Spherical method of calculation of the trasport coefficients for plasmas in uniform electric and magnetic fields

T. Chohra*, A. Boumeddane and M. T. Meftah

Univ Ouargla, Fac. des Mathématiques et des Sciences de la Matière,

Lab. Rayonnement et Plasmas et Physique des Surfaces, Ouargla 30 000 (Algérie)

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Abstract: The knowledge of the distribution function permits us to determine a number ofimportant parameters, such as, electron mobility, conductivity, etc. The purpose ofthis work is the development of methods for calculating the energy distribution ofelectrons EEDF in a gas of low ion density under the influence of uniform electric andmagnetic fields using the classical Two-term expansion where is expand in terms ofLegendre polynomials (spherical harmonics expansion). In this approximation, theBoltzmann equation takes the form of a convection diffusion continuity equation. The special configurations of the magnetic field parallel and perpendicular to the electric field are discussed in detail.

KEYWORDS: Boltzmann equation, Coefficients transports, Spherical method.

  1. Introduction

Fluid models of gas discharges describe the transport of electrons, ions and possibly other reactive particle species by the first few moments of the Boltzmann equation (BE). Transport coefficients may be rather specific for the discharge conditions. In particular, coefficients concerning electrons depend on the electron energy distribution function (EEDF), which in general is not Maxwellian but varies considerably depending on the conditions.

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  1. Conclusion

The Solutions the Boltzmann equation uniform electric andmagnetic fields, using the classical two-term expansion, and is able to account for exponential spatialgrowth model,electron-neutral and electron-electron collisions. We show that for approximations we use, the Boltzmann equation takes the form of a convection-diffusion continuity equation. To solve this equation we can use exponential scheme commonly used for convection-diffusion problems.

References

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