Asymptotic velocity of relativistic E × B drift

Tatsufumi Nakamura

doi:10.1063/5.0029013

Abstract

We have obtained the asymptotic velocity of a relativistic charged particle in static and uniform electric and magnetic fields with arbitrary orientations of the fields and with an arbitrary ratio of a = |E|/|B|, where the particle is assumed highly relativistic and has a constant velocity. The obtained solution corresponds to the relativistic E × B drift velocity of the guiding-center, which has features different from those of the non-relativistic drift velocity. The latter is given by vD/c = E × B/|B|2, but in the relativistic case, an additional drift motion exists in the direction that is perpendicular to both B and vD. The dependence of drift velocity on the angle between B and E is also modified substantially.

Highlights

Investigations of charged particle motions in electric and magnetic fields are important topics in plasma physics.1 The drift motion of the center of gyration, or the guiding center, of a charged particle in electric and magnetic fields that are static and uniform is a well-investigated case, which is known as E × B drift motion, and is still an important topic in plasma physics.2 Drift motions play crucial roles in various situations, such as the generation of energetic electrons in the magnetosphere, 3 plasma-bubble movements in the ionosphere,4 and particle and plasma dynamics in E × B devices such as Hall thrusters,5 magnetrons,6 and microwave-discharge neutralizers.7Relativistic charged particle motions in a constant electromagnetic field have been intensively studied so far
The charged particle is accelerated by the electric-field component that lies along the magnetic field for θ ≠ π/2, where θ denotes the angle between B and E,19 and is subject to E × B acceleration for θ = π/2.20 We find the following differences between the nonrelativistic drift velocity and the asymptotic velocity in the relativistic scitation.org/journal/adv regime: In the non-relativistic regime, if θ ≠ 0, the electric field accelerates the charged particle along the magnetic field, and the particle drifts in the direction perpendicular to both B and E at the velocity vD/c = E × B/|B|2, while simultaneously undergoing a gyration motion, i.e., cyclotron motion
We have obtained the asymptotic velocity of a charged particle in static and uniform electric and magnetic fields as a solution of the relativistic equation of motion

Summary

INTRODUCTION

Investigations of charged particle motions in electric and magnetic fields are important topics in plasma physics. The drift motion of the center of gyration, or the guiding center, of a charged particle in electric and magnetic fields that are static and uniform is a well-investigated case, which is known as E × B drift motion, and is still an important topic in plasma physics. Drift motions play crucial roles in various situations, such as the generation of energetic electrons in the magnetosphere, 3 plasma-bubble movements in the ionosphere, and particle and plasma dynamics in E × B devices such as Hall thrusters, magnetrons, and microwave-discharge neutralizers.. The drift motion of the center of gyration, or the guiding center, of a charged particle in electric and magnetic fields that are static and uniform is a well-investigated case, which is known as E × B drift motion, and is still an important topic in plasma physics.. We do not derive a solution for the particle trajectory, but instead, we obtain the steady solution of the velocity that is asymptotically reached when the accelerated particle becomes highly relativistic This solution corresponds to the relativistic extension of the E × B drift velocity formula, which expresses the velocity of the guiding center of gyration motion. This paper is organized as follows: In Sec. II, the solution for the asymptotic velocity of a charged particle in static and uniform electric and magnetic fields is obtained for arbitrary orientations of the fields.

ASYMPTOTIC VELOCITY

Comparison with numerical solutions

SUMMARY