosion processes have also been undertaken, reaching its

most sophisticated form in a sequence of radioactive surface

layer ablation studies that can track monolayer erosion

rates inside an operating accelerator as functions of

position and time.9 Such studies have identified the

cathode as the most vulnerable limiting component of the

thruster assembly and have helped to narrow the range of

cathode temperature and materials that will be required for

its satisfactory endurance.

Work on ion rockets proceeded slowly after being

proposed by Goddard until the 1950s, when researchers such

as Stuhlinger began to demonstrate their advantages and

practical devices began to appear. The basic principle is

to generate and accelerate a beam of positive ions

continuously for tens of thousands of hours. Extensive

studies of ion thrusters have been performed and their high

specific impulse capabilities make them most attractive for

missions to the planets and beyond.

Recently, Andrenucci and Paganucci10 conducted studies

and laboratory tests to produce enhancement of MPD thrusters

through cathode heating. The heat was provided by an arc

established between the inner surface of the cathode tip and

a thoriated tungsten electrode inserted into a blind hole

drilled along the cathode axis. The data obtained in their

experiments showed that the electrode thermal conditions

have a decisive effect on thruster thermal characteristics,

erosion, and instabilities phenomena.

In another related paper,11 the same authors performed

studies of scale and geometric effects on the performance of

MPD thrusters. In it they studied the performance

characteristics effects of gas flow, and geometry in

thruster efficiency and electrode erosion.

Most recent studies in the field in other similar

papers,12,13,14,15,16,17 are concerned with improving thruster

efficiency, by maximizing electrical energy conversion.

This dissertation deals with a similar aspect of

optimization, though not directly applied to MPD thrusters.



In order to asses the effects observed in the

experimental phase of this dissertation, certain theoretical

considerations need to be made to explain the physics of the

effect. Three basic points that need to be reviewed in this

chapter are, first, the physics of an arc, i.e., the

energetic of generation; second how a charged particle

deposits its energy in an arc-plasma; and last how this

energy might be distributed in the plasma and how it affects

the overall operation of an arc.

Physics of Arc Discharges

The arc discharge is, as a rule, self-sustaining, with

a relatively low cathode potential fall which is of the

order of the ionization potential of the atoms involved.

The small cathode fall is possible due to the particular

cathode emission mechanisms significant for an arc. These

mechanisms are capable of supplying an electron current from

the cathode, nearly equal to the total discharge current.

Arc cathodes emit electrons via thermionic and field

electron emission. Other processes of electron production

at the cathode, such as ion bombardment also exist.

Arc discharges is characterized by large currents that

are a few orders of magnitude larger than those encountered

in glow discharges. The cathode current density is also

much larger, typically in the order of 102 to 107 A/cm2.

These values are also a function of pressure and

interelectrode distance.

Arc cathodes receive large amounts of energy from ion

bombardment and ohmic heating and obtain high temperatures

either for the entire cathode area or, in some instances,

only locally in the form of a cathode spot. They are eroded

due to ion bombardment and suffer evaporation. The plasma

column, i.e., the region between the layers adjacent to the

electrodes, usually is in Local Thermodynamic Equilibrium

(LTE); however, in some instances, depending on the gas

pressure, deviation from equilibrium may exist. An arc is

said to be in equilibrium if the electron temperature is

equal to the gas temperature. For purposes of this

dissertation, the arc used in the experimental phase can be

categorized as a high pressure arc.

Electrode Phenomena

Certain phenomena occurring on the electrode surfaces

shall now be reviewed in order to explain the effects

observed in the experiments.

All surfaces in an arc receive energy by radiation from

the plasma and by heat transfer through convection of the

hot gases and vapor. The energy density received by

radiation, being typically not more than a quarter of the

total, is difficult to estimate because of the uncertainty

in the emissivity of the hot gas. An upper limit could be

set, for the purpose of estimating, by assuming that the

plasma acts as a blackbody knowing, however, that it is not.

The electrodes also radiate, yet the net power flow is from

the plasma, since in the upper limit the radiation power

received is proportional to the differences of the fourth

power of the respective temperatures of the surfaces

involved. In addition to radiation, hot neutral gas atoms

and molecules strike the surfaces and leave with somewhat

less energy, thus contributing to the heating of the

surface. However, the most important contribution is made

when two atoms of gas, or an ion and electron, re-associate

at the surface and give up their energy of dissociation or

ionization, respectively. Excited atoms or molecules,

especially long-lived metastables, can give up considerable

energy to a surface upon contact, then they return to the

gas as a neutral particle, usually with some excess kinetic

energy. Also three-body recombination of ions and electrons

occurs mostly on surfaces.

In gas discharges, the anode is essentially a positive

probe. It is heated in addition by electron and negative

ion bombardment. Usually the electron component dominates.


The voltage drop at the anode usually ranges from zero to a

maximum equal to the ionization potential of the atoms in

question. To this voltage must be added the work function,

which is the heat of condensation of the electrons. The sum

of these voltages times the anode current represents the

total electrical power input into the surface. The sum of

the electrical and nonelectrical input energies must be

balanced at the anode surface by the sum of heat conduction

into the metal, versus losses by radiation and evaporation

from the surface. Studies of this balance have been

conducted18,19 for a considerable number of metals, and

rather good estimates of both the temperature and

evaporation rate of arc anodes have been given.

The cathode, however, is the site of greatest

complexity for arcs. In addition to the previously

mentioned radiation flux and bombardment by neutral and

excited atoms or molecules, the cathode is bombarded by

positive ions and is subjected to high and continually

varying electric fields. Many of these processes are

illustrated in Figure 2.1. Multiple charged atoms of

electrode metal have also been found to be ejected from the

cathode, and some may have sufficient energy to make it all

the way to the anode.

Kinetic energy given up by the positive ion is J(+Vc),

where J is the current density and Vc is the cathode drop.

Some additional energy is given up in the neutralization of

* I

e: electron
R: Radiation
V: Vaporization
A: Atom
+: Positive Ion

Figure 2.1 Cathode Processes Affecting Energy Balance.






I I i I

Heat Out

Heat In


Heat In











the ion, as J(Vi-O)an where 0 is the work function and an is

a factor which is less than 0.5. The net effect on the

cathode is the emission of electrons as large as 90% of the

total current. The electron emission produced by thermionic

means represents a cooling effect in an amount equal to the

product of the thermionic current times the work function of

the surface. Ion bombardment is present in arcs but because

the ions have a relatively low kinetic energy, they are a

very inefficient way of producing electron emission.

Although data vary, for most metals positive ions are only

about 1% efficient, but with the low work function materials

they become about 10% efficient. Excited atoms such as may

occur in gases evolved from the electrode, especially those

in metastable state are effective in causing electron

emission.20 Photons from the plasma also cause electron

emission from the cathode. It seems that photoemission is

incapable of producing large currents -in most cases they

are restricted to a few microamperes per cm2. The idea of

field emission as an explanation of the nonthermionic arc

cathode spots was first suggested in the early 1920s. A

very high fluctuating field may be produced at the cathode

by the presence of the positive space charge.

Cathode Energy Balance

The cathode temperature, which is the main factor

determining the thermionic emission current, and the ratio

of ionic to electronic components are found from the system

of equations describing the energy balance at the cathode,

the charge production at the cathode layer, etc.

Calculations of this type are imperfect because the

processes are complex and numerous, and the data on

important parameters are incomplete. The results obtained

are mostly of qualitative value. A representative estimate

of one of the most interesting quantities, S--the fraction

of electronic current density of the total current--can be

obtained by constructing an energy balance in a simplified


Each ion carries to the cathode the kinetic energy in

the cathode fall Vc. A part of it, 13, is transferred to

the cathode upon impact; B1 is known as the accommodation

coefficient. When an ion is neutralized, the energy

released is equal to the ionization potential of the

resultant atom plus excess kinetic energy, minus the work

function 4 which is spent on removing the neutralizing

electron from the metal. A part of it, B2, is also

transferred to the cathode. The fractions 1-B1 and 1-B2 of

the energy remain with the outgoing atom. Not much is known

about the accommodation coefficients B1 of kinetic and B2 of

potential energy but certain similarities and indirect

arguments make it possible to assume that both are of the

order of unity. With each emitted electron, the cathode

loses the energy eo.

If we assume that the energy supplied by the ions to

the cathode is completely spent on electron emission and

material evaporation, and set B1=B2=1, we find:

je(0)=j+(VCI-0), S VC+I- (2.1)
Je 3+ Vc+I

The cathode receives from a plasma the heat conduction

flux Qt due to the temperature difference between plasma and

cathode. Another component is the radiant flux Qrad* The

heat entering the emitting surface of the cathode is

transported into the metal by the heat conduction flux Qh

because the opposite part of the cathode is colder. Some

part of Qrad, namely Qrad,c' is radiated away by the cathode.

The dimension of Q is that of power [W]. Dividing Q by

arc current i [A], we can denote q = Q /i [V]. The meaning

of each respective q is the energy per electron charge

transported by the electric current. The energy balance,

calculated per unit transported charge, is (for B1= B2 = 1)

qH = (1-S)(V+I-) +qT+qrad-S0-qradC (2.2)

When all of these factors are taken into account, the

value of S remains of the same order of magnitude as in the

estimate in (2.1). Detailed calculations of the balance,

involving other equations for quantities in 2.2,

demonstrated that as the arc current increases, the

temperature and the current density at the cathode also

increases but the cathode fall, and the fraction of ionic

current are reduced.

Note that when the fraction of ionic current is

calculated, one often evaluates energy balance not at the

cathode itself, via 2.1, but in the cathode layer. It is

assumed that the entire energy gained by the electrons

within the cathode fall goes into ionization, i.e., the

production of ions that subsequently reach the cathode.

This gives

I J+ Vc(2.3)
jeVc= j+I, S- (2.3)
I+V, 3 I+Vc

Emission Mechanism

The most obvious mechanism for the production of the

large electron currents at the arc cathode is thermionic

emission. The high temperature normally produced is a

result of the energy released by the impacting positive ions

that may come from the plasma but are more likely to come

from the cathode-fall region. If the positive ions are

produced in the cathode drop region, a high electron current

density relative to positive ion current density will be

necessary to produce the positive ions essential to maintain

the temperature. This is true because the efficiency of

ionization is much less than 100 per cent for single

collision ionization. Since the cathode drop is of the

order of ionization potential of the gas, many electrons

cross the cathode drop-region without making an ionizing

collision. It is probable that the cathode drop thickness


is of the order of an electron mean free path. It has been

reported in the literature that the electric fields

generated as a result of the positive ions created by the

electron ionization may have an effect on the work function

of the cathode material causing it to increase emission.

This similar case occurs in a fissionable cathode. A

surface layer of positive ions drawn from the discharge

column or produced artificially by fission fragments as a

result of nuclear reactions at the cathode surface produces

a very high electrostatic field at the cathode surface.

This effect is known in solid state physics as the Schottky

effect. This phenomenon has been studied extensively in the

early days of the transistor and gaseous electronics. The

effective reduction in work function due to an external

field has been found to be (in CGS units):

= -/ei" (2.4)

Substituting this effective work function of the

cathode in the presence of an electric field in the

thermionic emission equation gives the Schottky equation

j = 120 T2 e-e//kT (2.5)


j = je0.4389JE/T (2.6)

where jo is the thermionic emission current density in

amperes per cm2, and E is the effective field in volts per

cm. This effect will yield significant increases in current

for fields greater than 103 Volts per cm. Further analysis

of this issue will be discussed in chapter V. Surface

fields may be quite high in value with relatively low

average fields, owing to the presence of slight

irregularities, projecting crystal corners and

submicroscopic points. A 10% increase in the field at such

points above the average field for the surface may result in

the current density at these points being so great that

almost the entire emission will be from these points. A

most important mechanism that would create such large fields

and therefore cause field emission is that of a surface

layer of positive ions drawn from the discharge column. A

thesis of this dissertation is that a cloud of

semistationary positive ions produced by nuclear fission

products can be similar to this ion cloud drawn from the

plasma column.

In both cases, plasma induced and nuclear induced, such

a charged layer will produce a very high electrostatic field

at the electrode surface.

Analysis of the Arc Column

Suits21,22 applied the theory of the conduction-

convection heat-loss from solid bodies in fluids to the arc.

This has yielded relations that agree with the experimental

results. In his analysis radiation is neglected and all


energy lost from the column in free air is assumed to be by

conduction and convection. The arc column is considered as

a hot cylindrical solid body. This introduces some error,

since the convection currents are zero at the surface of a

solid, whereas the convection at the surface of the arc core

is a maximum. Since the heat loss within the arc column is

about 7% for most arcs22 it may be neglected for this


Suits proposes the following relation to express the

relationship between the thermodynamically determined


hD =C D3M2p2gAT (2.7)
-y- 1 R RT

where h is the convective heat transfer coefficient, D is

the diameter of the arc, k is its thermal conductivity, M is

the atomic mass of the species forming the arc, p is the

pressure, g is gravity constant, AT is the temperature

between the body and the ambient fluid, q is the viscosity

of the surrounding gas, R is the universal gas constant, and

a is a parametric constant which has been found to vary

between 0.04 and 0.25. In order to avoid the difficulty

arising from the large temperature variation within the film

surrounding the arc, a mean film temperature can be defined

Tf = Tambient+ A (2.8)

Replacing h by P/rDAT where P is the total power loss per

unit length,

h= E (2.9)

where E is the burning voltage gradient in volts per

centimeter and i is the arc current in amperes, then

equation 2.9 becomes

Ei=4.18 TkfAT C D3M2p2gAT (2.10)

where kf is the value of k at the film temperature. This

equation represents a similarity law for high pressure arcs

which depends only on the physical properties of the ambient

gas and arc temperature. At constant pressure the arc

temperature may be assumed independent of the arc, and

equation 2.10 becomes

Ei c D3" (2.11)

The arc current is given by

i = neeKeE (2.12)

where ne is the electron concentration, Ke is the electron

mobility, and e is the electronic charge. Computing the

equilibrium values from Saha's equation, ne is a function of

T only, then

i o D2E


where n finally solving for the gradient,

E o i-n (2.14)


n= (2-3a) (2.15)

For the extreme range ( 0.04 to 0.25 ) of a the calculated

values of n varies from 0.45 to 0.89, which compares

favorably with the experimentally determined values22. The

variation of the different parameters yield the following


ne o PB ; 3=1.44 (2.16)

D P Y +2a-1 (2.17)
D p- ; y=-23 (2.17)

E pm ; m=-a[3(B-1)-4] (2.18)

Plasma Temperature

Razier23 establishes approximate relations to determine

the temperature of an arc as a function of the power input

per unit length. If the power is fixed, Tmax in the arc

column is independent of its radius and depends to a small

extent on the heat conduction characteristics of the

surrounding gas in the electrical nonconducting peripheral


Razier further concludes that temperature is

insensitive to the method of cooling the arc and to the

organization of the discharge environment (free atmosphere

or a flow of a cold gas). Only the power input to the

plasma, exerts a direct effect on Tmax. The greater the

amount of heat that can be transported out of the cold gas

surrounding the arc, the greater the power that can be

introduced into it without "violating the steady state."

As a result of the strong dependence of conductivity on

temperature, high temperatures can be achieved only by a

disproportionate increase in power. Razier, further

enunciates the relationship between temperature and input


= Ei(VI/L) (2.19)
Tmax = 8 maxk

where Ei is the effective ionization potential of the arc

species, Amax is the maximum thermal conductivity of the arc

column, and k is the Boltzmann constant, and VI/L is the

power dissipated per unit arc length.

Anode phenomena

Processes at the anode are also complex and diverse.

In general, there is an anode fall of potential which is

usually lower than the cathode potential fall. The

temperature of the anode in a high pressure arc is equal or

greater than that of the cathode. A high electron space

charge is present at the anode end of the anode drop region.

This electron space charge is due to the incoming electrons

collected by the anode. At high gas pressures electrons are

emitted from the anode, owing to its high temperature, and

contribute to the space charge until driven back to the

anode. Positive ions produced in the anode drop region by

electron collisions move towards the cathode, the

concentration of positive ions increasing in the direction

of the cathode. At the cathode end of the anode drop region

the density of positive ions is high enough to nearly

neutralize the electron space charge, thus forming the

plasma constituting the positive column. Thus it is at the

anode that the essential positive-ion current is


An energy balance at the anode yields the following:

Pa = J (Va+40) (2.20)

where Pa is the power density (W/cm2) delivered to the

anode, Va is the anode drop, fo is the thermionic work

function, and j is the anode current density. Heat is lost

from the anode by conduction through the anode support, by

convection to the surrounding gas, and by radiation. If the

anode material is a relatively poor conductor, such as

carbon, conduction of heat through the solid may be

neglected. If in addition the convection loss to the gas is

neglected, the entire heat loss is by radiation according


(2. Pr=eaT4

where e is the emissivity of the anode material. For

equilibrium Pr = Pa then solving for the anode drop,

Va= ea4-0 (2.22)

Energy Deposition by Fission Fragments in a Gas

The passage of charged particles through matter has

been extensively studied for over half a century. It is not

surprising that the theoretical and experimental description

of alpha-particle and proton penetration phenomena is well

advanced as these are the charged particles with which most

experiments were performed before the discovery of nuclear


The theory of fission fragments ionization and other

ionizing particles is summarized by Northcliffe. If an atom

is given a velocity greatly in excess of the orbital

velocities of its electrons and allowed to enter a material

medium, these electrons will be stripped from the atom and

the bare nucleus will proceed through the medium, gradually

loosing energy because the coulombic interactions with the

electrons of the medium. At this point, where the particle

velocity is high, elastic or inelastic collisions with the

nuclei of the medium will be relatively rare and will add

little to the energy loss process. At first there is a

small but finite probability that the ion will capture an

electron in one of these collisions and a large probability

that the electron will be lost in the next collision; but as

the ion slows down and approaches velocities comparable to

the orbital velocities of a captured electron, the capture

probability increases and the loss probability decreases.

As the ion slows to velocities smaller than the orbital

velocity of the first captured electron, the capture

probability becomes very large and the loss probability

becomes zero. Meanwhile the probability of capturing a

second electron grows and the corresponding loss probability

decreases, so that with increasing probability the second

electron is retained. As the velocity decrease continues,

a third electron is captured in the same gradual way, and

then a fourth and so on. The major difference in the

description of the capture process for successive electrons

is the change in velocity scale necessary to match the

progressive decrease of orbital velocity of these electrons

within the ion.

Eventually the ion reaches velocities smaller than the

orbital velocity of the least tightly bound electron and

spends most of its time as a neutral atom. By this time its

kinetic energy is being dissipated predominantly by the

energy transfer arising from elastic collisions between the

nuclear fields of the ions and atoms, and a diminishing

amount of energy is being transferred to the atomic

electrons. The neutralized ion is said to be stopped when

it either reaches thermal velocities or combines chemically

with the atoms of the stopping material.

With respect to the medium into which the particle or

fission fragment is penetrating, most of the ionization and

excitation is caused by secondary electrons (delta rays)

produced during the initial coulombic stripping and

recombination interactions. This does not hold true,

though, for a heavy fission fragment near the end of its

track, where it is essentially neutral.

To calculate the space dependent deposition of energy

in a medium it is usual to start with a stopping power

relation. Using appropriate geometry one first calculates

the available energy per unit volume, and then using ion or

excited state generating terms, the kinetics of the system.

The Bohr stopping equation for fission fragments is24

-dE 2 e4 2 2 e4
S=2nNZeff- vLe + 2nrNZ1Z2 L (2.23)
mvy M2V2


N =atom density of the stopping material

M1,Z1=mass and nuclear charge of the moving fragment

M2,Z2=mass and nuclear charge of the stopping material
e,m =electronic charge and mass

v -velocity of the moving fragment

Z eff=effective charge of the fission fragment

vo =velocity of a Bohr orbit electron (2.2 x 108 cm/sec)

x =2 Zeff vo/v

Le =term for electronic stopping power

L, =term for nuclear stopping power

Lea =electronic stopping power for alpha particles of

comparable velocities.

The first term in the right hand side of equation 2.23

describes the electronic stopping power derived from

coulombic interactions. The second term describes energy

transfer by nuclear elastic interactions. It is standard

practice to ignore the second term since the amount of

energy deposited by nuclear interactions is small compared

to the total energy deposited. Thus using the first term

only of equation 2.23 the range of a fission fragment can be

determined. Assuming for the particle that E= 1/2 M1v2 and

that the Thomas-Fermi effective charge, Zeff= Z 1/3v/v0 is
valid, the fragment velocity follows from equation (2.27) as

a =-K(N,Z1,M1) (2.24)


e/ ^ 4 6.33X10-s 1/3 f 6Z /9
K(N,z1,M1)=2nN e4 6.33x108 1/3 62+1/ (2.25)
my 8M1 21/3

K is therefore a function of the mass and charge of the

moving fragment and the density of the medium, but is

velocity and space dependent. Solving this equation shows


v(x) =vi-Kx (2.26)

Solving this velocity-distance relationship for x when

v(x)=0 or v(R)=0, where R equals the range of a particle

with initial velocity vi, the result is

R(vi)=T (2.27)

Assuming the initial energy Ei=1/2M1vi2 and substituting

into equation (2.31) produces the well known square law

energy deposition relationship of a fission fragment,

E(x)=Ei(l-X)2 (2.28)

This relationship is therefore equivalent to the Bohr

stopping power equation using the Thomas-Fermi approximation

for Zeff with the nuclear stopping power term neglected.

Several authors using the general equation,

)E=Ei(l )n (2.29)

have disagreed with the n=2 value derived above. Axtman25

using the luminescence of nitrogen under fission fragment

bombardment, found n equal to 1.7. Steele20 used n=1.5 to

compute energy deposition by fission fragments in water.

Using this assumption Walters24 derives the energy

deposition relationship

dJe(z) CEpR1 3z2-2b2zln(bx)-b) (2.30)
tz_ 2


C : Fission Density. [reactions/cm3 sec]

Ep : Initial energy of the fission fragment. [ev]

R1 : Range of fission fragment in birth medium. [cm]

b : 1/Ar1

a : Bragg-Kleeman rule constant = pj/p2 (A2/A1)1/2, where

1 and 2 refer to media the fission fragments enter


p : Mass density. [gr/cm3]
A : Atomic weight. [gr/mole]

z : Track distance. [cm]

An almost identical empirical energy deposition

relationship can be derived, as previously noted, based upon

the relationship

x n
E(x) =Eo(l-x) ; 15n53 (2.31)

Both equations give similar results for small z, but vary

considerably for z approaching the range R2 in medium II.

This energy deposition function ignores any nuclear

elastic collisions; but if one calculates an ion production

source, a so-called "ionization defect" takes into account

this nuclear deposition, which is less effective in

ionization than coulombic interactions.

At this point researchers split to several different

techniques for generating source terms for a kinetic system.

Most studies have constructed an ion source term and used

the standard w values for fission fragment interaction with

various gases. These values include the ionization defect

and are experimental in origin.

Using the square law point deposition form of equation

(2.28), one can derive, simply by dividing by W, the

volumetric ion production rate:

l 1 dJe(z) CEpiRjilbz2-2bizln(biz)-bi) (2.32)
wi dz 2wi

where the distinction is made between the light and heavy

groups of fission fragments. Therefore,

IT(Z) = IL(Z)+ IH(z) (2.33)

The assumption that w [ev/ion-pair] is a constant value

over the entire path of the fragment is false, but if one

includes the "ionization defect" and views the target as a

whole, such as a plasma system, this approximation should

be close to the actual generation rate. Thiess27 approached

the problem in an unusual manner. Using the semi-empirical

energy deposition approach, a suggested alternative shown

above, he avoids the use of w values by calculating excited

states and ionization directly. This approach requires

knowledge of a complete set of cross sections for generating

the source terms for excited levels. Thiess modified Bethe-

Born cross section data based upon proton impact. Russell28

used another approximation, the Grysinsky electron

interaction cross section, for his excited state

calculations. Both authors clearly state that the use of


these cross sections may be entire invalid, but must be used

because there are no experimentally measured cross section

data available for such interactions. One factor that may

make the Grysinsky electron interaction approximation more

applicable than the others is the fact that about two-thirds

of the ionization and excitation is distributed to the gas

by secondary delta rays or fast electrons, rather than by

the primary fission fragment particle.

The range of fission fragment in a gas is a function of

the density of that gas and its molecular weight. Range

relations are strictly empirical and are derived from

measured data independent of straggling or other statistical


Range as function of pressure can be calculated using

the following equation:

R(cm) =KE2/3 (2.34)

where K =1.4 for most gases.

Experimental procedures such as those used in these

dissertation are based on cylindrical geometry. The average

chord length (s = 4 volume /area ) best represents the

distance that a particle if born on the surface or in the

volume of the cylinder would travel in a straight line

before it would again encounter the surface. For a cylinder

10 cm long and 1 cm in diameter the average chord length is

0.8 cm. Based on the above relationship the range of


fission fragments for the 'OB(n,a)7Li (Ea=1.77 Mev, ELi= 1.01

Mev) one finds that in helium at 0.3 atm, the alpha particle

has a range of approximately 4.7 cm and the lithium particle

a range of approximately 4.0 cm. A quick conclusion could

be that only a small fraction of the fission fragment energy

would be deposited in the gas. This is not necessarily true

for solid fission fragment sources, since a substantial

amount of fission fragments come from layers beneath the

surface of the source having deposited most of their energy

in the solid. The great majority of the fission fragments

do not leave the source with the typical 1.77 or 1.01 MeV

average energies that they are born with but with a smaller


A much better view of the energy deposition can be

gained by calculating the deposition profile at a particular

pressure. A calculation of the energy deposition utilizes

the square law deposition function and geometry used for

equation 2.32.

In order to proceed further, the fission rate must be

calculated as follows:

C = Rf = Ntao = Z (2.35)

Nt : number density of target nuclei

a : fission cross section

: average neutron flux

Z : macroscopic cross section.

For these operating conditions,

Average Thermal Flux:106 1/cm2sec, and

Fission Cross Section:3800 barns for B10, 580 barns for U235

From the previous equation,

dJe(z) CfEpiRli{b3z2-2b2ln(bz) -b) (2.36)
dx = 2


Cf :fission rate

Ep :most probable energy at birth

b :1/Arli

i :fission fragment group.

and the expression is in terms of energy per unit volume per

unit time.

Since this calculation takes into account only

coulombic interactions and ignores the nuclear elastic and

inelastic scattering of the particles when they reach the

neutral status, the energy deposition curve falls off very

fast. If the nuclear scattering terms were included, the

range would be extended slightly, but only a small addition

would be made to the deposition of energy at the end point

of the fission fragment path. The effect on the total

deposition would be small24.

One of the unknowns, as previously described involves

how the energy is utilized, what excited states or ions are

produced, and what photon emissions are coming from the

plasma generated by the fission fragments.

Since the fissile material that is placed in the

cathode is being constantly evaporated from the cathode

surface it is safe to say that the plasma column of the arc

is composed by that fissile material vapor, thereby forming

a volume source of fission. Upon application of the

previous relations to a volume of fissile material, it is

found that at the neutron fluxes used in this dissertation a

small fraction of the energy generated in the volume stays

in it. The total power produced by the volumetric source is

of the order of 10-5 Watts. Measurements detailed in

chapter IV show that in order to maintain the type of arc

used in this dissertation a power of a few kilowatts is


The one conclusion that can be drawn from such

calculations is that volume ionization or excitation by the

fission source, probably does not account for any changes in

the operation of arcs.

Butler and Buckingham29 state that for high energy ions

whose velocity is much greater than the thermal ion or

electron velocity, the loss rate of energy to the electrons

is larger than to ions by the factor (mi/me)(Pe/zi2Pi). For

helium this ratio is about 20. This could account for some

volume enhancement of energy, especially in the case of

fission fragment deposition. But Pe and pi are extremely

small in both cases and most of the energy transfer is to

neutral particles. This effect then, is not significant in

the tenuous plasmas described here. Since it has been


established24 that neutron fluxes do affect the operation of

glow discharges, and lasers, the changes occurring must be a

function of the irradiation of the electrodes. Data

describing these effects will be presented in Chapter IV.

Theory and Application of Plasma Diagnostic Techniques for
Temperature Measurements

Many techniques used for temperature diagnostics were

developed by Griem30, Hefferlin31, and Lochte-Holtgreven32.

The following discussion considers the relative line

intensity method and the conditions which are required to be

used for this method.

Local Thermodynamic Equilibrium (LTE)
A discussion of temperature diagnostic techniques and

their suitability requires examining the basis for plasma
temperature measurements. When collisional effects are
dominant, there is a possibility of detailed balancing
between collisional processes alone. "A detailed balance

implies that the distribution among bound levels is governed

by Maxwell-Boltzmann Statistics, and the free electron

velocity distributions being characterized by the same
temperature T,"31. Under this condition, the thermal

processes are said to be in local thermodynamic equilibrium


"[W]henever LTE prevails . processes involving free

electrons are predominant because their velocities are high

and cross sections at least not smaller than those used for

the corresponding reaction in which electrons are replaced

by ions. Time variations and spatial inhomogeneities may

restrict the validity of LTE, since one must obviously

require that in times of the order of the inverse excitation

or deexcitation rates there is no significant change in the

local electron temperature nor enough time for the atoms or

ions to diffuse into regions of different electron


It is a difficult task to make a detailed computation

of equilibrium satisfying conditions but it is still

necessary to evaluate the validity of the LTE assumption.

Without LTE temperature diagnostics become extremely


According to Schneider and Oertel33 there are basically

three types of validity criteria to be applied to laboratory

plasmas in which electron and photon interactions are

responsible for ionization and excitation:

I. Electron density must exceed certain minima.

II. Relaxation times must be short compared to times

characteristic of changing experimental conditions

III. The mean free path of atoms between equilibrating

collisions must be short compared to the distance over

which experimental conditions change noticeably.

For the arc examined in this dissertation, categorized as a

stationary, non-uniform plasma, the validity conditions I

and III must be satisfied.

The first criterion is satisfied mathematically by32

ne 9x10( f kT 12 [cm-3] (2.37)

where AE is the energy separation between the ground state

and the first excited state for which LTE is to be

considered. The basis for this expression is that radiative

transitions between the two states are less than 10% as

frequent as de-excitations by electron collisions.

The third criteria can be related to the electric field

in the arc through the energy gained by electrons between

collisions with ions. More important, one can establish the

agreement between the gas temperature and the electron

temperature. In this case the electrons are primarily

responsible for the excitation processes and thus define the

characteristic plasma temperature. The relationship between

these temperatures is expressed by

k(T-T) Mene e2E2 (2.38)
2 ) MiTei Me


Te:electron temperature [K],
Tg:gas temperature [K],

Tei:time between electron-ion collisions,[sec]

Me:electron mass,[Kg]

Mi:ion mass,[Kg]

ne:electron number density,[1./cm3 ] and

E: electric field [V/m]

This equation can be reduced to

Te-Tg Mi XeeE (2.39)
T 4Me[ / eJ

where the substitutions

ve= (2.40)


es_ 1 ; [cm] (2.41)

Great difficulty is experienced in determining a good

value for Qei. A reasonable estimate is between 10-13 cm2

and 10-14 cm2. For this condition the gas temperature is

within 5% agreement with the electron temperature for a

boron partial pressure of 0.3 atm. Until better interaction

cross sections are available, the task of making an accurate

computation of LTE remains a formidable one.

Relative Line Intensity Method

An estimate of a plasma temperature can be obtained by

comparing the relative magnitude of spectral emission from

two different excited states. The technique is based on the

measurement of line intensities and their ratio. It is

based on the following relationship:

where no is the particle density of the ground state of the

Ii iAi-j hv e-E/kT (2.42)

particular species, gi is the statistical weight of the

upper state, Ai_j is the transition probability for the

particular emission from state i to state j, U(T) is the

partition function, hv is the energy of the emitted photon,

Ei is the energy level of the upper state, and Ii is the
intensity density of the emitted line in (Watts/cm3

steradians). If one takes two lines from the same species,

provided that their difference in excitation energies is

large enough to produce the desired sensitivity, and

provided that the lines are not self-absorbed, the ratio of

the intensities of the two lines is given by:

-1 v2g2A2-2 exp(- E ) (2.43)
I1 vlglA T(2.4

from which a temperature can be derived.
The sensitivity of this method hinges on the energy

level separation of the two upper states of the lines that

are considered. If the lines used have upper states which

too close, then the method will not be very sensitive and

measurements will be meaningless unless the instrumentation

accuracy is very high.



The apparati used in the experimental phase of this

dissertation are described in this chapter. Theoretical

justification of methods and data used is provided and

calibration methods explained.

Arc Column and Electrodes

The device used to study arc plasmas is shown on Figure

3.1. It is a helium vortex stabilized plasma whose cathode

is at the inlet of the flow and the anode is correspondingly

at the exhaust. The anode is made of a tungsten insert

coupled to a copper jacket which is internally cooled. The

arc exhaust is connected to a catch tank which contains a

fine mesh capable of filtering fission products from the arc

exhaust. The catch tank is in turn connected to a vacuum

system capable of producing a vacuum of about 0.03 atm.

To allow for spectroscopic analysis of the ultraviolet

portion of the spectrum from the arc, the arc column was

inserted in a quartz cylindrical envelope which measured 57

mm in diameter, 4 mm in thickness, and 5 cm in length.

Bore for Charge of

Figure 3.1. Schematic Diagram of Vortex Stabilized Arc

Previous studies of fissioning arcs by Mack34, and

Randol35 utilized carbon-tungsten electrode systems. This

system was operated with no internal electrode cooling and

was restricted to low power input. Additional preliminary

work was performed in order to establish the stability of

the carbon electrode under the pressures designed for this

experiment. The stability of the arc was studied and

tungsten and carbon cathodes were monitored. Because the

light emission is dependent on arc stability it was of

critical importance to establish the time after which

measurements were possible. Therefore, the time to

stabilization, i.e., the time it takes for the arc voltage

and current to become static, was measured for different

electrode configurations. The stabilization time was

measured to be smaller for carbon than for tungsten. This

is partly because carbon has a specific heat than tungsten,

and therefore a better thermionic emitter per unit input

power. A bored hole in the center of the cathode allows for

the introduction of different fissile elements in the form

of powder or small pieces.

Helium is injected at an angle through the bottom plate

of the assembly, and exits through the top into a catch

tank. The bottom plate through which the cathode emerges is

internally water-cooled.

Spectroscopic System Calibration

Spectroscopic analysis was achieved by setting up an

incoherent fiber optic waveguide which would transport

optical information from the arc to a spectrometer located

in the control room 60 feet away. The waveguide consisted

of 64 quartz fibers of 100 micrometer in diameter.

Attenuation in the waveguide is wavelength dependent and

calibrations were performed using tungsten ribbon

calibration standards. The waveguide was focused on the

middle of the arc section were maximum intensity was


A Czerny-Turner type spectrometer with an overall focal

length of 48 inches was used for spectrometric analysis. A

schematic view of the spectrometer is shown on Figure 3.2.

The grating used was 1190 grooves per millimeter with a

blazing wavelength of 500 nm. The linear dispersion was

measured to be 0.644 nm per millimeter spread. The entrance

slit of the spectrometer was set at 20 micrometers. The

spectrometer could be run both in multiline or monochromator

mode. In the multiline mode, a series of waveguides were

positioned at the exit plane to detect two or more

predetermined spectral lines. In both observation modes,

each line was detected by a photo-multiplier tube (PMT)

(Hammamatsu Model R376) and photocurrent signals were

transformed into voltage signals using preamplifiers

(Hammamatsu Model C1053). The spectrometer grating was

Photographic Plate

Ught Guide I

Figure 3.2 Spectrometer/Data Acquisition Arrangement

driven by a stepper motor controller capable of variable

speed for scanning purposes. Calibration of stepper motor

position as a function of wavelength was performed. Curves

corresponding to wavelength calibration are presented in

Appendix A. Absolute intensity calibration was also achieved

through the use of a tungsten lamp calibration standard.

Measurements of intensity were performed at different

wavelengths and a total overall attenuation factor was

computed by taking into account the proper geometrical

configuration factors.

Neutron Generator

The experiments were performed at the Plasma

Irradiation Facility at I.N.S.P.I. (Innovative Nuclear Space

Power Institute) at the University of Florida using the

Kaman A-711 Neutron Generator. The Kaman A-711 generates

neutrons by means of the DT reaction which produces 14.7 MeV

neutrons. Moderation and thermalization of the neutron

spectrum was accomplished by placing graphite blocks in

front of the generator. In addition, the generator was

placed in a cavity inside a wax filled box. The arc assembly

was similarly placed in front of the generator inside a

cavity surrounded by a wax filled box. The resulting fast

to thermal neutron ratio was measured to be in the order of

1:10. The thermal neutron flux was measured to be 106/cm2


Data Acquisition

Arc voltage and current were monitored through a

Keithley Model 199 multimeter equipped with a scanner card,

capable of recording up to 8 channels of data. Software was

developed to control measurements through the GPIB interface

available for the multimeter by using modular language

software (LabView 2.0) produced by National Instruments Inc.

Arc intensity data sensed through photomultiplier tubes were

monitored through a Tektronics Model 2120 oscilloscope which

allowed for instant storage into hard media of all acquired

waveforms. Sample waveforms acquired using the oscilloscope

are shown in Appendix B.

Arc Iqnition

The arc's ignition mechanism is comprised of a remotely

operated solenoid valve with a latch switch, which opens

upon actuation of the valve. The latch switch is attached

to a plate which has the cathode incorporated into it. The

cathode plate is initially drawn up so that the cathode pin

makes contact with the anode back plate. Upon ignition, the

arc invariably took about 30 seconds to stabilize, i.e., the

current and voltage traces became static.



In this chapter results of measurements of arc emission

and effects related to neutron irradiation of fissile arcs

are reported. Arc spectra for different fissile elements

are also reported.

Local Thermodynamic Equilibrium (LTE)

Since most critical measurements performed hinged on

the fact that local thermodynamic equilibrium (LTE) be

present, it is incumbent to show that under the operational

conditions of the arc LTE was established. As stated in

Chapter II, the estimated temperature gap between gas and

electron temperature for the species used in our experiments

(both boron and uranium) lies between 5 and 10%. These

estimates are based on collisional cross sections which are

not very accurate to begin with but that are reliable within

an order of magnitude. It is also dependent on the applied

field of the arc. This field is that which is necessary to

sustain a nearly equilibrium plasma and is determined by the

energy balance of the ionized gas as a whole as explained in

earlier in Chapter II.

A small temperature gap such as the one found here

ensures a steady transfer of Joule heat from electrons to

the gas. If the gap were to exceed 50%23 one would have to

drop the assumption of equilibrium in all calculations

related to the arcs studied here.

Arc Spectra

Before any measurements were performed spectra of the

different fissile materials used in the arc were obtained.

Spectral range is from 240 nm to 500 nm. Photographic

spectra were taken for both boron, and uranium arcs and were

compared with standard mercury calibration spectra

previously determined to identify unknown lines. Spectra for

carbon and boron is shown in Figure 4.1 in the range of 240-

250 nm. Figure 4.2 shows the spectra of helium highlighting

the lines used in the spectroscopic analysis. Figure 4.3

shows uranium spectra highlighting the UI lines used for

analysis and Figure 4.4 shows the UII lines. Note that there

exists a very tenuous continuum in most captions, and the

presence of some nitrogen and oxygen lines, indicating the

presence of air in the system. Even though the system was

pumped to a vacuum before arc initiation some air leak is

still possible. The spectra from the boron arc shows the

persistent doublets at 249.7 nm and also the first excited

carbon line at 247.9 nm. These lines were used to observe

changes in their magnitude as a function of irradiation.

U to
0 C05

1.. 0%
(-4 (-4

Figure 4.1

Spectral Line Emission of Boron (249.7) and Carbon
(247.9 nm)



Figure 4.2 Spectral Line Emission of Uranium (417.1 nm)

Figure 4.3

Spectral Line Emission of Uranium (365.3 nm and
365.9 nm)



0% % C1
M C.) M .r

Figure 4.4

Spectral Line Emission of Helium (388.8 nm and

400.9 nm)



P C9


Irradiation Effects

Arcs were operated at a fixed electrical power input

for all experiments. The sequence of the irradiated runs

began by first igniting the arc and then firing the neutron

gun followed by turning off the gun, and turning it back on.

Voltage and current were monitored at all times.

As it can be seen in Figures 4.5 4.8, both boron and

carbon line intensities changed during irradiation. This

early indication of irradiation effects showed a sign that

the overall temperature could have increased since the lines

under observation have small principal numbers. This would

mean that since lower energy levels of the species were

being affected and given the separation between successive

states it would be very likely that higher levels would show

a similar effect, provided that no population inversion

would take effect. Successive irradiations of boron arcs

under different conditions showed similar results.

Plasma Temperature Measurements

The temperature of the arc with and without irradiation

was obtained from helium line ratio measurements. The

technique used is the relative line intensity temperature

method as explained in Chapter II.

The lines chosen for the temperature measurement were

the 400.9 nm and the 388.8 nm helium lines. The graph


6 2
Neutron Flux= 10 /cm sec



-_ Neutron Flux= 0

e 15


10 It-II-W-


Experiment Sequence
Figure 4.5 Boron Doublet Line Intensity as a Function of Neutron Irradiation.

6 2
Neutron Flux= 10 /cm sec


"c Neutron Flux= 0

20-- -- ----- ------


5. 5. -------i------- -- ---lii



o ,

6* I0f0l t C00o 0>0 r- NO ^ < tot- 0 0 r-I W r>-C 000. T-N M (O >O to0- WO -NO W in to

Experiment Sequence

Figure 4.6 Boron Doublet Line Intensity as a Function of Neutron Irradiation
(Continued Sequence)



6 2
Neutron Flux= 10 /cm sec





Experiment Sequence

Figure 4.7 Carbon Line Intensity as a Function of Neutron Irradiation.

Neutron Flux= 0

10 ----- ----- ---


Sv Mc i- or o a)Ct C iNOCT i- 00 i N C,), ) toi 00 0.T N o in) (D P.C 0000 T- N c') V in
i- v- i- r- r- v- N N N N N N N N N MCM 0C C C VC MC V V VM t V

S10 ---------


'5 1 -



Experiment Sequence

Figure 4.8 Carbon Line Intensity as a Function of Neutron Irradiation
(Continued Sequence)

showing the sensitivity of this line in the range between

5000 K and 20,000 K is shown in Figure 4.9. The

temperatures during the boron test runs are shown in Figure

4.10, and the uranium run temperatures are shown in Figure

4.11. The results show that the boron arc temperature

increased from -9,500 K without irradiation, to -11,500 K

during irradiation with a neutron flux of 106 n/cm2 sec.

This is a 20% increase in plasma temperature. The uranium

arc run temperatures increased from -8,100 K to -9,300 K, an

increase of 15%.

IV Characteristics

IV characteristics of both uranium and boron arcs were

monitored to obverse any changes in the characteristics for

each case. Figures 4.12 and 4.13 show the IV

characteristics of boron and uranium arcs under the

influence of neutrons and without. Figures 4.14 and 4.15

show the change in current in boron and uranium arcs as the

neutron flux was made to increase and decrease by

controlling the neutron generator beam current. The neutron

generator is designed to produce an output range 0.1% power

to 100% power, corresponding to 103 n/cm2sec to 106


Further evidence of the increase in current observed

during the temperature measurement experiments is observable

on a plot of current vs. arc input power.

co 0.06-



-2 1

Figure 4.9 Line Intensity Ratio of Selected Helium Lines
- .r 0 0 .. ... . . ... . ... . ..

0.00 - - ---

Figure 4.9 Line Intensity Ratio of Selected Helium Lines





6 2
Neutron Flux= 10 /cm sec

Neutron Flux= 0


1 2 3 4 5 6 7
Experiment Sequence

Figure 4.10 Boron Arc Plasma Temperature as a Function of Neutron Irradiation

110006 2
Neutron Flux 10 /cm se
Neutron Flux= 10 /cm sec


- 9000




6 2
Neutron Flux=10 icm sec

4 I

Neutron Flux= 0.0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Experiment Sequence

Figure 4.11 Uranium Arc Plasma Temperature as a Function of Neutron Irradiation.


6 2
+ Neutron Flux= 10 /cm sec
x Neutron Flux= 0


+ + + +4

40 50 60 70

Figure 4.12 IV Characteristics of Boron Arc Under Neutron Irradiation



6 2
+ Neutron Flux= 10 /cm sec
x Neutron Flux= 0.0

* x
C +






50 I I -I'
42 43 44 45 46 4

Figure 4.13 IV Characteristics of Uranium Arc Under Neutron Irradiation

+ ++

30 10 7
--*--- Current
29 Flux

28 106

27- a
i 26 105

25 x c


20 I 1 104

22 103


0 10 20 30 40 50 60 70 80 90 100 110 120 130

Time (sec)

Figure 4.14 Boron Arc Current as a Function of Oscillating Neutron Irradiation.

. --*- Current






S40- l i 6,080 102
n 9n 40 60 80 100




Time (sec)

Figure 4.15 Uranium Arc Current as a Function of Oscillating Neutron Irradiation.



Figures 4.16 and 4.17 show such plots for boron and uranium.

The effect was only observed when fissile materials were

introduced into the cathode pin. Previous irradiations of

tungsten and carbon arcs show little or no effect in the

monitored arc current. These observations are shown in

Figures 4.18 and 4.19.

Benchmarking Results: Particle Density Measurements

The uranium atom and ion densities can be obtained from

the measured line intensities, the helium line ratio

temperature measurements, and the above equations. These

values can be compared to the densities obtained by assuming

thermal equilibrium and using Saha equations30,31. The

results are shown in Figure 4.20. The calculated densities

for the uranium arc runs without irradiation, based on the

measured line intensities, are shown as the data points with

the appropriate error bars. The curves represent the

results of Saha equilibrium calculations for the range of

uranium pressures during the experiments. The results show

that the data lie in the region bracketed by the Saha

curves. This provides a good benchmark check of the

measurements and calculational methodologies.

Mass Transfer: Gravimetric Measurements

One of the key aspects of the uranium arc fission

reactor is the ability to minimize fuel loss from the

reactor via the electric field confinement. Data from the




0. +


* x

o +

35- +


+ x
x x
30 I -
1800 2000 2200 2400 2600 2800 3000
Power (Watts)

Figure 4.16 Boron Arc Current vs. Power as a Function of Neutron Irradiation

6 2
+ Neutron Flux= 10 6cm sec
x Neutron Flux=0.0


Figure 4.17 Uranium Arc Current vs Power as a Function of Neutron Irradiation





Power (Watts)





S10 6

2. 20

S10 5 25
C 0
o 0

CD 4
c 10
I- 15


102 -410
0 10 20 30 40 50 60 70
Time (sec)

Figure 4.18 Tungsten Arc Current as a Function of Neutron Irradiation.



0 IOII) I l u0

E 105


10 2
0 10 20 30 40 50 60 70 80 90 100 110 120 130
Time (sec)

Figure 4.19 Carbon Arc Current as a Function of Neutron Irradiation.

101 1 1
---- UI, Saha, 0.3 atm
......... UII, Saha, 0.3 atm
UI, Saha, 0.1 atm
...... UII, Saha, 0.1 atm
18_____ _____ UI, Measured

1 0 6 . . . .. .- - -- .

E 10

1015--- "7---
.io14. ---- - ..-4--

1000 10000 100000
Temperature (K)
Figure 4.20 Uranium Equilibrium Particle Density Population.
Total Pressures: 0.1,0.3 atm

uranium mass flow rate experiments are presented in Figure

4.21. The experiments were performed for a range of

currents from 20 to 30 amp. In addition, the physical

configuration of the uranium within the cathode pin was also

examined. Thus the uranium was inserted at various depths

into the pin to examine the impact on fuel loss rate. Due

to limitations in the scope of the effort, optimization of

operating parameters could not be performed. However,

Figure 4.21 indicates that the mass loss rate from the

electrode can be decreased to very low levels (order of a

few mg/cm2 sec), by proper electrode design.

Uranium recirculation and recovery was also performed

by operating the uranium pin as the cathode. In these

experiments, uranium atoms evaporating from the liquid metal

pool surface at the cathode tipare returned to this pool by

the effect of the electric field. Uranium loss from the

electrodes could thus condense on cold surfaces near the

electrode within the arc assembly. Thus, uranium either

exhausted with the helium, or was recovered within the arc

assembly. The results of these experiments are shown in

Table 4.1. The results show that up to 50% of the lost

uranium can be recovered in this manner.



E 40


O 3 Arc Current: 20 Amperes
0 Arc Current: 25 Amperes
A Arc Current: 20 Amperes

u 20


2 10

S0 1 2 3 4
Insertion (mm)

Figure 4.21 Gravimetric Measurements of Uranium Loss vs.

Insertion Distance and Arc Current

Table 4.1
Uranium Recirculation and Recovery






Average Insertion 0.0 1.0

Distance (mm)

Total Loss (grs) 0.220(100%) 0.391(100%)

Losses through Helium 0.193(88%) 0.179(46%)

Flow (grs)

Recirc. Uranium 0.026(12%) 0.211(54%)

Recovered (grs)



Following is a discussion of the experimental results

obtained. Possible explanations of the observed results are

varied and therefore subject to further experimental

verification. This chapter will attempt to explain the

effects reported in Chapter IV. First, the apparent

increase in line emission intensity which is claimed to be

caused by increased electron temperature. The increase in

temperature is also accompanied by a small increase in

monitored arc current, and therefore increased electrical

arc power input. Boron and uranium arcs were studied and

will be discussed separately.

Physics of Observed Phenomena

The observed increase in arc current in concurrence

with an increase of the neutron flux can be explained by

several well-known mechanisms. Walters24 states in his

investigation of the effect of thermal neutron irradiation

of He3 glow discharges, that the increase in current

observed in his experiments is due entirely to the ions

formed in the column and in the cathode fall which are


accelerated and are able to generate further ionization. He

further concludes that volume ionization in the column is

not enough to create the observed change in discharge


A similar explanation can be given in the case of an

irradiated arc discharge, but some of the physical

mechanisms actually differ. Arc discharges operate under a

different electric current regime (order of amperes as

opposed to milliamperes or even microamperes for glow

discharges), and need to generate electrons by thermionic

emission at the cathode to maintain arc conditions. The

energy required to raise the temperature of the cathode to

enable it to emit thermionic current is supplied by the ions

that are generated in the column, are attracted to the

cathode and subsequently heat it by collisions with the

solid surface. These ions are formed at a distance

approximately equal to the collision mean free path of the

thermionically emitted electrons. Now, in the case of a

cathode that is emitting fast particles via fission,

positive ions and electrons are created by the ionization

track generated by the fission products. The electrons

generated are repelled away by the cathode field, while the

positive ions are attracted by it. The ionization produced

by such fission products is considerably more efficient than

that of electrons due to their larger size, closer match in

mass ratios, and kinetic energy. As a consequence the


effective ionization mean free path is considerably shorter.

The resulting effect is the creation of a cathode fall which

is proportionately closer to the cathode than the electron-

induced cathode fall.

The fission products effectively produce a standing

positive charge cloud which hovers at a distance that is

equal to the ionization mean free path of the fission

product and maintained by the constant nuclear induced

generation of electron-ion pairs. The main loss mechanism

is represented by electron-ion recombination. The resulting

nuclear-generated ion cloud, induces a slight increase in

electric field by creating a corresponding image charge

behind the cathode surface. This field enhancement causes a

decrease in the work function of the material in accordance

with the Schottky effect. The reduction of the work

function at a given temperature causes an increase in the

thermionic electron current generated at the cathode and

therefore an increase in the overall arc current. This

phenomenon is well known for high current arcs 37-42

Figure 5.1 shows the enhancement factor as a function of

electric field for several temperatures. A small increase

in the electric field can yield a significant increase in

the electron current, especially at low temperatures.

In the next section a description of the proposed

mathematical model used to predict the arc current

enhancement is given.

2.0 9" '

/ 2500 K

o 3000 K

3500 K



102 103 104 105 106
Electric Field (V/cm)

Figure 5.1 Schottky Enhancement Factor as a Function of Electric Field

Mathematical Model

As stated earlier, the fission generated electron-ion

pairs effectively form a cloud of positive ions at an

average distance equal to the ionization mean free path of

the fission fragments, and this cloud results in an

enhancement of the electric field at the cathode surface.

This can be modelled by computing the field generated by a

charge in a shape of a disk at a distance away from its

surface equal to the ionization mean free path. Figure 5.2

shows the arrangement. To compute the electric field, using

Gauss's Law we obtain that,

I I 4= d (5.1)
s 4TEor 2

where a is the surface charge density (Coulombs/m2) and eo

is the permittivity of free space ( 8.85 x 10-12 F/m). The

scalar product in the integrand is resolved as,

i-dA=-i (Hpdpd#) =pdpd4 (5.2)

and from geometrical considerations,

pdp = rdr (5.3)

then 5.1 reduces to,

2n S S
r ardrd a r dr (5.4)
4nor2r 2eo r


Figure 5.2 Geometric Configuration of Disk Source Charge

IE Ip = E O In( + 1) (5.5)
2E 2

In this analysis 1i is the ionization mean free path of

the fission products in the gas, and a is the radius of the

arc column which for all purposes herein is equal to the

radius of the cathode surface. The ionization mean free

path is defined as:

i 1 (5.6)
a Ng

where ai is the ionization cross section of the gas, and Ng

is the gas number density. The ionization cross section is a

function of energy which peaks at the ionization energy of

the material and decreases slowly as a function of energy.

The ionization cross sections for boron and uranium are not

readily available in the literature. However, existing data

for other elements indicate that the ionization cross

section is directly proportional to the physical atomic

cross sectional area of the atoms undergoing the collisions.

Therefore it can be safely assumed at least within an

order of magnitude confidence that the ionization cross

section is of the order of na02 where ao is the atomic


The source of ionization can be computed by evaluating

the total ionization produced by the fission fragments

emitted by the fissioning species in the cathode. The total

charge density source is given by:

= eNfaf'thEqRf, 1 } (5.7)
w arecNg

where arec is the volumetric electron-positive ion

recombination coefficient, where Nf, is the number density

at the cathode temperature, of is the fission cross section

for the reaction, Oth is the thermal neutron flux, Rf,s is

the effective fission product range in the solid, Eq is the

effective energy released per reaction, e is the electronic

charge (1.6x10'19 Coulombs/charge), w is the electron-ion

pair yield per ionizing particle (eV/ion pair). In equation

5.7, the first bracketed term represents the charge

generation flux (Coulombs/m2 sec), and the second is the

average lifetime (sec) of the excess charge given by the

recombination time. It is to be noted that the effective

energy of the fission fragments is average energy of the

spectrum of fission fragments. As fission fragments leave

the surface of the solid they posses an energy spectrum

which is considerably softer. In fact sources in the

literature43 indicate that for the case of uranium dioxide

the spectrum is of the shape as that indicated by Figure 5.3

for the case of a uranium dioxide film which is larger than

the range of the fission fragments in the solid. This

spectrum can be approximated as flat with an average energy

of 50 MeV. A similar spectrum can be obtained for the case

of alpha particles and Li7 particles for the case of




c0 io

0 20 40 60 80 100 120 140
Observed Energy (MeV)

Figure 5.3 Uranium Fission Product Energy Spectrum From a Thick Source.

fissioning boron. The effective average energy of these

particles is then about 700 KeV.

Since the charge is being generated exponentially, the

effective field is the result of a volumetric charge

density, or conversely the sum of the field contributions

due to a series of disk charges. If we assume that the

charge is being generated at an exponential rate as a

function of distance from the cathode surface then the

expression for the charge density is given by:

a(x) = 0.528oo(ex/-I1) (5.8)

Then the average field contribution due to a volumetric

charge density source is given by integrating, namely,

0.52800 x/X+)
Average -1)n( +1) dx (5.9)
Ai average ii

where oo is the surface charge density computed above by


In the case of boron filled cathode and boron arc, the

fission fragments--Li7+ and He4--are colliding and ionizing

boron atoms which are evaporating from the cathode surface.

The ionization cross section for these processes is not well

known, but approximations can be obtained by obtaining data

for other materials with similar atomic mass and atomic

numbers. Massey and Gilbody44 report apparent ionization

cross sections for helium ions ionizing other helium ions,


argon, hydrogen, and molecular nitrogen. All cross sections

are in the order of 10-15 cm2. This supports the argument

that cross sections for atomic processes are in the order of

the atomic size a0o2, where ao is the Bohr radius.

Therefore a typical ionization cross section of 10"16 cm2

for He4 and Li7 would at least be within an order of

magnitude estimation. In the case of fission fragments from

uranium fission reactions, the same argument can be given

and an estimate of 10-16 cm2 can also be given for the

ionization cross section of heavy ions.

The recombination coefficient was computed by using the

formulism given by Hinnov, and Hirschberg45, which assumes a

hydrogen-like atomic structure:

arec =5.6x10-27 ne T-9/2

where T is in eV, ne is in cm"3, and arec is in cm3/sec.

This formulism although an oversimplification leads to the

best possible estimation of the recombination coefficient.

Table 5.1 shows the data used in evaluating equation 5.7.

Cathode Energy Balance

The number density of the evaporated gas is given by

the temperature of the evaporating surface and its vapor

pressure. The temperature of the cathode is also needed to

evaluate the work function reduction. In order to estimate

the temperature of the cathode surface an energy balance

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