Hypergeometric function representation of transport coefficients for drifting bi-Maxwellian plasmas

Abstract

We derive the momentum, parallel energy, and perpendicular energy collisional transport coefficients for drifting bi-Maxwellian plasmas by using the Boltzmann collision integral approach and present them in the form of triple hypergeometric functions. In the derivation, we write the drift velocity u of the bi-Maxwellian plasma in terms of parallel and perpendicular components (i.e., u = u‖ + u⊥), parallel and perpendicular with respect to the ambient magnetic field, and we consider the Coulomb collision interactions. We consider two special cases: first, when the drift velocity is parallel to the ambient magnetic field (i.e., u = u‖), and second, when the drift velocity is perpendicular to the ambient magnetic field (i.e., u = u⊥). For the first case, the transport equations and consequently the transport coefficients are derived and presented in the form of double hypergeometric functions; these results are consistent with the findings of Hellinger and Trávníček [Phys. Plasmas 16(5), 054501 (2009)]. For the second case, the transport coefficients are obtained and found to be in the form of double hypergeometric functions. When we combine these two special cases, i.e., for general u, the transport coefficients are shown to be in the form of triple hypergeometric functions. Also, we investigate the above problem by using another approach, i.e., Fokker Planck approximation. We obtain similar results for both approaches.