### 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.

Language | English |
---|---|

Pages | 296-299 |

Journal | IEEE Transactions on Plasma Science |

Volume | 47 |

Issue number | 1 |

Early online date | 28 Nov 2018 |

DOIs | |

State | Published - 1 Jan 2019 |

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### Keywords

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

### Cite this

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**Closed-form solutions for the trajectories of charged particles in an exponentially varying magnetostatic field.** / van Vugt, D.C. (Corresponding author); Kamp, L.P.J.; Huijsmans, G.T.A.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Closed-form solutions for the trajectories of charged particles in an exponentially varying magnetostatic field

AU - van Vugt,D.C.

AU - Kamp,L.P.J.

AU - Huijsmans,G.T.A.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

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.

KW - Closed-form solutions

KW - magnetic fields

KW - particle beams

KW - particle tracking

KW - system verification.

UR - http://www.scopus.com/inward/record.url?scp=85057423518&partnerID=8YFLogxK

U2 - 10.1109/TPS.2018.2878459

DO - 10.1109/TPS.2018.2878459

M3 - Article

VL - 47

SP - 296

EP - 299

JO - IEEE Transactions on Plasma Science

T2 - IEEE Transactions on Plasma Science

JF - IEEE Transactions on Plasma Science

SN - 0093-3813

IS - 1

ER -