The influence of plasma evolution on a kinetic scenario of collisional relaxation of a magnetized plasma

Abstract

For a magnetized plasma, a reduction of the two-time formalism [V.~I.
Erofeev, Journal of Plasma Physics \textbf{85}, {905850104} (2019);
V.~I. Erofeev, Contributions to Plasma Physics \textbf{62}, {e202100140} (2022)] to a highly informative scenario of redistribution of charged particles in momentum due to Coulomb collisions is reported. The consideration focuses on the standard case of an ideal classical ionized homogeneous plasma. It is found that the leading-order approximation of the scenario is consistent with the well-known generalizations of the Lenard--Balescu equation [A. Lenard, Ann. Phys. \textbf{10}, 390--400 (1960); R. Balescu, Phys. Fluids \textbf{3}, 52--63 (1960)] that take into account the leading magnetic field effect [N. Rostoker, Phys Fluids \textbf{3}, 922-927 (1960); M.H.A. Hassan, C.J.H. Watson, Plasma Phys. \textbf{19}, 237--247 (1977)]. A correction to the collision integral of this equation is developed that is due to time variations of plasma parameters.

Comment on ‘The influence of plasma evolution on a kinetic scenario of collisional relaxation of a magnetized plasma’

“…Erofeev claimed that Rostoker made an error in the calculation and that the same error also existed in the collision term developed by Hassan and Watson [3]. We have re-derived the magnetized collision term by virtue of the two-point correlation function in [1] and find that the results of Rostoker and Hassan and Watson are correct but the result of Erofeev is not.…”

“…In a recent paper [1], Erofeev studied the influence of plasma evolution on the collision term of a magnetized plasma. It is surprising that when the corrections due to plasma evolution are neglected, the result is different from the Rostoker collision term [2].…”

Reply to Comment on ‘The influence of plasma evolution on a kinetic scenario of collisional relaxation of a magnetized plasma’

“…in accounting for the particle time retardation effect.) Note that the above mistake does not violate the estimates [1] for the characteristic inverse times of particle redistribution in momentum that correspond to different terms of the particle collision integral.…”

“…Paper [1] was devoted to the calculation of the two-point correlation function ⟨δN α (r, p, t) E(r ′ , t ′ )⟩ that drives the time advances of the distribution function f α (p) of charged particles of species α in a homogeneous non-relativistic magnetized plasma. Within the collision integral of the corresponding evolution equation, the spatial Fourier transform of a specific data of the two-point correlation function,…”

“…To correct the kinetic equation (30) in paper [1], the structures (nω Bα ) / (p ⊥ v ⊥ ) that supplement the 'entry' operator (k • (∂/∂p)) n should be removed 1 . The correct form of the generalized Rostoker's kinetic equation is…”