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

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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.

Original languageEnglish
Article number8544029
Pages (from-to)296-299
Number of pages4
JournalIEEE Transactions on Plasma Science
Issue number1
Early online date28 Nov 2018
Publication statusPublished - 1 Jan 2019



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

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