JPRS ID: 10216 TRANSLATIONS THERMOPHYSICAL PROPERTIES OF WORKING MEDIA OF THE GAS-PHASE REACTOR BY V.K. GRYAZNOV, ET AL.

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JPRS L/ 10216
24 December 1981
Translation
THERMOPHYSICAL PROPERTIES OF WORKING P"EDIA
OF THE GAS-PHASE NUCLEAR REACTOR
By
i V.K. Gryaznov, et al.
~
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JPRS L/10216
24 December 1981
THERMOPHYSICAL PROPERTIES OF WORKING FiEDIA
OF THE GAS-PHASE NUCLEAR REACTOR
;
i Moscow TEPLOFIZICHESKIYE SVOYSTVA RABOCHIKH SRED GAZOFAZNOGO YADEFNOGO
REAKTORA in Russian 1980 (signed to press 1 Aug 80) pp 6-63
[Chapter 1 from the book "Thermophysical Properties of Working Media
of the Gas-Phase Nuclear Reactor", by Viktor Konstantinovich Gryaznov,
- Igor'L'vovi.ch Iosilevskiy, Yuriy Georgiyevich Krasnikov, Nina Ivanovna
Kuznetsova, Vladimir Ivanovich Kucherenko, Galina Borisovna Lappo,
Boris Nikolayevich Lomakin, Georgiy Alekseyevich Pavlov, Eduard
Yevgen'yAvichson and Vladimir Yevgen'yevich Fortov and edited by
V.M. Iyevlev, Atomizdat, 1,800 copies, 304 pages]
Editor's Preface......... ~ 1
Chapter 1. TheYmodynamic Properties 4
1.1. General cnaracteristics of the behavior of thermodynamic
functions of working media 4
1.~. Asymptotic methods of describing the thermodynamics of a
weakly imperfect plasma 14
1.3. Thermodynamics of a strongly imperfect plasma 19
1.4. Component composition of partially ionized imperfect plasma...... 31
1.5. Consideration of the effect of the medium on the state of
atom: Mode:i calculations by the Hartree-Focl: and 'I'homas- 38
Fermi method
1.6. Method of calculating the composition and tnermodynami.c
functions of a multicomponent imperfect plasma 45
1.7. Discussion of the results of calculation. Comparison to
data of other calculations 55
Chapter 2. Transfer Coefficients of Imperfect Plasma....................... 63
2.1. Qualitative description of heat, mass, pulse and charge
transfer processes in a gas-phase nuclear reactor 63
2.2. Kinetic theory of weakly imperfect plasma 69
2.3. Theozy of nonequilibrium processes in imperfect media..,......... 79
2.4. ModeZ approaches to determination of electron transfer
coefficients of imperfect plasma................................. 89
a [I - USSR - K FOUO]
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N'ok oFN�10nL USH: ohi.v
2.5. Effect af transfer coefficients of a multicomponent imperfect
plasma 99
2.6. Method of calculating transfer coefficients of imperfect
plasma. Discussion of results of calculation........... 105
Chapter 3. Optical Properties of Gases and Plasma 117
3.1. Radiation transfer in a gas-phase nuclear reactor. Ele-
mentary absorption processes in a plasma of working media......., 117
3.2. Deceleration absorption on ions and atoms 119
3.3. Photoionization of atoms, ions and molecules 120
3.4. Absorption in atomic lines .....o....,....... 127
3.5. Molecular absorption .�..........o........o.. 130
3.6. Effect of imperfection on optical properties of plasma......... 135
3.7. Discussion of inethod and results of calculating optical
characteristics of working media 141
Chapter 4. Generation and Diagnosis of Imperfect Plasma 145
4.1. Characteristics of experimental investigation of imperfect
plasma 145
- 4.2. Electric methods of producing an imperfect plasma................ 149
4.3. Dynamic methods in physics of imperfect plasma 157
- 4.4. On condensation of an imperfect plasma............... 165
4.5. Comparison of experimental and calculate3 data on
thermodynamics.............~...~~~~~~~~~~~~~~~~~~~~~~~~~r~~~~~~~� 171
4.6. Comparison of experimental a:.d calculated data by
transfer coefficients.............. 177
4.7. Comparison of experimental and calculated data by
optical properties...........................................o... 180
Chapter 5. Thexmoghysical Properties of Working Media of Gas-Phase
- Nuclear Reactor 186
Bibliography .......................o................. 288
The present state of the theor.y of estimatian
optical properties of gases at high pressures
of experimental investigations in the physics
or partially ionized, is ana1T�zed. Numerical
thermophysical properties of plasma of workin
alkali metals, uranium, hydrogen and mixtures
and pressure range are made.
of *hermodynamic transfer and
and temperatures and the state
of non-ideal plasma, completely
calculations are made of the
g media used in gas-phase nuclear--
of them--over a wide temperatu;�e
The hook is survey ancl referencc in nature and will be useful both to specialists
involved directly in the gas-phase nuclear reactor and to engineers and scien-
tific workers specializing in various fields of the physics of low-temperature
plasma.
b
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EUITOR'S FOREWORD
Moscow TEPLOFIZICHESKTYE SVOYSTVA RABOCHIKH SRED GAZOFAZNOGO YADERNOGO REAKTOFA in
- Russian 1980 (signed to press 1 Aug 60) pp 3-5
[Preface by Correspanding Member of USSR A^ademy of Sciences V. M. Iyevlev from
the book "Thermophysical Properties of Working Media of the Gas-Phase Nuclear Re-
actor", by Viktor Konstantinovich Gryaznov, Igor'L'vovich Iosilevskay, Yuriy
- Georgiievich Krasnikov, Nina Ivanovna Kuznetsova, Vladimir Ivanovich Kucherenko,
Galina Borisovna Lapgo, Boris Nikolayevich Lomakin, Georgiy Alekseyevich Pavlov,
Eduard Yevgen'yevich Son and Vladimir Yevgen'yevich Fortov, Atomisdat,1,800 copies,
304 pages]
[Text] The proposed book is survey in nature on the thermophysical properties of
- materials and contains re=erence material on the thermodynamic, transport and op-
tical properties of vapors of alkali metals, uranium, hydrogen and mixtures of
them over a wide temperature and pressure range. The indicated survey and refer-
_ ence material were compiled with respect to interests related to investigating the
_ possibility of develnpment and the anticipated characteristics of a nuclear reactor
of an essentially new type--the gas-phase nuclear reactor (GYaR) and 1lso of power
plants with Lhis type of reactor. Interest in investigp.tions of the gas-phase nu-
clear rea:,tor, including study of the properties of thE- working media, is deter-
mined by the assumed unique properties of this reactor, useful for many applica-
tions. It can be used both in large electric power plants and high-temperature
production systems and in space power plants, engines and so on. Electric pnwer
plants with GYaR have a number of advantages which include [1-4]: high efficiency,
increased heat dissipation temperature, i.e., the capability of discharging heat
into the aiY rather than into water without significant deterioration of efficien-
cy, an increase of the nuclear fuel conversion ratio with low uranium charge in the
reactor, low accumulation of nuclear maLerials and so on. In this regard the gas-
phase nuclear reactor will possibly be the future basis for extensive development
of nuclear power engineering and technology. The contents of the book are not re-
lated dirECtly to processes in the gas-phdse nuclear reactor. However, it is
feasible in the preface to dwell briefly on the schematic diagram and some dis-
tinguishing features of GYaR that determine the characteristics of the approach to
study of the thermophysical properties of working media.
Different schemes of GYaR are now being investigated [1-4]. According to one of
the most promising of them, substantantiated by theoretical investigations and
model experiments, a GYaR is a cavity-type device. The fissionable material--
1
~
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uranitun in a gaseous state--is located in t-he center of the cavity surrounded by a
reflector-moderator. The working substance heated by thermal radiation from the
uranitun plasma passes bPtween the uranium and the cavity walls. Special measures
are employed--profiling c,f the velocity field, suppression of disturbances at the
- inlet of working media into the cavity, stabilization by a magnetic field and so
, on [3]--to reduce mixing of the uranium and working substance.
The principal advantage of the GYaR is the capabili'ty of heating the working sub-
stance to very high temperatures. The restriction here is only the need to have
a temperature permitted by the structural materials of the walls on the periphery
of the working substance. The temperature may reach tens of thousands of degrees
in some schemes far from the walls and also in the zone of the uranium plasma.
_ Therefore, one of the central problems in development of GYaR is that of establish-
ing the necessary temperature fields and concentration profiles in the reactor
cavity. Complex problems of magnetic hydrodynamics, diffusion and radiation and
convective heat transfer, 5olution of which is impossible withoiit a detailed knowl-
edge of all the transport characteristics of the plasma, arise in solution of this
problem. A knowledge of the optical properties of uranium and working substances
is of special importance since the main mechanism of heat transfer is radiant en-
ergy transfer.
The high temperatures of the uranium and working substance and the requirement of
the criticality of the GYaR make it necessary to have a pressure at the level of
hundreds of atmospheres in the reactor cavity. With these pressures and tempera-
tures of tens of thousands of degrees, the uranium and working substances, among
which alkali metals that provide high conductivity and absorption of radiation
play the important role, are in a state of a so-called strongly imperfect plasma,
i.e., in a state of single- or multiply ionized gas with intensive interparticle
interaction that significantly affects all the thermophysical properties of the
medium. The theory of this state of matter is extremaly complex and now contains
a number of unresolved problems, while the experimental information is very limited.
Therefore, unlike problems of traditional thermophysics, not only proper sampling
, of all the input data but, which is no less important, critical selection of the
most reliaole methods now available of calculating the thermophysical properties
of the working media in a strongly imperfect plasma are required to calculate the
thermodynamic and transfer properties. This circumstance has been reflecteii in the
fact that a considerable part of this book is allocated to analysis of the princi-
pal problems of the theory and current state of genEration and diagnosis of a non-
ideal plasma.
It should be noted that experimental investigations of an imperfect Plasma have not
yet been conducted adequately and this is related to the complexity of generation
and diagnosis of this plasma. Theoretical investigations of an imperfect plasma are
also far from complete and the collective of authors hopes that the outlined re-
sults will be used in further development of investigations on the physics of a
nonideal plasma.
The book is constructed in the following manner. The first three chapters are
devoted to a survey of the curren" state of the theory and selecting the method of
calculating the the modynamic, kirietic and optical pr.operties of an imperfect
General problems of the thermophysics of an imperfect plasma are considered in these
2
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chapters; therefore, the outlined material may also be used in other fields of
physics of hi.gh-temperature gases and plasma. These fields include the thermo-
physics of strong shock waves, powerful MF-ID generators, heavy-current discharges,
the hydrodynamics of scattering of dense vapors in laser thermanuclear fusion and
- so on. The fourth chapter is devoted to a survey of experimental methods and re-
sults obtained on the thermophysics ofan imperfect plasma. Finally, chapter 5
contains specific results of calculations of the thermophysical properties of the
plasma of working media: gaseous alkali meta'.s, uranium and also mixtures of al-
kali metals with uranium and hydrogen.
Thp participation of the authors in direct writing of the material was as follows:
V. K. Gryaznov--sections 1.5 and 1.6, I. L. Iosilevskiy--sections 1.1, 1.3-1.7 and
_ 4.5, Yu. G. Krasnikov--section 1.2, N. I. Kuznetsova--sections 3.1-3.5, V. I.
Kucherenko--sections 2.5 and 2.6, G. B. Lappo--sections 3.1-3.5 and 3.7, B. N.
Lomakin--sections 4.1-4.7, G. A. Pavlov--sections 2.1 and 2.3-2.6, E. Ye. Son--
sections 2.1-2.6, 3.6 and 4.6 anu V. Ye. Forto�i--sections 1.5 and 4.1-4.7. The
numerical calculations were made by V. K. Gryaznov, I. L. Iosilevskiy, V. I. Ku-
cherenko and G. B. Lappo.
Since the book is mainly survey and reference in nature, one should turn to the
cited bibliography for more detailed study of the theoretical problems and exper-
iunental methods of the generation and diagnosis of an imperfect plasma. This book
on the thermophysics of an inperfect plasma is appearing for the firs'c time; there-
fore the authors will be grateful for responses and critical comments.
- The proposed book will be useful to specialists working not onl.y on development of
the gas-phase nuclear reactor, but also in other fields of plasma physics, MHD
generators, the physics of shock waves, some schemes of thermonuclear fusion and
so on.
3
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M'l)R OF'M'I('IAI, UtiM: lIVt.Y
TFiERMODYNAMIC PROPERTIES
J Moscow TEPLOFI7,ICHESKIYE SVOYSTVA RABOCHIKFi SRED GAZOFAZNOGO YADERNOGO REAKTORA in
Russian 1980 (signed to press 1 Aug 80) pp 6-63
[Chapter 1 from the book "Thermophysical Properties of Working Media of the Gas-
Phase Nuclear Reactor", by Viktor IGonstantinovich Gryaznov, Igor'L'vovich Iosilev-
skiy, Yuriy Georgiyevich Krasnikov, Nina Ivanovna Ku2netsova, Vladimir Ivanovich
Kucherenko, Galina Borisovna Lappo, Boris Nikolayevich Lomakin, Georgiy Alekseye-
vxch Pavlov, Eduard Yevgen'yevich Son and Vladimir Yavgen'yevich Fortov, Atomizdat,
1,800 copies, 304 pages]
[Text] 1.1. General Characteristics of the Behavior of the Thermodynamic Functions
_ of Working Medi3
Two approaches, which have become called the chemical and physical models [2],* are
usually employed to calculate the thermodynamic funcLl-ons of high-temperature media
in the range of parameters typical for the gas-phase nuclear reactor [1].
In most cases the simpler chemical model is considered where the presence of par-
ticles of specific varieties having a continuous energy spectrum is assumed before-
hand. The effect of the internal structure af the particles (bound states) tin
thermodynamic functions is taken into account by introducing individual statistical
sums (abbreviated statsums) [5]. This is the source of known difficulties related
to the conditional nature of dividing all degrees of freedom of the system into
translational and internal. in the practice of calculat3ng thermodynamic values,
these difficulties are gotten around by varikus types of "cuts" of the statsums on
the basis of one or another physical concepts.
A subsequent, but more complex approach to determination of thermodynamic functions
- is based on the physical -nodel where nuclei and electrans are considered and
coulomb interaction between them is taken into account on the basis of quantum-
statistical theory. In this case contributions to thermodynamic functions from
continuous and discontinuous spectra occur simultareously and are finite. These
problems are considered in section 1.2. When discussing the qua!.itative behavior
*The names methods of initial atoma and method of mixture are used for similar ap-
proaches in the theory of neutral chemically reacting gases [3, 41.
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of the thermodynamic characteristics of working substances of complex composition,
it is more convenient to use the traditional chemical model.
The problem of thermodynamic calculation can be conditionally divided into two
_ Parts. First, purely thermodynamic calculation with given, for example, pressure
p and temperature T of the remaining thermodynamic values such as density P, in-
ternal energy U, enthalpy H, entropy S and so on and also of differential charac-
teristics--specific heats Cp and Cv, the isentropic index Ys= (o In PI~ In P)s and
so on. Second, calculation of some important auxiliary values such as the composi-
tion and individual contributions of different subsystems, for example, free chdr-
ges, atoms, moleculPS and so on. A knowiedge of these values is in principle not
compulsoxy for calculation of the thermophysical properties, but the existing ap-
proximate methods of calculating these properties rely in most cases on using them.
It follows from the results of numerous approximate calculations that the general
behavior of the thermodynamic characteristics for working media in the range of
" parameters p= 0.1-102 MPa and T= 103-105 K[1] is determined first by processes
of ionization and recombination of atoms and ions and second by formation and dis-
sociation of different :nolecules, while at low temperatures it is determined by the
gas-liquid phase transition. Tae effect of the nonic:leal na`ure on the behavior of
the total thermodynamic values of working substances is not felt as strongly as an
_ their composition. Although all the indicated processes may actually proceed si-
multaneously, it is useful to judge separately the effect of each of them on the
course of thermodynamic functions.
,
n'
i,~ r ~
,f I
- -r ~
i-
: j foorma
r
Li =1 i`+P. J
~ ~ ~`0,000f
I /
~i r~ Ir 1U ;'r 40 6u fllll 11 10''K
Figure 1.1. Thermodynamic Equation of State of Lithiwm Plasma. Results
- of calculation (the possibility of condensation and formation
- of molecules was not taken into account)
;j specific band in tl:e plane of thermodynamic parameters, for example, p, V or
p, T and so on, can be set into aareement to each of these processes. The posi-
tion and slope of this band are dependent on such parameters as ionization energy,
- energy of dissociation and sc- on. As an illustration, let us consider the process
' of ionization of lithium. Like all alkali metals, secondary ionization in lithium
proceeds with a filled electran shell; therefo.re, the first and secand ionization
potentials diff.er significantly (see Table 1.1, section 1.6), while the primary
and secondary ionization bands are clearly distinguished.
The dependence of the dimensi.onless value--the lithium compressability factor
Z= pV/RT (R is the gas constant and V is the molar volume) on temperature is
*
The thermodynamic calculations presented in the given r.,ook were made by using a
- special rrogram described in [6].
5
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presented in Figure 1.1. The range of an ideal gas behavior (Z = const) and the
range of transition separating them corresponding to primary, secondary and ter-
tiary ionization, can be clearly distinguished in the low-pressure range, i.e.,
at low densities. :ks pressure increases, these processes shift toward the higher
temperature range and in this case both ionization bands are split and superimposed
on each other so that, for example, the section corresponding to ideal singly ion-
ized lithium essentially disappears.
Thc: foregoing on the thermal equation of state p(V, T) is also valid with respect
to the caloric equation of state U(p, T). This is illustrated in Figure 1.2 on
the example of hydrogen. The value pv = pp-1 is used as the independent variable
here, which permits clearer determination of sections of ideal gas behavior, where
~V - consl.
U 2-1 I The constant constained in this relation is dependent on selec-
tion of the point of reference and is expressed by dissociation ana ionization
energy.
in' (1) aa'M ~Jo - Naea A/ b~u
~
/ j La3 ~Nl
10 ~ ~ N~ib Hb i 6
~
-v-anooi Mna
o,f Nna
-.-rooMna
e r2 a 4 sp,,f 1'e-
Key :
Flgure 1.2.
1. Ideal gas
Caloric Equation of State of Hydrogen U(p, V). Results of
calculation. Lines corresponding to ideal gas behavior
:l
2 PV I cunsl are noted
7fie behavior illustrated in Figures 1.1 and 1.2 on the isobars is qualitatively
preserved upon intersection of the dissociation or ionization band along the iso-
chor, isotherm, isoenthalpy o-r isoentropy. Specifically, such differential char-
acteristics as, for example, specific heat, have a characteristic burst in this
case (Figure 1.3). The ionization band and general course of lines T, H, U and
- S= const intersection this band are depicted schematically in Figure 1.4 in co-
ordinates p, V.
The enthalpy-entropy diagram on which dissociation or ionization bands can also be
distin3uished is important for practical purposes (Figure 1.5).
6
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d
~
- S H=N';~ __II
� {
u� 1
. 0
rn' to' fo'
- Figure 1.3. Specific Heat of Hydrogen [114]
~
V
Key:
7,K
pV
S-r.onat
nonoca (1)
UOflU3Q!{!fU
~
- - V
Figure 1.4. Qualitative Behavior of "Lines x= const (x = T, H, U, S and
so on) IIpon Intersection of Isolated Ionization Band
1. Ionization band
The general cnurse of thermod}�namic functions presented above is correctly de-
scribed qualitatively within the chemical model [5], based on solution of the known
system of equations of chemical and ionization equilibrium using heats of.dissoc:.a-
tion, ionization and excitation energy. It is important to kno~r~ with this approach
how sensitive the total thermodynar.iic values ar.e to selection of the method of tak-
ing the internal degrees of freedom and the effect of imperfection into account.
This is shown in Figures 1.6-1.10 on the example of the thermal and caloric equa-
tions of state of cesium. It is obvious from the figures that the ambiguity re-
lated to the differPnces between the methods suggested in the literature [71 of
taking the contribution of excitec. states of an atom into account is not reflected
in the qualitative behavior of the curves within the ionization band (this conclu-
sion is retained for dissociation). The effect of this intersection ~s felt to a
greater ~.egree with an increase of press when, as already noted, the ionization
and dissociation bands are shifted to the higher temperature range.
If quantum effects are not taken into account, the interaction between charged
particles can be characterized by the dimensionlesc parameter y or by parameter P
more convenient in problems of theory.
7
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pv
7 � cnnst
i
i
1!-cOnsl
a-
~
`
=con
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A
M'OR OMMI('IAL l1tiE: UNILY
(1) .

: 0 7-50� 10'
w F ~ '

40
/
~
fU 90
/
15 ~ !-IS�l0''K
10 12
0 (2)
f0 15 5,/1,m/2�K
_ Figure 1.5. Enthalpy-Entropy Diagram for Hydrogen-Potassium Mixture
(H2 + 3 percent K): solid lines--isobars; dashed lines--
isotherms
_ K:ey :
1. J/g 2. J/g�K
.
k7, 1 ,on ~ kyyn ~ (1.1)
r� 2- x2~ 4 n njel/k'1'.
Sap ,
Here e is charge, k is Boltzmann's constant, rD is the Debye radius and nzar and
E is the total concentration and stan for charged particles.
zar
4dhen calculating tne total thermodynamic functions, the effect of coulomb interac-
tion is doubly manifested. On the one hand, it is present in the form of direct
corrections to the values of internal snergy and pressure. On the other hand, it
is indirectly reflected in thermodynamic properties due to a shift of ionization
equilibrium because of effective variation of the i.onization potential. In the
; range of weak imperfection I' � 1, the corresponding corrections are given by the
known Debye-Hueckel approximately [8]� In this case corrections to the vaZues of
energy and pressure are negative and proportional to the first power of parameter
I', while the degree o� ionization increages. Accordins to this, the typicaY trans-
ition in the ionization rang2 is smoothe3 over in the thermal and caloric equations
- of state (see Figures 1.6-1.10) and the corresponding peak is also smoothed as a
function of the specific heat or compressability on temperature. Let us emphasize
that the "inclusion" of charge-charge interaction monotonically increases the in-
ternal energy or enthalpy in a considerable part of the ionization band in the
caloric equation of state U= U(p, V) i.mportant for some gas-dymamic problems
(adiabatic flows) (see Figure 1.9).
8
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l.' I
1, N
1,6
Figure 1.6. Thermal Equation of State of Cesium in Ionization Band (iso-
core v= 500 cm3/g). Calculation in ideal gas approximation
with regard to different number of excited states of cesium
in statsum (1.71): 1--ground state; 2--
3--
(u-~I~~),
'm?K
10
Ni,
U~
!
0
f ? 'f l1,M11u (l)
Figure 1.7. Caloric Equation of State of Cesium Plasma on Isochor v=
= 500 cm3/g. See Figure 1.6 for notations.
Key:
1. kJ/kg
2. t4Pa
When the ionization band intersects, for example, along the isochor (V = const),
the parameter of imperfection 1' does not behave monotonical'- and reaches a specif-
ic maximum value [7]. This value increases with a shift to tne higher density
range. The effect which charge-charge interaction has on the general course of
thermodvnamic functions also increases in this case within the given band. The
range where parar,:eter 1' ? I can be conditionally called the range of strong imper-
fection. The forms and specifically the characters of correction for imperfection
in this range was discussed by many authors (see, for example surveys [9-121). It
is now clear that the given problem is closely related to the role of excited states
of the atom and other particles and with the sequential approach the contributions
from discontinuous and continuous energy spectra of particles should be interXelat-
ed, as occurs, for example, in the physical model of a plasma where both contribu-
tions are calculated simultaneously (see section 1.2).
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f'� 015 1 z p,Mfla

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- pV - ~ - - - _
1-
1,~9
/,G
f0`~ ' + J
,
~~5 > z p, Mna
Figure 1.8. Isochor o� Cesium v= 500 cm3/g. Calculation of system of
ions, electrons and atoms (in ground state) with different
corrections for imperfection: 1--ideal gas; 2--ring (Debye)
approximation in large canonical ensemble (1.84, 1.85) ; 3--
correction as in sing le- component model (431 (see also Fig-
iares 1.16 and 1.17)
(u-1pV),
io'K 4-W
NZ
7
i
o ~ z p,Mna (a)
Figure 1.9. Caloric Equation of State of Cesium Plasma on Isochor v=
= 500 cm3/g. See Figure 1.8 f.or notations
' Key :
1. kJ/kg
- A large numbe'r of papers [13-161 is also devoted to the problem of the role of
interaction of char:ged and neutral particles. The effect of this interaction is
manifested differently according to existing concepts. First, bound complexes of
neutral and charged particles which are regarded as a separate variety of parti-
� cles, for example, H-, H2 and H3, Li-, Li+, Li2 ar.d so on, are formed in the case
- of sufficiently strong attraction at close distances. The calculations show that
inclusion of these particles in the calculation is weakly reflectcd in the total
thermodynamic characteristics. Second, there is the effect o� charge-neutral in-
_ teraction unrPlated to formation of an individual variety of particles. The fol-
- lowing dimensionless parameter is used for the characteristic of this part of the
contribution of interaction.
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= io tk,1~ \
i ka ~
(1)I ~ 2
J
qb
- 0,4
\
~
,
1~ll)i-- f0lp iQJ V~CMi/8 (2)
Figure 1.10. Fosition in p, v-Plane of Isoentrapy of Cesiinn s= 1.9 kJ/(kg�K)
_ When Using Different Corrections fnr Imperfection: 1, 2 and 3--
- as in figure 1.8; 4--ring (Debye) approximation in [N, V, T]-
group. Summation of intra-atomic states in 1-4 to energy Ek <
< I - kT
Key :
1. kJ/kg 2. cm3/g
~kT J'(1) (f) rrr, (1.2)
where np is the neutral particle concentration and (P(r) is the potential o= charge-
- neutral interaction. The equality of this parameter to unity conditionally limits
the range where charge-neutral interaction appreciably shifts the ionization equi-
librium. Different estimates made for alkaii met::_s [16] yield a typical figure
on the order of approximately -0.5�10'21 eV�cm3 for the value I(D(r)dr eontained in
expression (1.2). Calculations using this value show that consideration of the in-
teraction of charged and neutral particles in the greater pa.r.t of the range of in-
'.erest to us weakly affects the general course of the total thermodynamic functions,
leading to some smoothing of the course of these functions discussed above in the
low-temperature part of the primary ionization band. The diagrams of state of hy-
drogen, lithium, cesium and uranium with the range of strong imperfection noted on
titem due to charge-charge and charge-neutral interaction are presented in Figures
1.11-1.14. The give diagrams were plotted on the basis of calculations (see Chap-
ter 5) where the indicated interactions were already taken into account. However,
in view of the approximate nature of our knowledge of the potential 0(r) itself in
[1.2) and also due to the approximate nature of the corrections that describe these
interactions, the abovP estimate of the role of these interactions may be
inaccurate.
The interaction between neutral particles can also be described within two mechan-
isms. Formation of a new variety of neutral particles, for example, molecules, may
have a significant effect on the general course of the thermodynamic functions in
the low-temperature range. This is primarily related to hydrogen (see Figures 1.2
and 1.11) and to a lesser degree to the alkali metals and is related directly to
the values of the dissociation energy of H2, Li2r Na2 molecules and so on (see
- Table 1.1).
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DV
kT
1,5
I
10 fo1 103 f04 v,cM'%z (1)
- Figure 1.11. Diagram of State of Hydrogen. `I'he range of strong imperfection
is noted (r > 1). Dashed zone considered in this paper (p < 50
MPa): solid lines--isotherms in approximation of ideal gas H+,
e and H; dashed lines--additional consideration of formation of
H2, H2 and H
Besides this effect, an interaction not leading to formation of bound states (the
term "imperfection" is usually applied to this latter part) is considered separ-
ately in the chemical model. Estimates and calculations :how that, being limited
only by consideration of molecule formation, we introduce an error to the equation
of state in the low-temperature range 4,000 K) in the range of pressures of in-
terest to us.
A qualitatively important manifestation of particle interaction, primarily of neu-
tral particles, is the gas-liquid phase transition. According to existing esti-
mates [17, 181 and according to experimental data, the critical parameters of alka-
li metals are located in the range of parameters: Tkr = 2,000-3,500 K, Vkr = 50-
300 cm3/mole, pkr = 10-60 MPa and Zkr = PkrVkr/RTkr - 0.1-0.2. Statistical
measurements of the equation of state of cesium vapors in the sub- and near-critical
- range T s Tkr = 2,050 K have now been made (19, 201. There are no static experi-
ments in neutral cesium vapors at supercritical temperatures, but comparison of
recent experimental data at T 5 Tkr [20] to the generalized diagram of compressabil-
ity for nonmetals [21, 221 shows satisfactory agreement (Figure 1.15). If one as-
_ sumes that the noted agreement is retained at T> Tkr with accuracy sufficient for
estimates in the temperature range where thermal ionization is low, one can direct-
1y compare the equation of state characterized by the diagram of compressabili*y
indicated above to the results of thermodynamic calcul.ation that do not take into
account interatomic interaction (except for formation of biatomic molecules). The
boundary where the difference becomes sufficiently large can be conditionally taken
= as the boundary of the range of strong imperfection due to neutral-neutral inter-
action. This comparison was made for isotherms T= 2,000 and 3,000 K in Figure
1.15 and for isobars P= 10 and 20 MPa in Figurce 1.13.
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(1) J .
Kl~ BfX~Q311l1A
io-z o6~rnr.mc(2)
. p-50Mfla
rz2
r-f
zo ~ r=0,5
~ fn
~
>o-4 rQa (3) 1 j
\01> `v l
2 J s fo 20 r,1o1K
Figure 1.12. p-T Diagram of Lithium. Saturation boundary and range of
strong charge-charge interaction (dashed line) and charge-
neutral interaction (wavy line)--~natm(Do = 0.5 (1.2)) are
noted
Key:
1. g/cm3 3. Gas
2. Two-phase zone
It follows from diagrams 1.12 and 1.13 that the high-temperature part of the
boundary of the two-phase zone, including the vicinity of the critical point, is
- in the zane where, besides neutral particle interaction, charqe-neutral and charge-
charge interactions are also strong. The hypothesis has frequently been advanced
in the literature [9, 141 that there may be an appreciable difference of the gas-
liquid phase transition in alkali metals from the phase transition in nonmetals
due to this and, moreover, that there exists an independent "plasma" phase transi-
tion. The presently available experimental information does not yet indicate the
presence of any qualitative anomalies in this range (see sectior. 4.3 for more
detail).
- Compared to the alkali metals, uranium has a higher boiling poILnt (approximately
4,000 K). The critical parameters of uranium, according to existing estimates,
are such that (pkr = 600 MPa, Tkr z 11,.500 K and pkr = 5.3 g/cm3 [18, 23, 24)).
the entire range of pressures of interest to us is subcritical. Yn this regard
the overall pattern of thermodynamic functions in the temperature range of
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,
A6yxi_Pa3riap 06nncnr2~
i f -f0 y

.
~ r-2
/
1 / r"I
r-rr,s
(3) 1 ~
I ~

2 3 4 S
Figure 1.13. p-T-Diagram of Cesium. The notations are the same as in Figure
1.22: 1--calculation by method of section 1.6; 2--smooth ap-
proximi:tion of experimental results [20]; 3--generalized equa-
tion of state for nonmetals [21, 221 ("Obert and Nelson diagram")
Key:
1. g/cm3 3. Gas
2. Two-phase zone
T 5 104 K is divided into two sections: a gas behavior range limited by the curve
of equilibrium and a gas-liquid transition range. ~he condensation boundary separ-
ating them is experimentally known in a limited temperature range (T < 2,500 K),
due to which the results of approximate extrapolation are used in practical calcu-
lations related to higher temperatures [23, 25]. The validity of this extrapola-
tion in the case of uranium is especially needed in substantiation and experimental
check since, as can be seen from Figure 1.14, the high-temperature part of the
curve of equilibrium is located in the range of a strongly imperfect plasma, which
according to existing concepts, may lead to violation of the known enipirical rules
which are the basis of the extrapolation indicated above,
1.2. Asymptotic 14ethods of Describing the Thermodynamics of a Weakly Imperfect
Plasma
Unlike ordinary gases, the forces of interaction between particles are long-range
- in a plasma, due to which the effects related to interaction may be significant at
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(1) (3)
� ~+d ~~~?/~Ms
~n~xyr~j.�mn oAnncnr~,
(2)
r'2 f0-f
~
,
z%~~. 8
/ ~ ~ 1 6
~
io1a r-t 4
a ~
6
s
i ~ P.
, \ Mnu
! f0-r
20
6
1lr~y
f0 .s
rn .t (4)
s s R io 20 Jo r,lo~c
Figure 1.14. p-T-Diagram of Uranium. Solid lines--calculation by method aE
section 1.6; dashed lines--calculation using fewer known levels
([105]) and with regard to imperfection according to (1.24-1.30,
1.33); dash-dot line--calculation from [106]; the wavy lines
denote passage through secondary and tertiary ionization (I--
- xU++/xU+ = 0.5; iz--xU+++/xU++ = o.s)
Key:
1. Nuclei/cm3 3� g/cm3
2. Two-phase zone 4. Gas
low temperatures (T - 104 K) even at charged particle concentrations of n� 1018
cm'3. Moreover, quantum-mechanics effects are manifested in an imperfect plasma:
- first, effects of electron generation may occur and second, when the particles in-
teracting by coulomb's law are at short distances, their relative motion should be
described quantum mechanically rather than by using laws of classical mechanics.
The degree of imperfection and quantum effects in a two-component plasma can be
characterized by two independent dimensionless parameters
Y _ ezlL�'n A,xj~ (1.3)
where E is some mean energy, n-1/3 is the average distance between particles,
nS (lnt~z/k7' irie)~/' is the average de Broglie wavelength of the electron and xD is the
_.....c uepye radius (1.1). A set of these parameters, dependent on the particle
mass and the sizes of the charges, occurs in a multicomponeiit plasma.
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pV
RI
0,9
0,8
0,7
UU0 \
_ rson .
0,6 1
0,5 1
/
p,4
rv
o,j o
2000-
1 2030
~
~
~
~
1
1
1
1
5 ~ f0
15 � p,Mllu
Figure 1.15. Equation of State of Cesiun Vapors in Low-Temperature Range:
- I--smooth approxi.mation of experimental results [20]; I7--
, generalized equation of state for nonmetals [21, 221 ("Obert
and Nelscn diagram"); III--calculation by method of section
1.6; IV--�Cs condensation boundary
If the temperature is high, then E~ kT and condition y� 1 can be written in the
form n1/3 � kT/e2. Assuming, for example, that T x 104 K, we find that this con-
= dition is fulfilled at concentrations less than 1020 cm 3. At low temperatures
n~ /2rtr� (pF - ra (3n2ij)' is the Fermi pulse ) and the condition y� 1 reduces to
the tollowing:
lt'/.� 2 (I/3n2)'/-ni,.e'/1i'� '
It is fulfilled at electron concentrations greater than 1023 cm-3.
If k7' < Ry (Ry - ntPr'/lta2), then conditions are initially achieved with an increase of
plasma density when Y� 1 then Ae'Xp z 1 and the electrons are then degenerate.
One can consider the thermodynamics of a weakly imperfect, strongly imperfect non-
degenerate and then degenerate plasma according ta this sequence. The inverse
pattern is observed with an increase of density at kT � Ry: the plasma is initial-
ly degenerate and coulomb interaction then becomes significant. Provided that
Ry/kT � 1, the particle motion is quasi-classical. However, bound states may make
an appreciable contribution to the thermodynamic functions. In the inverse limit-
ing case Ry/kT � 1(the Born case), the interaction between particles is consider-
ably quantum in nature and can be described by means of perturbation theory.
The degree of electron degeneration is described by the known parameter rAe. If
nA3 � 1, then degeneration can be disregarded. 4?e note that if parameters (1.3)
are taken as independent, then Ry/kT and n/le will be functions of them:
16
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- .

- 1 �.TOOU K ~
~ - - _
~
.
2000
. \ . _ i _
.
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Ily/k7'. 4nzy'/(nPxj))a; lil1~ (Aexl,)3/(h7[y)'/' (1.4)
Let us consider the thermodynamic properties of a plasma with charged particle con-
centrations up to 1020 cm-3 at comparatively l.ow temperatures (approximately 104-
105 K). Under these conditions the parameter of degeneration nAe will be small and
the plasma can be regarded as Boltzman. Pareuneters (1.3) may be less or on the
_ order of unity, however the first of them (where one should assume E- kT) plays
the main role since it achieves values of approxiuia!:el.y 1 more quicicly with an in-
crease of charged particle density [9l. Moreover, since the first of parameters
(1.4) can be greater than unity, the contribution from bound states must be taken
into account. The existing results in equilibrium theory of this plasma lead to
an expression for the coulomb part of the thermodynamic potential ASt in the form
of an expansinn by the value t - A--' exp (la/kl) 126--3151
AS21kTV -At". + pL2 ln CV -1- Dt'/' liI t Et"., (1.5)
where V is the vol �me of the system, u is the chemical potential of the particle
and A, B, C, D and B are the coefficients of expansion by value ~ dependent on l.em-
perature. The two first and the foiirth terms of this expansion describe the con-
tribution from the continuous spectrum to A52. The third and fifth terms cantain
the contribution from the discontinuous spectrum. Strictly speaking, this contri-
bution was calculated for a hydrogen plasma. However, the results may also be'
applicable for two-component systems where hydrogen-like ions are present. More-
_ over, there is an approximate method [36] that permits application of formula
(1.5) by using the chemical model to calculate a multicomponent plasma where nuclei
or hydrogen-like ions with charges of different multiples are present and multi-
- electron bound states may occur.
Formula (1.5) was found on the basis of the quantum-statistical approach where the
method of Green functions and the diagram technique were used. There is now an
extensive literature on this problem [37-39]. The quantum-statistical approach was
first used in Vedenov and Larkin's investigations [26, 27] to determine the thermo-
= dynamic functions of a plasma. Let us dwell below on the main results found within
- the indicated formalism.
It is convenient to use the large Gibbs statistical group, where the thermodynamic
_ potential 0 is a functicn of variables T, U, and V to construct the complete
the�-modynamics of a system of many particles in quantum mechanics. The expression
- for the value of SZ, where the coulomb part AS2 is contained in the form of (1.5),
was found in [29, 35]. Formulas for a two-component plasma have the simplest fozm.
Since these formulas are required for further considerations, let us write them:
- Q1k7'V = p/k7' & -I- T 0 -I- fv) -
n e~ ' n 1-~- I n 2 n t� Y(1. 6)
4 n' ( kT 4 j/2 ( kT
' -F- 2 exp (!/kT - rqi); ~
j 3 r - 4 1'' ~2C In 4C - 35 \ _ 9 r3; (1.7)
y ~ 8 { 9 12 j 44
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~
gn eXP L'n/k7) wr'1[(1-F%)lkT l: (1.8)
n
- ~Q Q ~ gn exp E.10) o)ns) - E.)/kTI; (1.9)
in)
- 1' _ e' (k7,-i ~v i~ fU HD = AJi ~J1T~-~ /blZ~ -I' b.~ e'� (1.10)
_ The following functions are contained in expressions (1.8) and (1.9) in the sums
for the discontinuous spectrum w,(,' ) (x) eap (-x) - x eap (-x) ~x = ~ kT
I �
allCl
W,~,2) (x) = i[ 1--- ex1) x)] - 5 xF ( I; I I/4; -x) - 3 x exp(-x),
3 21 7
- having the meaning of weight functions and which ensure the convergence of these
~ su:ns. The value of gn, which p'-ays the role of the statistical weight of an iso-
lated ion (gn = 2n2 for hydrogen, where n is the main quantum number), is intro-
- duced under the sign of the sum in expressions (1.8) and (1.9) to use formula (1.6)
not only for a hydrogen plasma. Formula (1.6) can be used in some approximation in
this form for calculation of a non-hydrogen plasma as well. In this case the ex-.
perimental or approximately calculated values must be taken for the energy levels.
i
The value F (1; b; -z) _(h - 1)~ e sx (d - x)b-Z dx at (b > I) is a hypergeometric degen-
erate function, I is the ionization potential, En is the excitation energy of an
isolated particle and C= 0.5772 is an Euler constant; the exchange corrections
were taken into account in (1.6) with accuracy up to terms approximately Ae o D
inclusively.
Zf the equations for charged particle concentrations are added to (1.6)
a kTV (a0lar-I)r.v ~a = l ~ e),
n
(1.12)
then we find t.he equation of state of a plasma in parametric form. The internal
energy U is found from the relation
1/ 1 l r1Sa 11 k7'V k7,V-(j1 ()T (l~ -L k7V I ~`~C
v L vZu ) T,V (1.13)
1 Ce a -t.e
We note that the number of ions and electrons determined from relation (1.3) char-
acterizes the total number of particles both free and bound into pairs in the con-
sidered physical model of a plasma. The chemical model is usually employed in
practice where the ions and electrons are regarded as free, and, moreover, there
is the concept of atoms whose number is determined as the sum of the numbers of
18
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,
bound ion-electron pairs. The question of how to go from the physical to the
chemical model of a plasma is discussed in [2, 32, 34, 361.
Let us describe the expressions for charged particle densities both for the in-
ternal energy ensuing from relations (1.12) and (1.13):
~
I n 2
2 1 2 ~ 32 ( l-}- 1 2 1 f A; n-I-
n, _ it, - (CI-I- Z.) ~
(1.14)
+ -2 C~Z.A:Q exP (//kT - � I ~pl :
j� 20 l~' ~Il 4 Ifi3 I~' i�a
- 2 i- -2 ( (i0 > -44
kTv - 2 G' f ( 1 I - ~ I' (1 3f n -I '~iv) - ~ (1 1- 1 -2' 2 ) Y,
x i-1- 1/k7' I I'Aexn -I- ~3kT
\ ~
2 ~~.n:(~ exli (I/kT� Pxi)
( -4
(r in Q i 9~ ~ - dT -1 4r, _ ~17 110)
d7 ~
(1.15)
(1.16)
If /1e*D 1 ir~teractions at short distances r- e2/?cT begin ico play
the determining role in a formation of the second, collective part of the shielding
could. It is known from study of a similar situation in simplified coulomb models
[41-43] that the charge-charge correlation function is no lor_ger described by the
simplest expression cf (1.18) as the imperfection increases. Additional terms of
type (1.18) with parameters dependent on the behavior of interaction potential at
short distances initially appeared in it and, beginning at some moment, it acquires
an oscillating nature. The shielding and interaction radii (1.18, 1.19) are al-
_ ready otherwise dependent on the thermodynam.ic parameters than the Debye radius
(1.1) in the range of strong imperfection (I' z 1).
In a single-component model the analytical approximati.ons developed to the present
time permit one, despite the absence of a small parameter, to describe rather ef-
fectively the range not only of weak, but of strong imperfection as well. However,
in the more complex case of a system with charges of different signs, for example,
in the model of charged solid spheres [44, 451 when the depth of the attraction
potential appreciably exceeds the value kT
tnin (Drj (r) < - k'/', (1.21)
A significant part of the charqes, combining into pairs, no longer participates in
- collective shielding. In this situation the met,hods suitable for a single-compon-
ent plasma become hardly effective. One of the procedures that permit one to take
this fallout into account qualitatively consists in additional introductian of a
new variety of composite neutral and charged particles. Mutually impermissible
- sections of the phase space appear for charges remai.ning in the discharge of free
charges at short dis'cances [46, 47]. This is necessary so as to exclude the physi-
cally identical states and can be taken into account by effective correction of the
coulomb potential at short distances [46, 481. It must be emphasized that, first,
this co rrection depends on the selected meth.od of separating the atoms and com-
posite ions and thus depends on the thermodynamic parameters. Second, this cor-
- rection is not paired, i.e., the interaction in a system of free charges ceases to
, be binary-additive. One can estimate the dimensions of the corresponding correc-
tion. Let, for example, states of the elec*ron-ion pair wzth binding energy ex-
ceeding the value kT be related tc the atomic charge. In this case the radius of
effective correction of the coulomb potential for free ions and electrons corre-
- sponds by an order of magnetude to the nimension of thE range where 4)kul(r) ! T,
Figure 2.7. Dependence oP Viscosity of Sodium on Temperature at p= 50 MPa
_ (dashed line--possible behavior of curve)
KZI(M:c)J
(1) 10"1 1 5U%
10-;
lO-s i 1111 111 1 , 1
4 s e 12 2o r, 103c
Figure 2.8. Dependence of Effective Diffusion Coefficient Dnn on Temperature
at Pressure of 10 MPa for Mixtures with Different Potassium
Content
Key:
1. kg/(m�s)
Let us estimate the electric field and space charge occurring due to the effect of
thermoelectric forces during motion of an inhomogeneous ionized medium in a gas-
phase nuclear reactor. The value of the ratio a;cr - 102 uV/K; a field E� 1 V/cm
occurs in the working w lume of the reactor at temperature gradients af approximate-
ly 104 K/cm and the heat and mass transfer in a gas-phase nuclear reactor by the
electric field must be taken into account because of this since the values of the
corresponding terms (approximately E*) in relations (2.7) and (2.8) are on the or-
der of terms approximately oT and aca. The value of the space charge found from
_ the Poisson equation (p* - DE) is low compared to the mean concentration of charqed
particles and consequently the dependence of the thermophysical properties of the
- plasma in a gas-phase nuclear reactor on z can be disregarded. An axial magnetic
- field, whose typical value of magnetic induction is 102 T, does not lead to any
- significant anisotropy in the transfer coefficients: the parameter is wt - B.e/m < 1
- since the electron collision frequency is v- 3�1013-1014 s-1.
2.2. The Ki.netic Theory of a Weakly Imperfect Plasma
- The working substance and the fissionable material are partially ionized at temper-
s atures of approximately 103-105 K and pressures of 10-1 to 102 MPa under the oper-
' ating conditions of a gas-phase reactor. It is Complicated to describe th.is system
69
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'Aa,
Bnvm
ios
.
AQ'J
f03
W
4 E B 12 20 T,
Figure 2.9. Dependence of Effective Coefficient of Thermal Conductivity an
of Potassium and Hydrogen Mixture (10 percent potassium) on
Temperature Along Isobars
Key:
- 1. w/m
_A .

Hin/iM�10
10l
f0�
f0-'
4 6 B 12 20 T, f0'K
Figure 2.10. Dependence of Effective Coefficient of Thermal Conductivity
- of Potassium and Hydrogen Mixture on Temperature at Pressure
_ of 50 MPa
Key:
1. W/(m�K)
kirietically. The energy thresholds of the different types of transformations (ion-
ization, dissociation and excitation) are comparable to the thermal energy of par-
ticles; therefore, a large number of inelastic processes that affect the transfer
coefficients occur in the plasma. Thus, calculation of the transfer coefficients
of a real plasma may be only model in nature, based on the theory of simpler sys-
tems. One of them is a system of charged structureless particlesJ therefore, let
us initially consider the kinetic theory and types of collision integrals of a
_ completely ionized plasma. Let us then discuss the coll;sion integrals in a multi-
variety particle system raith internal structure and also the effect of excited
particles and inelastic collisions on the transfer coefficients.
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Key :
1.
. 2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Figure 2.11. Diagram of Findinq Kinetic Coefficients of Gases and Plasmas
Lieuville control
BBGKI chain
VKk' method
Approximation of pair collisions
Polarization approximation
Control for VKF
Methods of molecular dynamics
Boltsman KU
Klimontovich KU
Lenard-Balescu KU
Leriard-Balescu KU of imperfect plasraa
Landau KU
(Klimontovich)
Landau KU of imperfe::t plasma (Klimontovich)
Transfer coefficients
The literature devoted to different problems of the kinetic theory of structureless
particle systems with short- or long-acting potentials is rather extensive (see,
for example [9-161); therefore, let us limit ourselves here mainly to enumeration
of the results. The sequential stages of calculating the kinetic coefficients in
~ gases and a plasma are shown schematically in Figure 2.11. The initial point of
- kinetic theory is the Lieuville equation, which on the one hand, as a result of
sequential integration by coordinates and pulses of particles, leads to the chain
of BBGKI equations (Bogolyubov, Born, Green, Kirkwood and Ivon) and on the other
yields formal expressions for the transfer coefficisnts by time correlation func-
tions (VItF) (see section 2.3) for a similar discussion of the latter method).
The chain of equations for s-partial distribution functions is
ja lls J f NljXai., ...dCN1 (2.12)
r
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where V is the volume of the system and xk =(rk, pk) is the coordinate of the
particle in the phase space of coordinates and pulses having the form.:
N- (0) Y U,I j, --v-.s S0,,..j_jf,+jdxS+r (2.13)
1 v~
Here eP = p2/2m. Calculatir:. .,f the elect,s.c conductivity of a low-temperature
plasma [58] in staircase .pprnxii;;ition, which takes into account the multiple
charged particle interactions, yie'Lds a result coinciding in accuracy with the
approximation of [20] and correspor..ling to the coulomb logarithm.
The method of Green functions was used in [59] to calculate the corrections to the
electric conductivity of a Lorentz gas and the corresponding diagram tect.tnique was
developed in [60].
The effects of nongair scattering when the electron wavelength Ae and the scatter-
ing amplitude lrq (q is the scattering cross-section) are comparable to the distance
. between scatterers N-1/3, were taken into account in [59]. Expansion of the colli-
sion frequency was found with respect to parameter NAeq as a result
v,,/f v( I-1- a,t u,t' -1- ayLa In t).
2,4. Model Approaches to L',etermi_nation of Electron Transfer Coefficients of an
Imperfect Plasma
The kinetic theory of gases, valid in the limiting case of locally strong potentials
at na3 � 1(a is the radius of rotential action), and of a plasma for integrally
weak potentials (1' � 1) was developed in section 2.2. The state of inethods of cal-
culating transfer coefficients expressed by timP correlation functions was analyzed
in sectior: 2.3. E'or systems with weak interparticle interaction, both approaches
- `.o determination of the transfer prorcrzies are equivalent but in individual cases,
-1
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following the second approach, one can calculate analytically or niunerically the
transfer coefficients fu.- systems with strong interartion. The latter is possible
for a weakly ionized plasma, sing le- component plasma and dense neutral systems
[51-56]. Strict methods cannot be used to calculate the transfer coefficients of
a multicomponent, cl:emically reacting, imperfect plasma. Therefore, the electron
- properties of transfer of an imperfect completely, partially and weakly ionized
- plasma are considered in the given section on the basis of model concepts and the
transfer progerties determined by heavy particles are considered in the next
section.
The chemical model, according to which a plasma consists of a specific number of
components: free electrons, ions, atoms, molecules and so on, is usually employed
to calculate the transfer properties of an imperfect plasma. Let us analyze the
influence of different effects on the electron transfer coefficients of a partially
' ionized plasma with strong coulomb interaction--electric conductivity and thermal
ENg', using Frost foxmulas (2.97) which should be regarded as model with respect to
an imperfect plasma. The collision frequency of elect rons and heavy scatterers is
1 9
v~. - v ~ Qen~ (U) 11n _1- (Z,) n, u3 ( n~ L (2.67)
e
Here L(t) is the coulomb logarithm that describes collective effects in a plasma
and Y6,a are the correcting factors (section 2.6). Comparison of data on electric
conductivity, calculated with respect to (2.97) and (2.67) and on the adopted
version of composition (section 1.7) (L(1') = ln[1 +(3 X2/I')2]) to the experi-
mental results if [61-63] shows an excess of theory over experin,ent. It is diffi-
cult to achieve agreement by varying L(1') but since the given procedure has no
definite physical meaning, main attention should be devoted to the contribution
of non-coulomb effects (to electron scattering on excited atoms, to inelastic elec-
y~ tron collisions, to "the finite dimensions" of ions and so on) to crllision fre-
quency. Manifestation of non-coulomb effects distinguishes electron transfer in
an imperfect plasma and is unrelated directly to the long-acting nature of coulamb
forces.
The partially ionized imperfect plasma has a temperature of 1-3 eV in the experi-
ments of (61-631. If the material of the plasma has low ionization potential (for
example, an alkali metal), then a significant ::raction of the neutral atoms in the
plasma is excited. The result of ineasuring thc electron scattering cross-section
on a sodium atom in the first excited state (3 p) is known for electron energy of
4 eV (64]: a cross-section of e- 3 s is less than that of 3- 3 p by a factor of
2-3. Such a considerable difference indicates Y.he need to modify expression (2.67)
for a partially ionized plasma of alkali metals:
- Ye p nn I bf o QeP E'XO EAT). (2.68)
Qn i
Here Qn is the statsum of a neur.ral atom and Qe1~ is the transport cross-section
of elastic electron scattering on an atom in the i-th excited state, the energy
and statistical weight of which is Ei, gi. The fraction of excited atoms is
negligible and their effect on the length of the free path of electrons should be
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disregarded in a partially ionized plasma of inert gases at temperatures of 1-3
eV. Let us investigate in more detail the effect of electron scattering by excited
atoms on the collision frequency on the example of a partially ionized cesium and
litihium plasma. Elastic scattering of electrons in the 6 s, 6 p and 5 d states of
the cesium atom (the energy of these states is 0, 1.4 and 1.8 eV, respectively) and
scattsring in 2 s and 2 p states of lithium (energy of 0 and 1.8 eV) for a lithium
plasma should be taken into account in the temperature range of 1-3 eV when calcu-
lating the electron transfer properties for a partially ionized cesium plasma. The
electron scattering cross sections on excited lithium and cesium atoms were calcu-
lated in Born and Glauber approximations in [65]. The basis for using the indi-
cated approximations is good agreement of calculated and experimental data on
elastic scattering of electrons with energy > 1 eV on lithium, sodium and potassium
atoms in the ground state [66]. The exchange interaction of impinging and valency
electrons and the orbital polarization of the latter are disregarded in Glauber
approximation. Estimates show that these simplifications are valid for E> 1 eV.
Assuming that the atom of an alkali metal consists of a base with charge +le and a
valency electron, let us write the electron scattering amplitude on the atom (-Fnlm)
in Glauber approximation (in atomic units):
2 [ 1, (b, r) u,,n~ (r) e"b d2 G(ir;
Fnnt - ,1
l' (b, r) 1- exp s) J;
~
x (b, S) V (b, r, t) dt;
-m
V ~ - ~
(2.69)
unlm is the wave function of the valency electron, v and k are the velocity and
wave vector of the scattered electron, q= 2k sin 6/ 2, 0 is the scattering angle
and n, 1 and m are the quantum numbers. Expression (2.69) is written in a coordin-
ate system whose origin is located in the nucleus of the atom, z k, and r, r�' are
the radius vectors of the atomic and scattered electrons. Let us expand them:
r= s+ z and r' = b+~, where s and b are projections of r and r' onto the xy-
plane. The wave functions of the valency electron calculated by the Hartree-Fock
method (see section 1.4) were used when calculating the e cross-sections of lithium
and cesium. If the square of the radial part of the wave function is represented
in the form
~~r
2 nini ct f 21 }-I - L~ r
RI
x u, r e
r--i
then equalities (2.69) can be simplified since for Fn00 We have
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i" -
~ "0/ 12,-" , vc, - !~e (9. X)
Fnuu ~ ~ 4 a! (A r 1 '
la_=yno
!
n/2
jo c~,, X> s91�k 1' do o~~~_ _~q= ~.~g~ u, x
5ill o (X' + a= C(g2 0)4
0
s,t
X ~ / L \ 2 Irt j d~U ( l- sin 2t3 cos (p)Irl
/ 1
2n ~ cos U j '
1
(2.7o)
Here ci is natural numbers, n= 1/v and Fnlm for 1, mgi 0 are represented similar
to (2.70) [65]. The total and transport elastic scattering cross-sections are
calculated in the standard tarnner by the scattering amplitude [48). 'The results
of calculating the total Qnlm and transport Qrl~lm elastic scattering cross-sections
of electrons by Born and Glauber methods in the energy range of 1-10 eV on cesiun
and lithium atoms in the ground and excited states are illustrated in Figures 2.12
and 2.13, from which it is obvious that the elastic scattering cross-sections in
the ground state is one-half to one-third those in the excited states. The iso-
therms of electric conductivity (Figures 2.14 and 2.15) were calculated with re-
gard to this effect [65].
Q
0 2 4 6 B E,sB(1)
Figure 2.12. Elastic Scattering Cross-Sections of Electrons in 2 s and 2 p
States of Lithium Atom: 1 and 4--Born method; 2 and 3--
Glauber method
Key :
1. Electron volts
The next non-coulomb effect which influences the transfer coefficients of the
plasma is the difference of the electron and ion i.nteraction potential (ve1) at
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Q~"nn z
~ o
2
io3
S
z
in?
5
2
n
FOR OFFICIAL USE ONLY
~
Figure 2.13. Elastic Scattering Cross-Sections of Electrons in 6s, 6p
and 5d States of Cesimn Atomz (the Born method)
Key:
1. Electron volts
- short distances from the ion nucleus from the law zie2/r. Thus, the typical dimen-
sions of ion cores of heavy cesium and xenon ions comprise approximately 5 ap,
- which is comparable to the shielding radius of charges in a pZasma. The effect of
a finite dimension of an ion on the electron collision frequency was taken into
account in [671 by the quantum defect method [68], which is based on the analogy
of motion of a slow free electron and a weakly bound electron in the field of an
_ ion core. The radial part of the wave function of a free electron with pulse k and
orbital moment 1 has asymptotic form (r upon scattering on an ian with charge
zie [48l :
siii kr In kr - l-f- arg I'
k )
( I l-~kt Yi(2.71)
\
where Yr litn nA 'n (A,)) k!' 11
,
A,0
Here the quantum defect 0= n- n', n is the main quantum number of state, the
_ binding energy of the electron in whicki is equal to (2n'2)-1. Correction to the
transport coulomb cross-section, determined by the quantum defect method, comprises
C671 approximately 25 A2 for cesium and xenon ioris at electron energies of 1.5-2
eV. Rest=ictions of the quaatum defect method include the following: relation
_ (2.71) is valid at E-~- 0 and the potential ve1 is coulomb far from the ion nucleus.
'I`he effect of a finite dimension of a cesium ion was considered for QM in [69] by
_ the simplified model: Born approximation was used, the potential ve1 at short dis-
- tances frcim the ion nucleus was approximated by the exponential potential and in
this case AQU) - 50 A2 was found at e- 2 eV.
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,lUi
rt,iM I - -
isa
1.01(
� 18200
i00 � i 1 /5000
rlUU00
9 00 I oB00 . ~
60 - 9:00 9000
/0000~
- '
0 f0 20 S/l . %~0 p,tttlct
_ F.igure 2.14. Comparison of Calculated and Measured Values of Electric
Conductivity of Cesium Plasma Along Isotherms (experimental
- points are data of (611)
~t,1L~` - . . _
CM IN,
~ 'T -
r~n
100

~b~~d
o---~o-
12500 .':0
2o . 10 /jo p,rJnu
Figure 2.15.
Isotherms of Electric Conductivity of Lithium Plasma Without
Regard (upper curve) and With Regard to Scattering on Excited
Atoms
Description oi a two-particle electron scattering process on an ion, free of the
deficiencies of the quantum defect and model method [69J, is possible on the basis
- of the phase function method [70] which petznits accurate calculation of the parti-
-I cle sca*_tering phase during its motion in a yiven potential. Let us write the
equation for the scattering phase dl(r):
11
dr -k UC, (r) Icos 6i (r) ji (kr) sin 61 (r) it r (kr) I 6i (0) = 0.
In this equation jl(x) and nl(x) are the known Riccati-Bessel functions [70] and
the asymptotic expression for the radial part of the wave function is determined
by the scattering phase
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The use of the phase function method requires that the short-range Part vei(r)
be given accurately and the long-raage par*_ of ve1(r), according to model concepts,
should be selected in the form of the Debye potential. Consideration of the "fin-
ite" dimension of ions leads to a reduction of the calculated values of electron
transfer coefficients and is manifested more strongly, the greater the degree of
ionization and imperfection of the plasma.
Let us discuss the effect of inelastic electron collisions such as excitation and
ionization of atoms by an electron impact on the collision frequency of electrons
with heavy scatterers. Data on the excitation and ionization cross-sections of
alkali atoms by electron impact, presented in the literature, permit one to con-
clude that the excitation cross-sections at corresponding energies of the imping-
ing electron are c.omparable in value to elastic cross-sections of electron scatter-
ing on atoms in the ground state [64]. Thus, because of the high population of
excited levels of neutral atoms in a partially ionized imperfect plasma of alkali
m2tals under conditions of [61-63], the indicated inelastic process appreciably
increases the electron collision frequency and accordingly reduces the transfer
coefficients. Variation of collision frequencies, based on physical concepts [71],
will be described by addition if a term of the following form to ve
v. vI Q. (U) no ( 2. 7 2;
u
where Qed is the excitation cross-section of a neutral of vaL-iety a(the atom in
different exc;ited states belongs to different varieties here) and na is the concen-
tratian of neutrals of variety a.
The next effect of significance in a fully or partially ionized perfect plasma is
the correlation of particles on which electron scattering occurs. Z'he contribution
of correlation degends on the degree of orderedness of the scatterers. In the lim-
iting case when the scatterers are fuliy ordered, as occurs in metal, the electron
- is scattered simultaneously on the entire chain of atoms; therefore (due to inter-
ference), the length of the electron path increases sharply. The high electric
_ conductivity of inetals both in the solid and molten states is naturally explained
_ by this effect. There is partial order in a dense gaS or plasma and inter�erence
effects should lead to an increase of the length of electron flight and according-
- ly to an increase of plasma conductivity. The effects of correlation are taken
into account by the Ziman formula for the collisiori frequency of an electron [78]
- with other particles
I 2kniex
v` ~vn , 4k f Q(" (k) u(k) k9 d k,
u
(2.73)
where the structural factor a(k) is determined by the equilibrium correlation
function of ions gii(r) [721:
u(Ir) = 1-f- 4nn si~ kr (g, , (r) - I J i2rlr.
J
(2,74)
Calculation of the effect of correlation on the coulomb logar.ithm with nonlinear
~ '
- Debye correlation function [72] b`i+ (r) = Lxp - e exp(xr)I
the coulomb logarithm (see Figure 2.16).
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yields a correction to
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When calculating the electron transfer coefficients of a partially ionized imper-
- fect plasma, determination of composition [73], different from thp traditional
composition (section 1.7), is used. The composition of the plasma used in [73]
to calculate the electric conductivity of a plasma of inert gases, is based on
specific division of the energy spectrur.i of electrons in the plasma. The energy
spectrum [73] was found on the basis of the classical expression for the density
of electron states calculated in the "close neighbor" approximation, when electron
interaction with its surroundings is replaced by inY,eraction with the nearest ion,
while interaction witti remaining particles, as weaker interac�ior_, is taken into
account by methods of perturbation theory. The "atoms"--electron-ion states with
high negati -m energy ( kT) are determined in the electran energy spectrum, and elec-
tron scattering on them is considered as that on a single particle. The excited
atoms (VA) are states with energy from -kT to ez/rsr; tsr is the average dystance
between piasma particles, quasi-bound states (KS) are formations with enzrgy froro
-e2/i�Sr to zero and collision complexes (SK) are elect:ron-ion pairs with positive
energy. Scattering of free electrons excited atoms, quasi-bound states and colli-
sion complexes is equivalent to scattering on a coulomb center. Besides free elec-
trons, charge transfer in a partially ionized plasma is accomplished, according to
[73], by electrons bound in quasi-bound states and collision complexes by means of
' the collision mechanism. Collision transfer occurs due to the fact that the motion
oF electrons in the quasi-bound states and collision complexes, w3iich accordingly
occurs along segments of elliptical and hyperbolic orbits, is intinite since the
- nearest ion is replaced during electron motion. In a weakly imperfect plasma the
main contribution to charge transfer is made by free electrons and in an imperfect
plasma by electrons belonging to quasi-bound states and collision complexes. The
disadvantages of the described approach should include some arbitrariness in selec-
tion of the mechanisms of electron scattering on excited atoms, quasi-bound states
and collision complexes; therefore, agreement of the model to experimental data
_ in electron conductivity of a weakly imperfect and partially ionized imperfect
plasma of different materials [73] is conclitional.
lsin,
- Figure 2.16. Effect of Ion Correlation on Coulomb Cor.:ponent of Electric
_ Conductivity of Plasma
The concept of the composition of a partially ionized imperfect plasana, as can be
clearly seen from the previous discussion, is not the only one. For electron
transfer in a partially ionized plasma of inert gases in the range of parameters
considered in the given section, electron scattering on excited atoms and inelas-
tic collisions with p?asma particles are insignificant and consequently in this
- case a model that does not use the concept of plasma composition can be formulated.
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Let us describe one of the possib'.e single-electron models of this type, based on
concepts of quasi-classical theory of a continual course [74]. Let u, assume that
a plasma consists of electrons and ions. According to the continual course theory
(TKP), the electron moves in "au':horized" paths in a random, effective potential
V(r) created by fluctuations of_ ion density; the fluctuations of V(r) are not de-
N
pendent on the presence of a:i electron at a given point V(r)___ ~ v,.j (r - Ru)�
a_i
Here R. is the radius vector of 'che ion and summation i.s carried out ror all ions,
and ve1 is the electrr~n-ion interaction potential.
According to TKP, the
tron energy remaining
space is divided into
space (we denote it b
tential distribution
authorized paths satisfy the condition V< E(E is the elec-
during motion of the constant). For any energy E, the entire
authorized azid forbidden, the fraction of the authorized
t
y c(E) ) is equal to I . F(V) dV , F(v) is the po-
_ c,
function and by definition [74):
F ~N `i11t, . . .dRnr1Y/ (R, . . .RN) 8(V - V
J
W is the probability of a given ion configuration in a random potential and 0 is
the volume of the system. F(V) has a Gaussian form provided that in the sphere of
influence of potential ve1 there are sufficiently many ions and W= 1:
r dr.
-i c ~ )
(V) - n-~~'a� exp V'/av~~ o~ 2ni f V2
The main contribution to F(V) is made by ion fluctuations in a sphere with effec-
tive radius rp; therefore, the c4ndition that the electron moves in V(r) like a
e9 hz
m~ . In
classical particle is the inequality av n'/' 2 , where 1= nir~
o s o
the left side of the inequality is the depth of the typical potential hole and in
the right side is the energy of the ground state of the electron with respect to
the bottom of the hole. It is qualitatively clear that there is some energy Ec,
beginning with which at least one authorized path penetrates the entire system of
- scatterers, i.e., electrons with E> Ec contribute to electric conductivity and
those with E"' Ec are localized. Determination of Ec and c(Ec) in the given ran-
- dom potential is one of the purposes of TKP. Another inportant value is the per-
colation probability P(E), determined as the conditional probability that the
point belongs to an unrestricted path if it is in an authorized sFace. At E< Ec,
P(E) = 0 and P(E) rapidly approaches unity at E> Ec; therefore, it is usually
- sufficient to assume that P(E) = 8(E - EC). It was established in [75] that
c(Ec) = 0.17 (i.e., Ec _-0.68 Qv) for F(V) in Gaussian form and is not dependent
on the form of vei(r) and it is necessary only that sufficiently many ions be lo-
cated in the effective sphere of a two-particle potential.
Let us determine the electric conductivity of the plasma, following simple
concepts:
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_ W
? I exp (P�r) I T (E) P (E) exP (-Flk7) EcIF. ~
3 �n~ k%' .2.75)
c
y Here p(E) is. single-electron density of states, T(E) is the time of the free path
ecxual to 1/v (v is electron velocity) [74]
E
I 2
't !1l
(E) c (E) SdV mt (E -1~-'/. f + ~ :
_,0
' 1 is the ordinary gas-kinetic length of the path--1/niQei~(E ' V), Qe1~ can be cal-
culated by the phase function method and one can easily take into aacount the ef-
fect of the finite dimensions of ions,Xdescribes scattering from the edges of
authorized paths, a - - when E The analysis a (E) : a - rCc (E) [1 - c (E) ]'1 was
made in [74]. Un3er the conditions considered in thQ given section, 1-X at E< 0.
The single-electron density of states p(E) is determined in quasi-classical approx-
imation in the following manner [74]:
1l(E) ~ (1n,'he, I s I E V (l)1'1. W (R1 . . .RN)(j1tl . . .ll~t/y.
saN
The density of states was calculated provided that W= 1 and n>j/n > 1 [751:
(E) J 2\ 1. ( 2nh2 ) l~ Qu11 eXP E12Qu) 0-'12 ( v2 F
ao
l ) ~ ~ l
where D_3/2(x) is tlle function of a parabolic cylinder.
of a non-Debye completely ionized plasma was calculated
to (2.75). In this case Ec in (2.75) was assumed equal
to the length of the free path related to reflection of
of authorized zones was not taken into account; neverth,
are in satisfactory agreement with experimental results
The'electric conductivity
in [76] by a model similar
to zero and thc correction
electrons from the edges
aless the results of (76]
in the range I' < 0.3.
We note that the Poisson distribution function for F(V) and the corresponding
variables p(E) and Ec should be used in some cases (when the condition n� 1 is
violated) for an imperfect plasma instead of the Gaussian distribution function
of potential and the density of states and the value Ec corresponding to it.
In concluding the given section, let us briefly discuss the existing concepts of
electron transfer in vapors of inetals at subcritical pressures and near-critical
densities. The indicated range, let us call it the ttansition range, is character-
ized by qualitative variation of the electron properties of inetals upon variation
of density near the critical range. Experimental investigations of the transition
zone were conducted on mercury [77-80] and.cesium [7, 81-831. It is shown that
variation of electron properties and metal-dielectric transition occur rather
smoothly in mercury while a Mott type transition probably occurs in cesium [84].
The transition zone is roughly divided by density into two zones si.milar in prop-
erties to a metal and to a plasma--the gaseous zone. Model determination of the
98
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interface of these zones in cesium vapors was conducted in [84] and in this case
the experimental data of [81-83] were used. The subStance is a dense plasma in
the gaseous zone. The use of precise approaches to describe its properties is dif-
ficult since interaction be::ween the plasma components is strong. Minimum values
of conductivity of inetal vapors on the subcritical isobar are apparently achieved
in the gaseous zone. The models [85-87] are essentially oriented toward a part of
tne gaseous zone sufficiently remote f.rom the critical point (O.lpkr < p< 0.4pkr)
with low degree of ionization, where neutral interaction has the main effect on
the thermodynamic properties of the plasma. Interaction of charged particles with
neutral particles and between each other under these conditions without affecting
the thermodynamic characteristics of the meditun, significantly snifts the ioniza-
tion equilibrium, i.e., it is reflected in the properties of the elecrron tr�nsfer
in the plasma. Separation of electrons into free electrons, i.e., those partici-
pating in the transport mechanism of charge transfer and localized electrons, is
carried out by different methods in the models of [85-87]. In [85] the localized
electrons are des,�ribed by "fluctuations"--formations occurring due to localization
of electrons on Fluctuations of density;localization is interpreted in the sense
of (2.75) in [87]. Selection between the indicated approaches cannot be made due
to the paucity of experimental data.
2.5. Effective Transfer Ccafficients of a Multicomponent Imperfect Plasma
When designing devices in which the working substance is in the plasma state, one
must solve the problem of h,,~at shielding of the surfaces touching the plasma. The
thermal fluxes generated by the plasma are determined by the profiles of co:nponent
concentrations in the plasma space. Consequently, when investigating heat trans-
fer of a multicomponent plasma with restricting surfaces in a gas-phase nuclear
reactor, in tne cYiannels of MFID generators and behind the shock wave trailing af-
ter a spacecraft during its motion at hypersonic velocity in the atmosphere ot a
- planet, correct consideration of multicomponent diffusion is important. In the
indicated cases the plasma should be consiflered as a cheMically equilibriiuti and
= quasi-neutral plasma, i.e., one should use LTR approximat:.on and turii from inves-
tigation of the diffusion of components to investigation of the diffusion of chem-
ical elements (see (2.8)). Diffusive heat transfer described b. effective coeffi-
cients of thermal conductivit,y in (2.7) has a significant effect on the convective
thermal flux and the gas-dynamic characteristics of plasma flow. The coefficients
of transport thermal conductivity (a') and shear viscosity (r1) are also required
to close the system of gas-dynamic equations (,2.1)-(2.5).
The definition ar_d general propertis of effective t.ransfer coefficients are dis-
~ cussed in the given section. A inodel is suggested far calculation of effective
- transfer coefficients, shear viscosity coefficients and transport thermal conduc-
tivity of an imperfect plasma, by means of which the tables of values of the trans-
fer coefficients of a plasma of alkali metals, uranium and tneir mixtures were
calculated over a broad range of paramaters (see Chapter 5).
Formal determination of effective transfer coefficients of i.mperfect media by
phenomenological coefficients and investigation from general properties are pos-
sible by means of iinear thermodynamic3 0� irreversible processe by gradients
[88]. Effective transfer coPfficients can also be determined by time correlation
functions on the basis of une of the versions of the theory of nonequilibrium
99
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processes discussed in section 2.3. Let us use the first approach as the most il-
lustrative and one leading most rapidly to the goal. Let us formulate the ex-
pression for production of entropy (o) of a multicomponent imperfect plasma in LTR
approximation, i.e., with rpspect to chemical elements [21
1 Na av
/
a q07~ ~ E ia /~p " - zoE'1 - T ni! dx~ (2.76)
~
a-1
According to the second principle of thermodynamics Q> 0. Expression (2.76) was
found by the standard method [8E1, 21 when using the ohpnomenological laws of con-
serva*_ion ~n the form of (2.1) - (2.5) ,Iia _(du/ aea)p;,,cb4cu is the specific chemical
potential of the element a, u= u(p, s, {ca}, z). For transformation of (2.76) to
a more convenient form, let us substit.ute the Gibbs-Dyugem relation T0 (�.17) _
pIE~~- (hal7~ \7T and the symmetrical tsnsor of viscous stresses in the forni of
N
- (2.9) into the given expression and let us use the candition ~ ia = 0 , then
- 0-i
Nu- I
a-- ~~�q'VT--r ~ i�[VTm, (2.77)
a=i
_ I -(I lVv F H, _,T)
7'
ri'he chemical element "electrons" whose charge per u;iit mass is ze =-e%ne (the
remaining values of za are equal to zero) is determined in (2.77)s
If - 1/2 (vvi/[3xj -1- I/38,jpvY. q' = q - Elraia;
ha is the specific enthalpy of the chemical element. Let us rewrite (2.77):
U- jIXJ~ ~ , here ji is flu:ces and Xi is thermodynamic forces. Ths fluxes are
linear functions of thermodynamic fcrces: ji = aigXk and thuR:
Q= Z aikXhXi,
l.k
(2.78)
aik is the pLienomenological transfer coefficients of (2.78). The fluxes and ther.-
modynamic forces in (2.77) are linearly independent of each other and consequently
Q is a positively determined qsadratic form that satiisfies the Silverster criterion,
according to which all the major minors of the matrix compiled from phenomanologi-
cal coefficients are negative. Another property of aik is the symmetrical or anti-
syrmetrical nature with respect to subscripts i and k in an isotropic medium--On-
sager reciprocity relations [89]. The symmetrical nature of aik occurs in the
case if the parameters of state denoted by subscripts i and k are at the same time
even or odd functions of the velocities of all particlesj the antisymmetrical na-
ture occurs when parameters ji and Xk have different evenness [89]. The
100
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recipmcit%� relstions arcl zlso valid tor linearly dependent fluxes and thsrmo-
dynamic forces [881.
,he phenomenological transfer equations ji = aikxk generally link the fluxes and
T
thermodynamic forces of clifferent tensor dimensionality. However, if ji and Xk
have different tensor dimensionality, the Descartes components ji and Xk are trans-
formed differently during transformations of rotation and reflection of the coor-
dinate system. It may be that the fluxes will not be dependent on all the thermo-
dynamic forces due zo the properties of symmetry of the considered system. The
given sta*_ement is called the Curie principle [88]. The values of ji and Xk of
different tensor dimensionality are unrelated to each other in an isotropic medium.
The result of the isotropic nature of the medium is that the values of aik are
scalar; moreover, proc.;iction of entropy in the form of [2.77] can be divided into
_ three terms--scalar 6p, vector Q1 and tensor Q2, each of which is negative. In an
- isotropic medium for mass flow of a chemical element and q', we have:
N,1 f ( e
' q' a~ TT O T ~Ila E*
1.
yj l
~-i
Na "1 .
V t e T2 Ta'ub OT E'`
6=1
(2.79)
It is obvious from the Onsager reciprocity relations and the positive_nature of
the vector term in production of entropy that 111,11=(1btj- (Iv4>O and
= aaa > 0; since aUQIT2=a� (see (2.11)), then a> 0 and the positive definition of
shear and volumetric viscosities follows from Q0, a2 >0.
Let us determir.e the effective diffusion coefficients and thermal conductivity of
a multicomponent i.mperfect plasma. Provided that the pressure in the plasma is
constant, let us express AT(Ua - un) by the gradients ca (let us disregard terms
of approximately oZ) and, having substituted the derived expregsion into (2.79),
we will have (I~~(1t� - 1~~)/~)l'e1j,.r.r b rc u --~~a)~
N,j. . 1
vaDvcb -1- UA pT - DaE*;
NQ- 1
l )uG - r aa/ Iib;
r-~
Na-1
!i t `I
l)� - m T L~ uae
~ 6-`l
In similar fashion for thermal flux:
101
ll T
dj
FOR OFFICIAL USE ONLY
aaQ �
7''
(2.80)
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N 1
- 0l X1)V 1'+ ~ k avCa - Xt:E*,
o-l
N 1
a - hJ 1)u ,
U(h
a=-1
N~-1 (2.81)
~1, ~ uTb j18 - (Il p Ilr~
- Dbol ~
a ~ ~ a
b-=1
NJ-1
OCQQ (ho - ~la~ Do ~ �
7'rn~
~ - 1 E 1
a-1
Formulas (2.80) and (2.81) are convenient when investigating the properties of
effective transfer coeff icients.
_ Let us consider the consequence of the positive nature of production of entropy a.
for a two-component mixture and let us introduce the notations ---;L � IT)aQa Iio, Xn=
~ - - (li�- /iJ U,,,,.7ta=A� then ~-X�Vra (the terms approximately E* are omitted for simplicity). After substituting q' and ia into the expression for
(2.77) and after simple transformations using the copdition of stability with re-
spect to diffusxon [88]: ua > 0, we find j1)�a > AaVo . It obviously follows
from (2.80) and (2.81) that jTp". ; thereforp,
ir) D,, > AaDa . (2.82)
One can also as.certain the property of having a fixed sign of the effective dif-
fusion coefficient: -Daa > 0; DW has no specifa.c value. The limiting relations
Da (T, p, ca) = 0) = Da (T P, ca = 1) = 0 are valid for the effectiive thermo-
diffusion coeffici.ent; the law of the approach of Da to zero at ca 0, 1 depends
on the composition of the mixture, temperature and pressure.
In the case of a mixture consisting of three or more chemical elements, clear re-
- lations between the effect of transfer coefficients from the condition al > 0 can-
not be found in general fo rm. For example, for a three-element plasma a symmetri-
' cal positively specific matrix with the elements /:11(~o =~i Db It~T corresponds
~ ta the vector term of production of entropy in the form of (2.77):
l>uu n Dba b, pbb b ~
n,~ -T~ ; f4l2 ._7, - Ita 'I- T It,,, f~y, _ T I1D ~
7� T T T
l)ob a ~~a a ')b b . ll� a L 1)b b
�
-7,- �b, ~ ~1a -,7. ILU f- I, i40~ A13 = �b _r' 1L6~ (2.83)
I ( D4jb o /)un a_ ~~G6 6 _ Uba bl
A2' 2 \ r ~~a Fis -T - ~ T �bl �
- Calculating the determinant or the major minors of matrix (2.83) and the thermo-
dynamics derivatives ua in some approximation, one can find the relations in the
form of inequal.ities between the effective diffusion coefficients and thernull
conductivity--a. Investigation of a matrix of type (2.83), corresponding to ol
102
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in the fonm of (2.76), and of the relationships between the effective diffusion
and thermal conductivity coefficients i-s apparently infeasible since the latter
are expressed by Dab, Da, Da, Ha and ua (compared (2.81) and (2.80)
- The Onsaqer reciprocity relations for phenomenological transfer coefficients also
placP speci_fic restrictians on the Pffective diffusion coefficients. The matrices
of phenomenological coefficients aab - a, ub '_u and D~ - D are obviously relateu~
to each other (see (2. 82 D= -au, a -DU 1; since a= a, then
(2.84)
I ! ,
Calculating the tY:ermodynamic derivatives i.n the matrix U and setting the corre-
sponding elements of the left and right sides of (2.84) equal to each other, one
can find the relations between the effective diffusion coefficients in the form of
equalities.
The thermodynamics of irreversible processes, linear in gradients, does not yield
a formula for calculation of transfer coefficients since it is phenomenological
- theory. The theory of nonequilibriiim processes (section 2.3) lir.ks the transfer
coefficients to the corresponding correlation functions, calculation of which is
difficult fer an imperfect plasma. Let us formulate the model approach to calcu-
lation of the effective transfer coefficients of a multielement imperfect plasma
[901, based on the chemical model of a plasma and used in calculation of the tables
- of values of effective coefficients given in Chapter 5. The mass fluxes of cherniczl
- elemem`.s are deternu ned by the mass fluxes of the plasma components (see (2,E))�
Let us introduce the expressions for the mass flux of a component and also of a
convective thermal flux which follow fi�om ti1c exF-r
tD ti
~p
M
~
4m
~
.
.
~
.
Q
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1
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+
cn
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+
+
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1
+
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+
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~
O~i ^
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M
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rn
1
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1
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+
+
1-
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g
.
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f
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t 7
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1~
tn
cn
N
t~Ap
p~
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,
.
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w m m M z'~.~' Z Z ;Z z d ~
\
316
FOR OFFICIAI. USE ONLY
d
tp
w
0)
r.
3
O
r-4
ri
W
O
b
~
4
C'.
U
~
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FOR OFFiCIAL USE OIVLV
a
Y
~
~
0
~
I o
0
I ~
u
I 0
O
O
O
~
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U
0
M
N
tn
N
pr-1
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E~
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I
I
I
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o

l4
+
0
+

+
1
C2,

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M
M
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r
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o
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m
h
.
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+

+

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+
q
+
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OMi
o
p~
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n
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Ci
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LA
t-:
Q1
,
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c
0
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.
.
I~
"9I"
1
1
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to
d.
a0
uA
N
tn
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00
t~
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M
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M
O)
OO
to
M
LV
to

1
a
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Gl
~
~
ui
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r-1
~
H
+ 1
1
+~+2 +i -
I
+
N
O)
c0 (7) tO ~
N l0 ~
cv"!a~o
v
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ry
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1~ ~f N
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O
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a
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r
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p
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C
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~ O~
ry
Q
I
0 Q
+ 1
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1
N
b g
~ M
+ + 7
q
7
4
1

~
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c0 O ~ P
01
N
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O
O M N
~ ~j ~
~
l0 Op LA
Qt~ a~pp
p
Qy'
~ ~S
~
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ry
Q
~
~ q Q
~ ~
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O O
+ 4'
O O O
'f' + +
M q M
y.
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O
to to
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`r N
~ fM-
l~] ~ j
n M~
~
p
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I

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o 0
.

C ~
N
co
~
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M GO
h ~
~ OI
+ +
 g
~
~
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I I
-

+
ry
~
o
o~ ~
~�t
~
~ 1 ~ 1 ~
~
o
-1-
!3 O
-f- +
N
q
QM
I ~
~
I
T
-1-
~ ~ ~ ~ ~
~
~ I ~ A D p
~ g 00 ~
g ry
~
~�y -In ~~f' ~Iyc,
u V V V V V G. ~N h~ Lr ~.1 .t b tl
.1
232
FOR OFFlCIAL USE ONLY
UI
C!
d
N
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B
~d
~i
0
N
N
E
a
N
b+
td
a
tn
13
3
0
~
~
W
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~
~
r-1 jJ
~ U
u
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o
o f
CC3

~
+
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+
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j-
n
O
14
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M
t
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0
0
O
ap

p N
o0
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a~
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U
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ui
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~
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o
0
4-
I 1
I
Cl

V' M
4- + +

M
o
C-1
N
t- tD
p
~j
tD O, O
~
N
~
QM M

Of
~A
0) tD ^
^ ~ ~
0
+
~
~

+
00
c,j
00
oD o0
N 6a
c+~
c00p
~n
~
~
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n
u~
~
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~
1N~
M
0e0~ 04
tp N
dp
0
t
0
~
OS
~
1
F
+
+
+
T
7
7
`
0
+
+
7

M
M
O O
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~~d'
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M M
M
e~

~
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b
o

1
1
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1 00 to
n 00
Oi O
~
a~0
n
~
~
N
~
cp
~
. .
.
. .
.
C'!
~
cla
cM`!
-4:
c�v
I l
~ C14 go o4D *D
~
N
t0 t0 er
~
N
7 I ~+M�
pp
N N~~t'+`p~ 00 ln 1D My1(f+~~ p~ QQ cM~ ~y~
M a0 M ~n ~ ~ O~ 'O O~ ~ p~ u~ t0 00
I I . I + I -1-a
u c'3 c'3 t'3 c'~ t'3 a.c -1~ F:~ c tl.i
233
FOR OFFICIAI, USE ONLY
a~
~
a
~
~
~
wl
O
~
~
~
a
S
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0
0
N
0
0
N
O
M
w
Y%
T O
u ~
a ~
cb
~
0
~
z~ -
a~
0
9
.r.,
~
0
U
u
~
~ p
v p
H
+
~
q
i

+
+
+
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+
j
rn
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0
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ry
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cli
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t~G
d'
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ti CV
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ry
n
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M
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I
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7
7
7
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T
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i
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-r 0)

OMi
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C'j OD
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t0
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.00
V~ M
M
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V)
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4
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4
f
 
.1 .r b tl1
249
FOR OFFICIAL USE ONLY
~
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w
G+
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3
O
rl
r-I
tH
O
~
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J
U
u
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~
ro
m
0
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~
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U
ui
ui
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H
+
-f- ~ I
F- 1 -1-
ti wp.r ~o 0eee~~o~ rn~
00 j
..y 0
o, ~ .
?
Ci Ci w
qq
u~~y
+ + + -o}-
N C
O ~ ~
+
~
~ ~ ~ ~
N
~ N
C'!
c
.
.
1
+ T -1- F-
I 1 ~
-1- ~
5~D~ 0 Np~
C~+.
op
~ f
" ~
t
~0 Ci $
V
~
~ 1 1 ~ 1 I
+ +
1 t ~
+ 7 . ~
.Ya ^ M c M ~0 ~ C ~ ~V M M
~ Op ~ p

~
M
t"" Q~
ry 00 V.
M q M
Q1
R
J
T
-
M
C7
~ ,
~y
I - p
8 CV
2
CI!
.r p
r~rn,
7 1 I 1 1
, g -F-Y
~ O o~0 ~o � Q
~ CY d: . ry
MG 2 e~i CV
3 ~ ry ~
~ cb ~
v~
~ O o0
tc .
~ ~ ~ � 1 ~ 7
1
q ~ N
1 ~ ~
N O
1 1 1 1 ~
~
� ry �Q i M ,n
ts rn
~ ~ ~ t` `r~
CY
o~ v in
~ ~ N ~ N ~
.
~
4
f
b tl
.la
250
FOR OFFIC[AL lJSE ONLY
N
btq~
W
~
a
3
0
4
ri
W
0
0
ro
~
~
'i
~
U
u
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500010014-0

APPROVED FOR RELEASE: 2047/02/09: CIA-RDP82-00850R000504010014-0
FOR OFFICIAL USE ONLY
~
~
a,
0
~

4J
r.
O
U
u
~
N
W
.-I
-2
H
~
O
~
II
~
N
O i ~

6t~ag
1 Q
I
N~v~
O O O C d
"F'
~
g
M��
O
; �
c0 t-
~ 0
c0 O)

'd' EO
~p~
. O
N t~
4~ N~
~ N N
0
F
Q~ ~A
Gi
UR
i
~

Z;+++
~1q
+i
�
O .t
+}i ~
tO M
lO O~i
~ O
pcp y
~ M Qi oD ~O
~ ~D
~ n
CV ~ ~
. ry ~p e} .
t~

.91110 -1�03
T=
7000 K: Pu=5c
%
.9160 4-02
.1105 -4-03
.1240 +03
.1592
.1928 -F01
.2164 -1-02
.3697 -1-04
.2648 -}-04
.2137 -F04
.2.168 -1�01
.20:35 -}-01
.I805 4-0I
~i -.1202 �1-05
-.8148 -t 04
-.5801 -}04 ~
.1437
.8:129
.1079 -F 01 '
.2239 -02
.2986 --02
.3394 -02
.3921 - -02
.5766 -02
.6ffi8 --02
.4364 02
.6147 02
.6278 � - 02 I
3194 02
.3184 � 1n2
.2400 -1-02
.1711 ---02
.1660 - - 02
!1567 - O:i
--2523 �--02
-A575 --02
---.5720 �-02
.1974 -06
11362 --Of
.7156 -07 ,
.7149 02
.1491 -01
.1718 -00
.Tldfi 02
.9582 -4-02
.8848 -}-02
-.I Ofia -01
t 482 - QI-
--.1506 - 01
.1214 q-05
.1563 1-05
.1480 -}-05
.3980 -F03
.2870 -1-02
.2710 -{-41
T-A000 K: ~U=50%
.8075 -1-02
.9920 -E02
.1164 +03
.1231
.1533 +01,
j1804 -t 02
.4921 -{-04
3509 -}-04
.2697 1-04
.2532 -F-01
.2150 -1-01
.1879 01
-.1401 -}-05
-.I()84 05
--.7818 4-05
.2935
.7651
.IHm, -1-01
7l'
Az
~t
a
I)vu
f)U
1)E
u
U
).T
XF
x R
% I
11,ennenne, nr
10 I 100 ` 600
.`1R52 --02
.8013 --02
.A564 -02
.4A9G -{.Q2
.'1425 ---02
--.1711 --02
.1577 ---(N3
.1'll7 --01
.1156 -1- 03
--.Ifi59 -01
~ .2247 -{�05
.bfi20 102
.3527 02
.9740 - 02
.I(H)7 --UI
.7769 -1-02
.1779 -t12
--.5584 -02
.J750 --07
.1950 -01
.1343 -}-07
-.2007 -01
.2435 q 05
.4750 -}-01
[Continued on following page]
266
FOR OFFICIAL USE ONLY
.1239 +03
�9749 -}-02
.2422 +(M
.1740 -{-01
-.6679 -4-05
.3ac2 +oi
.3768 -02
.8940 -02
.9135 -02
.2992 -F02
;1015 -02
-.fi2fi4 -02
.6275 -O7
.1999 -01
.1261 -{-03
-.1733 -01
.2152 -}-05
.7610
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500010014-0

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500010014-0
FOR OFFICIAL USE ONLV
- Table 5.6. [Continued]
flapaweTp
M
P
h
s
h~
Ti
X'
~F.
A
a
/)uu
I)T
11
Uy
kU
I r
~E
R
M
P
h
s
h;
r
~
1l'
~E
0
a
nuu
r
I1
nF

~u
).r
;LF.'
).R
Jlaerene, .r
I ~ I 10 I
r- io 00o x; pu=sox
.7053 -t-02
.8203 -}02
.1009 +03
.8.56t3 -01
.1025 -}-01
.1281 -}-02
.6876. +04
.6336 -}-04
.3940 +04
2751 -{-01
.2357 -}-01
.2017 4-01
-.1582 - f 05
I 455 -I-05
- ~M48 05
.2060
.6946
.I539 +01
.5561 -03
.2052 -02
.3510 -02
.7052 -02
.1241 -01
.1880 -01
.7637 -02
.13:10 -01
.1950 -01
.5075 -}02
.6802 +02
.6912 +02
.2768 --02
.3704 -02
.3675 -02
- -.5193 -07
-.21140 -02
-.4761 -02
.480:1 -07
.1258 -Oti
.1269 -06
2416 -02
.4868 -02
.1613 -01
ii679 A�02
.9351 -}-02
,1969 +03
-.5511 -02
-.1599 -01
-2734, . :1
.2490 -}-05
.3689 +05
' .4761 -E05
.7210-}04
.2740 -}-03
.1570 +02
T-1
2 000 K: Pu=50
%
.6280 +02
.7217 + 02
.8792 +02
.6351 -6I
.7500
.9424 -I-01
,.9731 -104
.7294 -F-04
.5344 04
.3008 -101
.2631 +01
.2143 +01
- ;1552 0.5
-11632 + 05
-.1430 +05
.esis
.4571
.125e +oi
.1616 -03
i~ .7551 -02
.7798 -02
.5210 -}-02
.3281 -02
-.278:3 --03
.14A3 -07
.28G5 -02
- 2fi73 -{-02
--.7075 - 02
.3105 -F 05
.3280 -t 05
.1101 -02
4 569 -01
.1643 -01
.8347 -}02
.4691 -02
-.I1.72 -02
.6551 -07
.36Aa -02
.3445 +02
-.1439 -01
.5(KJ7 -}-05
.1220 +04
100 I b00
.3083 -02
.2835 -01
I .2946 -01
.1037 +03
.b697 -02
-.37b4 -02
.1093 -06
.1100 -01
.1869 '+03
-.3081 -01
.7371 +p5
.5750 +02
IContinued on following page]
267
FOR OFF[C1AL USE ONLY
.1127 +03
.72*II 02
.3351 +04
.1842 +OE
-.9733 '-{-04
.2874 -}-Qt
.4104 -02
.1987 -Ol �
.2030 -01.
.5900 -}-02
.2528 -02
-.6173 -02
.9021 -OT.
.2141 -01' .
.2275 +0:1
-.2858 -01:
.4T63 -f 05
.2590 +Oi
.1013 01
.5616 -f 02
.4367 +04
~1933 +Ol
-.1237 05.
.24i7 +ot
.4207 -02
.3471 -Ol' .
.3548 -41" .9458 +02'
.4742 -02
-.5769 -02
.9776 -OT .
.1650 -Ot :
.2872 +03:
-.3911 -Ot .
.817G +05�
.8G10 +01
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500010014-0

APPROVED FOR RELEASE: 2007102/09: CIA-RDP82-00850R000500010014-0
FOR OFFICIAI. USE ONLY
Table 5.6. [Continued]
ilapaweTp
M
P
h
a
h,
r
n
v
a
Duu
Ur
u
DE
u
At)
).r
iE
XR
M
P
h
s
h~
r�
vi
0
a
Duu
r
1)T
D~
AU
).T
0
XR
ns.armNe. .T
7'-1
b 000 K; Pu =.ri0
%
.5579 -{�02
.6053 02
.7307 -{-02
.4500 -01
.5030
.6298 -{-01
.1971 +05
.1155 -1-05
.8133 -J04
.3309 401'
.2845 -}-QI
.2348 -F01
-.145iA -{-05
-.I612 -1-05
-.1665 -}-05
.1147
.3453
J&ri2
.6118 -04
.3034 -03
.1885 -02
.9323 -02
.1785 -01
.3975 -01
J400 --02
.1890 -01
.4086 -01
.57I15 (Yl
.NAUf, -}-02
.1434 -I-03
.4004 --02
.5827 --02
.8459 -02
-.2307 - 0:1
--.6511 --03
-.2564 -02
-.1766 - 08
.9181 -08
.5113 -07
.3526 -02
.2162 -02
.3048 -02
-.9296 02
-.1095 -}-03
.3638 -}-01
-.1579 -02
-:1203 -01
-.3808 -01
,4262 4-05
.691ri -105
.6916 +05
.6730 �t 05
.4840 A-04
.2620 + Ql
T=2
o0oo K; Pu=5a
�,6
, .5447 �1-02
.5527 +02
.5831 02
.3264 --QI
.3398
.3766 -1-01
,1647 -}05
.1569 -1� 05
.1395 -{-05
.3468 +01
.3090 -F-01
.2684 +01
-.1830 +05
-.1800 -E05
-.1797 -}-05
.6562 --01
.2072
.647-1.
.7659 -04
.1502 -0 i
.1504 -01
.7349 +02
.5261 -02
-.:f268 --07
�--.9136 --08
.4178 --02
-.2198 -{-03
, --.IFi08 --02
.7081t -1-QS
.9710 -1- 05
.1601 -03
.24G8 -01
.2474 --01
.1037 +03 .7335 -02
-.6534 -03
-.3954 --OB
.4608 --02
-.3230 4-03
-.IR,ifi -02
.1071 -{-06
.8920 -1-04
.5943 -03
.5068 -01
.51G4 -01
.167b -{-03
.1148 -01
--.1769 -02
.1974 -08
.7541 -02
-.4AA7 -}-03
-.1646 -01
,1780 -I-06
.7680 A�Q1
500
.8G24 -}-02
.38U9 -F02'
.6246 --04
.2070 +01
-.1526 -I-05�
.1886 +01
.3822 -02
.fi005 -OC
.GIG4 -OE
.1572 + OT
.8621 --02
-.5022 -02
.6251 -OT
.3446 -02
.1984 +03
-.5644 -Ol
, .1442 -}-06
.3670 4-02
.6565 -1-02
.2192 -F-02-
.1135 -}-05.
.2368 +01
-.1850 05�
.1363 +Ot.
.2018 -02:
.9427 -01
.9754 -01.
.2438 + 01.
.1554 -01
-.3969 -02:
.2240 -07'
.2b36 -03=
-.b3U8 -}-03
--.594U -01
.2614 -}-06
.1200 + 03
[Continued on following page]
268
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500010014-0

APPROVED FOR RELEASE: 2007102109: CIA-RDP82-00850R000500010014-0
FOR OFFICIAL USE ONLY
Table 5.6. [Continued on following page]
n..~~l"oe. .T
n.p.metv
M
r
h
s
h,
r
~
a
a
1'uU
UT
U
[)1j
111
xT
),h
71k
M
P
h
s
h~
r
I I 10 1 too
T=-2
5 00o K; Pu=50
X
.4954 -}02
.5399 A-02
.5547 -}-02
.2369 -01
.2625
.2806 -}-01
.2,361 4-05
.1871 -F-05
01712 + Wo
.3178 -}-01
.3223 01
.2826 -}-01
-.2528 -}-05
-.2388 -}-05
-.2269 +05
.45'90 -01
.1350
.4249
.9454 -04
.1929 -03
.4784 -03
2048 -01
.34211 --01
.6449 -01
.20fr1- --01
.3427 - 01
.6467 -01
.8112 -1-02
11219 + 03
.1878 -{�03
.6201) --02
.87951 - 02
.1326 -01
-.3732 01
--.8177 --01 .
-.1926 -02
-.4493 -08
-.5502 -08
--.6313 -OS
.1900 (Yl
.5553 --02
.1005 -01
-A000 -403
.-.6026 f 03
--.9508 103
-R1910 02
-.5335 ---02
--.5989 -02
.9759 -I 0:'i
.1549 -{-06
.2512 -1-06
.38,50 -1-06
.2570 -1 05
.2275 +04
T-=
30 000 K: Pu =fi0
% .
,4152 4�02
.4893 -1-02
.5:02 -1-02
.1654 ---01
.1975
� .2242 -}-01
.3824 +05
.2674 -}-05
.2051 -{-05
.4313 -01
.3511 +DI
.2948 +01
-.5867 4-05
-.3543 -}05
-.3i26 -}-05
.3558 -01
.1016

vi
x'
XE
v
a
VUU
pii
UY
XI l
;Lr
)Lf:
XR
[Continued on following page]
.221G -03
.4335 --01
A3G7 --A)
.12!)8 +03
.9914 - 02
- -.8Gfi5 - 01
--.HIIB --08
.fiA37 02
--.9381 -{-03
� ..I020 -01
.20(li �t Oti
.7700 -}-05
.6266 -03
.8093 -01
.All3 -~~I
.2078 -{-03
.149''., - -01
-.219ri -02
--.510-11 --08
.IIfi9 --�01
-.1540 -}-04
-.1182 -01
.3346 -}-08
.6620 04
269
.g306 -04
.2574 --01
.2fiIG -01
.8765' �1�02
.7i42 --Q2
- 294) --01
- -.7:l28 ---08
.2!121 -02
-.4701 -1�0:1
- -.1257 - -01
.12fi3 -F-Ofi
.23G0 �}07
FOR OFFICIAL USE ONLY
soo
.5773 +02 �
.1523 -}-02
.15G5 -}-05
.2550 -{-01
-.2168 -}-05
.9476
A209 -o2
.I148
.I158
.2752 03
.1891 -01
-.3907 -02
-.1495 -08
� .8812 -02
-.1368 -�-04
-.2507 -0I
.3674 -}-Ofi
.398U 03
.5558 -I-02
$1199 -}-02
.1867 +05
.2660 +01
-.2938 -{-05
.6682
,i4 10 -02
.1366
.13G8
.2979 -I-03
.209T -01
-.4268 -02
I -.8730 -08
.1577 -01
-.2208 04
=-.1550 -01
.4821 +06
.1010 -}-04
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500010014-0

APPROVED FOR RELEASE: 2007/02109: CIA-RDP82-00850R400540010014-0
Table 5.6. [ContinuedJ
.6929 -04
.4127 -01
.4141 - QI
.i1i7 +m
!Iri51 02
-.2IK09 U3
--.I71fi - OA
h4I1 � 02
-.6228 -I 03
--.9079 - 02
.20fi3 -}�OG
.127U +(19
I

nsomeMNe. .T
-
_ .
n.r,MeTp
i
io
ioo
~ coo
T =
40000 K; (1u = bO%
.
M
.3351 -}-02
.3879 A-02
.4536 -{-02
.5038 -}-02
p
.9988 -02
.1170
.1401 +01
.7980 -}-01
h
.6821 +05
.4991 4-05
.7661 -{-05
' .2902 +05
s
.blfil 4-01
.4180 -E01
.3404 -}-01
.2950 -}-QI
h"
-.11,46 -}-Ofi
-.931,7 -}-05
-.5981 -}-05
-.5128 }-05
f
'.2482 -1-05
.6664 --01
11908
.4004
4
x'
XE
0
a
Dt~u
UT
U
nE
u
k(i
)LT
kE
X R
T=
.1938 01
.5ll:l -02
.14G8 -1-03
.9557 -{-02
--..6tY13 4-04
.1171
.5'JG4 -�03
jI 135
� .1145
.2251 -1 Oa
.1771 --QI
--.21 99 02
--.Ifi47 -O7
.IIH3 - 01
-2815 A-Q4
-A4a3 - 01
.4974 Ofi
.2940 05
.1250 -02
.IAA6 �
. I R~)fi
.:i316 -1-01
.2472 - 01
-.4944 --02
--.1761 -07
2156 -01
-.4 41 3 -}-04
-.4837 -01
.7419 +06
.b200 -F04
Table 5.7. Thermophysical Properties of Potassium-Hydrogen Mixture
(1) (lapawetp
M
P
h
s
h,
r
~
kE
a
a
nKx
uT
K
Dti
)LT
A'K
xE
XR
FOR OFF'ICIAL USE ONLY
.IA:IA -03
.6285 -01
.G1162 01
.14!IG -1 03
.1244 --01
--.5931 - 0:f
-�-.8710 OB
.4159 - 02
--.i ir7 104
-.18fi4 01
.3027 -}-Ofi
.97A0 -1-06
(2) AasneHee, er
10
( 100
~ 600
-4000 K; N=
346
'
.2521 -4-01
.2905 01
.30;1I -}-01
.7432 --01
.8,564
.41fr8 +01i
-.5488 -}-05
-.7887 4-05
-.8523 -{-06
.7317 -1-02
.6016 -}-02
.5407 �1�02
-.9389 -}-05
-.1331 -{-06
�
-.1436 -{-06
.2379
.4692
.7623
.4288 -03
.84fi2 --0'l
.1167
.3949 -101 .
. 1868 _ .03
.....:4570 - �07
.9f57 - 07
.fiA74 - 02
-.1 I'lfi
.765fi �1�01
.IIIA �104
.2G40 -1-0fi
Key:
1. Parameter
[Continued on following page]
.5918 -O:i
.8912 -�02
.9R37 --0I
.2447 �101
.781'l - � 04
. -.4118 _ 01
.78G2 --07
.41fi5 --02
-.9923 -01
.4490 -;-02
.3238 -{-03
.6410 -1-04
270
FOR OFFICIAL USE ONLY
.6563 -b3
.8602 -02
.442;f -��UI
.121:f -1�01
.15Z8 -04
-A989 -Oa
.190T -07
' .19fi8 y-02
-.4175 -01
.f82G -}-02
.,ri3ri6 +02
.1990 -1-03
.6691 - 03
.8;i42 -02
.250!1 -�01
.674G
.7G72 -�08
-.5207 --03
.4915 =-08
.11?9 -Q2
, -.l998 --Ol
~ .7567 -}02
--.b449 +01
.187i1 -E 02
2. Pressure, atcnospheres
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500010014-0

APPROVED FOR RELEASE: 2007/02109: CIA-RDP82-00854R000540010014-0
FOR OFFICIAL USE ONI.Y
Table 5.7. [Continued]
Ilu
&wet
I
nn.,"iNe, .r
p
p
~
I
to
100
600
T
= hooo K; pK = 3X .
h1
.IfiOf, +01
.I839 -{-01 .2409 -}01
~ .2753 -}QI
p
.3790 --02
.4339 -01 .5682
.3247 01
- h
.6259 -1-05
.2615 +05 -.3312 +05
-.5670 +05
s
.1099 03
.9225 -}02 .7029 --02
.6038 --02
h~
.8502 -}-05
.3454 -}-05 -.6047 .{-05
-.9915 -}-05
r
.1200
.2804 .6071
.1026 -}-01
Ti
.31"S -Al
A886 -03 .7003 -03
.7761 -03
X'
.1020 - 01
.1069 -01 .1133 -01-
11107 -01
2642 - 01
.9115 -01 .9916 -01
.6205 -0 t
o
.7921 -1-011
.6098 -f lll .3671 -{-QI
.2277 4-01
a
.420-1 --03
.2140 --03 .1133 -03
.4049 -04
nKK
--.5235 U:)
-.4266 -11,3 -.4967 -Q9
-.5609 -03
DK
.6643 - - U7
.7804 -07 .8179 -07
.4490 -07
1K
.1374 01
.1128 -01 .7082 -02 '
.4824 -02
XT
--.1553 -01
-.8119 -01 -.9494 -01
-.5776 -01
IK .
-.3061 �4-02
-.3436 -}-01 .3792 -{-02
.6073 +02
;LE
.;1800 +04
.2735 +04 .1011 -1-04
.3556 +03
IR
.7550 4�06
.4380 -}-04 .1600 +03
.1820 -{-02
T =
6000 K; OK = 3�,{,
hi
'
.1572 +01
.1626 +01 .1033 +01
.2349 -}01'
P
.3095 -02
.3198 -01 .3601
.2310 -}-01
' h
.8234 -{-05
.7234 -}05 .2732 -F05
-.1476 +05
~
.1135 +03
.9979 -}-0`l .8129 +02
.6799 -}-02
h,'
.1081 4-06
.IOOfi -}06 .3676 -}-05
-.3169 +05
r
.9509 --01
.2611 .6305
.1177 +01
iq
.3951 -03
.4474 -03 .6377 -03
.8156 -03
X
.1238 - 01
41270 --01 .1339 -01
.1387 --01
iy
.1474 --UI
.9301J -01 .9458 --01
.9663 -01
a
.1024 1-02
.1003 4-02 .7190 -}-01
.4890 -i-01
a
.6441 - 03
.5013 -03 2835 -03
.1319 -03
nKK
-.7 730 O;l
-.6821 -0:3 --.5049 --03
-.5649 --03
/)Kr
.5736 - 37
.5878 -07 .7792 --07
.8318 -OT
DK
118(N) --01
.1887 -01 .1433 -01
.1080 -01
;.r
-2072 _.-0';
-.2065 --01 --.8245 --01
-.8771 -01
AK
-.5662 -f Q'l
-.3266 �h02 .3329 -1-02
.3148 -f-02
.5983 � I 04
.6308 Q4 .3n4 _I qq
.l Q-32 -1-04
Aq_
.IIW -1-07
.9230 -1-04 .2640 -}-03
.3W -1-IM"
[Continued on following page]
271
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500010014-0

APPROVED FOR RELEASE: 2007/02109: CIA-RDP82-00854R000540010014-0
FOR OFFICIAL USE ONLY
Table 5.7. [Continued]
nY(IiNlip
M
P
h
s
h,
1'
AiMllNNt, T
10 100 ' 500
T
J;'i66 -1-01
.2G;f9 - 02
.9668 -{-06
.I157 +O;i
.I,'l?5 +Oti
.71(il --01
= 70()0 1(;
.1582 -4�01.
.2fi68 -01
.9354 (15
.107f -}03
.12fi8 -1 U6
.2148
3%
.1706 -}-01
.2877
.7224 -}-05
.aezs +o2
.1029 406
.5679
11
.4555 -...03
.4810 . 0.3
i'
.I-Iti'l --01
.1505 -QI
~E
.
.1520 -U I
.2051 01
o
.I I95 .102
.1249 �1-02
a
.fipfil - -I):i
.6374 -03
UKK
--.9366 --0,3
-.7927 --03
UK
.5421 07
.6490 - 07
UK
.2072 --01
.2425 -01
iT
--.4777-03
-.5666 ----(Yl
71K
-.7711 -t-02
-.5305 -F02
A F
.8018 -I U4
.9468 -1-04
~R
.1910 +I)8
I .2810 1-05
T
c 80(N) K; O
M
.1564 -I UI
K
.1571 -1-01
P
.2:1(Ni --02
.2317 --01
h
. i i oi 4 oo
. iWn -}-os
s
.1176 +03
.1051 +03
h,
.1489 -I��
.1476 -{-0i;
f'
.55 71 - ()I
.1709
. 5'161i -03
.538:1 --�0~
.I692 ...01
.1743 -OL
~z
.6726 UI
.1931 - 01
Q
.I276 02
.1426 4-02
a
.6547 - -03
.704:1 03
UKK
---.1030
t-.9645 -03
nK
.626l - 07
.5325 - 07
UK
.2199 --01
.2727 -01
),T
2917 03
-
1996 - 02
xK
- --.93;13 �102
--7062 �1�02
xE
!J9G'l - q1
f
.I'llfi -1 1)6
.1570 �1 IMI
.8740 -1-05
[Continued on following page]
272
FOR OFFICIAL USE ONLY
.5970 - O:f
.1552 - 41�
.b457 -01
. 1064 02
.4735 -O:i
-.6011 -03
.5789 -Q7
.2180 --01
~
-.3994 - 01
-.2394 -E02
.82'l0 -E 04
.5650 -1-03
.16'l4 +UI
.2397
.9914 +Q5
.918A 1-02
.139fi 06
.487b
.6106 - 0;!
.1795 -01
.3416 --01
. 1389 +0`l
.6166 -03
-.75;14 -ll3
.5117 -07
.2787 -01
-.1744 --01
-.3890 -102
.1241 -1-05
.1300 -1-p4
.2001 -}-01
JG87 +QI
.3241 -E05
.7527 +02
.4357 -}-05
.1063 01
.792fi - Q:3
.Ifilfi - pL
!J430 41,
.7G90 -{-Ol
.2G95 --�03
-.5894 -03
.7975 -07
.1744 -01
-.7935 -01.
.2128 -}-01
.5198 -}-04
.5360 -{-U2.
.1792 -1-01
.1323 -1�01
.7227 -1-05
.eoc i +n2
.1048 -}-OG
.9497
.76b5 -Q7
.1837 -UIl
.fi941 -01
.1097 -{-02
.4065 -03
-.6600 -03
.6262 -07
.2369 -01
-.b174 --01
---.1947 +02
.9473 +04
o56c +n2 ,
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500010014-0

APPROVED FOR RELEASE: 2007/02109: CIA-RDP82-00850R400540010014-0
RQR OFF'1C1AL USE ONLY
Table 5.7. [Continued]
ReexeNSe, ar
n.p,meTn
I
i I
to
too ~
soo
T=
10 000 K; PK = 3%
M
.1540 -F01
.1561 -I-01
.1579 -{-01
.1635 -}-01
P
-181J -02
.1842 ---bl
.1665
.9655
h
.1522 -1-06
.13414 -106
.I 34 I, -FOfi
!1235 06
s
.1221 -1-03
.1085 4.03
.9579 -4-02
.8638 -}-02
h,
.2310 --06
.1994 OG
.1877 4-06
.1768 4-06
f
.5026 --01
.1216
.3458
.7143
q
.GS;Ifi --0~
.6746 --03
.7183 --03
.8112 -03
k'
.2227 01
.2265 ---01
.2326 --01
.2357 -01
7LE
.2849 --01
.2374 --01
.27.38 -01
.4067 --01
~r
.2051 �1-02
,1779 -102
.175:1 -1-02
.1583 J-02
ct
.1099 02
.BM8 03
.7953 -03
.6358 - 03
� UKK
--.5162 --03
--.9930 - 01
--.1037 -02
-.89I9 -03
pK
.I493 _ pg
.8830 -07
.5407 -07
.4997 -07
pK
.1191 � -01
.2671 --01
.3189 -=-01
.3400 -01
iLT
--.6814 02
-.3154 -02
--.5fl65 -.02
-.1932 -01
XK
-B207 -1-02
--.8473 �1-02
-.5660 -}-02
-.3588 4-02
)LE
.I468 +p,
.1762 -,'-05
.2000 -F05
.I871 -{-05
1lR
.4020 4-08
.40ra0 �1� Ofi
.6400 4-04
.3530 --03
T=
12O110 K; PK=
3%
M '
.1428 01
~ .1524 4-01
.IfiGI -}-01
~1590 -}-01
p
.1406 -02
.1500 --01
.1536
.7826
h
.2588 +OG
.1903 �}-Ofi
.1684 06
.1596 -{-06
s
. 1317 03
. I 13 I-}- 03
.9890  02
.8967 02
h~
.4034 -1-06
.2928 --06
.2510 -1-06
.2392 --06
1'
.6160 -01
.1282
,2879
.5581 '
q
.7410 --03
.8070 --01
.8606 -03
.9308 -03
X'
.2821 --01
.2978 01
.2977 -01
.2971 -01
xE
.6105 -01
.4021 --01
.3389 -01
.3745 --01
Q
.3673 -{-02 .
.3152 +02
.2423 -}-02
.2068 4-02
a
.2094 - 02
.1651 - -�02
.1161 '--02
.8585 -03
DKK
-.001 - - 03
-.5565 --03
-.1011- --tYl
-.I066 -02
DK
.112fi'l --Ofi
1I1269 (Ni
.8416 07
.5840 - 07
UK
.3536 02
.1368 --01
.3165 --01
.3799 -01 '
),r
=.4965 -01
-.2904 -01
.1689 -01
-.1605 -01
),K
-3129 -{-012
-.6699 -}-02
-.8164 -}-02
-.5144 +02
1lE
.2586 -}-06
.2781 05
.2923 -{-05
.2838 +05
XR
.1320 4-08
.4710 +06
.1490 -{-05
.9810 �}-03
[Continued on following page]
273
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500010014-0

APPROVED FOR RELEASE: 2047/02/09: CIA-RDP82-00850R000504010014-0
FOR OFFICIAL USE ONLY
Table 5.7. [Continued]
nR.ArxMe, o.
n.p.~eTp
I
1 I
10
I
100 '
600
r=
16000 K: PK -3�% .
M
.1083 +01
.1351 -F01
.1493 -}01
.1543 -1-01
p
.8579 03
.1070 01
.1180
.6091
h
.6621 -f Ofi
.3658 -1-06
.2541 +06
.2231 +06
s
.I613 �{-03
.1260 +03
.1052 -}-03
.9436 -}-02
h;
.10.15 �}-07
.5723 -I (K'i
.3963 -1-06 t
.3470 -F-06
f
.7260 -�01
.1572
.3184
.6351 .
Iq
.6202 - 03
.91;10 - O:I
.IUri'J 0'l
.I135 --02
ll'
.3015 01
.4190 01
.4562 --{ll �
.4449 -01
kE
.1160
.8751 =-01
.6209 - 01
.5190 =01
o
.6813 -1-02
.6790 �102
.5441 + 02
.41181 -4-02
u
.3651 -02
.3653 -02
.2787 --02
.1913 -02
DKK
-.7243 ---04
--.2499 -03
.692P --O:f
-.I017 -OZ
UK
.5485 07
J218 - 07
.1006 --06
.8014 -07 ,
UK
.8040 ---01
.3655 -02
.1610 -01
.2862 -01 ~
-.9383 -UI
.4191 --01
--.7553 -01
-.5606 -01
X K
-.5181 -4 02
- .8105 -I-02
--.1303 A 03 ~
-.1379 -}-03 ;
1,E
.4999 -}-05
.5443 05
~
.6085 -{-05 '
.6620 -4-05
hR
.1210 -}OA
.3880 -fOG
~
.1710 -4-05 ~
d760 -}04
T =
20000 K; PK
= 3%
M
.8190
.9507
.1222 01
1378 +01
p
.4867 -03
.5705 --02
.7365 -01 .
.41010 .
h
.1270 -1-07
.9739 4 06
.6738 406
.4196 -}06
s
.1912 E03
.1606 �103
.1232 403
.1055 -}-03
h,
1995 -107
.1529 -1-07
.9064 -f Ofi
.6673 -}-06
I'
.5043 --01
.1459
.3501
.5965
q
.1392 --03 '
.5827 --03
.IIfiO --02
.1429 --02
il'
.2820 - 01
.5070 �--01
.7866 -01
.8961 -01 ,
aE
.4459 - -01
.1116
.1327
.1210 '
o
:IAI'l4 -1-03
.I282 -1-03
.1358 +03
.1206 +03
a
.54 bR 02
' .6828 -'02
.7209 - 02
.6109 -02
DKK
-.5722 ---04
-.1264 -03
-.4056 -03
-.8146 -03
DK
.6077 --08
.2454 -07
.5647 --07
.6974 -07
I~K
-.4097 - 04
.3678 -01
.3571 -02
.1132 -01 ;
7Lr
---.1723 - 01
-.9106 --01
-.1715
-.1872 .
XK
-.I IU9 -1 03
--,11707 -}-03
--.2773 -1-03
-.3579 +03 ,
llc
.9359 -105
.1265 -1�06
.I691 OG
J691 -}-08
XR
.I I10 -1�0!)
.1000 -1 07
.2050 �1-05
.2010 -{-04
.
[Continued on following page]
274
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500010014-0

APPROVED FOR RELEASE: 2007102/49: CIA-RDP82-00850R040500010014-0
FOR OFFICIAL USE ONLY
Table 5.7. [CuntiiiuaLi]
ITapaMt7'p
M
p
h
s
hc
r
ll'
a
a
DKK
Dr
K
�K
j
;LK
XF
XR
M
P
h
s
hc,
r
q
A'
6
a
DK!c
1.) K
nE
K
~r
JLK
;Lr�
XR
.
T= 30 000 K: flK = 3%
AIISJIlIIkl, 01'
~ 10
lo0
.78W
.7990
.8490
.3116 --03
.3176 --02
.3419 -01
.1627 �1-07
.1582 -F-07
.1418 +07
.2119 +n3
J865 -4-03
,1680 -f-03
.2423 -}-07
.2425 4-07
.2222 -{-07
.2289 � -01
.7213 _-pl
.2222
.7209 ---04
.1551 - 03
.521 5 -01
.5529 --QI
.79('~', --01
.1278
.5581 ni
.e708 -QI
.1415
.15A6 -F03
2045 -f-03
.2726 -1-03
.8526 -02
.1091 - 01
.1449 -01
-.4678 -Qq
--1275 -O:i
-.3098 --03
.1901 --.09
--.3066 -OS
.6645 -08
-.1214 --02
-.9092 -03
-.2214 --03
-.4081 -02
--.160 -pl
-.6560 --01
-.6514 �1-02
--.2797 -}-03
-.6597 Q3
.2059 -}-Qfi
.28;'~9 -f -06
.4031 +OG
.7850
.1319 -0
. .1919 -1�0
.220f -t-0
.2735 -}-0
.iac,, --o
.109G --0,
.9G10 --01
.9615 -01
2149 -{-03
.-i-i� -ni
--.4476 - 04
.1202 -OA
--.117J
--.4797 ---02
.A4b0 +-02
.3(iSA 4 OG
[Continued on following page]
.3940 -I-UB
.2570 -{-06
T= 40 00() K, p
=
396
K
.7RA8
.79A~1
3 .2341 -02
.2402 -.01
7 .1894 --07
:1832 -}-07
3 31954 --03
.17()0 -~-03
7 .2784 -~-07
.2763 �1-07
.4~ -oI
.1292
.1651 - 03
.3270 --03
.1312
.1937
.1317
.1971
.2727 -}-03
1477
r
.3625 -}-03
.
-01
.1946 -01
- 94f,3 - 04
-.2370 -03
.1429 �--(16
.2742 -09
-.2530 02
-.2857 -02
-1822 -OZ
-.25al -01
--.G853 -}-02
-.4626 -1-03
4872 -1-Of,
.6822 -106
.40`~() �1 ~
~
~
.,3070 -+-07
275
FOR OFFICIAL USE OPILY
600
.9622
.1981
.I146 -~-07
.1346 --03
.1829 07
.4G04
.I 171 - (NZ
.1877
.2247
.3~IA9 --03
.IGf5 -p 1
-.6160 -03
.1789 -p7
.1015 -02
-.187~!
-.1040 -}-04
.5074 -}�p6
.8670 -{-p4
.8294
.1270
.1705 07
.1508 --03
.2fi23 �-~-07
.2850
.6963 -03
.2780
.3075
.4530 --03
.2420 -01
-.5436 -03
.8415 -09
-.2iso -oz
-,8444 -01
-.1263 -{-04
.8932 -}-b6
.9190 05
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500010014-0

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500010014-0
FOR OFFICIAL USE ONLY
Table 5.7. [C:ontinucd]
1 iBpaNlTP
J(asnenne, er
I 1 10 1 100 1 600
T -
400.1 K; OK = 1
0�r6 �
D1
.3610 -}-01
.4650-1-01
.5345 +01
Q
.1065 ---01
.1371
.1576 +01
h
.2489 -1-04
-.2601 -}-Ou
-:1859 1-05
~
.5187 -}02
.4008 +02
.3313 +02
-.381 I -1-04
- J3fi6 -1-05
-1330 �{-Ofi
r
.I 651
.3343
.6701
'q
.5:315 03
.7229 -03
.9099 ---03
i'
.7601 --42
.7635 --(Yl
.7205 0'l
1~E
'1950 - UI
.8140 --01
.3611 --01,
Q
.41115 -1 01
2805 -4 01
.1302 -i-01
a
.2465 - 03
:1025 - 03
.2515 - 04
!)KK
01
--.HORH �03
---.9215 07
1)K
.1328 - OG
.1072 - .(Hi
.2284 07
UK
.446:1 02
.2921 ---02
.1477 ---02
kr
--.9603 01
--.dN5:1 01
--.3810 --01
1lK
.I:i;IU -1.02
.8445 +02
.1265 -}-03
iF
.1518 +04
.726314-03
2671 A-03
XR
.6990 -t 05
.1560 +04
5610 �1-02
T-
5 000 K; OK = 1
0�,{p
1u
.2994 -4�01
.3430 -}-01
.44 ifi 1-01
P
.7070 -02
.81(X) --01
.1052 1-01
h
.1611 4-05
.1636 -{-05
-.14:35 -F05
s
5955 -1-02
.4954 4�02
.3849 -1-02
hc
.!K)84 }-05
.3744 05
-.5977 -1-05
r
.1872
.4074
.8725
71
.419:1 03
.5915 - .p3
.8334 --03
X,
.9674 - 0?.
.9862 -02
.9864 -�02
XE
.231'l -01
.7610 --01
.Rlrll --UI
R
.1126 -f�02
.8209 1.01
.4589 �1-01
a
.fi 17.:1 03
.4082 07
. 1650 ---0:1
Kt(
� .8687 - 03
.
-.7707- O;i
--.41274 - 03
/)r
K
.9657
07
.II151 -O(i
.10!1,1
p(i
~)r
K
e990 - 02
.78r1 ---02
.5330 -02
Xr
01
-�-.6799 -01
--.8249 -11t
XK
-..5777 1 02
_ J064 -101
.7122 �1-02
xF
.4442 {04
.3685 4 04
.IA52 -I 04
_ XR
fifil0 - } 05
.1440 .104
.5370 A-02
[Continued on following page]
276
FOR OFF[CIAL USE ONL'i'
I .5593 +01
, .8247 -}-01
-.4192 -}-05
.29A6 q-02
-.1435 -}-06
.I178 +01 ,
.8305 -03
.6!IG9 -02
.'lOfi9 -0)
.7fi13 �
.AOIQ -05 ;
--.91565 -01
--.I(NYl -07
.99NJI -03
-.1843 -01
�1393 -{-03 ,
.1215 1-03
.5'l40 -}-01
.5092 -}-01 ,
.6012 -}-01 '
-.2676 -}-05
.3321 J-02
-.9914 -{-05
.1533 -}01
.9287 - 03
.9:)69 -02
.5053 -01 ,
2A34 �}-01 i
.6889 --Oq j
--.1041 --02 .5856 --07
.39fi4 -02
-.5131 �-01
.1136 +03
.9563 +Q3
.2840 +01
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500010014-0

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500010014-0
MOR ()FF1('IA1, IItiM: ONI.Y
Tab1e 5.7. [Cnntinued]
j(..aexe, .r
flmpowetp
1 I 10 I 100 I 600
T =
sooo K; aK = 10
%
M
.2896 -{-01
.3030 -}-01
.3598 -}-01 ,
.4359 -{-01
p
.5703 -02
.6971 -01
.7089 '
.4295 -}-01
h
.4877 -}-05
.4195 +05
.1143 05
-.4517 +05
s
.6187 -{-Q2
.5417 -}-02
.4428 -1-02
.3725 -}-02
h,
.1128 -{-06
.I062 -1-06
.3967 -F05
-.3004 -{-05
I'
.1646
.4092
.9211
~
.1658 -}-01
' 71
.4(MJ1 --03
.5172 -03
.7482 -03 .
.9432 --03
x'
.1212 - 01
.1238 --01
.1253 -01 '
.1233 -01
7~E
.1412 �01
.2901 ��-01
.7828 -01
.7862 -Oi
o
.I6:15 �1 nl
.1650 A-02
.IOtiQ -F02
.7163 -{-O1
a
.8876 - 03
.8098 ~3
.4478 -03 :
2116 -03
I)KK
--.1778 02
--.9933 O:f
--.9255 -03 ~
-.1054 -02
DK
.IOGO --OG
.8317 -07
.1049 -06 '
.IIQ7 -06
DK
.1273 01
.1358 --U I
.1096 - - 01
.8869 -02
xT
-.G417 -03
---.1787 -01
-.6884
-.7463 --01
1lK ,
-.I 1:19 03
-.6545 +02
--.2668 -{-01 ~
.5911 -1-02
1lE
.725I -{-04
.8131 -}-04
.5906 -}-04
.3525 '-}-04
1lR
.1400 OG
.2490 -}-04
.9400 +02
.1280 -}-02
T =
7000 K; OK - 1
0%
M
.2872 -}-01
.2926 +01
.3180 -{-01
.3723 +01
p
.9917 -42
.4946 -01
.5379
.3150 '-}-01
h
.5744 +05
.5419 -{-05
.4144 +05
.2046 -{-05
s
.6322 -}-02
.5615 -}-02
.4800 -}-02 :
.4110 -}-02
h~
.129ti OG
.132fi -~-Ofi
.1077 �1-Ofi
.4667 -E05
r
.1206
.3618
.8771
.1605 +01
11
.4507 - 03
.511i!) --03
.6904 --03
.9039 -03
x'
.145;1 - 01
.1521 0)
.1547 -01
.1533 -01
kz
.15(YI 01
.1966 -01
A685 -01
.7761 -01
0
1940 +02
.2151 -{02
.1738 -1-02
.1326 -}-02
a
.105 .5 - -02
.1152 -02
.8280 -03
.46,50 -03
IIKK
� �.IBili 02
--.1400 -02
-.IOGG -02
--.1086 -02
VK
I110'l - Qli
.9197 -~7
.7769 -07
.IOGO -06
DK
15:f3 --01
.1k~85 --01
.1733 -01
J457 -01
xr
.7764 ---04
--.5193 --02
-.3458 -01
-.6580 -01.
aK
-.1701i 403
-.1100 -}-03
--.51�I:1 -}-02
.1772 -E01
AE
.995() -1-04
.1268 0:'i
.1186 +05
.8312 -E04
1lH
5180 -{Ofi
.fi010 -F04
2200 -1-03
,1860 .}.02
[Continue3 on following page]
277
FOR OFFICiAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500010014-0

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500010014-0
FOR OFFICIAL USE ONI.Y
Table 5.7. [Continued]
. Aunex
we, at
I
flapamerp
1
10
!00
T =
eooo K: aK = 10
,c
M
.2866 -{-01
.2890 +01.
.3017 +01
= p
.42:10 -02
.4275 -01
.4470
h
.6515 -f-05
.6347 -1-05
.5644 -}-05
s
.6424 +02
.5739 -}.02
.5002 -1-02
h:
.I482 -1-06
.1510 +Oti
.1453 J-06
C
.1001
.2999
.7886
~
.5099 -03
.5524 -03
.6865 --03 ~
.1694 � -0l
.1801 -01
.1880 -01
xz
.1713 01
.1953 -01
.3171 --01
o
.21 B2 -1� O2
.2594 -1 02
.2467 -1� 02
ce
.1174 --02
.1377 -02
.1203 -02
_ UKK
-.1136 -02
-.I$26 --02
-.I328 -02
DK
.9932 -07 ;
.9394 -07
.7294 --07
DK
.11711 -01
.2234 -01
2346 -01
7lr
.2245 --03
-.1845 -02
-.1722 --01
k K
-2235 4-03
-.1568 -{-03
-.7990 --02
7lE
.1267 405
.1691 -F-05
.1854 +05
IR
.1860 +07
.1790 -1 05
.3800 A U3
-
T
= 10000; PK=
IOg/o
M
.2841 �1.01
.2867 -{01
.2911 -{-UI
p
.3354 ()2
.3390 - 01
.3455
h
.8,101 �I 05
.7976 105
.7641 105
s
.6632 �4 02
.6920 1 lY2
a226 -}02
h,
.2130 -1-06
.1917 -f Oli
.I907 -hOG
, 1'
.GEIU:i (ll
2031
.6694
t~
.6409 0:1
6715 01
.7G38 -03
.2212 UI
.2368 01
.2571 -01
aE
2406 --01
2433 01
.2885 --01
o
.2716 -{-02
.3I39 �I-02
.3-173.+02
a
.1468 --02
� .I1;76 ---02
.1767 -02
I)KK
--.19:i3 -U'l
.2-109'--02
-.1993 -02
/)K
.1829 --06
.1074 -06
.8232 --07
- !)K
.I645 01
.2668 --II
3316 -01
kT
- 71153 02
-.9696 --04
- .6G2G -(Yl
I K
- �.2265 �t 0;1
--.2:f:14 +03
---.1178 -{-03
AE
.IN94 �105
2643 -105
.3190 05
Ak
IO80 +OR
.1180 106
.1730 +04
[Continued on following page]
278
~ FOR OFFICIAL USE ONLY
{00,
.3338 +01
.2474 -}-01
' .4170 4-05
.4394 -}-02
.IU92 -}-06
:IH72 -{-01
.870fi --43
.1852 -01
.5894 --01
.19U4 -}-02
.7716 ---03
-.I 192 -02
.8263 -07
.2036 -01
-A3&5 -01
--.4003 +OZ
.l9R2 -}-05
.326Q 02
.3034 +01
jI802 -101
.6967 -4-05
.4709 + UZ
.1819 --1-OG
.IIG2 -}-UI
.9U53 --03
.'15J4 -01
.392:) -111
.310A -}-0'l
.1411 -U2
-.i6i9 -n2
.G8G0 -OT
.3159 -01
1982 - Ol
-6705 .10'l
.30�14 -}-05
.I I,2U -1 03
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500010014-0

APPROVED FOR RELEASE: 2007102109: CIA-RDP82-00850R000500010014-0
FOR OFFICIAL USE ONLY
Table 5.7. [Conti.nued]
Ilopsuerp
M
P
h
s
b~
I'
~
XE
a
a
DKK
Ur
K
vK
~r
)1K
),F:
hrt
M
P
h
s
h~.
t'
~E
a
a
VI(K
VK
DK
xT
1I(
xe
XIl
Jjesaeure. Ar
I
' tp
I 100
- T -
12000 K; pK =
1oK
.2657 +01
.2819 -}-01
.2876 -f-01
.2618 --02
.2778 -01:
.2842
.1364 �F06
.1036 -F06
.9400 +05
.7102 -}-02
.6130 +02
.5386 -{-02
.3961 -{-O(i
.2769 -1�06
.2401 A�U6
.GRAI --01
.I615
.4430
.7361 -03
.8053 -03
.8903 -03
.2747 - 01
.2998 -01
32G7 -01
.4546 --01
.3470 -01
.3483 -01
A097 -1�02
.3991 -1-02
.4208 4-02
.2215 - 02
.2134 -02
.2150 -02
--.64-18 0;1
-.1837 --02
---.2449 -02
.224U --QG
.IHfiS -Oti
.1043 -06
.6307 - -02
.2109 -01
.3737 -01
. _.I IGQ 01
�-.3781 -01
-.6824 -02
- -.845Q -I 02
--.1921 A-OJ
--.1473 4�03
.2802 �1 Ilfi
.3504 -1�05
.4501 +05
.
7' =
15900 K: OK =
10%
.2034 -1�01
2521 A-01
.2771 A-01
.1611 --02
.1997 ---01
.2196
.341i1 +06
.1925 06
.1355 -1-06
.Hl;:f!) 02
.6784 -1-02
.5690 -F02
.1034 .107
.5681 A-00
.3860 +06
.7341 ---01
.1647
.3673
.6181 - 03
.9262 -03
.1102 -02
.:l(X% --01
.4101 --01
A657 --01
.9611 --01
.7404 -01
.5739 -01
.6876 02
.70:'ifi -}(Y2
.64II -}02
.3672 02
.3798 --02
.3342 -02
1754 . Il;i
� -.fi49fi --03
--.1815 -02
.9881 - 117
.I657 -OG
.I646 -06
1 12fi 112
.6629 - 02
2558 -01
5159 01
- -.fi40'l - 01
-.4367 -01
9577 1112
--.1404 -103
--.1884 �1 03
51177 115
.6162 05
.7321 05
.1250 -1-08
.31511 -{-(6
1120 1 08 .3150 106 .5890 -1-04
.1290 -1�05
[Continued on following page]
2.79
FOR OFF[CIAL USE ONLY
600
.2940 1-01
.14b5 -E01
.8921 -}-05
.4888 -{-02
.2:i80 -FOG
.9027
.1016 -02
�.3410 -01
' .3972 -01
.4(191 -}-02
.1926 -02
-.21 a3 -02
.1776 -07
.4053 -01
-1393 -01
-.5090 -}-02
.47fi4 05
.34~A �E03
.2859 -E01
.1134 +01
.1207 06
.5120 -}-02
.3347 -{-06
.6A83
.1229 -02
.4H62 -01
.5302 -01
.5859 -{-02
.2832 -02
--.2409 -.02
.iifis -os
.4IG7 -01
-.3495 --0I
-.8G4`l 02
.7902 -{-05
.1p90 -{-G4
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500010014-0

APPROVED FOR RELEASE: 2047/02/09: CIA-RDP82-00850R000504010014-0
FOR OFFi('IAI, l1SF ONI.Y
Table 5.7. [Continued]
Jlrsrea
re, &r
I
, n.p.Merp
1 I
10 I
100 ~
600
T=
20 000 K; PK = l
O%
M
.1552 01
.1792 -}-01
.2288 -{-01
.2571 -}-01
p
.9221 -03
.1076 -01
.1380
.7746
h
.6599 -1-06
.5082 +06
.3014 +06
.2214 4-06
s
.1050 +03
.8585 -f-02
.6625 -{-02
.5688 +02
hc
.1996 -1-07
.1520 -{-07
.9046 -1 06
.6639 -1-06
T
.5047 --01
.1465
.3581
.6284
t)
.1566 -Q3
.6034 --07
.1229 --(Yl
.1574 -02
7l'
.2797 -01
.4981 01
.7771 -01
.9037 -01
kE
.4382 --01
i1059 '
.1257
.1174
a
.1029 4-03
.1286 �107
.1388 -1-03
.1279 -{-03
a
.5160 --�02
.68,19 --02
.7371. -02
.6507 -02
UKK
-iII II -03
-.2581 - 03
-.BfiG'l -03
-.1158 --02
DK
.9127 -08
-.4411 --07
-.1011 -Of,
.1218 --OS
DK
2441 -04
.i3196 -03
.6563 --02
.1977 --01
lLT
-.1084 -01
-.6357 �-01
-.1328
-.1504
AK
-2(Y)fi 4�03
-.3119 -}-03
-.4555 -}-O:i
-.4950 �4-03
bE
.9372 +05
.1274 -}06
.1646 -}-06
.1833 -}06
AR
.1130 -}-09
.1030 J-07
.2070 1�05
.1870 �1-04
-
T
000 K. OK =,1
0%
M
.1475 �{-01
.151M -E01
.1605 -1-01
.1813 401
p
.5820 - - 03
.5983 --02
.650 -01
.3736
- h
.8860 +06
.8410 -}-06
.7429 -}-06
.6005 -}-06
s
.1142 �}03
.9986 �}02
.8442 -1-02
.7207 +02
h;
.2414 �1-07
.2426 -{O7
.2222 -F07
.1828 �1-07
C
.234.1, --01
.7292 -01
2230
.4631
q
.1832 ---04
.1919 --0~
.6174 ---03
.1317 -02
.5167 -O1
.7716 - 01
.1264
.1860
iE
.524(i 01
.81 I I- 01
.1460
.2221
o
:1529 +03
.2011 -1-03
.2716 -{-03
.3149 -}-03
a
.8488 --02
.I089 --01
.1450 --01
.IG(ili --01
_ UKK
--98I8
--.2338 -�0;1
--.5907 --03
-.101 --02
UK
.II IH - OB
.4B20 ---09
'1231 -07
.3210 --07
UK
--.1801 --02
--.1494 -02
-.1490 -03
.2117 --02
- xT
--.6861
--.2286 --01
-.5946 -01
-.1659
),K
-.5261 102
--4619 �1-03
-.1207 -}IM
-.I866 -1-04
AE
.1973 -106
.2805 -1-06
.4026 -f-06
.5103 -}-06
XR ~

.4070 408
.2570 -}-06
.8650 -}-04
[Continued on following page]
280
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500010014-0

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500010014-0
FOR OF'F7CIAL USE ONLY
Table 5.7. [Continued]
n.mme. .T
IlapeYetp
.I (
10
I 100
( 600
T = 40000 K; PK =
Ipy(e .
M
.1447 -1-01
.1466 +01
.1494 -}01
.1491 -}-01
p
.4276 --03
.4354 -02
.4497 -01
.2390
h
.1092 -1-07
.1042 -}-07
.9914 -}-06
.9101 -{-06
s
.1200 -1-03
.1057 +03
.9162 +02
.8104 +02
h,
.2739 �1-07
.2785 -1-07
.2753 -}07
2623 -}-07
r
.1367 - oi
.42W oi
.1319
.28e7
ri
.Ill:lB O:f
.1705 - 0~
.3770 -03
.8531' -03
- A'
.8502 - 01
.1212
.1844
.2710
XE
� .8549 01
.1219 - 01
.1886
2994
o
.1979 03
.2596 � f 0:)
.3518 -1-03
~ .4466 -}-03
a
.i IbriQ _01
.I462 --01
.1943 --01
; .2424 -01
UKK
-.9076 ._pq
--.1845 -03
-_.4445 --03
-.1016 --02
UK
.2320 --(18
.2850 -08
.1844 -08
~ .3471 -08
1)K
--.3241 -02
--.39011 -02
-.4624 -02
-.3555 -02
JlT
--.1092 --01
-/l 117 -01
-.356h -01
-.9626 --01
AK
.3863 -}-03
.1227 -f-03
-.5774 -F03
-.2089 -}-04
AE
.3326 +06
.4635 +06
.6824 -F06
~ .8812 -}-06
7lR
-
.4340 -F-09
.3190 +07
.8300 -}-05
T =
4000 K; PK = 50K
M
.1485 -E02
.1770 -}-02
.1989 -1 02
.2118 -1-02
p
.4385 ---01
.5224
.5875 +01
: .7137 +02
h
.:1673 �104
-.1233 +04
--.3698 -{�M
~ -4403 -}-04
s
.13:13 -1-0'l
.l(IJ;i -{02
.9296 -1-01
.8470 -1-01-
hc
.5498 � 1 11, .
-.8901 12
-.1114 4-13
~ -.1425 -1-13
.
.2676
.5325
.1200 J-01
.2804 -}01
q
H985 - 03
.1093 --02
.1178
.1171 -02
.:19I 1 - 02
.3455 --02
.1074 02
.295$ -(Yl
- Az
.3470 -01
.11,10 01
.145:1 01
.8440 --02
o
A726 -I AI
.2293 -F01
~I054 J-01
.8138
a
2125 03
.8101 -04
.2286 --04
i1084 -04
1)KK
- .'1G78 -02
-.3135 --02
-.3410 -02
-.3478 -02
f)K
.4212 - -07
.3089 -07
.1704 -08
.7428 -08
!)K
.7816 03
.4948 -63
.2715 -03
.2692 -03
AT
- .14fi5 01
-.3420 --01
-.1521 -01
-.7787 -02
kK
.4486 -102
.3244 +03
.4679 -1-03
.5068 03
1lt
IAII -4-04
.1053 -f04
.4965 403
.3693 -}-03
- XR
.41:f0 -t 04
.2200 +03
.7450 1-01
.6530 -}-00
(Continued on following page]
281
FOR OFFIC[AL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500010014-0

APPROVED FOR RELEASE: 2007/02109: CIA-RDP82-00854R000540010014-0
Table 5.7. [Continued]
FOR OFFICIAL USE ONI.Y
n.P.we,p
J(saAeu
xe, ar
I
10 100 ( 600
~
7' =
5oou K; OK = 5
0X
_
M
.1269 -1-02
.1430 -}02
.1731 -{-02
.1953 1-02
P
.3016 -01
.3391
.4109 -F01
.2334 -}-02
h
.1088 �1-05
.6725 -1 04
.1438 -1-04
-.9488 -}-03
s
.1496 -102
.1271 -1-02
.1043 -1-02
.92.14 -}-01
.1079 +06
.4876 -105
--5277 -{-05
-.9539 1�05
j
.3332
.6834 .
.1518 J-01
.3195 -1 01
.6566 --03
J629 03
.1-I09 02
.1251 -02
~
.5744 --02
.55:39
.4728 --01
.4275 -02
~E
.9629 - - 02
.2599 - (11.
.2978 - -UI
.1949 --111
Q
.I311 +02
.8:187 1-01
.4325 +01
.JIIiH -f-Ql
a
.7171 --01
.41;11 -03
.1529 -03
.8222 --01
L)KK
--.3~100 ---42
-.3145 --02
-.3641 -02
-.3930 -02
UK
.4469 -07
.3392 -07
.3200 -07
.1760 - 07
DK
.1626 -02
.1493 -02
.1044 -02
J827 -03
1Lr
--.7 t 7'l -02
-.2571 -01
-.3163 -01
-2079 -01
ILK
-.2287 -}-03
--.5297 -{-02
.2730 -}-03
.4294 + 03
)LE
.4891 -}-04
.4418 04
.2651 +04
.1941 +04
~R
.6390 �{-04
.2660 +03
.1020 +02
.1040 +01
T
6000 K; OK = 50
%
M
.1148 -1-02
.1218 -1-02
.1478 +02
.1722 4�02
P
.22R!1 -_01
.2547
.2943 1�01
.1721 �+-02
h
.1691 -105
.1253 105
.7789 -1-04
.3864 -104
s
.IGUG -102
.1377 .102
.I-I;iJ �102
.101I �f 02
h;
.1382 -106
.1236 -}OG
.5221 1-05
--.2092 + OFi
f'
.3264
.7347
.I619 -f U)
.3218 -{UI
11
.45H0 - 03
'
.7965 - 02
~E
.8701 --02
Q
.zzx2 -I o2
a
i 1i234 - 02
DKK
---.4580 _ 02
Ur
K
.7544-07
nE
K
.2,1G7 -02
~r
.1976 --02
XK
- .:1913 -1�03
XE,
.8391 -1-04
XR
.9260 �1-04
.7H2G 03
.8143 -02
.1270 -01
.194G -}-U2
J89G -03
-.3740 -02
.3734 -07
.272U -02
--.1195 -01
---.2607 -103
.97b0 -{-04
.3801) U3
.iin2 --u~
.7425 --02
.2732 -01
.1246 -}-02
.4G88 -03
--.3164 -02
.3336 -07
.2299 -02
-.2737 -01
--.2768 +02
.7G81 +04
.2020 -t0`L
.1278 -02
.(i5fi3 -02
' .'1869 -01
.950H -{-UI
.1868 -03
-.41G5 -02
.:510 -07
.2176 -02
--.295L --01
.2324 -F03
.G73U -}-04
.2H3U q-01
[Continued on following page]
282
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500010014-0

APPROVED FOR RELEASE: 2007/02109: CIA-RDP82-00854R000540010014-0
Table 5.7. [Continued]
FOR OFFICIAL USE ONLY
ndp.me,p
1(menexMe, �r
ioo 1 600
T- 7000 K; pK - s
oK ' .
M
.1077 -10'l .1187 - f 02
.1333 -1 02
p
.1845 --01 .2043
12295 -1-01
h
.2174 -1-05 .1736 -{-05
.1302 -1�05
s
.1680 -4-02 .1451 -{-02
.1240 02
h;
.1475 -t-06 .1566 06
.1243 +06
- I'
.2749 .6989
.1604 -}01
t~
.3917 -03 .6410 -07
.9967 -03
.1039 - 01 .1 I 1 G--- 01
.1101 --01
A~
.1061 --01 .1242 -01
.1944 - -01.
a
3016 -1-02 .3103 -102
.2278 -}-02
at
.1626 Il'l .1657 (12
.1010 02
UKK
-.629q - 02 .4857 --IMI
--A222 - -02
I )T
K
-
.9241 - 07 .5442 - 07
.3016 07
DK
.3151 02 .3946 -02
.3798 -02
xT
. ..i735 - o:l .8268 --0'l
-.1955 -QI
XK
- -.595!1 -10;1 3788 J-03
--.2105 -}-03
Ak
. i I'.I:f -{05 1591 --05
.1534 -1-05
1~R
2780 -t 05 .7150 -}-03
.3670 -}02
T = 8000 K: OK = 6
09f,
- M
.1018 102 .1123 -1-02
.1250 -}-02
p ~
1570 - 01 .1700
.1898 +01
h
.2504 -}-05 .2159 A-45
.1717 -F05
s
.1725 -1�02 .1508 -}-02
.1295 -{-02
h,.
.1572 -1�06 .1747 +06
.1667 +06
. 1'
.2203 .6165
.1497 -F01
~
.3985 -03 .5680 -03
.9172 -03
7.'
.1268 - 01 .1426 -01
.1519 -01
iz
.1277 - 01 .1475 --01
.1843 -01
a
.;iSbQ -f Om .4201 +02
.3623 -E02
- a
.1905 02 .2263 - 02
.1718 -02
UKK
- .781%7 --0'l --.6280 -02
---.6008 --Q2
_ DK
.I046 - Ofi .6807 -01
.3483 --07
UK
3661 - U2 .4912 - -02
,5366 --02
' T
i
- J118 - 0' --.5657 -02
V
--4671 -01
K
--.5103 �f-03
-.8182 �103
-.2792 +03
� kE
.I;'rt(i -10'# .2200 -I Q5
.2462 �1-05
R
.9050 -105 .17;I0 -104
.6300 -1-92
[Conti.nued on following page]
.1519 +02
.1317 +02
.9(KJ9 -}04
.1090 1-02
.6102 -}-05
I .3042 -}01
.I187 -02
.9890 -02
.2833 - 01.
.1657 -1-02
.5382 -OJ
-.439G --0'l
.3456 -07
.3fi41 -n2
-.2774 --01
-.1093 -}-02
.1231 A�U2
.4800 -{-O!
.1386 -}-02
.1058 +01
.1370 +06
.I153 +02
~ .1265 -{-06
.27J4 -}-01
.1148 -02
.1412 -�01
.2487 -01
.2904 02
.942G --03
-.4805 -02
.2t169 ---07
.51b1 -02
-.23b3 -01
-:1307 1-03
.ai4o -Hos
.84120,-}-4i
283
FOR OFFICIAL USE 01VLY
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Table 5.7. [Contiriued]
n.p.MeTp
Aasrexxe, ar
io
I
[Continued o., following page ]
284
FOR OFFICIAL USE ONLY
600
T=
10000 K; OK=60%
M
.I032 -1-02
.IUfiI -}-02
.1151 -1-02
.1247 -1-02
P
.1130 -01
.1281
.1410 -{01
.7694 A-01
h
.3000 -}-05
.2807 +05
.2404 -1-05
.1077 -}-05
s
.1780 -}-02
.1580 -F02
.1372 -}-02
.1232 -}-02
h,
.1942 -}-06
.2018 06
.2142 +06
.2032 -}-06
1'
.1443
.4391
.1190 -{-01
.2212 -}-01
~
A7fr1 ---03
.5647 --U3
.8433 - --03
.1122 _._02
.1711 --Ill
2(Y19 --01
.2437 01
.2497 -02
~y
. I 7'l3 ----01
.2044 - - 01
.2514 0'
.2809 -01
a
A401 102
5782 -102
.6144 -I 0'l
.5307 -1-02
ac
.'l:flil - 112
.3124 --02
.3179 -02
.2221 -02
UKK
1012 -01
---.9227 -11'l
-.7206 -02
--.6230 -02
UK
.I'll:i ---UG
.9007 - 07
.5006 - 07
3165 -07
UK
A509 - 02
.6614 - ~ 02
.t)f199 -02
.8356 - 02
7lT
.4325 03
-.2373 -03
--.1376 --01
-2178 -01
AK
---.1243 +(M
-.8212 -1-03
-.2723 -}-03
-.7488 +02
XE
.2328 +05
.3411 -{-05
.4535 +05
.4560 -}05
1lR
.9010 -}-06
.1190 -}-05
.2540 -}-03
.2590 -E02
�
7' =
12 000 K; OK - 5
0%
M
~ .1009 -1-02
.1039 -1-02
.1 09g -{-02
.1174 -}-02'
P
~ (100 -01
.1042
.1120 -}-01
.6065 1-01
h
' -}-05
.3342 -}-05
2990 -}-05
.2664 +05
S
.1845 +02
.1629 -}-02
.1425 -}-02
.1284 -}02
h,
.3180 +06
.2460 -F06
.2526 -E�06
.2585 -4-06
r
.1034
.3157
.9187
.1810 -{-01
71
.55H3 -01
.6396 - 03
.8622 -03
.1146 --02
)L1
.2142 QI
.2622 ---01
.3380 --01
.3758 -01
.2337 - 01
.2666 - 01
.3401 -91
.3890 -01
a
.5271 +0'l
.6926 +02
.8324 -}-02
.7794 -}-02.
a
.2825 - -02 1
,3730 --02
.4408 --02
.3572 --02
UKK
J402 02
-.1140 -01
-.1085 --01
-.8141 --02
L)t
.IGUG -Ofi
a1,127 - fM
.F656 --07
.4106 -07
1)K
.4411 - 02
.7839 -02
.1094 --01
.11G6 -01
),T
. .5901 01
--.9994 -03
-.1078 -01
-2181 -01
IK
---.1250 -1-04
-.1012 4-04
-11680 -1-03
.2955 -}-03'
xE
.3263 -1-05
.4733 +05
.6781 -}-05
.7488 -105
.1400 -~07 j
~
.6310 -1-05
.9020 A 03
.6790 -f-02
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Table 5.7. [Continued]

. . . Asuxexne. ar
_ IlRpOwetp
(
~
I 10
I ICO
T ~
ib 000 K: P K = 509fi
M
.8515 +01
.9R50 01
.1049 -}-02
P
.6757 --02
.7881 -01
.8543
- h
.7288 +05
.4712 4-05
.3869 4-05
s
.2105 -{-02
.1729 +02
.1489 -F02
h,
.10()9 -F-OT
A933 +06
.3407 -}-06
r
.7933 -01
.2171
.6328
-
.4933 --Q3
.7529 ---113
.9885 --03
~
.2436 ---01
.:I510 -01
.4786 -01
~E
A264 - 01
.4183 -.01
.4983 -01
~
.711,79 �102
.8746 -1-02
.1085 -}-03
_ fz
.3825 -02
A692 -(Yl
.5774 --02
/)KK
. 24:I0 -02
-.8621 -02
--.1246
_ -01
/)K
.1175 - 06
.1532 06
.1004 - 06
1)K
.1361 - 02
.59112 -02
.1290 -01
xr
--.5448 - 01
-.5284 -02
-.1183 --01
7lK
-.4809 +03
-.7502 +03
-.1670 +03
;,F
.52.58 4� 0.5
.7164 4-05
- .1044 06
XR
.1330 +08
.3250 sj
I .1340 +04
T = 20 000 1(; PK =
50�.fi'
Ni
.6993 +01
7769 4-01
.9300 +01
p
.4156 -02
.4672 --01
.5677
h
s
.1292 : f (Ni
2438 4-02
.I078 +Ofi
.6751 +05
.
.2052 402
.1651 4�02
- h'
.I!r,IG -}-07
.1517 -407
.8533 -1-06
I'
.5075 -01
.1517
.4162
q
.1917 -03
.5619 --03
.1142 --02
h'
.2659 -01
.4457 --01
.722E --0I
l~x
.:IBIS -01
.7420 � -pl
J294 - 01
n
,1010 +03
.1319 -1�0,1
.1593 -F03 - I
a
.5411 - U2
.7018 --02
.8473 -02
1) KK
-.6d198 -�03
-:I!M,7 -02
--J427 -02
DK
.I101 --07
.6779 -07
.I094 -06
UK
.8060 -04
.1013 -02
.6917 -42
XT
--.3850 -02
-.2575 -01
-.5405 -01
I K
--.9239 +03
- �.IOJS +04
830 +03
;,E
.9390 +05
.1297 +06
.18i4 -}-06
XR
.1220 J-os ~
: i8so +07
.2060 -1-05
[Contin-.:ed on followii g page ]
285
FOR OFFICIAL USE ONLY
600
�1106 02
.4570 +GI
.3479 -}-OS
.1044 -}02
.3281 +06
.1306 +01
.1275 -02
.5706 -01
.b801 -01
.1113 -f 03
.5516 -02
-.1131 -01
.6107 - 07
.1548 -01
-.231-1 -01
.121G +04
,1234 -{-06
.2G90 -{-03
.-A
.1016 -E02
.31N3 +01
.5343 +05
.1449 +02
.G022  06
.8413
, J 5G7 -02
.9187 -01
.1054
.171Q +03
.8780 -022
-.1257 -0)
.1014 -OG
.155N -01
-.5745 -01
.2487 -{-04
.2276 -{-06
.1170 +04
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Table 5.7. [Continued]
I I
-
� Aanneuwe. ar
APBNlTQ
1
1
10 1
loo ~
500
.
T= 30 UclO K; ~K 50%
M
.6013 �4-01
.6493 +01
.7100 -1-01
.7845 -}-01
P
.2,178 -02
.2rM -01
.2882
.1626 1-01
h
.2402 -{-0(3
.I054 -}-OG
.I556 +OG
.IQ69 "-}-OG
s
.2874 -}-02
.2419 -1-02
.2010 -}02
.1742 -}-02
hc
.2139 4-07
.2437 -}-07
.2220 -{-07
.1815 -4-07
I'
.2fi55 -01
.7810 -01
.2290
A830
Ti
AE
rt
a
KK ,
J)K
K
;Lr
A K
XF.
XR
A
M
P
h
s
hc
r
11
A'
),E
~i
a
DKK
J)K
1)K
Xr
AK
X r:
XR
.7275 -04
.37H2 -UI
.;1y25 --01
.12fi9 �1-U3
.N'l76 --02
---.4204 - A3
.1608 � 08
. -�.!2!19 -02
--,I1385 --01
-.1023 +04
.1674 +Ofi
T-
.5451 -h01
.1615 -02
.3G04 -}-Ofi
�7212 -}-02
.9797 -}-07
.ir,9i! --oi
.fG19 -M
.fi492 _ .01
.55Al --01
.114Q �1-O;f
-.in49 - oi
~ .47fi1 --01
.19'l8 OS
- I fi94 --02
2584 � 01
.4372 -1-01
.2507 � 1 Ofi
.27GT 03
.1i137 � -01
.G9G7 -�OI
.IA20 OZ
.IQAO --01
. I11'lG --02
.:1194 - 08
I 370 - 02
--.41290 -01
--.7243 -}-03
.2578 +OG
.51,30 -1-08
000 K; OK = b
.5819 +01
.17:14 -01
.2995 -}-06
.2723 -}-02
.2A04 -}-07
.-wU - ot
.1144 --0;1
.Afi01 -_01
.8725 --01
.
:2075 -1-03,
.14()9 �01
. .9:146 03
.28(KJ - OA
-.2538 - 02
-.15A7 - 01
.4669 -}(14
.:i832 - f 06
.ao4n A os
286
.85:fA - 03
.IIAI
.1349
.2GG7 A-03
- -01
.1455
--.2930 --02
- - 07
.1586
-.9842 --04
-.5138 -QI
, -A274 -}-U4
.39N2 -}-OG
.3130 (16
.1672 -02
.1768
.2051
.3t4A -I-O:!
.1671 -01
--.6;146 -02
.3787 -07
.2505 -02
-.109fi
--.5177 �}-04
.5172 Ofi
.9630 -}-(M
.6166 +01
.1868
.2588 -F06
.2306 +02
.27fi1 +07
.1485
.G65G -F01
.1027 41
.2181 +08
�2002 +02
.2G25 +07
.3130
.429fi - 03
.1449
.Ifil4
.3011 Q3
.I9'l7 - 01
- .21,74 02
.4489 OA
--.3A90 --02
- 01
.6174
.11173 04
.6914 -}-06
.4640 07
FOR OFFiCtAL USE ONY.Y
.1 2W -n2
.2354
.25GG
.4110 -{-03
2451 �--QI
--A7fi0 - Oi
~.9'l50 ---08
~
- .3093 - 02
--,I 29fi
-.2821 �{-OR
.8372 -V 06
.IU10 +OG
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Notations in Bibliography
ZhETF
--,7ournal of Experimental and Theoretical Physics
ZhpMTF
--Journal of Applied Mechanics and Engineering Physics
ZhPS
--Journal of Applied Spectroscopy
Yj
ZhFIQ1
--Journal of Physical Chemistry
ZhTF
--Journal of Engineering Physics
DAN SSSR
--Reports of the USSR Academy of Sciences
TVT
--Thermophysics of High Temperatures
_ UFN
--Advances of the Physical Sciences
_ TMF
--Theoretical and Mathematical Physics
Trudy MAI
--Proceedings of the Moscow Aviation Institute
Trudy FIAN
--Proceedings of the Physics Institute, USSR Academy of Sciences
Preprint IPM
--Preprint of Institute of Applied Mathematics
IQzF'TI
,
--Khar' kov Physicotechnical Institute
MZhG
--Mechanics of Fluids and Gases
JQSRT
--Journal of Quantuan Spectroscopy and Radiative Transfer
Phys. Rev.
--The Physical Review
Rev. Mod. Phys.
--Reviews of Modern Physics
287
-4
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BIBLIOGRAPHY
Bibliography to Preface
1. Second Sympositun on Uranium Plasmas, Research and Applications, Atlanta,
Georgia, 1971.
2. "Dinamika i upravleniye atomnym raketnum dvigatelem" [Dynamics and Contirol of
a Nuclear Rocket Fhgine], edited by B. N. Petrov, Moscow, Atmoizdat, 1972.
3. Iyevlev, V. M., ?ZVESTIYA AN SSSR. SERIYA ENERGETIKA I TRANSPORT, No 6, 1977.
- 4. Thom, M. G. and F. K. Shwenk, RAKETNAYA TEKHNIKA I KOSMONAVTIKA, Vol 16,
No 1, 1978.
Bibliography to Chapter 1
1. Iyevlev, V. M. IZVESTIYA AN SSSR. SERIYA ENERGETIKA I TRANSPORT, No 6, 1977.
2. Ebeling, W., PHYSICA, Vol 43, 1969.
3. Shpil'rayn, E. E., K. A. Yakimovich et al, "Teplofizicheskiye svoystva
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- Izdatel'stvo standartov, 1970.
4. Semenov, A. M.-and E. E. Shpil'rayn, "Equation of State of A Chemically Re-
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State of Gases and Fluids], Moscow, zzdatel'stvo Nauka, 1975.
5. Gurvich, L. v., G. A. IQzachkuruzov et al, "Termodinamicheskiye svoystva in-
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Moscow, Izdatel'stvo AN SSSR, 1962.
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_ kotemperaturnoy plasmy" [Thermophysical Properties of Low-Temperature Plasma],
- edited by V. M. Iyevlev, Moscow, Izdatel'stvo Nauka, 1976.
7. Fortov, V. Ye., B. N. Lomakin and Yu. G. Krasnikov, TVT, Vol 9, No 5, 1971.
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Mechanics], Moscow, Izdatel'stvo Nauka, 1964.
_ 9. Norman, G. E. and A. N. Starostin, TVT, Vol 8, No 2, 1970.
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Izdatel'stw Nauka, 1971.
288
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11. Kudrin, L. P., "Statisticheskaya fizika plazmy" [Statistical Physics of a
- Plasma], Moscow, Atomizdat, 1974.
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Dissertation for poctor of P',ysicomathematical Sciences, Izdatel'stvo IVT
AN SSSR, 1972.
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Vol 44, No 11, 1966.
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tr.anslated from English, Moscow, Izdatel'stvo Energiya, 1970.
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26. Vedenov, 1. A. and A. I. Larkin, ZhETF, Vol 36, No 4, 1959.
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289
FOR OFFICIAL USE ONLY
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_ 30. DeWitt, H. E., JOIJRNAL OF MATHEMATICAL PHYSICS, Vol 7, No 4, 1966.
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34. Vorob'yev, V. S. and A. L. Khomkin, TMF, Vol 8, No 1, 1971.
35. Krasnikov, Yu. G., ZhETF, Vol 73, No 2, 1977.
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teorii polya v statisticheskoy fizike" [Methods of Qu,antum Field Theory in
Statistical Physics], Moscow, Fizmatgiz, 1962.
38. March, N., W. Young and S. Sampantchar, "Problemy mnogikh tel v kvantovoy
mekhannike" [Problems of Many Bodies i.n Quantum Mechanics], translated froni
_ English, Moscow, Izdatel'stvo Mir, 1969.
39. Isihara, A., Statisticheskaya fizika" [Statistical Physics], translated from
English, Moscow, Izdatel'stvo Mir, 1974.
40. Fradkin, Ye. S., in "Kvantovaya teoriya polya i gidrodinamika" [Quantum Fie1d
Theory and Hydrodynamics], Trudy FIAN, Moscow, Izdatel'stvo Nauka, 1965.
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ar..d T. Murphy, PHYSICS OF FLUIDS, Vol 12, No 7, 1969; del Rio, F. and H. De-
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No 6, 1966; Hansen, J. P., Phys. Rev., Vol A8, No 6, 1973.
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Chasovskikh, V. P., "investigating Equilibrium Properties, the Structure and
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