- Détails
- Catégorie parente: AST Annales des Sciences et Technologie

**Low-frequency electric microfield distribution **

Thouria CHOHRA^{*} and Mohammed Tayeb MEFTAH

*Laboratoire LRPPS, Faculté des Sciences et de la Technologie et des Sciences de la Matière, Université Kasdi Merbah Ouargla, Ouargla 30000 (Algérie)*

**Abstract:**

The knowledge of the electric microfield distribution in multicomponent cold plasma is a necessary condition to solve several problems. In particular, the calculation of the spectral line shapes for an ion, taken as radiator in plasma consisting of neutrals and ions point is one of these problems requiring such distribution. In this work, we are interested in the electric microfield distribution in two-component cold plasma. To reach this goal, we used a useful method based on ”cluster expansion”, widely known in statistical mechanics, in the independent particle approximation. Here we only use the first term of the Baranger-Mozer formalism. The main interactions used are ion-ion and ion-neutral interactions.

**Keywords: **Microfield distribution function, Two-component cold plasma, Cluster expansion, Baranger-Mozer formalism.

**Introduction**

The knowledge of the probability distribution function for electric field in a multicomponent ionized plasmas is a prerequisite to the solution of a number of problems, in particular that of the calculation of the broadening of spectral lines in plasmas [1-7]. In relation to this problem, various theories of the electric microfield distributions have been formulated. The primary aim of these efforts has been to include ion-ion correlations with various orders and thus to improve the original work done by Holtsmark [5].

Since then, severalefforts have been made to improve the statistical description of microfield distribution. The first theory which goes beyond the Holsmark limit and which is based on a cluster expansion similar to that used by Mayer [8] was developed by Baranger and Mozer. In this approach the microfield distribution is represented as an expansion in terms of correction functions which has been truncated on the level of the pair correlation. The latter is treated in the Debye-Huckel form which corresponds to the first order of the expansion in the coupling parameter. The theory of Baranger and Mozer was improved by Hooper [9, 10] and later by Tighe and Hooper [11, 12] based on Broyles' collective-coordinate technique [13]. They reformulated the expansion of the microfiled distribution in terms of other functions by introducing a free parameter which was adjusted in such a way to arrive at a level where the resulting microfiled distribution did not depend on the free parameter anymore. A further improvement of this model was made in Ref [14-16] considering a Debye-chain cluster expansion. Afterwards the Baranger-Mozer second order theory was extended by including higher order corrections, like triple correlation contribution [17].

One distinguishes two parts in the electric field, which are the high-frequency and the low-frequency components. The high-frequency component is that part of the electric field whose time variation is governed by the motion of the electrons. While the time variation of the low-frequency component is governed by the motion of the ions. The problem of low-frequency component of cold plasmas is the subject of this paper. Here the plasma is represented as collection of N particles (ions +neutrals) shielded, which interact with each other through an effective potential. The effective potential includes the effect of ion-electron interactions.

The paper is organized as follows. In Sec 2, we define the system and parameters of interest as well as the theoretical model to calculate the microfield distribution in (TCICP). The theory of Baranger-Mozer for the computation of low-frequency thermal electric microfield distribution is extended here to the cold binary mixture plasma (neutrals + ions). The system we deal with consists of ions and neutrals immersed in a uniform neutralizing background. The total system is assumed to be in thermal equilibrium and neutral at all. The numerical results are given in final section.

**References**

[1] B. Held and C. Deutsch; Phys. Rev. A**, **Vol. **24**, 540 (1981).

[2] B. Held; C. Deutsch and M. M. Combert; Phys. Rev. A, Vol. **29**, 880 (1984).

[3] M. Baranger and B. Mozer; Phys .Rev., Vol. **115**, 521 (1959).

[4] M. Baranger and B. Mozer; Phys .Rev., Vol. **118**, 626 (1960).

[5] J. Holtsmark; Ann. Physik, Vol. **58**, 577 (1919).

[6] C. F. Hooper; Phys. Rev. A, Vol. **149**, 77 (1966).

[7] H. R. Griem; '*Spectral line broadening by plasmas*', Academic Press, (1974).

[8] J. E. Mayer and M. G. Mayer; '*Statistical Mechanics*'; Wiley; New York (1940).

[9] C. F. Hooper; Phys. Rev., Vol. **149**, 77 (1966).

[10] C. F. Hooper; Phys. Rev., Vol. **165**, 215 (1968).

[11] R. J. Tighe and C. F. Hooper; Phys. Rev. A, Vol. **14**, 1514 (1976).

[12] R. J. Tighe and C. F. Hooper; Phys. Rev. A, Vol. **15**, 1773 (1977).

[13] A. A. Broyles; Phys. Rev., Vol. **100**, 1181 (1955); Z. Phys., Vol. **151**, 187 (1982).

[14] C. A. Iglesias and C. F. Hooper; Phys. Rev. A, Vol. **25**, 1049 (1982).

[15] A. Y. Potekhin, G. Chabrier and D. Gilles; Phys. Rev. E, Vol. **65**, 036412 (2002).

[16] H. B. Nersisyan, C. Toepffer and G. Zwicknagel; Phys. Rev. E, Vol. **72**, 036403 (2005).

[17] A. Davletov and M.-M. Combert; Phys. Rev. E, Vol. **70**, 046404 (2004).