Abstract
We derive the collisional momentum and energy transport coefficients in Maxwellian plasmas with a general drift velocity with respect to the ambient magnetic field by using two approaches, the Fokker-Planck approximation and Boltzmann collision integral. We find the transport coefficients obtained from Fokker-Planck representation are similar to those obtained by using Boltzmann collision integral approach, and both results are presented in a closed form in terms of hypergeometric functions. This has been done for drifting Maxwellian plasmas with special emphasis on Coulomb collision, i.e. inverse-square force. Also, we calculate the transport coefficients for two special cases, firstly, when the drift velocity is parallel to the ambient magnetic field (i.e. u = u∥, and zero perpendicular drift velocity), and secondly, when the drift velocity is perpendicular to the ambient magnetic field (i.e. u = u⊥, and zero parallel drift velocity). It is worthy to mention that, up to our knowledge, none of the derived transport coefficients for the above mentioned case are presented in closed form and in terms of hypergeometric function.
Highlights
Transport equations based on an isotropic Maxwellian distribution function were first derived by Tanenbaum (1967), Burgers (1969), and reviewed by Schunk (1977)
They obtained these transport equations by using Boltzmann collision integral approach and presented them in terms of the Chapman–Cowling collision integrals (Chapman and Cowling, 1970). These coefficients are valid for arbitrary temperature differences between the interacting gases, and are restricted to small relative drift velocity between the interacting gases. We removed the latter restriction and calculated transport coefficients for general drifting Maxwellian plasmas that are valid for arbitrary drift velocity differences as well as for temperature differences between the interacting plasma species
We derived these transport coefficients for two special cases, the first one, when the drift velocity is parallel to the ambient magnetic field and the second one when the drift velocity is perpendicular to the ambient magnetic field
Summary
Transport equations based on an isotropic Maxwellian distribution function were first derived by Tanenbaum (1967), Burgers (1969), and reviewed by Schunk (1977) They obtained these transport equations by using Boltzmann collision integral approach and presented them in terms of the Chapman–Cowling collision integrals (Chapman and Cowling, 1970). We removed the latter restriction and calculated transport coefficients for general drifting Maxwellian plasmas that are valid for arbitrary drift velocity differences as well as for temperature differences between the interacting plasma species We derived these transport coefficients for two special cases, the first one, when the drift velocity is parallel to the ambient magnetic field and the second one when the drift velocity is perpendicular to the ambient magnetic field.
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