http://www.geocities.com/gary23428/LowTemperature/THERMIONICCONVERTERS.htm


I THINK THIS IS SOME OF THE MICRO BASED THEORY/APPLICATION BEHIND THE MACRO
ENGINEERED LASER-EM-MICROWAVE AND OTHER ENERGY TECH BEING TESTED AND
DEPLOYED AGAINST US AS ONE ASPECT OF THE CHEMTRAILING....WHEN ENERGY IS
CREATED ON SUCH A LARGE SCALE THROUGH DEPLOYMENT OF BARIUM PLASMAS AS ACTIVE
AURORAL ANTENNAE AND ENERGY GENERATION FIELDS, THEN A RELATIVELY SMALL
AMOUNT OF ENERGY FROM GROUND BASED MOBILE OR STATIONARY UNITS IS ALL THAT IS
REQUIRED TO CONTROL IT.  WHOLE CITIES CAN THEN BE SUBJECTED TO
ENERGY/BEHAVIOUR CONTROLS/ EXPERIMENTS.  GOD KNOWS WHAT THE POPULACE AT
LARGE HAS BEEN INFECTED WITH, TO REACT WITH THESE VARIOUS ENERGIES IN
BEHAVIOUR MODIFICATION TESTING ON BROAD SCALE.  THE INDIVIDUAL HUMAN TEST
SUBJECTS AND OUR KNOWLEDGE OF THEIR INDIVIDUALS PREDICAMENTS IS BAD ENOUGH.

Chapter 1

THERMIONIC CONVERTERS AND LOW-TEMPERATURE PLASMA

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

1. Methods of Direct Conversion of Thermal to Electrical Energy

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:

1. Thermoelectric generators (TEGs)

2. Thermionic converters (TICs)

3. Magnetohydrodynamic (MHD) generators

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)
(Th - Tc) where a n and a p are Seebeck coefficients and Th and Tc are the
hot- and cold-junction temperatures.

Two types of losses reduce efficiency in thermoelectric generators: thermal
(as a result of the thermal conductivity of the materials) and electrical
(related to the ohmic resistance of the material). The combined effect of
both losses is a decrease in efficiency below that of an ideal heat engine.
Each of the losses can be reduced separately by varying the current in the
load. To reduce the fraction of losses due to thermal conductivity, the
current must be increased; to reduce the fraction of losses due to internal
resistance, the current must be decreased. As indicated by A. F. Ioffe, the
most promising materials

2

for developing thermoelectric generators are semiconductors

Fig. 1.1

The thermionic diode converter (Fig. l.2a) has a hot cathode (the electron
emitter) and a cold anode (the electron collector).* The left hand branch of
the diode current-voltage characteristic (i.e., when a negative voltage is
applied to the anode with respect to the cathode) is employed in electric
power generation.

A negative applied voltage does not mean that the electric potential
difference between the electrodes obstructs electron flow through the
converter. If the anode has a work function less than the cathode, a
negative internal voltage occurs across the interelectrode space only if the
negative applied voltage, or load voltage, exceeds the contact potential
difference (Fig. l.2b).

For the moment, one can consider an ideal diode (no space charge or gas in
the interelectrode space) with the linear potential distribution shown in
Fig. l.2b. In this case the current in the external circuit decreases below
the cathode emission current only when the applied voltage exceeds the
contact potential difference, because only then are emitted electrons
reflected by the field back to the cathode. The current-voltage
characteristic for this ideal diode converter is shown in Fig. l.2c.

For real thermionic converters with a vacuum in the interelectrode space, an
important advantage is the absence of thermal conduction losses across the
interelectrode gap. Irreversible heat losses, which reduce efficiency, in
this case consist primarily of thermal radiation. However, the relative heat
losses due to radiation may be reduced by increasing the current density in
the TIC or by reducing the electrode emissivity.

The main disadvantage of the vacuum TIC is the retarding potential created
in the interelectrode space by the electron space charge. Positive ions,
which compensate for the negative charge of the electrons, are therefore
introduced into the interelectrode space to increase the current through the
converter. With these added ions, a plasma forms between the electrodes. The
state of this plasma may depend significantly on converter current, and
various operating modes of the plasma thermionic converter are distinguished
as a function of the plasma state.

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)

3

Fig. 1.2

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.

In Magnetohydrodynamic (MHD) generators, thermal energy is converted to the,
kinetic energy of a conducting gas (or low-temperature plasma) flow. The emf
occurs because of the effect of the magnetic field on this flow (Fig. 1.3).
There are open-cycle MHD generators, where the working fluid is the fuel
combustion product (to which is added easily ionized additives to increase
electric conductivity), and closed-cycle MHD generators, in which the
working fluid is a plasma of some optimum composition (heated by a special
heat exchanger).

In liquid metal magnetohydrodynamic generators, the emf occurs in the liquid
metal, to which the gas of the device has transferred its kinetic energy,
rather than in a plasma flow. MHD devices are included with systems for
direct conversion of thermal to electrical energy, since they do not require
a separate, conventional electric generator.

Non-mechanical devices for obtaining electric power also include solar
photocells, which use the energy of solar quanta, and fuel cells, which use
various electrochemical processes at the electrodes. We will not discuss in
detail these last two devices.

Methods for direct conversion of thermal to electrical energy have a number
of important advantages compared to ordinary methods. First, there is the
essential simplicity and the absence of rotating

4

parts that must withstand large dynamic forces and must be manufactured with
great accuracy.

Second, there is the possibility of using higher operating temperatures. As
is well known, the maximum efficiency of a heat engine increases as the
temperature difference between the heat source and the heat sink increases.
The blades in steam turbines, which come into contact with chemically active
water vapor and which sustain large mechanical stresses, do not permit an
increase of steam temperature above 550° C. The MHD generator and the TIC
can operate at higher temperatures and, therefore, can use the high
temperatures obtained from chemical and nuclear fuels more effectively. The
MHD generator and the TIC, and also the TEG to some extent, can operate
either independently or as a high-temperature topping cycle to ordinary
generators to increase the total conversion efficiency.

Fig. 1.3

Third, the TIC and the MHD generator (and to a lesser extent the TEC) may
operate efficiently at high heat rejection temperatures. This makes them --
especially the TIC -- very promising for use in space, where heat must be
rejected only by radiation and where it is desirable, therefore, to have the
heat rejection temperature high in order to reduce radiator weight.

Fourth, the efficiency and the weight per unit output power of the TIC and
TEC become considerably less than that of conventional mechanical power
plants at low output power levels. This makes the TIC and the TEC very
promising for use in autonomous low-power plants.

2. The Efficiency of Direct Conversion of Thermal to Electrical Energy

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

(2.1)

regardless of the specific properties of the working fluid and regardless of
the cycle used. Carnot derived this expression for the efficiency of an
ideal heat engine by considering the conversion of heat to mechanical energy
using a cycle consisting of two adiabatic and two isotherms of an ideal gas.

Formula (2.1) is easily obtained if the concept of entropy, as a function of
the state of the material, is introduced from the very beginning. Then, the
heat taken away from the heat source is

(2.2)

5

and the heat transferred to the heat sink is

(2.3)

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

(2.4)

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 
(dSc = dSh), 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
(dSc > dSh), 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. *

3. The Main Operating Modes of Thermionic Converters

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
eVB (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.)

Fig. 1.4

The development of a device with such small gaps between heated surfaces of
such large area is a very difficult engineering problem. Therefore, the most
promising converters at present (especially for large outputs) are plasma
converters,

_____________________________________________

*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/Tc-1/Th) 

6

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
le 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/le « 1 because the
extent of filling the well is not dependent on the ratio d/le.

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 TC × 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.@

With surface ionization, a fraction of atoms incident to the cathode surface
return as ions. In the case of a dense plasma, this mode is called the
diffusion mode, because the electrons and ions move away from the cathode by
a diffusion process. In this case the cathode work function must be
sufficiently high to obtain the required number of ions. However, an
increase of cathode work function also reduces the cathode electron
emission.

________________________

*A characteristic feature of the Knudsen mode is its greater instability. As
a result of the long path lengths and differences in electron and ion mass
and flight velocities, fluctuations may be amplified rather than attenuated,
creating intense noise or resonant oscillations.

@
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.

7

In the diffusion mode the voltage drop in the volume cannot be large,
otherwise the ions would not be able to reach the collector to neutralize
the negative electron charge in the entire interelectrode space. Therefore,
in the diffusion mode (as in the Knudsen mode with surface ionization), the
current reaches saturation at a very low applied voltage, and as the applied
voltage increases, the voltage increase appears primarily in the anode
sheath. These effects limit the output current in the diffusion 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
Vex in this case may be considerably less than the ignition voltage Vig
(Fig. 1.5, curve 1).

Fig. 1.5

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/le 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 arc mode is the most promising mode for practical application because of
the possibility of obtaining large currents. Therefore, the low‹voltage arc
mode with a dense plasma is employed almost exclusively for present
operating converters and for converters presently being designed.

__________________________

*In a Knudsen plasma, these effects are much weaker than in the arc mode,
and current saturation is more closely approached.

8

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 Eion, the ratio of energy expenditures
for formation of ions Pi to the total energy extracted at the load PL = j VL
(VL is the voltage on the load) is roughly given by

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

Converters have been described in the literature in which the ions are
obtained by using auxiliary ion sources, rather than by using part of the
output voltage applied to the interelectrode space to produce the ions. In
this case the use of easily ionized cesium is not necessary; inert gases can
be used which have very small thermal electron scattering cross sections
(the Ramsauer effect). However, TICs operating with such strongly
non-equilibrium plasmas so far have not been developed.

4. The Efficiency and Power Density of a TIC

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 
eVL < (f C - f A), there is current saturation (segment I in Fig. l.2c):

(4.1)

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

(4.2)

Here 
VL is the voltage on the load, fC and fA are the work functions of the
cathode and anode, and TC is the cathode temperature.

In the saturation segment (I), the energy carried away by the electrons from
the cathode is

(4.3)

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

9

In the segment II of the characteristic, the energy carried away from the
cathode by the electrons is

(4.4)

The radiation energy losses are

(4.5)

where 
TA 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

(4.6)

The component emissivities e
C and e A are for the cathode and anode separately.

The useful power in the load and the efficiency of the converter are
expressed by the following formulas:

(4.7)

(4.8)

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

(4.9)

If radiation losses are much greater than the energy carried by the
electrons, this point of operation becomes the point of maximum efficiency,*
and for this case

(4.10)

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)

_______________________

*In practice this extreme is avoided. For more details, see e.g. [2].

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

10

to obtain optimum cesium coverage. In our example
PL » 13 W/cm2 is obtained at f A = 1.7 eV and js= 10 amp/cm2. The
evaporation heat of the electrons from the cathode is Srad » 34 W/cm2. At e
= 0.3, Srad= 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/TC < f A/TA. With this inequality, from (4.10) we find

(4.11)

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 js = 10 amp/cm2 without seriously reducing the
TIC performance. 

The high efficiency of the ideal converter can also be achieved with a
plasma converter operating in the Knudsen mode, because ion formation losses
may be reduced to a negligible value (for example, with surface ionization).

Inevitable losses related to the passage of current through the gap occur in
a dense plasma, and part of the contact potential difference must be
sacrificed in order to increase the current of the converter. These losses
cannot be characterized by some constant ohmic resistance, because the state
of the plasma and of the pre-electrode sheaths vary continuously with
current. Calculation of the output and efficiency in the arc mode is an
important problem and is considered in the following sections of the book.

For a dense plasma, it is frequently more convenient to calculate the
efficiency of the converter by considering the energy transferred to the
anode rather than the heat removed from the cathode. If ion current to the
cathode can be neglected compared to the electron current, then

(4.12)

where 
TeA is the electron temperature near the anode.

5. Requirements for Electrode Materials and TIC Designs

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

11

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. 

Another way to limit plasma losses is to reduce the cesium pressure by using
cathodes with higher cesium adsorption energies. If we proceed with the
concept that cesium adsorbed on materials with a higher work function is in
an ionized state, then the adsorption energy should increase as the vacuum
work function of the surface increases. Experimental investigations have
confirmed this expectation, and emitters with a maximum vacuum work function
are now being used extensively, for example, tungsten with a (110) preferred
orientation and rhenium. The work function of the surface and the adsorption
energy can be increased by using electronegative additives: oxygen,
fluorine, etc. And in practice, introduction of some amount of oxygen into a
TIC does increase the conversion efficiency.

However, with oxygen it is not yet possible to obtain the required stability
of properties for long periods of operation.

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.

A thermionic diode is a low-voltage source with high current densities.
Therefore, a large number of diode converters must usually

12

be connected in series to suppress relative resistance losses and also to
make the conversion of direct to alternating current more convenient. These
connections present special engineering difficulties if the converters are
in a reactor core. One possible design for a multi-element TIC is shown
schematically in Fig. 1.6.

Fig. 1.6

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.

6. Prospects for Using 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 U
235 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

13

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.

7. The Plasma in a TIC

Low-temperature plasma find extensive practical application in various
gas-discharge devices: gas-filled diodes, thyratrons, plasmatrons,

_____________

*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 Earth¹s surface so as to overcome the force
of the Earth¹s 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].

14

mercury vapor rectifiers, fluorescent tubes, glow discharge tubes, arc
furnaces, welding equipment, and during the past few years, MHD generators,
plasma engines, etc. However, even though the physics of low‹temperature
plasmas is one of the oldest branches of physics, the theory of the
phenomena involved in the passage of a current through a plasma has not
reached such a state of development that the current-voltage and other
characteristics of plasma devices can be designed with sufficient accuracy
for application, as is done for electron tubes and transistors.

We shall now attempt to enumerate the most important factors which we feel
cause the lag of the theory of plasma devices behind engineering
requirements.

First, there is the very large number of elementary processes which occur
simultaneously in the plasma: elastic scattering, excitation and
de-excitation of the energy levels in the atoms, ionization and
recombination, excitation of vibrational and rotational energy levels in
molecules, charge exchange, formation of chemical compounds and radicals,
etc. Despite the large amount of experimental work, the cross sections for
many of these elementary processes are not known. This frequently makes it
difficult to distinguish the important phenomena from the secondary
phenomena.

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. 

Finally, the phenomena in the electrode-plasma transition sheaths are
usually more complicated than the phenomena in the volume, because they are
strongly non-equilibrium in nature. Direct experimental investigation of
these electrode sheaths is very complicated and, in fact, is only beginning.
Therefore, many conclusions about the interactions of the plasma and the
electrodes (for example, about the nature of the processes in the cathode
spot) have no firm experimental basis

15

and are, in part, merely theoretical conclusions.

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. 

Correct description of the electrode sheaths is of great importance.

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 fC <
m , part of the emitted electrons return to the cathode (Fig. l.7b). When
the case fC> 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*).

Fig. 1.7

With passage of current, the height of the barrier and the electron
concentrations may undergo great changes. To derive these changes,
approximate boundary conditions were derived, and subsequently employed
successfully, which permit "joining" the solutions in the plasma volume to
those of the strongly non-equilibrium electrode sheath region.

______________

*"Ion rich" and "electron rich" are the terms usually employed in the US
thermionic literature.

16

Thus, it is possible to obtain a closed system of differential equations and
boundary conditions for this problem. These were solved by computer, and in
some cases, solutions were obtained in analytical form as well.

The simplest problem, calculating the diffusion mode of the TIC, where the
volume ionization can be neglected, was solved first. A solution was then
obtained for the arc mode TIC with a weakly ionized, dense plasma. It was
recently possible to consider an even more complicated case, that of a
strongly ionized plasma between the TIC electrodes.

Experimental methods for investigating (diagnosing) a plasma in the narrow
TIC gap were also developed simultaneously, which permitted quantitative
comparison of calculations and experimental data. Quite satisfactory
agreement between theory and experiment was obtained. This in turn
stimulated further development of the theory and further improvements in the
experiments and in the methods for diagnosing TIC plasmas.

The results of these investigations--of the volume and electrode processes,
and also of the calculations of the state of the plasma in TICs--are the
main content of most of the chapters in this book. One may hope that this
outline of methods and results will be important not only for TICs but for
other devices which also utilize low-temperature plasmas.

Investigation of the problem of the maximum achievable conversion
efficiencies in TICs leads naturally to the consideration of the
low-temperature plasma as a thermoelectric material for the direct
conversion of energy. From this point of view, a slightly non-equilibrium
plasma can be characterized by a dimensionless thermoelectric figure of
merit:

(7.1)

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] 

(7.2)

The thermoelectric-emf of a plasma, a , and electrical and thermal
conductivity's, s and k , are determined primarily by the free electrons,
even with a small degree of ionization. Therefore, the thermoelectric-emf is
given by

(7.3)

where m 
= kT ln(Ze/ ne?) is the chemical potential of the plasma, Ze = 4.82 x
1015T3/2 the sum over states for the electrons (partition function), ne? 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:

(7.4)

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

17

in the range 
2-3. 

Thus, we have for the thermoelectric figure of merit:

(7.5)

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

Thus, a low temperature plasma, as was first pointed out by A. F. Ioffe, is
essentially an ideal material for converting heat to electric energy. In
principle this makes it possible to bring the efficiency of a plasma diode
close to that of an ideal heat engine.*

But in reality, direct use of formulas (7.2) and (7.5) to calculate the
efficiency of a plasma TIC is not correct, because the state of the plasma
varies intensively when the current passes through the converter. The
electron concentration and temperature change, and significant voltage drops
develop in the cathode sheath barrier. Still, the high value of the
thermoelectric figure of merit for a slightly non-equilibrium plasma is
helpful for understanding in a general way why the plasma TIC can have high
efficiency despite the apparent strong non-equilibrium state of the
operating modes.

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.

18

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. Gil¹bert, 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,