Thermodynamic and Transport Properties of a Dense Semiclassical Plasma
T.S. Ramazanov, K.N. Dzhumagulova, M.T. Gabdullin, A.Zh. Akbarov
Al Farabi Kazakh National University, IETP, Tole bi, 96a, Almaty, 050012, Kazakhstan
Abstract. The thermodynamic and transport properties of dense semiclassical partially ionized plasma were investigated
on the basis of the pseudopotential models taking into account screening and quantum-mechanical effects. The internal
energy was calculated using RDF. The electrical conductivity and diffusion are obtained on the basis of well known
Keywords: dense semiclassical plasma, internal energy, transport coefficients, electrical conductivity, diffusion
PACS: 52.25. Kn, 51.10.+y, 51.20.+d, 52.25.Fi, 51.30.+i
The investigation of kinetic and thermodynamic properties of the dense semiclassical plasma is important for the
study of the astrophysical objects and realization of different technological applications.
In this work we consider the dense semiclassical partially ionized hydrogen plasma consisting of electrons, ions
and atoms. Number density changes in the range of 1020 1024 3 e i n = n + n = ¸ cm- and the temperature domain is
5´104 ¸106 K .
It is convenient to describe plasma state with dimensionless parameters which characterize the physical values.
Coupling parameter • characterizes the potential energy of interaction in comparison with the thermal energy:
( )2 / B G = Ze ak T , where 3 3 4 e a = pn is the average distance between particles. For weakly coupled plasma
G <1. The density parameter is the relation of average distance to the Bohr radius: / S B r = a a , where
B e a = h e m is the Bohr radius. The degree of degeneracy for the electrons is measured by relation of thermal
energy to the Fermi energy: / 2(4 / 9 )2/3 5/3 / B F s Q = k T E = p Z r G, where F E is the Fermi energy for electrons.
The condition Q³1 corresponds to the state of weak and intermediate degeneracy.
The various approaches are used for description of plasma properties with different values of parameters. At the
calculation thermodynamic functions of nonideal plasma there are difficulties connected with taking into account of
interaction of particles. The knowledge of the interaction potentials is necessary. Such potentials should take into
account the specific effects existing in the considered area of densities and temperatures. The pseudopotential model
taking into consideration the quantum-mechanical and screening effects was
In order to determine mass transfer in the plasma, one needs to calculate diffusion coefficient of electrons.
We have calculated the diffusion coefficient using the Chapman-Enskog method:
where ij W is the collision integral; n is the density of particles.
Results of the diffusion coefficient calculations are presented in figure 4.
We can see that the partially ionized plasma has lower electrical conductivity and diffusion than the fully
ionized one. Such behavior of the curves can obviously be explained by large amount of electrons in fully ionized
plasma. While the relative number of atoms in plasma is not high the values obtained for fully and partially ionized
plasma are not strongly different. Discrepancies with other theories can be explained by different methods used for
calculation of the coefficients and different pseudopotential models for the description of interparticle interaction. In
the papers [6-8] the transport coefficients were calculated by the dielectric response method of one and two
component plasma approximation. In the papers  the collision frequency by Ziman formula was calculated. The
Coulomb and effective pair  potentials were used in the papers  and , respectively.
Figure 3. Electrical conductivity of fully and partially ionized
plasma at 1 s r = .1 – ; 2 – ; 3 – ; 4 – Spitzer theory; 5
– our results for fully ionized plasma; 6 – our results for
partially ionized plasma.
Figure 4. Diffusion of fully and partially ionized plasma at
1 s r = . 1 – ; 2 – ; 3 – Spitzer theory; 4 – our results for
fully ionized plasma; 5 – our results for partially ionized
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4. T.S. Ramazanov and K.N. Dzhumagulova. Kiev: Proc. Int. Conf. PLTP-03, 2003, pp. 5-1-61.
5. T.S.Ramazanov, K.N.Dzhumagulova and M.T. Gabdullin, Einhoven, The Netherlands: ICPIG, 1 42 (2005).
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