This chapter is introductory. In it the characteristics of the TIC and the operating principles of plasma diode converters are briefly considered.

Modern society requires the most diverse electric power sources. Along with high-power power plants, there are requirements for autonomous power plants with low output (watts-kilowatts; for automatic radio-relay lines, remote meteorological stations, marine buoys, etc.) and with medium output (kilowatts-megawatts; for expeditions, manned arctic stations, military installations, etc.). In particular, special requirements are placed on the power systems for spacecraft, where heat can be rejected only by radiation and where the weight of the plant is severely limited.

At the present time, electric power from high-power thermal and atomic power plants is obtained using steam boilers and turbogenerators, while the generators in mobile and low-power plants operate with internal combustion engines. The thermal energy in all these units is initially converted to mechanical energy; the mechanical energy is then converted to electrical energy. Despite the great success achieved in perfecting these electric power plants, some deficiencies in the conversion processes themselves remain uncorrected. Therefore, during the past decade there has been great interest in so-called direct (i.e. non-mechanical) methods for converting thermal energy to electrical energy.

Research in direct energy conversion is being pursued in three main directions:

The electromotive force which occurs in a material under the effects of a temperature gradient (the Seebeck effect or thermoelectro-motive force) is the driving force of the thermoelectric generator (Fig. 1.1). The TEG is a thermocouple (or several thermocouples) with high efficiency. The thermoelectric—emf, directed from the cold to the hot end in the positive branch and the vice versa in the negative branch, occurs because of the effects of the temperature difference. The resulting emf is E = (a _n + a _p) (T_h - T_c) where a _n and a _p are Seebeck coefficients and T_h and T_c are the hot- and cold-junction temperatures.

The optimum output voltage of a TIC is about equal to the contact potential difference, and consequently, does not exceed 1 - 2 volts. T. Therefore, to obtain sufficient electrical output power compared to the radiation losses, it is necessary to have high current densities (on the order of 10 amp/cm²). The requirements of having a large contact

*In the US thermionic literature the terms emitter and collector are used rather than cathode and anode, T. Because of the kinetic energy of the emitted electrons, greater output voltages are available, but this leads to considerable decrease in current, output power, and efficiency (see segment II in Fig. l.2c)

potential difference and very high emission current densities lead necessarily to the use of high cathode temperatures (in the range of l800-2200° K). Thus, the thermionic diode is a high—temperature, low-voltage electric power source, with high current density. The use of positive ions to neutralize the space charge does not change this basic character of the converter, because ion formation and the passage of current through the plasma introduce losses of electrical energy and therefore can only reduce the output parameters of the TIC.

Carnot showed that the efficiency of a heat engine which takes heat from a heat source of temperature T_h and discharges the heat to a heat sink at temperature T_c may not be greater than

where dS_h is the decrease in entropy of the heat source, and dS_c is the increase in entropy of the heat sink. The efficiency of the engine is then

If the cycle is not accompanied by friction losses, viscosity losses, heat conduction losses, ohmic resistance losses, etc., the entropy of the system does not change (dS_c = dS_h), and the efficiency of an ideal heat engine (2.1) is obtained.

As a result of irreversible losses in a real device, there is always an increase of entropy (dS_c > dS_h), and therefore, the real efficiency of (2.4) is always less than of (2.1). To obtain high efficiency during direct conversion of heat to electrical energy, the irreversible energy losses (primarily the result of internal electrical resistance and of direct heat transfer between the heat source and the heat sink) must be reduced. *

The working fluid in the thermionic converter is a gas of free electrons in the interelectrode space, either in a vacuum or in plasma. Vacuum and plasma TICs are different in character. In vacuum TICs the charge is transferred only by the electrons. These electrons create a negative space charge between the electrodes, and as a result, a retarding field develops which deflects some of the emitted electrons back to the cathode. The vacuum mode is efficient only with very small spacing between the electrodes. If this spacing does not exceed several microns, the height of the potential barrier eV_B (Fig. 1.4), which impedes the electron flow, remains small at the required currents (» 1-10 amp/cm²). (At smaller currents, the vacuum TIC is inefficient because of relatively large radiation losses from the cathode.)

*In order to imagine entropy more vividly, one can, for example, assume that there is no absolute thermal insulation between the heat source and the heat sink. The change of entropy D S, related to the flux of conduction heat Q, is then equal to D S = Q(1/T_c-1/T_h)

where the negative space charge is neutralized by positively charged ions. Cesium which has the lowest ionization potential (3.89 eV), is usually employed for the ions.

TICs with Knudsen or with dense plasmas are distinguished by the nature of electron motion in the converter. The Knudsen plasma mode of operation occurs when the mean free path of the electrons l_e is greater than the interelectrode distance d. In this case the electrons and ions move in the electric field created by their own presence, essentially without collision. Usually, most of the potential variation occurs near the electrodes, and there is at most a weak field in the interelectrode space. The electron and ion concentrations in the interelectrode space are essentially equal.* If the potential distribution is non—monotonic, i.e., if a potential well for ions or electrons forms in the space, then the carriers of the corresponding sign will fall into the well as a result of infrequent collisions and remain there for a long time-until they obtain, by further collisions, the energy required to escape from the well. This effect is appreciable even at d/l_e « 1 because the extent of filling the well is not dependent on the ratio d/l_e.

In the Knudsen (direct flight) mode, the entire electron emission current can be removed at the collector with a sufficiently large ion concentration. With practical gap widths, however, the direct flight mode can be useful only if the converter currents are not too high. When the current density reaches tens of amp/cm², the electron scattering from the ions becomes appreciable because of the large concentration of carriers.

To provide emission currents greater than 1 amp/cm² at T_C ³ 1500° K for currently available cesium adsorption cathodes, the cesium pressure must be increased so much that the mean free path of the electron, for practical gap widths, becomes less than the interelectrode distance. In such a dense plasma, the electron and ion drift velocities are low compared to their thermal velocities. Under these conditions, the plasma properties excluding the narrow pre-electrode regions are determined by macroscopic parameters, e.g., heat conductivity, electron and ion mobility, and diffusion coefficients.

The dense plasma mode (as well as the Knudsen mode) is classified, in addition, by the method for ionization-surface ionization or volume ionization.@

@In most of the US literature, the surface ionization mode is referred to as the unignited mode, and the volume ionization mode as the ignited mode.

When there is an electric field at the emitter, which accelerates the electrons into the interelectrode space and increases their energy, ion generation in the volume begins to play the dominant role. This mode, when the main ion source is within the interelectrode space, is called the low-voltage arc or arc mode [1]. The potential and plasma density distributions in the arc mode develop in such a way as to provide sufficient ion generation and to move the ions to the electrodes. A region of sharp potential variation, the cathode drop, forms near the cathode and the main ion generation occurs in the space near this region. At low cathode temperatures, the arc must be ignited to go from the diffusion mode to the arc mode, and to bring this about, it is necessary to reduce the load voltage, or even to apply an external voltage to the converter. After ignition the arc operates at lower voltages, and the extinction voltage V_ex in this case may be considerably less than the ignition voltage V_ig (Fig. 1.5, curve 1).

At high cathode temperatures, the transition from the diffusion mode to the arc mode occurs without ignition; volume ionization increases gradually as the voltage in the gap increases (Fig. 1.5, curve 2). In the arc mode the cathode is not the main ion source; therefore, its work function can be reduced appreciably, to allow the emission of large currents. The cesium pressure must be increased to several torr (or more) to reduce the work function by cesium adsorption. Under these conditions, the ratio d/l_e for practical gap widths is always large compared to unity. The current in the arc mode does not saturate but continues to increase with applied voltage because of the Schottky effect at the cathode, because of a decrease in electron backscatter to the cathode, and because of an increase in ion current to the cathode.* As the current in the arc mode increases, a state of ionization equilibrium is quickly established in the interelectrode space, during which the rate of ionization (at a given point) becomes equal to the rate of recombination.

The actual energy expended for ion formation in the arc mode does not significantly reduce its efficiency. This is obvious from the following simple analysis, which is directly valid for a Knudsen arc. The thermal velocity of ions is a factor of (m/M)^1/2 less than that of the electrons (where M is the mass of the ions and m the mass of the electrons); therefore, each ion in transit compensates for (m/M)^1/2 electrons. Since the energy expenditure to form the ion is of the order of the ionization energy E_ion, the ratio of energy expenditures for formation of ions P_i to the total energy extracted at the load P_L = j V_L (V_L is the voltage on the load) is roughly given by

At V_L = 1 V this ratio is approximately 10^-2.

It is convenient to begin consideration of converter efficiency with the simplest case--the ideal TIC. With space charge and anode emission neglected, the current-voltage characteristic (see Fig. l.2c) consists of two segments. As long as the load voltage is less than the contact potential difference eV_L < (f _C - f _A), there is current saturation (segment I in Fig. l.2c):

where j_s is the cathode emission current density. In the opposite case eV_L > (f _C - f _A), there is an exponential dependence of current on voltage (segment II in Fig. l.2c):

Here V_L is the voltage on the load, f _C and f _A are the work functions of the cathode and anode, and T_C is the cathode temperature.

where 2 kT_C is the average kinetic energy carried by emitted electrons and S_eva is the heat of evaporation for electrons emitted from the cathode.

where T_A is the anode temperature, s = 5.67 x 10^-12 eV/cm⁴deg⁴ (Stefan-Boltzmann constant), and e is the effective thermal emissivity of the system, equal to

The component emissivities e _C and e _A are for the cathode and anode separately.

The useful power in the load has a maximum at the break in the ideal current-voltage characteristic (if f _E - f _C > kT_C). At this point the voltage on the load is equal to the contact potential difference:

It is obvious from these simple formulas that greater useful power and efficiency can be obtained by reducing the anode work function. In a plasma TIC a low anode work function is achieved by introducing cesium vapor. Cesium adsorbed on the anode surface can be optimized to provide work functions in the range f _A = 1.5 - 1.7 eV.

Emission current densities of approximately 5-10 amp/cm²@ are typical for TICs. A cathode with a work function f _C » 3 eV, for example, will emit this current at 2000° K. Cesium adsorption is also used to obtain an optimum cathode work function. However, since the rate of desorption increases very rapidly as temperature increases, the cesium vapor pressure on the cathode must be increased to several torr (or more)

@Resistance losses along the electrodes become increasingly severe at greater current densities.

to obtain optimum cesium coverage. In our example P_L » 13 W/cm² is obtained at f _A = 1.7 eV and j_s = 10 amp/cm². The evaporation heat of the electrons from the cathode is S_{rad »} 34 W/cm². At e = 0.3, S_rad = 27 W/cm² and h » 21%.

Expression (4.8) for h has one disadvantage: it clearly does not follow from (4.8) that the diode efficiency cannot exceed the efficiency of the Carnot cycle. This is related to the fact that when deriving (4.8) we disregarded emission from the anode, which is permissible only for f _C/T_C < f _A/T_A. With this inequality, from (4.10) we find

It is obvious from these considerations that the anode temperature does not affect efficiency as long as the emission from the anode is low compared to cathode emission. This means that the anode temperature (the cooler temperature) may be high without an appreciable reduction of efficiency and of output power. This is very important for spacecraft, where heat rejection must be accomplished by radiation. In our example, anode temperature can be increased to 1100° K for f _A = 1.7 eV and j_s = 10 amp/cm² without seriously reducing the TIC performance.

where T_eA is the electron temperature near the anode.

It was noted above that anodes with a minimum work function and a cathode with some optimum work function (2.0 to 3.0 eV, depending on the cathode temperature) are required for TICs. A low anode work function is usually provided by cesium adsorption. A work function of 1.7 eV is easily achieved with cesium adsorption on a cold electrode, but in a

number of cases, a work function as low as 1.5 eV can be achieved by optimizing the anode temperature.

The situation is more complicated with respect to the cathode. For prolonged operation, the cathode should be made of refractory metals (for example, W, Mo, Re, or Ta), but all these materials have a work function of more than 4 eV. To provide the required emission current, it is necessary that an adsorbed layer which reduces the work function be maintained on the cathode. Cesium can be used as the adsorbate in this case, also, but cesium has a rather low adsorption energy, and therefore, rather high pressures are required to provide a low work function.

However, as pressure increases, the electron scattering in the plasma increases, and consequently, the voltage drop across the TIC increases. To minimize this loss, designers try to reduce the inter-electrode spacing, insofar as this is compatible with the requirements of reliability. Electrodes can short-circuit as a result of possible slight deformations at high temperatures during prolonged operations. It is especially difficult, for example, to maintain a small gap (of about 0.2 = 0.3 mm) for TICs inside a nuclear reactor, because of fuel swelling due to the accumulation in the fuel of fission products and other structural defects.

It has been suggested repeatedly that the required cathode work function could be provided by using materials with higher adsorption energies, for example, barium or strontium, leaving to cesium only the function of compensating for the space charge. But unfortunately, these materials, adsorbed on the anode, increase the anode work function f _A above that obtainable with cesium. For example, the work function of Ba is 2.3 eV compared to 1.8 eV for Cs. An increase of f _A has the same negative effect as an increase in the voltage drop across the plasma. The use of semiconductor electrodes in the TIC is limited by the requirement that the voltage losses in the electrodes not exceed one-tenth volt at current densities of the order of 10 amp/cm².

To reduce thermal radiation losses, it is desirable to have an anode with a low thermal emissivity. However, the anode may be covered by a layer of material evaporated from the cathode. Therefore, it is difficult to obtain an effective emissivity e less than 0.2 in real converters.

The nuclear fuel is enclosed in a metal jacket, which functions also as the converter cathode. The heat from the anode is carried off by a liquid-metal heat-transfer fluid, which must be insulated from the anode. The jumpers which connect the elements in series should provide not only minimum electric and thermal losses but also the high mechanical stiffness that the entire structure requires in order to maintain a small gap between the electrodes. Very severe requirements are placed on TIC insulators. They must operate at rather high temperatures in contact with active metal vapors (cesium or even barium) and in a number of cases must also tolerate large doses of nuclear radiation. The ceramics Al2O3 or BeO are the usual insulating materials in TICs.

Most intriguing are the prospects for using TICs for atomic power in space. At the present time, semiconductor solar cells are employed for long-life, autonomous electric power sources on almost all spacecraft. But as the output increases, the mechanical systems for deploying large photoelement surfaces in space and for orienting them become very cumbersome. It is assumed that the maximum output for photoarrays is 10-50 kW [3]. However, there are applications which require greater electric power. Television broadcast directly to viewers without relay stations on Earth, for example, can require an electric output at the satellite of 100 kW to several hundred kW [4].

The problem of using atomic power for spacecraft propulsion is of enormous importance. This becomes clear immediately if the energy of the fragments obtained from the fission of a U²³⁵ nucleus (1.66 x 10⁸ eV) is compared to the energy of chemical reactions, measured in several eV per molecule (for example, an energy of 2.5 eV for the formation of an H₂O molecule). Thus, a lightweight atomic reactor contains an enormous amount of energy, the release of which should be adequate for very long—term spacecraft expeditions.

Prospects of manned flight to Mars [5] and other planets at a distance of hundreds of millions and billions of kilometers depend on the development of nuclear-powered rockets (for comparison, recall that the distance from the Earth to the Moon is equal to 385,000 km). There are problems related to the development of a reactor adaptable to operation

under space flight conditions, but no less important are the problems of proper utilization of the reactor energy to impart the maximum thrust with minimum expenditure of the working fluid in the propulsion engine. The reactor energy can be used simply to heat the gas discharging from a propulsion engine. Even in this case, a specific impulse of up to 800 sec* can be obtained by using the lightest gas H₂, an improvement over chemical fuel [6]. A considerably greater specific impulse than can be obtained by heating hydrogen to fuel-element temperatures can be obtained by using ion or plasma (electric propulsion) engines. This, however, requires some method of converting the nuclear energy, liberated in the form of heat, into electrical energy. In this case, TICs are highly promising because of their lightness and high efficiency at high radiator temperatures.

Yet another advantage of the TIC is noted in [5], where the possibility of using TICs in a system designed for a manned expedition to Mars is discussed. A nuclear reactor with thermionic fuel elements has a good impedance match to an arc plasma propulsion engine; therefore, they can be combined directly without a voltage converter. This is fortunate because this voltage converter would have to operate at a high temperature, i.e., close to the radiator temperature. The authors of [5] conclude that a system consisting of a fast-neutron thermionic reactor having an efficiency of 13% and electric power density of 12 W/cm², combined with an arc thruster which accelerates lithium to a specific impulse of 5000 sec, is quite capable of performing the task of moving a spacecraft from Earth orbit to Mars orbit and back for a proposed manned flight to Mars. @

The prospects for using TICs with chemical fuels are very intriguing. TICs in time could compete successfully in efficiency and weight with internal combustion engines to produce electric power for large autonomous power plants with outputs up to 10 kW. The main difficulty here is the need for development of high-temperature materials which could withstand prolonged contact with the fuel combustion products [8]. As of now, successful operation for 330 hours of a converter heated by incandescent gases with an emitter temperature of 1450° C [9] has been reported.

*The ratio of the ion impulse (imparted to the rocket) to the weight of the working fluid on the Earth (P/mg) is called the specific impulse, i.e., the rate of gas flow is equal to the specific impulse multiplied by the acceleration of gravity. The specific impulse for engines operating on ordinary fuel does not exceed 300 sec, but the combination of liquid hydrogen and liquid oxygen yields 400 sec.

@Electric propulsion engines have a very low thrust compared to chemical engines. This is related to their low power. Therefore, electric engines are unable to be launched from the Earth’s surface so as to overcome the force of the Earth’s gravity. Injection into Earth orbit should be accomplished by chemical engines. However, electric engines may operate for a very long time compared to chemical engines; therefore, they may gradually accelerate a spacecraft to much greater speeds in interplanetary space [7].

Second, there is the extreme variability of the plasma. The plasma is easily set in motion, and its electrical conductivity varies by many orders of magnitude under the influence of external effects (electric and magnetic fields, pressure gradients, etc.). Instabilities, which can occur in different ways-increased noise level, turbulence, striations, regular large-amplitude natural oscillations-easily occur in a plasma. High-temperature plasmas are especially unstable; but even with a low-temperature plasma, where the stabilizing effect of the collisions is stronger, it is not always possible to assume that the plasma is homogeneous and quiescent.

Third, the special nature of Coulomb forces acting in the plasma should be emphasized separately. Coulomb forces easily reach very large values with only slight deviations from space charge neutrality, and they decay slowly with distance, so that they act directly on a large number of plasma particles. The collective motions due to Coulomb interactions are manifested in the form of plasma (Langmuir), ion-acoustic and other waves. If these oscillations are excited above the equilibrium thermal level, they can play an important role in the scattering of individual particles, as in beam relaxation and in the development of macroscopic instabilities.

Fourth, the system of differential equations which describes the state of a quiescent (steady-state) plasma can be solved in analytical form only in the simplest cases. In most cases of interest, their solution has only recently ceased to present insurmountable difficulties, because of the use of electronic computers.

Theoretical and experimental investigations of the TIC plasma have permitted, perhaps for the first time, the calculation of the state of the plasma during the passage of an electric current--by using only experimentally measured cross sections of the elementary processes, and without any a priori assumptions about the nature of the distribution of temperature, potential, density or other parameters of the plasma. It was possible to achieve this because of a number of favorable circumstances, the most important of which are the following: the simple geometry of the problem (one-dimensional flows); comparatively small deviations from equilibrium of the electron and ion distribution functions in the main volume; the narrowness of the gap, as a result of which a positive column with striations is not formed between the electrodes; the large equilibrium emission from the cathode which prevents the occurrence of spots; and the low voltages across the plasma, which do not exceed 1-2 volts in practical operating modes.

Consideration of electrode interaction with the plasma can begin with the case of thermodynamic equilibrium where net current is equal to zero. If the cathode work function f _C is greater than the chemical potential of the plasma m , then a space charge layer forms near the cathode which accelerates the emitted electrons and retards part of the emitted ions (Fig. l.7a). In the opposite case f _C < m , part of the emitted electrons return to the cathode (Fig. l.7b). When the case f _C > m occurs, the TIC is said to be overcompensated (excess ions, or ion rich*); when the case f _C > m occurs, the TIC is said to be under-compensated (electron rich*).

This thermoelectric figure of merit determines the decrease of converter efficiency below the efficiency of an ideal heat engine (2.1). For a small temperature difference, we obtain [9]

where m = kT ln(Z_e/ n_e?) is the chemical potential of the plasma, Z_e = 4.82 x 10¹⁵T^3/2 the sum over states for the electrons (partition function), n_e? the electron density, and r the average flow of electron kinetic energy (in units of kT). The latter is dependent on the scattering mechanism and usually has the value 2-3.

The ratio k /s for an electron gas is given by the Wiedemann-Franz law:

where L is some number dependent on the scattering mechanism, usually

in the range 2-3.

If we assume that T = 2500° K and n_e? = 10¹³ cm^-3 then we obtain ln(Z_e/n_e?) » 18 and zT » 200.

In the preceding calculation, we neglected radiative heat transfer, which actually may significantly reduce the effective zT of conversion. This neglect, however, is not of importance, because in principle, the absolute value of radiation can always be reduced by using materials with low emissivities. Also, the importance of radiation can be minimized by reducing the interelectrode distance and by increasing the current.

*It is obvious from formula (7.5) that the positive ions do not affect the thermoelectric Q-factor of the plasma, since this ideal working fluid is essentially a free electron gas. It follows from (7.5) that the diode may also operate with a non-equilibrium concentration of the electrons, as in the case of a low-temperature plasma with inert gas ions.

References

1. a, N.D. Morgulis, Termoelektronnyy, plazmennyy preobrazovatel, energii, Gosatomizdat , 1961, Language, Call Number, LCCN, Dewey Decimal, ISBN,ISSN,

b, N.D. Morgulis and P.M. Marchuk, Ukrayin. fiz. Zh., 1, 59, 1956. The main operating modes of thermionic converters, low-voltage arc or arc mode, Language, Call Number, LCCN, Dewey Decimal, ISBN,ISSN,

2. N.S. Rasor, Journal of Applied Physics, 31, 163, 1960. The efficiency and power density of a TIC, Language, English, eng, Call Number, QC1.J83, LCCN, Dewey Decimal, 530.5, ISBN,ISSN, 0021-8979

3. a, G.F. Tape, Proc. 2nd Int. Conference on Thermionic Electrical Power Generation, Stresa, p. 1407 , 1968. Prospects for using TICs, Language, Call Number, LCCN, Dewey Decimal, , ISBN,ISSN,

b, Yu. L. Danilov, ibid., p. 1417. Prospects for using TICs

4. W.A. Ranken and E.W. Salmi, 3a, p. 185. Prospects for using TICs

5. R.W. Bussard and R.D. DeLauer, Fundamentals of Nuclear Flight, McGraw-Hill, New York, 1965. Prospects for using TICs, Language English, eng, Call Number TL783.5 .B79 LCCN 64025371 ,,r852, Dewey Decimal 629.4223, ISBN,ISSN

6. L.A. Gil’bert, Elektricheskiye raketnyye dvigateli, Voyenizdat, 1968. Prospects for using TICs, Language, Call Number, LCCN, Dewey Decimal, ISBN,ISSN,

7. M. Latouche-Halle, 3a, p. 81. Prospects for using TICs,

8. P.K. Shefsiek and J.P. Angello, Thermionic Conversion Specialists Conference, Carmel, p. 521, 1969. Prospects for using TICs, Language, English, eng, Call Number, TK2955 .T4412 1969, LCCN, 88197004, Dewey Decimal, 621.31,243, ISBN,ISSN, -

9. A.F. Ioffe, Semiconductor Thermoelements and Thermoelectric Cooling, Infosearch Ltd., London, 1957. Prospects for using TICs, Language, Call Number, LCCN, Dewey Decimal, ISBN,ISSN,

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