IEEE TRANSACTIONS ON SCIENCE, VOL. 19, NO. 6, DECEMBER 1991 1191 Thermionic Energy Conversion Plasmas

Ned S. Rasor, Senior Member, IEEE

(Invited Review Paper)

5, T, Abstruct- The history, application options, and ideal basic C performance of the thermionic energy converter are outlined. The basic plasma types associated with various modes of con- EMITTERn verter operation are described, with emphasis on identification and semi-quantitative characterization of the dominant physical processes and utility of each plasma type. The frontier plasma HEAT IN HEAT OUT science issues in thermionic converter applications are briefly qE - -qc summarized.

I. INTRODUCTION HE thermionic energy converter is a nonmechanical CURRENT J Tgaseous-electronic device for converting heat directly into electric power by thermionic electron emission. In its LOAD simplest form-i.e., the diode shown schematically in Fig. l- are emitted from a hot electrode and collected OUTPUT POWER = qE - qc by a colder electrode at a higher potential energy (lower electrical potential). Part of the heat removed from the emitter Fig. 1. Basic thermionic energy converter. by the evaporating electrons is rejected to the collector by the condensing electrons, and the remaining part is converted into of scientific issues addressed, the detailed qualification and electric power in the load as the electrons return to emitter documentation required for a comprehensive review is not potential. possible here. Key publications are cited, however, which in- Although thermionic converter operation usually is de- clude comprehensive review of and reference to the supporting scribed in physical electronic terms (i.e., as a plasma- detail. electron tube), the heat-power engineer may prefer to consider Table I summarizes the variety of technological options and thermionic energy conversion as a thermodynamic heat applications associated with thermionic converters. This article engine cycle. The thermionic cycle is similar to a modified is concerned primarily with the physics of the various types of Rankine (steam engine) cycle that uses electrons directly plasma employed to conform to the constraints of particular as the sole working fluid [l]. The emitter is the “electron options and applications. The various plasma types summa- boiler” and the collector is the “electron condenser,” which rized in Table I1 will be described and their characteristic develop an electrical pressure (potential) difference to produce advantages identified with particular applications. electrical work rather than a vapor-pressure difference to produce mechanical work. Although the efficiency of the ideal thermionic converter at practical power densities is about 11. BRIEFHISTORICAL PERSPECTIVE 60% of the Carnot thermodynamic limit, the technology on The history of thermionic energy conversion and its appli- which present applications is based achieves about 25-35% of cations is summarized briefly in Table 111. The possibility of Carnot efficiency. Advanced thermionic converter types have using electron emission for energy conversion was recognized been investigated that can more closely approach the ideal by sev+eral scientists and inventors after the discovery of converter-efficiency limit. by Edison in 1885, the discovery of the The purpose of this article is to provide a perspective electron by Thomson in 1897, and the quantitative physical of the nature and scientific characterization of the unique description of thermionic emission by Richardson in 1902. and remarkable plasmas occurring in the various modes of The confluence of high-temperature materials technology, the thermionic converter operation associated with different appli- development of nuclear heat sources, and the emerging need cation requirements. Because of the large number and variety for efficient and compact electrical power sources in space in Manuscript received September 26, 1989; revised August 21, 1991. This the mid-1950’s led to the first experimental demonstration of work was partially supported by the U.S. Department of Energy, and by the practical levels of thermionic power generation by Marchuk Strategic Defense Initiative Office of the U.S. Department of Defense through in the USSR in 1956, demonstration of the more practical the U.S. Air Force Wright Aeronautical Laboratories. The author is with Rasor Associates, Inc., Sunnyvale, CA 94089. ignited mode of converter operation by Wilson in the U.S. in IEEE Log Number 9104419. 1957, and demonstration of converter operation in the core

0093-3813/91$01.00 0 1991 IEEE 1192 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 19, NO. 6, DECEMBER 1991

TABLE I SUMMARYOF THERMIONIC CONVERTEROFTONS

APPLICATIONS: Envi ronmnt Nuclear In-core/Ex-core/On-core Nuclear Radioisotope reactor Moderated/Fast Fossil fueled Topping Auxi 1 iary power

Solar __-___ Power conditioning

TABLE I1 MATRIXOF THERMIONICCONVERTER PLASMA TYPES

PLASMA SOURCE I VOLUME SURFACE INJECTION I

" TRIODES SPACINGiMFP RATIO d/X

of a nuclear reactor by Grover et al. in 19.59, all apparently objectives and was planning to construct a test reactor. The acting independently. USSR, however, began ground testing its low-power TOPAZ Early consideration was given to the use of thermionic thermionic reactors in 1970, and ground-tested eight versions converters in solar and radioisotope space-power systems. by 1983. By 1965 it was clear that the emerging thermionic technol- In 1Y73 the US. terminated its entire space nuclear-reactor ogy could not displace the well-established photovoltaic and program, including thermionic reactor development. From thermoelectric technologies in these applications. By 1965, 1973 to 1983 U.S. thermionic technology development was however, the basic physics of the ignited mode of converter directed toward application to fossil-fueled terrestrial power operation was understood sufficiently, and the practical tech- systems. Since performance in the ignited mode of operation nology was developed sufficiently, to permit initiation of that had been used in the reactor application was marginal at engineering development of in-core thermionic nuclear reactor the lower temperatures required for fossil-fueled applications, systems in the US, USSR, West Germany, and . basically new types of converter operation were developed The multiple modular redundancy and high heat rejection during this period, involving advanced electrode and plasma temperature capabilities of in-core thermionic space reactor technology. systems give them inherent and decisive advantages over In 1983 work was resumed in the US. on space nuclear- turboelectric systems in reliability, development cost, and reactor systems in response to the greatly increased electric system weight. power requirements of prospective military space-based sys- The US. and USSR took substantially different approaches tems. Major emphasis has been placed on recovering the 1973 in thermionic reactor development. The former concentrated thermionic fuel element technology and extending it to meet on perfecting the thermionic technology through interative the 7-10 y lifetime requirements projected for a variety of development tests of thermionic fuel element (TFE) modules. military systems [2]. Alternate approaches also were explored The USSR essentially froze the thermionic technology at for applying advanced converter technology to innovative the 196.5 level and proceeded immediately to construct full- thermionic reactor systems [3], and for applying advanced scale thermionic reactors for testing. By 1973 the US. had very-high-temperature nuclear fuels to achieve the high power achieved its thermionic fuel element lifetime and performance densities required in multimegawatt applications [4]. RASOR: THERMIONIC ENERGY CONVERSION PLASMAS 1193

TABLE Ill HISTORICALSUMMARY OF MAJORTHERMIONIC ENERGY CONVERSION PROGRAMS

US THERMIONIC PROGRAM

BASIC PHYSICS ELEMENTARY CESIUM IGNITED CESIUM DIODE EXPLORATION DIODE CONSOLIDATIO

SOLAR,RADIOISOTOPE THERMIONIC NUCLEAR FOSSIL-FUELED APPLICATIONS & NUCLEAR REACTOR FUEL ELEMENT (TFC) SYSTEM EXPLORATION DEVELOPMENT I I II I 1957 1965 1973 1975 1983 IYM5 1990

USSR THERMIONIC PROGRAM (ESTIMATED)

c~~~~~~~~~~v~FB~~~~u~~~~~~L

TOPAZ REACTOR TOPA7 FLIGHT TEST TOPA7 SOLAR, RADIOISOTOPE TOPAZ EXPERIMENTS SYSTEM DEVFLOPMENT DEPLOYMENT APPLICATIONS e NUCLEAR REACTOR REACTOR ' REACTOR DEW. e TCST EXPLoRAT1oN DEVELoP"ENT TFE DEVELOPMENT HIGH POWER IIEACTOIt EXPLORATION

WESTERN EUROPEAN PROGRAMS -1 I IGNllED MODE IGNITED MODE4 BASIC PHYSICS IGNITED CESIUM DIODE CONSOLIUATION' CERMET EMITTER' EXPLORATION 1 41

THERMIONIC NUCLEAR' FOSSIL FUELED APPLICATIONS F02~'~L{~~~~U3 FUEL LLEMENT (TFE) DIODE DEVtLOPMENT5 DEVELOPMENT 1 1 POWER 1 I 1 -73 1965-73 19/75 1482 1985 1990

1- W. Geniiany, FranLe, Eurdtoill 4- Sweden 2- W. Gerniany, Netherlands 5- Netherldndr 3- W. Gennany

In 1987 and 1988 the USSR announced operation and testing in earth-orbit of two of its 6 -kW TOPAZ thermionic reactor systems [5]. The USSR identified thermionic reactor systems as the basis for fulfilling its future space electric- power system requirements into the megawatt region [6]. Because of the continuity and central coherence of its scientific support, the basic physical research on thermionic energy conversion in the USSR has been more coherent, more thorough, and much more completely documented in scientific publications than that in the U.S. The U.S.'s basic work, being tied primarily to a variety of transient engineering development Fig. 2. Motive diagram for ideal diode thermionic converter. programs, has been chaotic and poorly documented, but has been generally more innovative and more directed toward problem solving as a result. characteristics in subsequent descriptions of practical converter operation. The motive diagram in Fig. 2 shows the potential energy 111. THE IDEAL DIODETHERMIONIC of an electron as it moves from the emitter to the collector. CONVERTER AS A REFERENCECASE To be moved from the emitter into the gap, an electron must Before discussion of the plasma effects, it is useful to define overcome a potential energy barrier known as the emitter work the ultimate thermionic converter performance limits imposed function 4~.A similar barrier, the collector 4~, by electron emission and heat-transfer processes, independent exists at the collector. of any plasma effects. This ideal case thereby serves as a If no collisional or space-charge effects occur in the inter- basis for quantitative identification of the plasma-imposed electrode space (e.g., in a very close-spaced diode), an energy 1194 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 19, NO. 6, DECEMBER 1991

I I IDEAL DIODE7 I I I J; \ 1 IGNITED DIODE I €9.5 WITH VB=O

OUTPUT \ SATURATION CURRENT \ REGION DENSITY J

\ OBSTRUCTED REGION \ VB-, \ ‘\ \ \ \ IGNITION \ PO 1NT UNIGNITEO DIODE \

vo OUTPUT VOLTAGE V

Fig. 3. Comparison of ideal and cesium vapor diode thermionic converter electrical output characteristics (transition points circled).

1000 1200 1400 1600 BOO 2000 1000 1200 1400 1600 1800 2000 EMITTER TEMPERATURE (K) EMITTER TEMPERATURE (K)

(a) (b) Fig. 4. Performance equivalent to ideal diode thermionic converter (IS = @c for ideal diode). Solid lines = maximum efficiency; dashed lines are for J = 10 A/cm2. barrier V + $c must be overcome to move an electron from The total heat that must be supplied to the emitter is the emitter across the gap to the collector when the electrode potential energy difference (output voltage) V is greater than qE = qe f qr -k qL (3) the contact potential energy difference V, = $E - $c,as may where be seen in Fig. 2.’ When V is less than V,, a barrier $E must be overcome. Neglecting electron emission from the collector, the qe = J(~E+ 2kTE) = heat removed by electron emission, output current density of the ideal diode thermionic converter, qr = m(T; - TA) = heat removed by thermal radiation, therefore, is given by the Richardson-Dushman equation as qL = heat conducted down the emitter lead, J = AT; exp[-(V + $C)/kTE] for v > V, (I) E = net thermal emissivity of the electrode system J = AT;€!X~[-$E/~TE] S Jl for v < v, (2) 20.1 - 0.2, = 5.67 x 10-12W/~m2K4= Stefan-Boltzmann constant. where A = 120A/cm2 - K2, IC = (116OO))-’eV/K is c the Boltzmann constant, TE is the emitter temperature, and The energy conversion efficiency is therefore J,’ is the zero-field, saturation emission current density. A current-voltage characteristic for the ideal diode converter 7 = J(v - vL)/qE (4) from (1) and (2) is included in Fig. 3. The output power density where VL is the voltage drop across the emitter lead. It can JV is given in Fig. 4(a) for different collector work functions be shown that for maximum efficiency, VL=V/lo, qL?qE/10, 4C. and qe=3qr. Maximum efficiency and efficiency at a constant In this article the term “voltage” refers to the potential energy difference typical current density are given in Fig. 4(b) as a function per electron, not to the electrical potential (the potential energy per unit charge). Accordingly, the voltage V in electronvolts (eV) is numerically equal of emitter temperature, and the power density at maximum to the potential difference in volts. efficiency is included in Fig. 4(a) for different collector work RASOR: THERMIONIC ENERGY CONVERSION PLASMAS 1195 functions $e. More detailed descriptions of the ideal diode, including the effect of collector emission and the conditions Nlobluml#o=4.1 eVkA for maximum power and maximum efficiency, are available 1 elsewhere [7]. Turqsten (#o*4.6sV) In a real thermionic converter, electron energy losses in the Computed Valuer - interelectrode space and electron current scattered back into the emitter both cause a reduction in output voltage from that of an ideal diode converter at a given output current density. These effects can be conveniently characterized by defining a quantity VB,which when substituted for in (1) defines the ideal diode equivalent to any given output current J and voltage V at emitter temperature TE;i.e.,

J = ATiexp[-(V+ VB)/~TE]. (5)

The back-voltage VB(also called the "barrier index") therefore characterizes the performance of any real thermionic converter relative to tabulated parametric performance data for the ideal diode converter, with VB = 4~;e.g., Fig. 4. It is analogous to the back-EMF in electrical machinery or to the back-pressure in mechanical heat engines.

IV. THERMIONICCONVERTER PLASMAS i \ Typical collectors AND THEIRANALYTICAL DESCRIPTION - I (I"II'I''I1I'IIII' A. Nature of Thermionic Converter Plasmas An inherent aspect of thermionic converter operation is the existence of a high electron current density between the elec- trodes, corresponding to a minimum electron density of about 1013cm-3 for an output current density of 10 amp/cm2. The emission-inhibiting electric field of the resultant electron space immersed in cesium vapor at pressure charge can be suppressed either by making the interelectrode

gap approach the associated Debye length (w 1 pm), or by interposing a plasma of this or higher density between the electrodes at much larger spacings (100-1000 pm). Because the sole function of the plasma in a thermionic with the temperature T and "bare" work function $,, of the converter is to transport the electron current efficiently between surface, where p, = 7.5 x 106 torr, = 0.75 eV, and the electrodes, with a minimum of current attenuation and h is the temperature of the liquid cesium vapor source. potential drop, it tends to be nearly equipotential within about TR As shown in Fig. 5, the work function is nearly uniquely a tenth of a volt, to be highly energy and charge conservative, characterized by qho and the temperature ratio T/TR in the and to be only a few electron mean-free-paths thick. As region of significance for thermionic converter emitters (4~22 a result, the thermionic converter plasma is primarily one eV). In the region of significance for collectors (& < 2 eV), dimensional, and its state and characteristics are determined however, basic understanding is inadequate and the database primarily by its interaction with the bounding electrode sur- is entirely empirical. faces. It is necessary therefore to characterize this interaction Because transport and ionization in the plasma also depend in some detail in order to describe the plasma characteristics. on the cesium pressure p, it is clear that the electrode and plasma properties interact strongly through Fig. 5 and (2) and B. Electrode Work Functions and Emission (6). Furthermore, the work functions given in Fig. 5 have The electrode work functions determine both the potential a dependence on plasma density due to the Schottky effect at the boundaries of the interelectrode gap, and the flux of arising from high electric fields in the positive ion sheaths and electrons into the gap. The practically successful between the plasma and electrode surface. These effects are electrodes are those that depend on cesium adsorption to obtain understood and adequately characterized [9], [lo]. There are low work functions when immersed in cesium vapor. strong indications, however, that additional electrode/plasma By considering the adsorbed layer as a thermal equilib- interface processes affect the collector work function in an rium between atomic and ionic states of cesium (i.e., a important but unknown manner. two-dimensional partially ionized plasma), a formulation is The electron thermionic emission into the interelectrode gap obtained [SI that correlates the work function 4 of a surface J, is given by (2). The positive ion thermionic emission into 1196 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 19, NO. 6, DECEMBER 1991 the gap is given by the Saha-Langmuir equation: excitation, and ionization properties, and a first-principle eval- uation of their quantitative effect on local and overall plasma properties for experimental confirmation over a wide range of conditions. The numerical integration of these equations across the plasma is quite complex and has been performed where p 2 1.3 x 1Ozopcm-2s-1 is the arrival rate of cesium atoms at pressure p in torr, and V, = 3.9 eV is the ionization by a variety of approaches [13]. Such rigorous calculation of energy of the cesium atom. the state of the plasma interior can obscure more significant For a neutral plasma, the densities and random currents of effects at the plasma boundaries, however. the electrons and ions are equal, such that at equilibrium, In the alternate or “phenomenological” approach [lo], [14] the same transport and continuity boundary conditions are J, = aJis, where a = (MTe/mTi)1/2~500- 700, and M and m and Ti and T, are the ion and electron masses applied to the plasma, but the plasma itself is represented and temperatures, respectively. Equations (2) and (7) can be algebraically by a simple macroscopic model having the combined [8] to define the work function & of an electrode average properties that conform to the boundary conditions. emitting a neutral plasma, which is included in Fig. 5 and also Because of the relative insensitivity of converter character- is known as the electrochemical potential of the plasma. istics to the details of the local plasma state, this approach characterizes converter operation to the degree required for preliminary converter and system design evaluation. While C. Directed Current at Boundaries not as rigorous and versatile as the fundamental approach, the The fact that the plasma energy distribution must be asym- phenomenological approach provides intuitive insight into the metrical and nonequilibrium at the plasma/electrode bound- physics of the dominant converter processes and is useful for aries significantly affects thermionic converter characteristics on-line converter diagnostics because of its relative analytical and has been examined in detail [ll], (121. A principal effect simplicity. results from the interaction of the half-Maxwellian energy The physics of the converter plasma modes listed in Table distribution of particles emitted into or out of the plasma I1 now will be summarized. at its boundaries with the full-Maxwellian distribution within the body of the plasma. This effect is adequately described V. IGNITED (ARC)MODE by the “directed current” approach [ 101 originally developed for description of neutron diffusion near boundaries. At any A. Description and Approach plasma boundary the total current of particles moving only to the right is The ignited or arc mode of converter operation is easy to achieve and employ practically, since it occurs spontaneously J+ = J, + J/2 (8) between elementary electrodes immersed in cesium vapor at and of the particles moving only to the left is practically achievable electrode spacings and temperatures. As a result, it has been the basis for all engineering applications J- = J, - 512 (9) to date. Its physics, however, is relatively complex. The phenomenological representation will be used here to where J, is the random current, and J is the net (drift) current identify and quantify the various physical processes which to the right. This result is obtained because by necessity, characterize operation in the ignited mode and which are J+ - J- = J. relevant to the description of other modes as well. Many sim- Equations (8) and (9) apply to both electrons and ions at plifying approximations are used in this intuitively tractable both the emitter and collector plasma/electrode boundaries. For representation. The consistency of the results of the phe- electrons at the emitter, for example, nomenological model with those of the more rigorous fun- damental model, however, provides a degree of confidence in J+ = JE + J-[I - exp(-VE/kTeE)] (10) the adequacy of those approximations [lo]. where JE is the electron current emitted to the right from the emitter; the second term in (10) is the electron current reflected B. Transition Point to the right by an emitter sheath of voltage height VE,and Te~ Fig. 6 shows motive diagrams for a plasma diode thermionic is the temperature of the plasma electrons at the emitter. converter operating in the ignited mode. In this mode, part of the electric power generated by the converter is dissipated D. Alternate Analytical Approaches internally in the interelectrode gas by collisional processes, Because of the dominance of electrode and boundary effects, heating the electrons in the gas to a sufficiently high tempera- two distinct approaches have been taken for analytical repre- ture so that they ionize the gas and maintain a neutral plasma. sentation of the plasma in thermionic converters. The most Electrons are retained in the plasma by sheath barriers VE and rigorous or “fundamental” approach is based upon numerical VC at the emitter and collector, but ions freely diffuse to the solution of the usual set of differential equations for electron electrodes and recombine on their surfaces. The voltage drop and ion transport and continuity in the plasma, subject to the across the interelectrode space, the arc drop Vd, sustains this boundary conditions described in Section IV-B and C. This process. A typical current-voltage output characteristic for the approach allows the inclusion of the fundamental transport, cesium, plasma-diode thermionic converter is shown in Fig. 3. RASOR: THERMIONIC ENERGY CONVERSION PLASMAS 1197

J‘ J; t b;V’

Fig. 6. Motive diagrams for the ignited diode thermionic converter. (a) Obstructed region. (b) Transition point. (c) Emitter saturation region.

The transition point (J’, V’) identified in Fig. 3-i.e., the neutralized by the ionization rate arising from the resulting point of maximum slope-has both practical and basic sig- arc drop Vd. Accordingly, Fig. 6(a) and (11) give: nificance.* It has practical importance, because it is near the points of maximum output power and efficiency. It has basic V = 4,q - 4~ - Vd + AV (13) significance, because it is where the zero electric field occurs and the emission current JE from the “virtual emitter” with at the emitter, as in Fig. 6(b); i.e., where the positive ions effective work function 4~ + AV is, from (2): generated in the plasma are just sufficient to neutralize the space charge of the zero-field saturation electron emission JE = AT’: exp[-(4r: + Av)/lcT~]= Ji exp(-AV/kTE). current Js’. It can be seen from Fig. 6(b) that the output voltage (14) at the transition point is given by 2) Particle Transport and Continuity: Rigorous description of the plasma requires solution of the transport equations V’ = 4E - 4C - Vd’ (11) for the plasma density n, electrical potential $, and electron temperature T, versus distance x through the plasma. For where Vi is the maintenance arc drop; i.e., the minimum arc drop that can maintain the ignited discharge plasma. electrons, Equations (2), (5), and (11) can be combined to give J=-- eXv [p%-dn + n-d$ + Knks] (15) 3kTe dx dx dx VB = 4C + Vi + Vd (14 with a similar equation for the ions, where e, A, U, and K where VL = lcT~ln(JL/J’). The back-voltage VB therefore are the electron charge, mean-free-path, average velocity, and arises from the energy loss at the collector surface 4c, the thermal diffusion constant, respectively. arc drop (plasma energy loss) Vi, and the voltage loss Vi Solution of the ion- and electron-transport equations, with due to the current attenuation by the plasma or by nonideal the set of boundary conditions corresponding to (8) and (9) in electrode surfaces. As shown in Fig. 3, the back-voltage VB the presence of the electron-confining sheaths, shows that the that characterizes the general performance of the converter is random electron current density in the ignited mode plasma is readily measured as the observed voltage difference between nearly an order of magnitude greater than the output current the transition point and the curve representing (5) with J, corresponding to n~lo~~cm-~s-~for J = 10 amp/cm2. VB = 0. Furthermore, it is found that the potential gradients within The transition point divides two major regions of ignited the plasma arise primarily from the electric field associated mode operation having significantly different plasma phe- with ion diffusion out of the plasma, rather than from electron nomenology: the obstructed region (V > V’),and the sat- transport through it. The electrical and thermal conductivities uration region (V < V’). of this high density plasma are so high and the voltage drop across it is so small (V, << 0.1 eV, typically) that, to a C. Obstructed Region very good approximation, the plasma can be treated simply as an equipotential and isothermal region through which the 1) Electron Potential Energy: In the obstructed region, electron current J diffuses. Accordingly, (15) with the d$/dx identified in Fig. 3 and represented in Fig. 6(a), there is and dT,/dx terms neglected is readily integrated to give the insufficient voltage drop between the electrode surfaces to ratio of the plasma densities n and random currents J, at the sustain the ignited plasma. The ignited discharge can exist plasma boundaries, for interelectrode spacing d, there, however, by erection of a negative space-charge barrier of height AV at the emitter. This barrier limits the emitter electron-emission current to the value JE, which can be

*All single-primed quantities refer to the conditions at the ignited mode The mass disparity between the electrons and the cesium transition point. atoms and ions is so great that ion currents in the plasma are 1198 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 19, NO. 6, DECEMBER 1991 negligibly small compared with the electron current J, and the plasma (V > V’) [IO]: energy transfer between them is negligible. The temperature of the atoms and ions is approximately equal to the mean temperature of the electrodes (TE + Tc)/2. The emitted electrons, however, are accelerated across the emitter sheath (v~~0.7eV, typically) and bombard and heat the electrons at the emitter side of the plasma to a much higher temperature (Te~-33O0K, typically). In order for the ignited mode to exist, this temperature must be sufficiently high to produce positive ions by impact ionization precisely as fast as they are lost by volume recombination and by diffusion to and recombination at the electrodes. The plasma typically is only = TO= V1/2k In (B;). if TO> T_s(nonLTE)(21) about 1% ionized at the emitter and 0.1% ionized at the TeE ET =- &e/k In if To < Ts (LTE).(22) collector in the obstructed region of the ignited mode. { s [$$I. 3) Energy Transport and Continuity: Detailed consideration The quantity R~4.5is a dimensionless constant involving of the cesium plasma stepwise excitation and ionization the constant ratio of the ion current at the electrodes to the process [15] shows that resonance radiation from the first average random ion current, and the ratio of the ion and excited state of the cesium atom is almost entirely trapped electron mean-free-paths. Equations (17)-(22), together with within the typical ignited mode cesium plasma, and the energy the Rasor-Warner formulation for the electrode work functions loss from the plasma by escape of other excitation radiation [8], are the basis of the widely used TECMDL computer model is negligibly small. As a result, the energy delivered to the of the ignited cesium diode thermionic converter [16]. plasma by the emitted electrons is removed almost entirely Equation (17) describes the attenuation of the emitted cur- by hot electrons reaching the collector or scattered back into rent JE by the plasma for electrode spacing d and electron the emitter. The heat removed by electron emission from the mean-free-path kO.O06/p cm for cesium vapor pressure p in plasma to the collector must be conducted across the plasma torr. The term in the square brackets is the current arriving by the electrons, resulting in an approximately linear electron from the interior of the plasma on the emitter side, which is temperature drop across the plasma to about T,c = 2100 K the sum of the current scattered back by the plasma and the current RJ reflected from the collector. This arrival current at the collector, typically. times the Boltzmann exponential in emitter sheath height VE 4) Volume Recombination and Local Thermodynamic Equi- and electron temperature Te~is equal to the current returning librium: A plasma cannot appreciably exceed the density at to the emitter from the plasma JE - J. The current attenuation which as many ions recombine locally as are produced locally. J/JE obtained from (17) is shown in Fig. 7(a) as a function In this condition, known as local thermodynamic equilibrium of the degree of electron scattering d/X. (LTE), the local plasma properties are equivalent to those Equation (18) describes the dependence of the arc drop that would exist in equilibrium with a hypothetical surface vd (the net energy loss in the plasma per electron) on the at the local electron temperature T, and emitting a neutral emitter temperature TE and the plasma boundary electron plasma. Accordingly, the local electron temperature in the temperatures Te~and Tee. The first term represents the plasma cannot fall below the value corresponding to T and net energy lost from the plasma via the hot electrons back- qhn in Fig. 5, where qhn is computed from (2) using the local scattered to the emitter. The second term represents the net electron temperature and random current density. energy lost via hot electrons reaching the collector. Fig. 7(b) In typical ignited converter operation, only the portion of shows that the arc drop decreases at large d/X as the increased the plasma adjacent to the collector is near or within LTE collisional ionization probability results in a colder, more and volume recombination has little effect on the output, efficient plasma until ion recombination in LTE is encountered. since most ion production occurs on the high temperature Fig. 7(c) shows, however, that the back-voltage VB or (emitter) side of the plasma. As the cesium pressure, spacing, “barrier index” (12) has a minimum value, giving maximum converter performance via (5) and Fig. 4, at about d/X = 8, and current density increase, the LTE portion of the plasma or pressure-spacing product pd = 0.06d/X~0.5torr-”. This expands toward the emitter and eventually can dominate minimum results from the competition between the decrease the entire plasma. Stepwise integration of the transport and in Vd (Fig. 7(b)) and the increase in V, (Fig. 7(a)) as continuity equations across the plasma becomes very difficult pd is increased. Remarkably, the decrease in Vd resulting (unstable) under these conditions, since the local ioniza- from the energy added by electrons emitted at higher TE is tion-recombination balance in LTE is exceedingly sensitive nearly balanced at all pd by the increased loss of electrons to the local density. . backscattered over a lower emitter sheath barrier VE,resulting 5) Summary of Obstructed Region Plasma Physics: The in a nearly constant VBN& + 0.45 eV over a wide range of combination of the above-described physical processes is pd and emitter temperature TE. summarized by the phenomenological model in the following Equation (20) shows that the electron temperature at the complete set of equations defining the state of the obstructed collector Tec is about 0.64 Te~,so the collector sheath RASOR: THERMIONIC ENERGY CONVERSION PLASMAS 1199

E ‘\

.8 .R 5

TR = 567 K .6 .6 d = .25 MM J ~ Va iev) 4 JE FUNUAMENlAL .4 .4 MODEL OUTPUT (IIRKtl4T UFNSITY TRANSITION POINT .2 .2 J (A/cM‘) (J’,V’l

0 0 .I .2 .4 .6 1 2 4 pd (torr-inm) 2

dlh 1 1 2 4 6 8 10 20 40 hO 80 1.0 I\ , , 5000 0 I I I I I .2 .4 ,6 .8 1.0 .R 4000 OUiPUT VOLTAGE V TeE ‘ 3000 .6 Fig. 8. Comparison of analytical models with experimental data for a planar =V) cesium vapor diode converter [lo]. .4 2000 2k(Tec- TE)Jc/Jdue to the energy absorbed in the plasma .2 by the cold collector electrons [lo]. The electron temperature To required to sustain a non-LTE 0 cesium plasma, given by (21), is characterized by two plasma pd (torr-mm) parameters, VI and B, that are derivable from the detailed kinetic analysis of the multistep excitation/ionization process (b) [15]. The “effective ionization energy” VI is found to be about 3.1 eV; i.e., at the energy level “bottleneck” above which dlh excitation is equivalent to ionization in a Maxwellian plasma. 1 2 4 6 8 40 10 20 60 80 The “ionizability factor” B~30is a dimensionless constant that includes the ionization cross section and the electron/ion mean-free path ratio, and is a measure of the ability of the plasma to produce and retain ions. A number of concepts have been proposed to improve the properties of the ignited mode plasma, including cavities or grooves in the electrodes to modify the ion production mechanism and additive gases to modify the scattering pro- cesses. None of these has been successful due to the relative insensitivity of the minimum VB to the disposable quantities included in the plasma characterization factors R, I?, and VI. .@6 .I .2 .4 .6 .8 1 2 4 Similarly, the use of state-dependent fundamental properties to pd (torr-mi) describe the plasma in the detailed fundamental model does not (c) give results significantly different from those obtained by the use of constant values of these three plasma characterization Fig. 7. State of the obstructed plasma in the ignited mode of converter operation; dependence on pressure-spacing product pd and emitter temperature factors. TE (computed from (17H22)). Dashed curves represent the LTE region for Although both analytical models satisfactorily characterize spacing d = 0.25 mm and the current density J shown. (a) Current attenuation J/JE and associated voltage loss V, (equation (12) and Fig. 3). (b) Arc ignited converter behavior in most respects, it can be see drop Vd and electron temperature Te~at emitter edge of plasma. (c) Plasma in Fig. 8 that both models fail to describe the experimental contribution to back-voltage (barrier index) I B . (I - or = I> + I ). volt-ampere characteristics properly in the obstructed region. The models predict a constant back-voltage VB below the height by (19) is Vc=1.09kTe~.It can be shown that the transition point, when in fact the back-voltage increases with collector back emission current Jc increases Vd by an amount decreasing current density. This discrepancy is important, 1200 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 19, NO. 6, DECEMBER 1991

since the practical operating point typically is in this re- -AV,2tkTe~,the output current increases primarily because gion, and this and related anomalies pose an uncertainty in the increase in emitter sheath height VE reduces the back- what basic processes actually dominate the important quan- scattered electron current. For -AV >> ICT,E, the approxi- tity V,. Because of the relative insensitivity of V, to the mately linear increase in output current is mostly ion current. detailed state of the bulk plasma, several hypotheses have been advanced to explain this discrepancy as arising from VI. UNICNITEDPLASMAS the plasmahurface interaction, including energy loss to the A. General Description electrodes by resonance radiation, incomplete thermalization of the electrons in the presheath region, positive ion trapping in The ignited or arc mode plasma just described is internally the nonmonotonic emitter sheath, discharge constriction, and maintained by impact ionization in a collisionally self-heated an anomalous Schottky effect at the collector. At present, this “hot” electron gas (T,>> TE).The arc drop and current issue is unresolved. A complete kinetic simulation model that attenuation associated with this inefficient process typically eliminates the artificial division of the interelectrode space into absorb nearly half the electrical power generated, increasing sheath and plasma regions might be required if the discrepancy VB by 0.4-0.5 eV, whereas less than 0.01 eV per electron is a sheath effect, or a detailed model of sheath field effects on is required to produce the plasma-sustaining ions themselves. the adsorbed layer is required if it is an anomalous Schottky Alternate means exist for maintenance of more efficient unig- effect. nited or “cold” plasmas (T,ETE) by energy sources outside the plasma, without dependence on collisional processes, such D. Saturation Region that V, + Vd5O.l eV (equations (12) and (18)). The motive diagram for the unignited plasmas in Fig. 9(a) For the conditions in the obstructed region and at the shows that in the region of greatest interest for thermionic transition point-i.e., for V 2 V’ as in Fig. 6(a) and (b), converter operation, ions typically are retained in the plasma the arc drop Vi is automatically that required for production by sheath barriers VE and Vc at the emitter and collector, and of precisely sufficient positive ions to neutralize the electron electrons freely diffuse to the electrodes; i.e., the opposite con- emission current. For V < VI, as in Fig. 6(c), however, an dition from that for the ignited plasma. The conditions in Fig. arc drop Vd = Vi - AV is imposed across the plasma that 9(b) and (c) are of interest also for converter diagnostics. Fig. is greater by AV than that required for plasma neutrality. 9(b) represents the condition at the transition point (J”,V”), Accordingly, this “excess” energy AV cannot be transferred where V, = 0, and Fig. 9(c) represents the condition at to the plasma electrons, since this would increase TeE and V > V”, where the collector limits the converter output, produce an excess of positive ions. The details of the ionization both of which are identified as regions in the electrical output and scattering processes in the emitter sheath are highly characteristics in Fig. 3. A rigorous description of unignited complex [ 121, but experimental data indicate that essentially all plasmas can be obtained by applying the appropriate boundary, of the excess energy AV is expended on production of positive transport, and continuity conditions described in Section V ions within the emitter sheath that are immediately swept into [ 161. An approximate description by the intuitively tractable the emitter instead of entering the plasma. To accomplish this phenomenological approach [ 171 is described below. the electron temperature at the emitter edge of the plasma rises For the general case of plasma maintenance, the net rate at to a value sufficient to approach a fully ionized plasma there which ions are supplied to the plasma is in the saturation region. Since the body of the plasma accepts only the electron Jzp = Jao - Jzb (25) energy required to maintain a neutral plasma, the remainder where of the plasma is essentially unchanged. Equations (17H22) therefore remain valid for that region, except that the emitter Jto = Jzs + Jm - Jzu - Jat (26) sheath is now: is the sum of the ion sources and sinks that are independent of the sheath heights, J,, is the thermionic emission current of VE = VA - AV for AV < 0 (23) ions into the plasma given by (7), ,Iaz is the ion current injected which with (13) and (17) gives for the output characteristics into the plasma by other external means, Jzu is the ion current in the saturation region, lost from the plasma by volume recombination, and Jat is the ion current lost by transverse diffusion to the plasma edge. Jzb Js J= . for V < V’ (24) is the ion current lost from the plasma over the bounding 1 + [g - 11 exp [E] electrode sheath barriers, which is exponentially dependent on VE and Vc. Computation of Jib using the boundary and with Te~equal to the temperature that approaches complete transport conditions described in Sections IV-C and V-C.2 ionization at cesium pressure (w 4500 K). The large positive sheath ion current into the emitter JiE=J,Av/K produces an intense gives, for the Practica1’y important condition Of heights (V = Vo), electric field at its surface that lowers the emitter work function #E and increases the saturation emission current J, > JL via the Schottky effect [9], [lo]. J= (27) The initial rapid increase in output current for V < V’ in Figs. 3 and 8 is dominated by the emitter Schottky effect. For Note that Jip = 0 for steady-state operation. RASOR: THERMIONIC ENERGY CONVERSION PLASMAS 1201

JE J =Urc J J" JE J --t - + --f + +

Fig. 9. Motive diagrams for general unignited thermionic converter plasmas. (a) Plasma saturation region (I7 < I."), ion- retaining sheaths. (b) Transition point (I- = I-"). (c) Boltzmann region (\- > 1.''); oc measured via (1).

Equation (27) shows that the output current in thermionic free paths for p in torr, and J, = env/4 is the random current converters with efficiently maintained unignited plasmas is density at the local plasma density n. understandably proportional to the strength of the plasma- In fact, the dependence of X on current density in (16) and sustaining ion source Ji,, and inversely proportional to the (28) implies a basic upper limit on attainable current density scattering factor 1+ id/X. The additional factor ( Js/J)TE/Ti in unignited plasmas; i.e., is important in all types of advanced converters employing unignited plasmas. It is a measure of the effectiveness of the J < J,,, = 4 x lO-'(l + Ti/T,)T,"/'/d. (29) sheaths in retaining the ions in the plasma, since the same For d = 1 mm, (29) suggests that J,,, is 2, 5, and 10 A/cm2 sheath barrier VEthat inhibits emission of J, from the emitter at T, = TE = 1000, 1500, and 2000 K, respectively. at temperature TE also inhibits loss of ions from the plasma Similarly, the effect of self-generated magnetic fields can be at temperature Ti. significant in unignited plasmas due to the large X and absence The exceptionally high J, >> J at exceptionally low cesium of electron-reflecting sheaths [ll]. As shown in Fig. 10, the pressure dlX5.1 needed for advanced unignited converters magnetic field arising from the output current is transverse to are contradictory requirements for electrodes that depend on the current flow through the plasma. To a good approximation, cesium adsorption. This dilemma inhibited the prospects for the effect of a tranverse magnetic field H (G) on output current practical application of such advanced converters. Recently, density for d>X (cm) is however, it has been found that use of an equilibrium mixture Jo of cesium oxide and cesium vapors permits J, >> 10 A/cm2 JN (30) to be obtained at very low cesium pressures, ~510-~torr. By 1 + 0.4(XH)2 increasing the adsorption energy for cesium on the electrodes where J, is the current density in the absence of a magnetic the adsorbed oxygen reduces the cesium evaporation rate, field. For a converter with coaxial cylindrical electrodes of and thus lower cesium pressure is required to maintain the length L cm and total field-free output current I,, the atten- adsorbed layer [ 181. Similarly, high emission currents can be uation of the total current I by the self-generated magnetic obtained at low cesium pressures using a mixture of barium field is and cesium vapors 1191. Adsorbed barium lowers the emitter IO work function without cesium adsorption, but unfortunately IN (31) it also gives a high collector work function (4~22.0eV). A 1 + 0.14( J,AL)+ ' description of various other vapor mixtures for obtaining high If electron-atom scattering is dominant (i.e., A,; << A,, in J, at low cesium pressures is given in [20, chap. 51. (28)), the magnetic current attenuation is I/Io = 75% for A comparison of (17) and (27) shows that output current a current density J, = 3 A/cm2 in a cylindrical converter attenuation by electron scattering is much greater in unignited having length L = 10 cm and cesium pressure p = 0.1 torr. plasmas, because of the absence of the large electron-retaining If Coulomb scattering is dominant, the magnetic attenuation is sheath VEat the emitter. As a result, converters with unignited independent of J, for J, << J,,,, and is 80, 40, and 20% at plasmas operate typically with d/El compared with d/X~8T, = 1000, 1500, and 2000 K, respectively, for L = 10 cm. It for ignited converters. Furthermore, the greater sensitivity to is clear, therefore, that both Coulomb scattering and magnetic electron scattering in the unignited plasma causes Coulomb effects must be considered in unignited plasmas. (electron-ion) scattering to be significant at high output current In fact, the strong interaction of these effects for J near J and low electron temperatures T,NTE,as summarized by J,,, gives rise to a potential for instabilities in the unignited discharge. A further factor in such instabilities is the Lorenz ponderomotive force on the plasma by the magnetic field. As shown in Fig. 10, this force tends to drive the plasma toward where X,,~O.O06/p cm and Li-3 x 10-9T,5'2/J, cm are the end opposite the current lead in a cylindrical converter, the respective electron-atom and electron-ion scattering mean producing a pressure drop along the length of the converter of 1202 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 19, NO. 6, DECEMBER 1991

FORCE ON PLASMAJXB M I I ll MAGNETIC ATTENUATION’U EMITTER 0

Fig. 10. Effects of self-generated magnetic field on thermionic converter plasma. Fig. 11. Comparison of experimental and computed characteristics of a planar cesium vapor diode converter in the unignited diffusion mode. Dots magnitude Ap = 4.8 x 10-5(JL)2torr for JL in A-cm [ll]. are experimental data; solid curves are computed using MASTERPC [16]. For JL = 30 A-cm, the resultant Ap = 0.04 torr becomes comparable to the total gas pressure employed in unignited C. Knudsen Regime plasmas. The possibility for electrical coupling to acoustic (organ-pipe) oscillations is apparent. The fundamental and phenomenological approaches using Various types of converter operation with unignited plasmas, the conventional macroscopic diffusion transport equations are associated with different means for providing the ions in (26), in surprisingly good agreement with experimental data, even will be described. when the electrode spacing d is as small as one electron mean free path, presumably due to multiple traverses of the gap by particles trapped in the plasma between the electrode sheaths. B. Dimsion Regime Nevertheless, for the essentially collisionless plasma regime In the diffusion regime of the unignited cesium vapor diode d << A, known as the Knudsen regime, the diffusion equations converter the ion emission current J,, given by (7) is the fail and the plasma is nearly homogeneous; i.e., there are dominant ion source J,, in (27), and Jlp = 0 at steady state. essentially no electric fields or particle density gradients in The plasma potential is such as to give a net neutral electron the body of the plasma. and ion emission into the plasma, whereupon 4~ + VEN&. The physics of the Knudsen plasmas has been explored and Accordingly, VE is essentially constant, unlike that in the described in substantial detail [ll], [21]. At first it might seem ignited diode, and is equal to the difference between the curves that converters operating in the Knudsen regime would be for and & in Fig. 5. Furthermore, for the condition in Fig. highly attractive, since when d << X and $EZ&, nearly the 9(b), the location of the transition point (J”, V”) identified in full emission current is obtained as output J-J, and the arc Fig. 3 is given by V” = 4, - 4~ and J’/‘v J, /(1 + f ), where drop V, and scattering loss V, are nearly zero, giving VBN~C, J, is given by (2) with dn substituted for 4~. as in the ideal diode converter. At the cesium pressures The basic thermodynamic constraint that the emission cur- required to obtain and a sufficiently low &, however, rent can be no greater than J, limits the performance in this the requirement d << X requires impractically small electrode mode to less than that in the ignited mode, except at very spacings and operation at very high temperatures. Also, at small electrode spacings and very high emitter temperatures the very high current densities J required for efficient high (TE22200 K). Because of its unique dependence on plasma temperature operation, Coulomb scattering (Aei in (28)) tends properties, however, the diffusion regime of the unignited to preclude efficient operation in the Knudsen regime, even cesium diode often is used for converter diagnostics; e.g., for with no electron-atom scattering (Aea). inference of emitter temperature, spacing, cesium pressure, Similarly, interest has arisen from time to time in the or collector work function whenever one of these quantities potential utilization of the spontaneous oscillations (typically cannot be measured independently. The most accurate diagnos- near 1 MH) associated with the ion transit time across the tics are obtained through comparison of the full experimental plasma that occur in converters operating in the Knudsen J versus V curve with that computed using the detailed regime. Aside from the interesting physics involved [ll], fundamental approach. As can be seen in Fig. 11, the MAS- [21], these oscillations apparently have no practical value for TERPC computer model [16] for the unignited mode precisely converter output, since they occur with amplitudes comparable represents the experimental converter characteristics, including to the dc output only at impractically low output currents and the approach to the ignited mode as the plasma electrons at the expense of a substantial arc drop Vd. are heated above the emitter temperature. Accordingly, the Although operation in the Knudsen regime with a plasma discrepancy that occurs in modeling the ignited mode (Section sustained by ion emission apparently has no practical applica- V-C.5 and Fig. 8) is uniquely associated with the fully tion, applications exist for Knudsen plasmas under conditions developed ignited plasma. known as the Knudsen arc. At sufficiently high output currents RASOR: THERMIONIC ENERGY CONVERSION PLASMAS 1203 and arc drops (Vd2l eV and 520.4 A/cm), the rate of ion production by electron impact becomes sufficient to produce a high-density electron-trapping plasma, even for d/X << 1 [ll]. The Knudsen arc has been applied as a plasma switch, the Tacitron [22], and as a fault current limiter, the Terma- tron [23]. These devices utilize the low arc drop (-1 V) at practically high current densities (0.5-5 A/cm2) and the practically high standoff (inverse) voltages (30-200 V) at- tainable with the cesium-vapor Knudsen arc. In addition, an arc in the quasi-Knudsen (quasi-collisional, d/XE1) regime is used to generate the injection plasmas for advanced types of thermionic converters discussed below.

VII. INJECTIONPLASMAS

A. General Description The plasmas in the ignited and unignited modes of the cesium diode converter are maintained by energy sources within the converter itself. The multiple constraints associated with these spontaneous internal processes limit converter per- formance and versatility of application. Advanced converter types utilize external energy sources to efficiently maintain the plasma by injection of electrons or ions into it under more optimum conditions. In addition, by modulation of the external energy source, such converters can be made to act as a switch or otherwise condition their own power output without Fig. 12. Schematic and motive diagrams for converters with injection type a separate output power conditioner. plasmas. P, is a power supply that generates the auxiliary voltage I>and current d, from a potential drop IT in the load circuit. (a) Electron injection It must be recognized that the simplified description here of triode. The auxiliary electron emitter e emits an ionizing electron current .J, unignited plasmas using (27) neglects the effects of volume into the plasma. (b) Ion injection triode. The auxiliary ion emitter i emits a recombination Ji, and plasma edge losses JZt.In practice, the positive ion current J,, into the plasma. (c) Pulsed diode. A pulse of voltage I ;. and current .J, injects ionizing electrons from the emitter into the plasma. converter design and operating regime are chosen to minimize these and other performance-limiting effects. For example, the output current of converters using injection plasmas is limited for V = V,: to only a few A/cm2 due to the importance of Coulomb scattering (29) at the relatively low electron temperature T, and large spacings d inherent to the injection process. Also, ion losses at the edges of the electrodes J,, can severely limit converter performance if the plasma is efficiently contained The ionization probability f and scattering factor d/X both by electrode sheaths, particularly for small-area planar diode increase with the pressure-spacing product, leading to an converters. optimum pressure near d/kl if the scattering and ionization cross sections are comparable in magnitude. Unfortunately, B. Triodes cesium has an electron-scattering cross section, at typical unig- 1) Electron Injection Triode: As shown schematically in nited plasma electron energies @X=0.006 torr-cm at 0.1-0.3 Fig. 12(a), a small auxiliary electron emitter can be placed eV), that is much larger than its ionization cross section, within the interelectrode gap to maintain the plasma. This because of resonance scattering by its loosely coupled va- type of converter often is called the “plasmatron” type, named lence electron; i.e., a partially ionized cesium plasma tends after the electron tube having this configuration. The electrons to be opaque to the low-energy output current electrons from the auxiliary emitter are accelerated into the plasma (large d/X) and transparent to the ion-producing high-energy by the applied voltage V, at an energy sufficient for a high electrons (small f), the opposite of what is desired. The probability of producing an ion; i.e., several volts as in the heavy noble gases, however, have this opposite property, Knudsen arc. The auxiliary ion current J,, in (26) thereby tending to be transparent to low-energy electrons (pkl is generated by an auxiliary electron current J, = Ji,/f, torr-cm) because of the Ramsauer electron diffraction effect, where f is the ionization probability per auxiliary electron. and opaque to the high-energy ionizing electrons. For this The auxiliary power required is P, = J,V, = JV;, where reason, argon, krypton, and xenon are favorable for production Vi is the “equivalent arc drop” across the external power of the electron-injection plasma, because V,is much less supply required to provide Pz, as shown in Fig. 12(a). If J,,, for them than for cesium vapor in spite of the higher V, Ji,, Jit, and Jip are negligible in (25) and (26), (27) gives, required (ionization energies 16, 14, and 12 eV, respectively, I

1204 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 19, NO. 6, DECEMBER 1991 versus 4 eV for Cs). However, cesium vapor at low pressure voltage to efficiently ionize the interelectrode gas. During a (lo-' - 10-1 torr) usually is added to the plasma to obtain negative pulse to the emitter, as shown in Fig. 12(c), the high- the low electrode work functions required so that production energy electron beam from the emitter produces a high density of the electron-injection (plasmatron) plasma is an exceedingly plasma by impact ionization in a quasi-Knudsen arc. Between complex quasi-Knudsen discharge. pulses, if ion loss is sufficiently inhibited by diffusion and Using the reasonably obtainable or near-optimum values ion-retaining electrode sheaths, the plasma decay time can be f = 0.1 - 0.5. d/X-1, V,z15 eV, cy = (MTe/mTz)1/2e500,much longer than the pulse repetition period, providing nearly and J/Js = 0.2, (32) gives Vi << 0.1 eV. The noble-gas continuous output power with a cold injection plasma. electron-injection type of converter therefore potentially can In the previously described steady-state plasmas, the net have substantially higher performance than the ignited mode rate at which ions were supplied to the plasma was zero; i.e., converter (Vd~0.4eV), especially at low emitter temperatures. production rate equaled loss rate, such that Jip = 0. If Jip is To obtain the assumed values of f, however, it is necessary not zero, the average density Ft of the plasma must change at to distribute auxiliary emitters over the entire electrode area the time rate no more than a few gap-widths apart. Since the gap width typically is less than 1 mm and the auxiliary emitter must dnldt = J,,/ed. (33) be heated by the emitter but be electrically insulated from it, It can be shown [17] that the average density for a sheath- the triode type of converter is structurally and technologically contained quasi-collisionless unignited plasma is, to a good quite complex compared with the elementary diode. approximation, 2) Ion Injection Triode: As described in Section VI-B, prac- tical operation of the cesium vapor diode in its unignited (34) (diffusion) mode is inhibited by the requirement that its output current is limited to less than Jn, corresponding to & in Fig. 5. This constraint arises because of the conflicting Accordingly, (27), (33), and (34) together can be solved for simultaneous requirements of a low emitter work function the time dependence of the electrical output characteristics. If 4~ for thermionic emission of electrons (2) and a high $E there are no ion sources (J2,= Jt, = 0), and ion losses other for thermionic emission of plasma-neutralizing positive ions than to the electrodes are negligible (Jzt= J,, = 0), (33) is (7). The constraint can be removed by providing, as in Fig. readily integrated to give the output current decay at constant 12(b), an auxiliary electrode in the interelectrode gap that output voltage V = Vo: injects positive ions into the plasma by thermionic emission of 3 positive ions (surface ionization). In order for there not to be a J = Jo/(l+ t/~)Ti (35) potential barrier for ion emission from the auxiliary ion emitter with high work function $,, a bias voltage V,z& - 4~ must where be applied between it and the electron emitter with lower work function $E, as shown in Fig. 12(b). The auxiliary power required is P, = Jz,V, = JV;, which combined with (27) as before gives (32), with f = 1. In this case the effective arc drop Vi is minimized and the output ri = v,d = ion transit time at average velocity vi and J, = power maximized when $,c-K = 3.9 eV, such that typically initial value of J. = V,e1 V. Since (32) gives vd << 0.01 eV for the ion injection The pulse power requirement is P, = J,v,r,/rd Jvi, triode, the electrical power required to maintain the plasma where J,, V,, and 7-z are the pulse current, voltage, and width, is entirely negligible in the ion injection triode, and the high and J is the average output current over the pulse repetition emitter temperature and close spacing constraints associated period Td. For J, = J,, therefore, the equivalent arc drop is with the diffusion mode of the unignited diode are removed. v; = Jsv, 7, / JTd. (37) As with the electron-injection triode, however, auxiliary emitters must be distributed closely over the entire electrode For a cesium vapor diode with typical values d = 1 mm, area and be heated by, but electrically insulated from, the emit- dlX-1, J,/Jo = 2, V, = 6 eV, and r, = 1 ps, (35) and (36) ter electrode. The complexity of this structure and the difficulty give a pulse repetition period Td = 4~~150ps for J/J0z0.5, in maintaining both high and low work function surfaces in and (37) gives VdeO.16 eV, which is significantly superior to cesium vapor in the presence of emitter vaporization products the ignited mode Vde0.45 eV. have prevented practical application of the ion-injection triode Several means are available to substantially decrease this to date, in spite of its superior performance potential. Vi,however. When several torr of a noble gas such as Xe or Kr is added to the cesium vapor, additional electron scattering is negligible, but the resulting diffusion gradient for the ions C. Pulsed Diode causes the average plasma density to be several-fold greater A type of converter that combines an injection plasma with than that given by (34). This effectively increases r2 and the much simpler diode structure is the pulsed diode. The therefore Td by the same amount, resulting in vi < 0.1 eV. plasma is maintained by applying to the diode electrodes a Also, since the plasma formation time is less than 0.1 ps, the continuous series of short (51 ps) pulses at a high enough pulse width r, could be substantially less than 1 ,us if shorter RASOR: THERMIONIC ENERGY CONVERSION PLASMAS 1205 pulses can be employed in practical configurations, further reducing Vi. It has been experimentally demonstrated recently in the USSR [24] that metastable vibrational states of nitrogen gas added to the cesium vapor can be excited during the pulse, and the plasma sustained long after the pulse by cesium ionization via collisional de-excitation of these states. The observed POWEP SYSTEMS plasma decay times reported are an order of magnitude greater than those for cesium vapor alone, but the nitrogen pumping (excitation) time is similarly increased. Accordingly, the ratio rZ:/rd in (37) is not substantially improved by this process. The auxiliary electrode voltage required for the N2 excitation CELL VZ=1 V is much less than the 6 V required for cesium TFE PAIR ionization, however, such that Vi << 0.1 eV might be possible. Furthermore, the much greater pulse width and lower pulse- Fig. 13. Modular versatility of in-core thermionic reactor technology. repetition frequency required might substantially improve the practical application of pulsed diodes to large systems. Attempts in the U.S. to verify these results have not been successful [25], suggesting that this approach may be de- pendent on conditions not yet identified. For example, N2 MAGNEl de-excitation must not occur at the electrode surfaces, so that OUTS I DE the different surfaces employed (adsorbed cesium in the U.S. REACTOR and barium oxide layer in the USSR) may be responsible for the different results. It is informative to note that the addition of nitrogen gas to 4-INSIDE the ignited cesium diode increases its arc drop [26]. Excitation REACT 0R COLLECTOR of the nitrogen by the high-temperature electron gas in the TANK ignited plasma is a parasitic effect that adds another electron energy-loss term to (18) for Vd without significantly increasing the total ion production rate.

EMITTERS TYPICAL)^ VIII. APPLICATIONS Fig. 14. Schematic illustration of the Thermionic Reactor with Inductive Coupled Elements (TRICE) concept. P = pulse generator; L = pulse-blocking inductor. A. Space Nuclear-Power Systems In-core thermionic nuclear reactor systems have an inherent converter. Improved understanding of the basic physics of the advantage over other systems, because the high-temperature plasma has provided analytical models for design evaluation heat source, the nuclear fuel, is suspended like the filament in and diagnosis of engineering test data, but has tended to a light bulb, isolated from the entire remainder of the system show that substantial improvements in the characteristics of which operates at conventional reactor coolant temperatures. the ignited plasma are not likely, as was concluded in Section Because the thermionic energy conversion cycle can operate at V-C. Basic improvement of ignited converter performance has the highest temperature attainable by the nuclear fuel, a high heat rejection temperature can be used to minimize the radiator been and probably will be obtained further through advances weight that dominates high-power space systems. Also, as in the surface physics of the electrodes, however. shown in Fig. 13, development of the basic cell and thermionic A recent study [3] examined the potential for substantially fuel element (TFE) enables production of a family of static improving the in-core thermionic reactor through use of con- space-power systems having high redundant reliability over a verters with the injection plasma described in Section VII. As wide range of power levels. shown in Fig. 14, the Thermionic Reactor with Inductive Cou- Because of this inherent advantage and modular versatility, pled Elements (TRICE) concept employs core-length pulsed use of the elementary, ignited-mode, cesium vapor thermionic diode converters that are coupled to the external load via elec- converter has been adequate to develop competitive thermionic tromagnetic induction, rather than by series connection of dc space-power systems for past needs in spite of the perfor- cells. In addition to potentially increased system performance, mance limits on the primitive ignited-mode converter (circa this greatly reduces the complexity of the cells and eliminates 1965). Accordingly, most work on thermionic space reactor the need for electrically insulating them from the liquid-metal systems to date has been concerned with the engineering coolant. The experimentally demonstrated inductive coupling development of components and integration of conventional requires cycling the converter plasma through four sequential ignited converters into various reactor designs [2], instead states: ignition pulse (quasi-Knudsen arc, Fig. 12(c)), unignited of research on improving the plasma characteristics of the plasma decay phase (35),plasma quench pulse (V- V, >> kTt 1206 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 19, NO. 6, DECEMBER 1991

40 I I CONvENTIoN4L I 1

im 2wo 2200 2400 2630 2m MW 3200 EMIllER TEWERATURE (K) EMIllER EWERATUE (13 Fig. 15. Analytically projected thermionic converter performance at very high temperatures (VHT). as in Fig. 9(c)), and stand-off phase (V << 0). The quench n pulse rapidly reduces the plasma density to a sufficiently CONVENTIONAL TFE CELL VHT CELL low value that significant current cannot flow during the POWER OUTPUT 71 watts (.I HP) 380 watts 760 watts subsequent magnetic flux reversal (inverse voltage standoff) ELECTRICAL 90 HWe/n3 180 t4ie/n3 phase required in an inductive coupling cycle. PONER DEHSITV Emitter temperatures in thermionic reactor designs have CELL EFFICIENCY -20-252 - 25-301 EMITTER LIFE -10 years 2500-I OKyear -1002800 OKhours been limited to about 1800 K, because of intolerable swelling TEMPERATURE J of the nuclear fuel at higher temperatures during the 5-10 y r.i” full-power lifetime and high fuel burnup required in previous EMITTER applications. Recently, however, applications have emerged which require much higher power densities for their feasibility, but for much shorter periods and much less fuel burnup. These Fig, 16. Comparison of thermionic fuel element cells for operation in the include power systems for military space systems, for elevation conventional and very high temperature regimes. of spacecraft from low earth orbit to high or translunar orbits by electrical propulsion, and for cargo transport in the manned there are as yet very limited experimental data for evaluation Mars mission. As shown in Fig. 15, the analytically projected of the validity of the present analytical models in this very power density attainable by thermionic converters at much high-temperature regime. higher temperatures is an order of magnitude higher than that in the conventional temperature regime, and at up to twice the efficiency [4]. Nuclear fuels developed for nuclear rockets, B. Terrestrial Power Systems both UC-ZrC and W/UO2 cermets, have operated for hours at Terrestrial thermionic power systems differ from space 2800 K, and potentially are stable for many months at 2400 power systems primarily in the availability of a low heat- K. Fig. 16 summarizes the revolutionary increases in power rejection temperature and in the much greater importance density and the efficiency potentially achievable; i.e., 1 hp of costs. The conventional ignited thermionic converter has from a cell the size of an AA flashlight battery, at efficiencies been unable to utilize the low heat-rejection temperature as approaching those of terrestrial power plants. do other heat engines, because this requires a collector work As indicated in Fig. 15, ignited-mode performance is function much lower than that attainable in ignited converters. projected analytically to be superior to the zero-arc-drop Furthermore, practical output at the present v~~2.1eV is unignited-mode performance up to about 2500 K. This obtained in ignited converters only for high emitter tem- somewhat surprising result occurs, because as the emitter peratures T~21600K, which requires expensive refractory temperature approaches and then exceeds the plasma- materials and high-temperature heat sources. For these reasons maintaining electron temperatures (i.e., as TE + Te~and Tec the conventional ignited thermionic converter is submarginally in (18)), the arc drop Vd in the ignited mode approaches zero competitive for terrestrial applications. and possibly becomes negative, as in Fig. 7(b). Furthermore, Detailed system studies have shown, however, that achieve- the existence of the electron-reflecting sheath VE in the ment of V~z1.6- 1.8 eV would make terrestrial thermionic ignited mode (17) reduces the effect of electron backscattering systems cost-effective and superior to alternative systems in compared with that in the unignited mode (27) at practically several applications. These include the topping of fossil-fueled large electrode spacings. It should be recognized, however, that steam power plants and cogeneration of electric power in RASOR: THERMIONIC ENERGY CONVERSION PLASMAS I207 process heat or gas turbine combustors [27], the efficiency no fundamental or practical limitations are known at present of which would be substantially increased, thereby reducing that make the following impossible: their fuel requirements and pollutants. While part of this 1) Thermionic converters operating with injection-type reduction in V, can be achieved by decreasing the collector plasmas in cesium-xygen vapor eventually may operate work function 4~ (12), it probably is necessary also to employ with steel or superalloy emitters at temperatures of converters using the advanced injection plasmas described in 1100-1300 K and collector temperatures of 500-600 K, Section VI1 for two reasons: first, the effective arc drop Vi in giving efficiencies of 15-20% at power densities of a the injection mode of operation can be significantly less than few W/cm2. Externally triggered, self-driven, inductive Vi in the arc mode (12); secondly, the much lower cesium ionizing oscillations might sustain the plasma and permit pressure in the injection mode is required for achievement of either dc or inductive ac output coupling. Applications: the low collector work function at low collector temperatures large and small fossil-fueled terrestrial power systems. Tc, since necessarily TR < TC (6). Inductive output coupling 2) Thermionic converters operating with ignited plasmas using the switchable injection plasmas also could decrease in cesium-oxygen vapor eventually may operate with thermionic module and power-conditioning costs. refractory metal emitters at temperatures of 1800-2000 Similar considerations apply to terrestrial thermionic nuclear K, and with low thermal emissivity collectors at temper- reactors. Utility power plants probably require the use of atures of 600-800 K, giving efficiencies of 20-25% at low-cost, low-temperature thermionic fuel elements without power densities of 10-20 W/cm2. Applications: long life expensive refractory metal emitters, especially if the entire (5-10 y) space and terrestrial nuclear power systems. TFE must be reprocessed upon refueling. The cost constraint 3) Thermionic converters with ignited or unignited plas- might not be as severe for naval reactors, however, permitting mas in cesium-oxygen vapor eventually may operate utilization of both the high-power-density ignited plasma at with known nuclear fuels at emitter temperatures of high temperatures for full power operation, and the low- 2400-2800 K and collector temperatures of 110G1400 temperature injection plasma with a low heat-rejection tem- K, giving efficiencies of 25-30% at power densities of perature to maintain high efficiency for low-power operation. 30-80 W/cm2. Applications: short duration (< 1 y) multimegawatt nuclear power systems for high-power density military and electric propulsion systems in space, IX. CONCLUSION and for compact silent naval propulsion.

A. Dominant Plasma Issues ACKNOWLEDGMENT There are still many peripheral issues that need to be Assistance by J. B. McVey in the performance of much of addressed for complete physical understanding and description the work described and in many helpful discussions during of thermionic converter plasmas. The following are felt by the preparation of this article is gratefully acknowledged. author, however, to be dominant frontier issues for substantial advancements in the field via plasma physics: REFERENCES SurfacelPlasma Interaction N. S. Rasor, “Thermionic energy converter,” in Fundamentals Hand- There is substantial empirical evidence in the form of book of Elecrrical and Computer Engineering, vol. 11, S. S. L. Chang, experimentally observed anomalies that Vj and & in Ed. New York: Wiley, 1983, p. 668. (12) are coupled by as-yet unidentified surface/plasma R. J. Bohl, R. C. Dahlberg, D. S. Dutt, and J. T. Wood, “Thermionic fuel element verification program -overview,” in Proc. 8th Symp. on interaction processes at the collector which inhibit low- Space Nucl. Power Svsr., (Albuquerque, NM), Jan. 1991, pt. 2, p. 636; ering VB by decreasing qbc [28]. see also, J. C. Mills and R. C. Dahlberg, “Thermionic systems for DOD Injection Plasma Properties missions,” in Proc. 8th Symp. on Space Nucl. Power Syst., (Albuquerque, NM), Jan. 1991, pt. 3, p. 1088. The physical description of injection plasmas is incom- N. S. Rasor, “Second generation thermionic reactor (TRICE)” in Proc. plete, especially in the details of the ionization process 2Isr Intersoc. Eneru Cc“. Eng. Conf., (San Diego, CA), Aug. 1986, vol. 2, p. 1337. and of the output current limitation and instabilities aris- N. S. Rasor, J. B. McVey, and R. C. Cooper, “Evaluation of thermionic ing from interaction of Coulomb and magnetic effects. conversion performance at very high temperature for burst power ap- Plasma Properties at Very High Emitter Temperatures plications,” in Proc. 22nd Intersoc. Energy Conv. Eng. CO$, (Philadel- phia), Aug. 1987, vol. IV, p. 1997. The properties of both the ignited and unignited plasmas Many articles on the development and in-orbit testing of the TOPAZ at very high power densities need to be defined both reactor systems were presented in: Trans. Con& on Nucl. Power Eng. in experimentally and analytically for emitter temperatures Space (Obninsk USSR), May 1990; see also, Proc. 7th (and 8th) Symp. Space Nucl. Power Syst. (Albuquerque, NM), Jan. 1990 and Jan. 1991 at which the temperatures and densities of the emitted (available through the AIP, DOE CONF 910116). electrons and ions approach those in the ignited plasma. N. N. Ponomarev-Stepnoi, “Nuclear power in outer space,” Atomnuya Energiya, vol. 66, pp. 371-383, June 1989 (English transl. available from Plenum); see also, G. M. Gryaznov et al., “Thermoemission B. Projections reactor-converters for nuclear power units in outer space,” Atomnaya Energiya, vol. 66, pp. 371-383, June 1989 (English transl. available Projections are hazardous, especially to the degree that from Plenum). they involve speculation. Whereas the detailed means for A. Schock, J. Appl. Phys., vol. 32, pp. 1564-1570, 1961; see also, G. N. Hatsopoulos and E. P. Gyftopoulos, Thermionic Energy Conversion, accomplishing the following projections are not yet defined, vol. 1. Cambridge, MA: MIT Press, 1973. there already are indications that they might be achievable, and N. S. Rasor and C. Warner, J. Appl. Phys., vol. 35, p. 2589, 1964. IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 19, NO. 6, DECEMBER 1991

L. K. Hansen, J. Appl. Phys., vol. 38, p. 4345, 1967. Antonov et al., Teplofiz 5s. Temp., vol. 27, p. 209, 1987 (in Russian). N. S. Rasor, “Thermionic energy conversion,” in Applied Atomic Colli- [25] J. B. McVey, “Improved pulsed ionization thermionic converters for sion Physics, vol. 5, H. S. W. Massey, E. W. McDaniel, and B. Bederson, nuclear power applications,” in Proc. 25th Intersoc. Energy Conv. Eng. Eds. New York: Academic, 1982, chap. 5. Conf. (Reno, NV), Aug. 1990, vol. 2, p. 357. F. G. Baksht et al., in Thermionic Converters and Low Temperature [26] S. V. Babko-Malyi, V. B. Kaplan, and A. M. Martsinovskii, “Thermionic Plasma, Moyzhes and Pikus, Eds. Moscow: Acad. Sci. USSR, 1973 discharge in a Cs + N mixture,” Zh. Tekh. Fiz., vol. 57, p. 2029, 1987. (in Russian) (English ed. by L. K. Hansen, Ed., Nat. Tech. Inform. [27] G. Miskolczy, B. Gunther, and A. E. Margulies, “Conceptual design Service, Springfield, VA, DOE-TR-1, 1978). of a thermionic topped steam electric generation plant,” in Proc. 13th F. G. Baksht and V. G. Yur’ev, Sov. Phys.-Tech. Phys., vol. 21, p. 531, Intersoc. Energy Conv. Eng. Con$ (San Diego, CA), 1978, vol. 3, p. 1976; see also, Sov. Phys.-Tech. Phys., vol. 24, p. 535, 1979; D. Hamm, 1893; see also, G. Miskolczy, C. C. Wang, and D. P. Lieh, “Thermionic J. P. Dansereau, R. Bouwmanns, and W. Coleman, “A time dependent combustor application to combined gas and steam turbine power plants,” model of a thermionic energy converter using a three scale asymptotic in Proc. 16th Intersoc. Energy Conv. Eng. Conf (Atlanta, GA), 1981, analysis of the electrode plasma boundaries,” in Proc. 22nd Intersoc. vol. 2, p. 1956. Energy Conversion Eng. Conf (Philadelphia), Aug. 1987, pp. 10-14. [28] G. L. Hatch, W. Rhiner, N. S. Rasor, and L. K. Hansen, “Status of N. S. Rasor, “Thermionic energy conversion,” in Applied Atomic Colli- research on advanced thermionic converters,” in Proc. 12th Intersoc. sionPhysics, vol. 5, H. S. W. Massey, E. W. McDaniel, and B. Bederson, Energy Conv. Eng. Conf (Washington, DC), Aug. 1977, p. 1563. Eds. New York: Academic, 1982, chap. 5; see also, F. G. Baksht et al., in Thermionic Converters and Low Temperature Plasma, Moyzhes and Pikus, Eds. Moscow: Acad. Sci. USSR, 1973 (in Russian) (English ed. by L. K. Hansen, Ed., Nat. Tech. Inform. Service, Springfield, VA, DOE- TR-1, 1978); G. N. Hatsopoulos and E. P. Gyftopoulos, Thermionic Ned S. Rasor (SM’66) received the B.S. degree Energy Conversion, vol. 2. Cambridge, MA: MIT Press, 1979; J. L. in engineering physics from Ohio State University, Lawless, Ph. D. diss., Princeton Univ., Princeton, NJ, 1980. the M.S. degree in physics from the University of V. Z. Kaibyshev, “A phenomenological model of the arc mode of a Illinois, and the Ph.D. degree from Case Institute of thermionic converter,” in Proc. 24th Intersoc. Energy Conv. Eng. Conf. Technology in 1955. (Washington, DC), 1989, vol. 2, p. 1149. During 1949-1962 at the Atomics International D. W. Norcross and P. M. Stone, J. Quant. Spectrosc. Radiat. Transfer, Division of North American Aviation, Inc. in Canoga vol. 8, p. 655, 1968. Park, CA, he conducted basic research on nuclear J. B. McVey, “TECMDL ignited mode planar thermionic converter radiation effects on reactor materials and on their model,” Rasor Assoc., Sunnyvale, CA, Rep. NSR-31/9@0775, Aug. ..Droperties from 4 to 4000 K. He was Proiect Leader 1990 (for ignited mode); see also, J. B. McVey and G. L. Hatch, “Indirect on programs for development and evaluation of emitter temperature measurement,” in Proc. 24th Intersoc. Energy Conv. high-temperature ballistic re-entry materials and fuel elements for the Pluto Eng. Conf (Washington, DC), Aug. 1989, vol. 6, p. 2859 (for unignited nuclear ramjet. As Director of the Energy Conversion Department he ini- mode). tiated and directed pioneering studies on thermionic energy conversion and N. S. Rasor et al., “Final report on TRICE program,” Rasor Assoc., engineering studies of its application to space nuclear power systems. As Vice Sunnyvale, CA, Rep. NSR-27-12, July 1988 (Contract No. DNA President-Research at Thermo Electron Corp., Waltham MA (1962-1965) he 001-85-C-0320). initiated and directed major basic and applied research programs in thermionic J.-L. Desplat, J. Appl. Phys., vol. 54, p. 5494, 1984; see also, J.-L. energy conversion. From 1965 to 1971 he consulted in the engineering physics Desplat, N. S. Rasor, and C. Dobson, “Cesium-oxygen electrode for J. of thermionic energy conversion, primarily for the Douglas Aircraft Company the TRICE concept,” in Proc. 22nd Intersoc. Energy Conv. Eng. Con& in Richland, WA, and Brown-Boveri in Heidelberg, Germany, and consulted (Philadelphia, PA), 1987, vol. IV, p. 2011. on cardiovascular devices at the Cox Heart Institute in Dayton, OH. He was R. Henne, “Features of a BaKs diode with plane polycrystalline the Founder, Chief Scientist, and Chief Executive Officer of Rasor Associates, MO electrodes for thermionic energy conversion,” DFVLR, Stuttgart, Inc., Sunnyvale, CA, from 1971 to 1990, where he initiated, directed, and Germany, ESA TT-171, Ph.D. diss., 1975, 131pp. A. G. Kalandarishvili, Working Medium Sources for Thermionic Power personally contributed in contract research and development of advanced Converters (in Russian). Moscow, Energoatomizdat, 1986, 184pp. physical electronic devices for production and control of electric power For a bibliography of more recent studies, see references in V. I. and related technologies and of cardiovascular devices. He is now, again, Kuznetsov and A. Ya. Ender, in Proc. 23rd Intersoc. Energy Conv. Eng. a Consulting Physicist in thermionic energy conversion, space nuclear power, Conf. (Denver, CO), 1988, vol. 1, p. 581. and heat transfer technology. He is an internationally recognized authority V. B. Kaplan et al., in Sov. Phys.-Tech. Phys., vol. 22, pts. 112, pp. in the surface and gaseous discharge physics of low-voltage, high-current 159-165, 166-172, 1977. thermionic discharges. He initiated and conceived related advanced devices J.-L. Desplat and M. Korringa, “Final report on high current Terma- and space nuclear reactor systems under investigation by several agencies. tron,” Rasor Assoc., Sunnyvale, CA, Rep. NSR-29, 1989 (Contract NO. Dr. Rasor has organized and participated in several U.S. and international N00024-86-C-5 167). scientific consortia and their related conferences. He is a member of the APS V. A. Zherebtsov et al., “Experimental and theoretical study of TEC and an Associate Fellow of the AIM. He is a founder of several high- pulse mode with Cs t N filling,” in Proc. 24th Intersoc. Energy Conv. technology companies, including Space Power, Inc. in 1983, and was its Chief Eng. Conf, (Washington, DC), 1989, vol. 2, p. 1137; see also, E. E. Executive Officer for three years.