Magnetic field effects on spatial relaxation of swarm particles in the idealized steady-state Townsend experiment

Abstract

The effect of a magnetic field at right angles to an electric field on spatial relaxation of a swarm of charged particles emitted by a plane source into a gas-the idealized steady-state Townsend experiment-is examined. The Boltzmann equation is solved using an adaptation of the "two-temperature" moment method, involving a Burnett function representation of the velocity distribution function, a technique which is valid for charged particles of arbitrary mass and is intrinsically of a "multiterm" nature. Results are presented for electrons in model and real gases, and are benchmarked against an exact analytical solution of the Boltzmann equation for a particular collision model. The application of a magnetic field significantly alters the relaxation profiles: in general, it can both enhance or retard spatial relaxation of transport properties. For methane gas, a multiterm analysis is essential to correctly account for the relaxation near the source, even though a two-term approximation may be sufficient when the magnetic field is sufficiently strong and hydrodynamic conditions dominate.

Periodic Electron Structures in Gases: A Fluid Model of the “Window” Phenomenon

“…The key factor in this successful outcome is the established heat flux ansatz, Eq. (5), and its subsidiary (6). The present results can be seen as providing not only an explanation of the window effect per se, but also as furnishing a fluid model of some generality, whose integrity has been stringently tested in a demanding problem.…”

“…Introduction.-The recent resurgence of interest in periodic electron structures in low-current, low-pressure discharges in gases [1][2][3][4][5][6] has been largely driven by the richness and novelty of the associated physics, in particular, the ''window'' phenomenon, a sharply defined range of voltages and gas pressures, within which electron properties oscillate, and outside of which properties simply decay monotonically in space, as illustrated in Fig. 5 of Ref.…”

“…The rigorous link between the microscopic and macroscopic pictures, as described above, is provided by Boltzmann's kinetic equation, which one solves for the electron phase space distribution function fr; v; t and obtains quantities of physical interest as velocity ''moments'' [1][2][3][4][5][6]11]. The solution must proceed numerically in phase space (r, v) without approximation or decomposition in terms of a density gradient expansion [11].…”

Рекуррентная Процедура Построения Неизотропных Матричных Элементов Интеграла Столкновений Нелинейного Уравнения Больцмана

“…Идеи Кумара нашли свое продолжение в работах ученых австралийской школы [5][6][7][8]. В этих работах моментный метод используется в основном для по-строения транспортных коэффициентов при движении заряженных частиц во внешних полях.…”

“…Кумар продвинулся также в исследовании структуры нелинейного интеграла столкновений. Он предложил использовать при расчете нелинейных МЭ преобразо-вание Талми, которое ранее успешно использовалось в квантовой теории.Идеи Кумара нашли свое продолжение в работах ученых австралийской школы [5][6][7][8]. В этих работах моментный метод используется в основном для по-строения транспортных коэффициентов при движении заряженных частиц во внешних полях.…”