Krook collisional models of the kinetic susceptibility of plasmas

Abstract

An assessment is made of Krook collisional models used to describe the kinetic behavior of collective oscillations, i.e., when Landau damping and collisions must be considered, as is often the case for low-frequency waves. The study focuses on an early energy-conserving model [B. D. Fried, A. N. Kaufman, and D. L. Sachs, Phys. Fluids 9, 292 (1966)] that is shown to be identical to a more modern version used in drift-wave stability studies [G. Rewoldt, W. M. Tang, and R. J. Hastie, Phys. Fluids 29, 2893 (1986)]. The inadequacy of the simpler, and often used, nonconserving model is illustrated. Comparisons are established with recent collisional studies of ion acoustic waves [V. Yu. Bychenkov, J. Myatt, W. Rozmus, and V. T. Tikhonchuk, Phys. Plasmas 1, 2419 (1994)] and electron plasma waves [C. S. Ng, A. Bhattacharjee, and F. Skiff, Phys. Rev. Lett. 83, 1974 (1999)]. A connection is also established with contemporary studies of condensed matter and quantum liquids [K. Morawetz and U. Fuhrmann, Phys. Rev. E 61, 2272 (2000); 62, 4382 (2000)]. A useful empirical fit is found that corrects the Braginskii susceptibility to incorporate the kinetic behavior associated with the Krook kinetic susceptibility.

Dielectric function of a collisional plasma for arbitrary ionic charge

“…To obtain qualitative descriptions of collisional regimes of a plasma the Bhatnagar-Gross-Krook (BGK) [18] collisional model in the kinetic equation for electrons has been widely used with or without number-conservation procedure [7,[19][20][21][22][23][24]. The appeal of this model is its simplicity, which in its original nonconserving form amounts to the replacement of ω → ω+iν in the argument of the plasma dispersion function, where ν is a model collision frequency.…”

“…[25,26] and [27,28], respectively, which yield analytic expressions for the permittivities in terms of combinations of the plasma dispersion function. However, for a completely ionized plasma, the model permittivity within the BGK approximation and the corresponding Drude model for the transverse permittivity [7,[22][23][24] lead to the significant deviations from the known limiting cases in the range of moderate and strong collisions [29][30][31]. For instance, it has been found that this model cannot reproduce the plasma permittivity in the strongly collisional hydrodynamic regime considered in Ref.…”

Final Report DOE Grant No. DE-FG03-01ER54617 Computer Modeling of Microturbulence and Macrostability Properties of Magnetically Confined Plasmas

“…We have recently completed an assessment of Krook collisional models. We found that not only the energy and number conserving operators but also the number conserving Krook operator are adequate to capture collisional effects in the kinetic regime compared to the Lorentz and Lenard-Bernstein collision operators which are more complicated to implement and calculate [LD11]. This effort will help greatly in guiding inclusion of collisions in our particle models.…”

Продольная Диэлектрическая Проницаемость Квантовой Вырожденной Столкновительной Плазмы

“…Конкретно, мы рассмотрим представление интеграла столкновений в форме стандарного модельного БГК-интеграла столкновений [11] (см. также работу [27], где проведено исследование этой модели). Тогда предыду-щее уравнение перепишется в виде…”