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474
INDEX
Accelerating fields thermionic emission in, 25-27
Accommodation coefficient in evaporation thermodynamics, 27-28
Additives
to cathodes, 11
electronegative, 42-47
electropositive, 39-42
Adsorbed atoms measurement of, 35-36
Adsorbed particles binding energy, 31
Adsorption
effect on work function, 30-33
kinetics, 30-31
Alkali metals
adsorption, 39
energy levels, 66-69
Alkaline earth metals on cathodes, 30
Aluminum oxide as insulating material, 12
Anode
atom flow from, 393
boundary conditions, 305
crystal structure, effect on ignition voltage, 345-346
temperature, effect on operating characteristics, 342-343
work function, 10-11, 344-346
effect on operating characteristics, 342-343
Anodes
cesium ionization on surface of, 269
electron energy flow to, 24
Fermi level, 3
temperature, effect on current-voltage characteristics, 282-283
effect on saturation current, 284
effect on TIC efficiency, 10
thermionic emission from, 50
work function in barium vapor, 42
Anomalous Schottky effect, 25, 300
Arc ignition, 368-372
Arc mode, 7-8
operation, 293-372, 321-326
atom and ion flow to cathode in, 357-360
current increase in, 336-339
discharge appearance in, 327
extinction of, 330-333
ignition of, 327-330
potential distribution in, 293, 296
with strongly ionized plasma, 347-357
transients in, 366-372
transition to, 326-333
Argon
effects on current-voltage characteristics, 360-365
electron scattering, 59 Atoms
Atoms
Boltzmann distribution, 119
charged-particle scattering from, 391-393
collisions with ions, 60-61
density in arc plasma, 293-294
desorption kinetics, 33-34
diffusion in plasma, 147-149
elastic collisions with electrons, 59-60
electron interactions with excited, 150-152
electron transitions in plasma, 124
energy exchange with electrons, 104-111
energy levels, 66-69
population balance of, 134-137
excitation-deexcitation processes, 61-66
excitation and ionization by electron collisions, 126-128
excitation levels in plasma, 119-120
excited-state populations, 123-124
flow from anode, 393
flow to cathode, 357-360
inelastic collisions with electrons, 61-66
ionization in electrode region, 202-204
475
ionization at hot electrodes, 167-170
ionization and recombination in plasmas, 123-134
photoexcitation in plasma, 128-129
radiation and absorption of light, 69-73
oscillator strengths, 71-72
recombination processes, 130-132
resonance excitation rate, 155-157
scattering by electrons, 296
temperature in arc plasma, 293-294
Auger effect in measuring adsorbed atoms, 36
Autonomous power plants, 1, 4
in space, 12-13
Auxiliary power plants (see Autonomous power plants)
Barium
addition to cathodes, 11
as additive, 40-42
adsorption on tungsten, 31-33
adsorption on (100) tungsten face, 36
heat of adsorption on tungsten, 31
heat of desorption on tungsten, 41
limitation on use as additive, 42
Barium oxide on cathodes, 30
Beryllium oxide as insulating material, 12
Bethe—Born approximation, 65, 124
Boltzmann distribution for atoms, 119
Boltzmann equation, 82
Born approximation, 65
Bottle-neck, 131
Boundary conditions
effect on TIC design, 259-262
effects on operating characteristics, 297-304
for LTE plasma, 309-313
for transport equations, 208-216
Calcium oxide on cathodes, 30
Carbon monoxide effect on electron emission, 46
Carnot efficiency, 4
Cathode
emission current, effect on operating characteristics, 339
surface-structure effects, 347
temperature, effect on current, 334
effect on current-voltage characteristic, 327-329
effect on minimum current, 331
effect on operating characteristics, 340
work function, current dependence on, 397
variations, 357
Cathode, nonuniform virtual cathodes on, 300
Cathodes
adsorbed materials on, 30-33
cesium adsorption on, 7, 9-11
electron emission, effect of space charge on, 299
electron evaporation heat, 10
electron flow at, 181-193
electron heat of evaporation, 24
emission current, 298
densities, 9
effect of geometry on, 301-302
effects of adsorbed atoms, 33
evaporation of, effect of chemical reactions on, 29
evaporation of atoms and molecules from, 27-29
Fermi level, 3
field intensity at, 298
heat transport from, 23-24
materials for, 11
oriented vapor-deposited coatings, 34
patch fields on, 24-26
surface energy, 29-30
surface-geometry effects, 301-302
temperature, effect on saturation current, 279-280
thermionic emission from polycrystalline, 25-26
476
virtual, 298-300
work function, 6-7, 35-36
effect of cesium adsorption on, 37-39
Cathodes, nonuniform effects on operating characteristics, 300-301
Central-station power plants use of thermionic converters in, 449
Cesium
adsorption on cathode, 7, 9-11
adsorption energy, 11
adsorption on germanium, 33
adsorption on tungsten, 31-33
binding energy of adsorption, 31-32
electron scattering, 59-60
energy-level populations in plasma, 138
energy-level transitions, 152
energy levels, 66-69
excitation cross sections, 65
heat of adsorption, 37-39
heat of evaporation from tungsten, 31
ion-atom interactions in, 61
ionization on anode surface, 269
ionization cross sections, 66
ionization in electrode region, 202-204
ionization potential, 6
ionization—recombination rates in plasma of, 137-141
quantum defects, 69
spectra, 68
Cesium oxide effect on electrode work function, 46
Cesium plasma
energy-level populations in, 162
equilibrium constants, 123
fast-electron distribution function in, 160-162
local thermodynamic equilibrium in, 325
particle equilibrium in, 120-122
partition functions, 121-122
Cesium pressure effect on operating characteristics, 342
Cesium vapor pressure effect on saturation current, 280-282
Charge exchange, 587-391
Charge-exchange interactions, 60-61
Charged particles
density in arc plasma, 293-296
scattering from neutral atoms, 391-393
transport in plasma, 90-95
Chemical fuels use of thermionic converters with, 13
Collectors (see Anodes)
Compensation parameter, 329
in Knudsen mode, 393-395
Contact potential difference, 24-25
Continuous-spectrum radiation, 72-73
Copper thermionic emission in cesium vapor, effect of oxygen on, 47
Coulomb collisions, 57-59, 83-84
in magnetic field, 92
Coulomb scattering, 393
Cross sections
for elastic scattering, 56
electron scattering by cesium, 60
for momentum transfer, 57-58
Crystals surface energy of, 29-30
Current
increase in arc-mode operation, 336-339
saturation, 279-282
variation with cathode temperature and cesium pressure, 331
Current-voltage characteristics, 304-307, 313-317, 354
in arc-mode operation, 321-322
in diffusion mode, 279, 286
effect of cathode surface on, 347
effect of cathode temperature on, 327-329
effect of coefficient of anomaly on, 338
effect of interelectrode spacing on, 341
477
effect of magnetic field on, 408
effects of inert gases on, 360-365
in Knudsen mode, 399-403
measurement of, 424-425
Debye length, 168-170
Debye radius, 58
Dense-mode operation, 6
Desorption kinetics, 30-31
Diagnostics (see Plasma diagnostics)
Diffusion equations for diffusion-mode operation, 271-279
Diffusion mode
calculations of, 16
operation, 6-7, 267-291
effect of magnetic fields on, 287-291
transition to arc mode, 326-333
Dipole moments of adsorbed atom layers, 45
Direct conversion, 1-4
efficiency, 4-5
Direct-flight mode (see Knudsen mode)
Distribution functions, 81-82
Doppler broadening, 77
Double-sheath mode, 333
Einstein coefficients, 69-71
Elastic collisions, 55-57
Electric field
electron distribution function in, 108-113
intensity, measurements of, 400-403
Electric fields distribution in plasma, 167-181
Electrodes
See also Anodes, Cathodes, and Probes
effect on diagnostic probes, 243-245
electron collisions with, 95-104
electron flow at, 181-193
interactions at, 167-216
ionization at, 167-170
materials of construction, 10-12
potential distribution at, 168-172, 204-208
semiconductor, 11
spacing, 11
effect on operating characteristics, 341-342
thermionic emission, 19-24
Electromagnetic radiation
continuous-spectrum radiation, 72-75
emission and absorption by atoms, 69-73
oscillator strengths, 71-72
flux in plasma, 142-145
interactions in plasma, 128-129
spectral broadening, 73-77
Electromotive force from Seebeck effect, 1-2
Electron current in arc-mode operation, 323
Electron distribution effect on ionization, 321
Electron emission for molybdenum in barium vapor, 42
Electronegative additives, 42-47
Electron-rich conditions, 15
Electrons
beam energy relaxation, 193-202
collisions, with atoms, 126-128
with electrodes, 95-104
with electrons, 95-97
with ions, 57-59
current in weakly ionized plasma, 87-91
distribution function, deviation from Maxwellian, 317-521
effect of inelastic collisions on, 149-162
in electric field, 108-113
for fast, 152-155
elastic collisions with atoms, 59-60
energy distribution function, 183-216
energy exchange in plasma, 104-111
energy flux in weakly ionized plasma, 87-91
evaporation heat from cathodes, 10
478
Fermi—Dirac energy distribution function, 19
field emission, 26
flow in cathode region, 181-l93
flow from plasma, 204-208
heat of evaporation, 24
inelastic collisions with atoms, 61-66
interactions with excited atoms, 150-152
kinetic coefficients, 95-104
kinetic energy flux, 23
mobility in plasma, 104
potential energy distribution at electrodes, 168-170
reflection coefficient, 181-l93
scattering, in arc plasma, 324-325
by atoms, 296
by cesium, 59-60
in interelectrode space, 39-40
by ions, 296
in plasma, 11
temperature, 310-313
in arc plasma, 293-296
distribution, 321-323
with ionization equilibrium, 326
probe determination of, 230
thermal conductivity in plasma, 104
thermal-diffusion ratio in plasma, 104
thermionic emission, 19-27
current, 21-23
in accelerating fields, 25
Richardson formula, 22-23
thermionic emission currents effects of adsorbed layers on, 45-47
transport equations, 208-216
Electropositive additives, 39-42
Emission current
effect of adsorbed atoms on, 33
effect on operating characteristics, 339
Emitters (see Cathodes)
Energy exchange between plasma components, 104-111
Energy levels population balance of, 134-137
Engineering problems, 423-449
Equations of state of arc plasma, 293-297
Evaporation thermodynamics of, 27-29
Extinction current, 333-334
Fermi—Dirac distribution, 19-20
Field emission, 26
Fluorine
addition to cathodes, 11
effect on electron emission, 46
use as additive, 42
Fokker-Planck approximation, 98-102
Gap
See also Interelectrode space length, effect on output, 50-51
potential distribution in, 400-403
Germanium cesium-adsorbed layers on, 33
Grizinski cross sections, 64-66, 124, 130
Hall effect, 93-94
Halogens use as additives, 43
Heat of desorption effect on electron emission, 45
Heat engines efficiency, 4-5
Heat pipes use of thermionic converters with, 436-439
Hydrogen
effect on electron emission, 46
quantum defects, 69
spectra, 68
Hydrogen plasma recombination coefficient for, 133
Ignited mode, 6
See also Arc mode
Inelastic collisions effect on electron distribution function, 149-162
479
Inert gases, 8
effect on current-voltage characteristics, 360-365
Inglis—Teller formula, 120, 122
Insulating materials, 12
Interelectrode space
potential distribution in, 269
space charge, 48
Interelectrode spacing effect on saturation current, 282
Ion current
in arc-mode operation, 323-324
calculation of, 337
dependence on boundary conditions, 302
dependence on device current, 319-320
Ionization, 132-133
energy expenditure, 8
local thermodynamic equilibrium, 325-326
rates of, 133-134
Ionization cross sections principle of detailed balance for, 125
Ion propulsion of rockets, 13
Ion-rich condition, 15
Ions
collisions with atoms, 60-61
collisions with electrons, 57-59
desorption kinetics, 33-34
electron collisions with, 95-104
energy exchange with electrons, 104-111
flow to cathode, 357-360
flow from plasma, 170-181
losses, 308
mean free path, 56
mean free time, 56
mobility in gases, 113-116
momentum transfer, 57
scattering cross sections, 56
scattering by electrons, 296
trajectories in undercompensated mode, 386
transport equations, 208-216
Isomite converter, 449
Isotopic heat sources, 445-449
Kinetic theory of plasmas, 81-116
Knudsen arc, 365, 408-418
Knudsen effusion chamber, 27
Knudsen mode
efficiency in, 10
operation, 377-418
compensation parameter in, 393-395
current-voltage characteristics of, 399-405
effects of magnetic field on, 405-408
monotonic potential distribution in, 378-384
nonmonotonic potential distribution in, 384-399
useful power in, 395-398
Knudsen plasmas, 6
Krypton
effects on current-voltage characteristics, 360-365
electron scattering, 59
Langmuir probes, 224-228
Light
continuous-spectrum radiation, 72-73
radiation and absorption by atoms, 69-73
oscillator strengths, 71-72
spectral broadening, 73-74
Liquid-metal magnetohydrodynamic generators, 3
Lithium
ionization cross section, 67
quantum defects, 69
Local thermodynamic equilibrium, 307-317, 325-326, 350-354
deviations from, 356
Lorentz force, 82, 91
LTE (see Local thermodynamic equilibrium)
Magnetic fields
effect on diffusion-mode operation, 287-291
effect on Knudsen-mode operation, 403-408
effects on arc mode, 365-366
480
effects on charged-particle transport, 91-95
Magnetohydrodynamic generators
closed-cycle, 5
open-cycle, 5
Materials of construction, 10-12
Matthiessen’s rule, 103
Maxwell distribution in arc-mode operation, 328
Maxwellian distribution deviations from, 149-162, 317-321
Metals
accommodation coefficients, 27-28
Fermi level, 19-20
mirror-image force, 20-21
patch fields in polycrystalline, 24-25
thermionic emission current, 21-25
in accelerating fields, 25-27
work function, 20
MHD generators (see Magnetohydrodynamic generators)
Mirror-image force, 25
Molybdenum
as cathode material, 11
electron emission in barium vapor, 42
thermionic emission in cesium vapor, 36
work function of anode, 344
work function vs. cesium adsorption, 37
Momentum exchange in plasma, 104-105
Momentum transfer, 57, 59
cross sections, 58
Monocrystals as cathodes, 30
"Narrow point," 131, 133-134, 159
Neon effects on current-voltage characteristics, 360-365
Nickel
oxygen adsorption, 44
thermionic emission in cesium vapor, effect of oxygen on, 47
Nodal-point method, l02-l04
Normal Schottky effect, 25-26
Nuclear power supplies in space, 12-13
Nuclear reactors
materials for thermionic components, 439-441
testing thermionic components in, 441-445
use of thermionic converters in, 428-436
Nuclear thermionic fuel elements, 12
Oscillator strengths, 71-72
Output
characteristics, 425
methods for increasing, 426-428
power, in diffusion mode, 278
Overcompensated-mode operation, 396
Oxygen
addition to cathodes, 11
adsorption, 43-47
chemisorption energies for tungsten, 44
effect on cathode emission, 47
effect on work function of tungsten in cesium vapor, 45
heat of evaporation from tungsten, 31
use as additive, 42-47
Partition functions for cesium plasma, 121-122
Patch fields in polycrystalline materials, 24-26
Peltier heat contribution to heat of electron evaporation, 24
Performance testing in reactor environment, 441-445
Photocells, 3
Photoionization, 125
Plasma, 13-17
atom diffusion in, 147-149
Coulomb collisions, 57-59
density distribution, 310-515, 321-325
with ionization equilibrium, 326
481
diffusion mode, 6-7
elastic collisions in, 55-57
electron scattering in, 11
electron temperature, 310-315
distribution, 321-323
energy exchange in, 104-111
equations of state, 304-307
in arcs, 293-297
frequency of, 221
instabilities in, 14
ion flow from, 170-181
ionization and recombination in, 119-162
kinetic equations of, 81-84
solution of, 84-87
kinetic theory of, 81-116
Knudsen mode, 6-7
local thermodynamic equilibrium in, 307-317, 350-354
oscillations in, 14
parameter distribution in, 313-317
potential distribution in, 309-313, 321-323
potential distribution with ionization equilibrium, 326
properties in diffusion mode, 279-287
radiation emission from, 145-147
radiation flux in, 142-145
space charges in, 14
state in arc-mode operation, 321-326
thermodynamic equilibria, 119-123
thermoelectric emf, 16
thermoelectric figure of merit, 16-17
as working fluid, 17
Plasma, hydrogen recombination coefficient for, 133
Plasma, inhomogeneous effects of, 129-130
Plasma, strongly ionized
in arc-mode operation, 347-357
equations for, 347-350
Plasma diagnostics, 16, 221-262
optical methods, 245-255
probes, 221-239
Plasma propulsion of rockets, 13
Polycrystalline materials
as cathodes, 30
contact potentials with, 24-25
thermionic emission currents, 25-26
Potassium
ionization cross section, 67
quantum defects, 69
Potential distribution, 309-313, 321-323
in arc-mode operation, 293, 296
in diffusion mode, 269, 275
effect of magnetic field on, 405
at electrodes, 167-181
in the gap, 400-403
measurement by probes, 230-235
with virtual cathode, 299
Potential distribution, monotonic in Knudsen mode, 378-384
Potential distribution, nonmonotonic in Knudsen mode, 384-399
Potential distribution, oscillating, 393
Potential wells filling of, 387-393
Power in Knudsen-mode operation, 395-398
Power plants use of thermionic converters in, 449
Pressure effect on operating characteristics, 342-343
Principle of detailed balance, 61-62, 86, 125
Probes, 221-245
comparison with spectral techniques, 255-259
current-voltage characteristics of, 222-223, 242-243
in dense plasma, 228-237
design of, 239
electron temperature measurement by, 230-235
Langmuir, 224-228
verification of results from, 237-239
Quantum defect, 69
481
Radioisotope heat sources, 445-449
Ramsauer effect, 8, 59
Rasor curves, 38-39
Reactor thermionic fuel elements, 12
Recombination rates of, 133-134
Recombination cross sections principle of detailed balance for, 125
Reflection coefficients, 181-193, 320, 336-337
effect on current-voltage characteristics, 321
Relaxation-time approximation, 84-91
Remote power plants (see Autonomous power plants)
Rhenium
as cathode material, 11, 426
evaporation rate, 43
Rhenium oxide
evaporation rate, 43
work function, effect of cesium oxide on, 46
work function vs. cesium adsorption, 37
Richardson thermionic current formula, 22-23
Rocket engines specific impulse, 13
Rubidium
ionization cross section, 67
quantum defects, 69
Rutherford cross-section formula, 58
Rutherford formula, 63
Rydberg energy unit, 68
Saha equation, 121
Saturation current
in diffusion mode, 279-284
for thermionic converters, 3, 8-9
Scattering in plasma, 84-87
S
cattering cross sections, 56Schottky effect, 25-26
anomalous, 300
in arc mode of TIC operation, 7
on emission current, 336-337
S-curves, 34
Seebeck effect, 1
Semiconductor thermocouples, 2
Semiconductors
limitations on use of, 11
thermionic emission, 23
Short circuiting, 285, 363
Slotted cathodes effect on emission current, 301-302
Sodium
ionization cross section, 67
quantum defects, 69
Sodium chloride, solid-vapor equilibria, 28-29
Solar photocells, 3
Solid—vapor equilibria, 27-28
Sonine polynomials, 97-98
Space charge, 48
distribution in plasma, 167-181
effect on cathode emission, 299
effect on cathode emission current, 333-336
neutralization, in thermionic converters, 2-3
in plasma, 14.
Space vehicles power supplies, 12-13
Spacecraft use of thermionic converters in, 429
Spectral broadening, 73-77
Spectral diagnostic techniques, 245-255
comparison with probes, 255-259
Stark broadening, 74-76
Steam turbines temperature limitations, 4
Strontium addition to cathodes, 11
Strontium oxide on cathodes, 30
Surface energy, 29-30
Surface ionization, 33-34
Tantalum
as cathode material, 11, 399-400
oxygen adsorption, 44
thermionic emission in cesium vapor, effect of oxygen on, 47
TEG (see Thermoelectric generators)
Thermal diffusion, 363
483
Thermal energy direct conversion (see Direct conversion)
Thermal-field emission, 26
Thermal, radiation energy loss by, 9, 11
Thermionic converters, 1-3
arc mode, 7-8
arc-mode operation, 293-372
cathode operating temperatures, 3
contact potential difference, 2
current density, 2-3, 6
current-voltage characteristic, 3, 8-9
design, boundary effects, 259-262
efficiency, 2-3, 8-10 16
electrode materials, 10-12
electron motive diagram, 5
energy balance, 8-9
engineering aspects of, 423-449
geometry of, effect on potential distribution, 398-399
interelectrode plasma, 2
operating currents, 5
operating modes, 5-8
output power, 2
output voltage, 2
plasma in, 13-17
potential distribution in, 293, 296
with virtual, cathode, 299
power density, 8-10
space-charge effects, 5
space-charge neutralization, 2-3
transport equations in, 208-216
useful power, 9
vacuum-mode operation, 47-51
current-voltage characteristic, 50-51
Thermionic diodes series connections, 11-12
Thermionic emission, 19-27
in accelerating fields, 25-27
current, 21-23
in accelerating fields, 25
from electrodes, 19-24
of molybdenum in cesium vapor, 36
Richardson formula, 22-23
from semiconductors, 23
of tungsten in cesium vapor, 35
Thermionic fuel elements, 432-436
Thermionic nuclear power plants, v
Thermionic reactors, 12-13, 428-436
Thermocouples, 1-2
semiconductor, 2
Thermodynamic equilibrium local, 307-317
Thermoelectric emf of plasma, 16
Thermoelectric emission effects of adsorbed layers on, 45-47
Thermoelectric figure of merit for plasma, 16-17
Thermoelectric generators, 1
efficiency, 1-2
Thomson cross sections, 124
Thomson theory, 63-64
Thorium, adsorption on tungsten, 32
TIC (see Thermionic converters)
Topaz nuclear power plants, v
Topaz-I thermionic reactor, 443-445
Topping cycle operation, 4
Transport equations
boundary conditions for, 208-216
in plasma, 87-91
for plasma with local thermodynamic equilibrium, 309
Tungsten
adsorption of elements on, 31-33
as cathode material, 11
evaporation rate, 43
oxygen chemisorption energies, 44
thermionic emission in cesium vapor, 35
work function, 40
in barium, 40-42
in cesium vapor, 40
effect of cesium oxide on, 46
effect of oxygen on, 44-45
variation of, 20
work function vs. cesium adsorption, 37-39
Tungsten oxide evaporation rate, 45
Tunnel effect in electron emission, 26
484
Undercompensated mode operation, 385-387
Unignited. mode, 6
See also Diffusion mode
Vacuum-mode operation, 47-51
Vapor-deposited coatings as cathodes, 34
Vapor-solid equilibria, 27-28
Virtual anode, 344
Virtual cathode, 333-336
position of, 300
Virtual cathodes, 298-300, 303-304
Work function
of adsorbed atom layers, 32-33
of anode, 10-11
effect of cesium adsorption on, 37-39
effect of cesium layers on, 35-36
effect of oxygen on, 44
for tungsten, 45
effects of adsorbed materials on, 30-33
effects on adsorption—desorption, 32-34
effects of cesium oxide on, 46
Rasor curves, 58-59
variation of, 20
Xenon
effects on current-voltage characteristics, 360-365
electron scattering, 59