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Submitted on 1 Jan 1979
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THE CONDUCTIVITY OF DENSE CAESIUM PLASMA NEAR THE SATURATION LINE
A. Lagar’Kov, A. Sarychev
To cite this version:
A. Lagar’Kov, A. Sarychev. THE CONDUCTIVITY OF DENSE CAESIUM PLASMA NEAR THE SATURATION LINE. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-691-C7-692.
�10.1051/jphyscol:19797335�. �jpa-00219328�
JOURNAL DE PHYSIQUE CoZZoque C7, supplgment au n07, Tome 40, JuiZZet 1979, page C7- 691
THE CONDUCTIVITY OF DENSE CAESRlM PLASMA M A R THE SATURATION LINE
A.N. Lagar'Kov, A.K. Sarychev.
I n s t i t u t e o f High Temperatures, U.S. S. R. Academy o f Sciences, Moscow, U.S. S. R.
The measurements of electrical conduc- ionization equilibrium of plasma.The semi- tivity of saturated caesium plasma/l/have conductors theory/4/helps overcome the demonstrated the extremely large values, difficulty.Let us consider the express- exceeding the results of the usual gas- ion for free-energy caesiwll vapuor with kinetic consideration by 5-6 orders of ions in a centre of it.!7e mill suppose magnitude. The mesusement s of conductivity that the concentration of
article
sN(3) at 20 atm./2/have shovm abrupt decreasing depends on co-ordinates.Such dependence in narrow temperature interval near satu- is due to the strong polarization attra- ration line and then according to the gr- ction of caesim atoms to the ion.In or- ovrth of temperature,relatively smooth in- der to take into account the expression creasing(Fig. ).The anomalious behaviour for the free energy is used which corre- of conductivity will be explained here sponds to the Van-der-Waals equation.with the formation of higher-order ionic Thus,the expression for the free energy clusters.The minimum at isobar arises due
to concurrence of two processes:the ionic clusters dissociation and thermal ioniza- tion of neutral atoms.
The influence of heavy ions on conduc- tivity for the first time was discussed by Leckenby and Robins/3/.They showed that the presence of the quadrarner sodiunl cluster would increase the conductivity of sodium vapour by an order of magnitude over that expected for the monomer.The a- tom of caesium has polarization constant which is larger than one for sodim,That is why the caesium vapour at high pressu-
follows
"1 - ~ ~ ~
9'
r p + ~pF = I
a.d t r
~"(-1
l ~ )+ m [& - 4'4p.1 (11
wherepis reciprocal temperature in ene- rgetical units,gthe total volwne,fiiis the volume with characteristic scale of atom-ion interaction, and
8
are the Van der-8aals parameters .The valueNIis the average concentration of particles in the volumeSiq,Mi =
N J ~-
$,N(.t)d$a -a4 -
'-*n/is the average concentration,V (%)is
, , .
the potential of ion-atom interaction from calculation/6/, € is dielectric per- meabil,i@~aking into account the decrease
, , . , , , , ,
re has to contain more heavy ions.The st- of potential due to dipols .interaction.
ructure of such ions is investigated very According to/5/ & ;
I +
$7wS)
badly,there are no data on theirrole in whereeis the polarization constant.For
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797335
C S
the value of d is 430 a;Let us suppose the concentration /1/(Z)is changed very -+strongly in the v ~ l u m e ~ ~ and in the v o l m blthe fluctuation
c ( ? ) 1 .
!ire will find such distribution of concen- tration in the total volumea,which corr- esponds to the minimum of free energy.Por this purpose let us find the change of free energy,due to ionic cluster formati-
on
p" fcl=~fdr'{/~ci,+/) pn[*]-
- Mqo - p ~ c y f l a
+ 13,U / F )
(C/O + I)/€}(2 1
The optimum fluctuation is found from the condition
g ~ h / t c = O .
1t satisfies the followinn eauation-
&C^/2
1 = fexp &B, 3 ' 2 ))- ])/(I+
e;rP g(z))/co) where / 3 ~ ( ~ ) = 4 ~ + ~q
-no - ~ x ~ - c ? N " p
$2)(3)
c ~ = I/dd
-
1At small temperatures the equation(3)can have three roots.The smallest and the largest ones are realized,that corresponcb to the phase transition from gas to liqu- id state inside the cluster.At high tem- peratures equation(3)has one root and there
is no transition inside c1uster.B~ means of free energy minimization we get the equation for concentration of negatively and positively charged particles.We supp- ose that electron-neutral atom and ion2 neutral atom interaction is dominant,wh- ile electron,electron-electron,ion-electr on interactions are negligible.So we have
dB where
r+/)
ce,
S
.r
+=- ~ ~ d z ' f k + f l ~ [ & - ] - d ~ " a ~ ,,,
The quantity dltcan be written analogical- ly.The calculations show that the concen-
tration of negatively charged particles has a deep minimum at isobar.This minimum corresponds tg the minimum of conductivi-
ty in Pig.The same methods as in /7,8/
were used for the calculat.ion of electri- cal conductivity of a dence caesium plas- ma.The reults are shown in Pig.
1.Renkert H,Hensel F.,Prank E.U.Ber.3un- senges,Phy~.Chem.,~,507(1971) 2.AleBseev V.A. et al.VI 1nter.Conf.High.Pres.Edosco~-J, 677(1975) 3.Leckenby R.E.,Robbins E.T.,
-
J. of Phys. ,lB, 441 (1 968) 4.Xrivoglaz 1vI.A.
Usp.Fiz.Nauk,lll,617(1973) 5.Leckner T., Phys.Rev., 158,130(1967) 6.Valance A., J.
Chem.Phys.,~,355(1978) 7.Lagarrkov A.N.
Sarychev A.K. JETP,E, 641 (1 975). 8.Lagarr Bov A,N.,Sarychev A.K.,Teplofiz.Vys.Temp., 16,903(1978).
0-experiment/l/at saturation line,-'--- experiment/2/, performed at isobar p=20 atm, 0-experiment/l/at 2073K and 2273K, 1-results of present work at p=20atm,2,3,
+results at =0.22,0.43,0.75 'respecti-
p.
vely, f, -critical density,--results at saturation line.
