Elliptic vector loci of average electron velocity of electron swarm in constant-collision-frequency model gas under ac electric and dc magnetic fields crossed at arbitrary angles

Hirotake Sugawara; Yuya Nakata

doi:10.1140/epjd/s10053-022-00346-1

2024 Impact factor 1.5

Atomic, Molecular, Optical and Plasma Physics

Molecular collisions, photoionization and dynamics: honouring Professor Vincent McKoy

Eur. Phys. J. D (2022) 76: 32
https://doi.org/10.1140/epjd/s10053-022-00346-1

Regular Article – Plasma Physics

Elliptic vector loci of average electron velocity of electron swarm in constant-collision-frequency model gas under ac electric and dc magnetic fields crossed at arbitrary angles

Hirotake Sugawara^a and Yuya Nakata

Graduate School of Information Science and Technology, Hokkaido University, 060-0814, Sapporo, Japan

^a sugawara@ist.hokudai.ac.jp

Received: 29 October 2021
Accepted: 13 January 2022
Published online: 15 February 2022

Abstract

The analytic solution of the average electron velocity vector $W (t)$ $\mathbf {W}(t)$ of an electron swarm in gas under ac electric and dc magnetic fields ( $E (t)$ $\mathbf {E}(t)$ and $B$ $\mathbf {B}$ , respectively) in a constant-collision-frequency model is extended to cover not only the known case of a right crossing angle ( $E (t) ⊥ B$ $\mathbf {E}(t) \perp \mathbf {B}$ ) but also the cases of arbitrary crossing angles ( $E (t) ⊥̸ B$ $\mathbf {E}(t) \not \perp \mathbf {B}$ ). The x, y, and z components of $W (t)$ $\mathbf {W}(t)$ are obtained as explicit formulae with the following parameters: the amplitude E of $E (t)$ $\mathbf {E}(t)$ , the angle $θ$ $\theta$ between $E (t)$ $\mathbf {E}(t)$ and $B$ $\mathbf {B}$ , the angular frequency $ω_{E}$ $\omega _E$ of $E (t)$ $\mathbf {E}(t)$ , the cyclotron angular frequency $ω_{B}$ $\omega _B$ (subject to the strength B of $B$ $\mathbf {B}$ ), and the electron collision frequency $ν$ $\nu$ . A basic feature that $W (t)$ $\mathbf {W}(t)$ draws elliptic locus in velocity space is unchanged even under $E (t) ⊥̸ B$ $\mathbf {E}(t) \not \perp \mathbf {B}$ , but the plane including the locus may tilt when $ω_{E}$ $\omega _E$ , $ω_{B}$ $\omega _B$ , or $ν$ $\nu$ varies. The derivation of $W (t)$ $\mathbf {W}(t)$ based on the analytic solution of single electron motion is detailed and fundamental behavior of the $W (t)$ $\mathbf {W}(t)$ loci is observed to understand the electron transport under $E (t) \times B$ $\mathbf {E}(t) \times \mathbf {B}$ fields.