Influence Of Correlations Of The Electric Field On Plasma Waves

A.I. Sokolovsky, A.A. Stupka
Dnipropetrovs’k National University, Department of Quantum Macrophysics,
Naukova Str., 13, 49050, Dnipropetrovs’k, Ukraine e-mail:
Abstract. Closed system of equations for electric field and hydrodynamic medium (many component plasma) has been
obtained taking into account binary correlations of the field. Statistical operator of the system was found on the base of
the Bogolyubov reduced description method and nonrelativistic quantum electrodynamics. Calculations were carried out
in the Hamilton gauge up to the first order of a perturbation theory in interaction. Corrections for the plasma frequensy
were found.
Keywords: equations for electric field and hydrodynamic medium, plasma frequency, Bogolyubov reduced description
method .
PACS: Plasma waves, 52.35. g; Statistical mechanics quantum, 05.30. d.
Coulomb electronic plasma is the most widespread through the simplicity of the model. In the system there are the
Langmuir (plasma) waves [1]. Below the known model is generalized by taking into account ionic basis, which is
assumed to be in a stationary state. More complete account of degrees of freedom of the longitudinal field is conducted
and new independent variables (second correlations of the field) are discussed. This allows deeper describing effects of
the delay than with the Landau and Balescu collision integrals [2]. It gives a possibility to estimate influence of the
mentioned on frequency of plasma waves.

The expressions (17) and (18) for frequency and attenuation constant show an impotence of ions dynamics via
coefficientξ , which corrected plasma frequency. Formula (18) contains new dissipative term connected with
correlations because coefficientθ , which can be a leading contribution compared with an ordinary expression [1].
Expression (17) for frequency contains interaction terms along with the sound velocity. Analogously to above
elaborated theory can be considered hydrodynamics of ion subsystem with electron subsystem is in an equilibrium
The work was supported by the State Foundation for Fundamental Research of Ukraine (project No. 2.7/418).
1. R. Balescu, Equilibrium and nonequilibrium statistical mechanics, New York, 1975.
2. Yu.L. Klimontovich, Kinetic Theory of Non Ideal Gases and Non Ideal Plasmas, Oxford: Pergamon Press, 1982.
3. A. Sokolovsky, A.Stupka, International Conference MMET’10, Conference proceedings, Dnipropetrovs’k, 2004, pp. 234-236.
4. A.I. Akhiezer, S.V. Peletminsky, Methods of Statistical Physics, Oxford, Pergamon, 1981.
5. A.I. Sokolovsky, A.A. Stupka, Condensed Matter Physics, 8, No. 4(44), 2005, pp. 685-700.

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