Closed-form solutions for the trajectories of charged particles in an exponentially varying magnetostatic field

D.C. van Vugt (Corresponding author), L.P.J. Kamp, G.T.A. Huijsmans

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We present a new reference solution for charged particle motion in a strongly inhomogeneous magnetostatic field. The solution describes both bound and unbound particle motion, which can be split into three regimes, the deflection, loop-deflection, and drift regime. We calculate the trajectory in terms of trigonometric and hyperbolic functions, resulting in simple analytical expressions for the particle position and ∇ B-drift velocity. This reference solution is useful to verify and compare the performance of kinetic and guiding-center charged particle pushers in inhomogeneous fields by verifying the conservation of two constants of motion, as well as the exact trajectory at any time.

LanguageEnglish
Pages296-299
JournalIEEE Transactions on Plasma Science
Volume47
Issue number1
Early online date28 Nov 2018
DOIs
StatePublished - 1 Jan 2019

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magnetostatic fields
charged particles
trajectories
particle motion
deflection
hyperbolic functions
trigonometric functions
conservation
kinetics

Keywords

  • Closed-form solutions
  • magnetic fields
  • particle beams
  • particle tracking
  • system verification.

Cite this

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AB - We present a new reference solution for charged particle motion in a strongly inhomogeneous magnetostatic field. The solution describes both bound and unbound particle motion, which can be split into three regimes, the deflection, loop-deflection, and drift regime. We calculate the trajectory in terms of trigonometric and hyperbolic functions, resulting in simple analytical expressions for the particle position and ∇ B-drift velocity. This reference solution is useful to verify and compare the performance of kinetic and guiding-center charged particle pushers in inhomogeneous fields by verifying the conservation of two constants of motion, as well as the exact trajectory at any time.

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