Motion of a charged particle in an axisymmetric longitudinal magnetic field that is inversely proportional to the radius

Abstract

An exact solution to the equations of motion of a charged particle in an axisymmetric magnetic field inversely proportional to the distance from the axis of symmetry is described and a FORTRAN code computing this solution is provided. This solution involves only elementary mathematical functions, however, it requires finding a root of a transcendental equation numerically. Although not particularly complicated in principle, this process is tedious in implementation as it requires considering several distinct types of solutions determined by the initial conditions as well as developing procedures for selecting the correct branches of the inverse trigonometric functions at multiple turning points. While this exact solution has been mentioned in the literature, its detailed description has been lacking. Program SummaryProgram title: BinvRCatalogue identifier: AEVC_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEVC_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 1681No. of bytes in distributed program, including test data, etc.: 62457Distribution format: tar.gzProgramming language: FORTRAN 90.Computer: Generic.Operating system: Unix-like.RAM: 100 K bytesClassification: 4.14, 4.3, 19.Nature of problem:Tracing the motion of a charged particle in a particular magnetic field.Solution method:Implementation of an analytical result.Restrictions:Particular form of the magnetic field.Running time:0.03 second for 1000 points