Charged-Particle Orbits in Varying Magnetic Fields

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Abstract
A solution for the paraxial orbits of charged particles in varying magnetic fields is given. The magnetic field is assumed to be azimuthally symmetric but is allowed to vary arbitrarily with time or axial distance. The instantaneous guiding center and radius vector of the orbit are given in terms of the initial guiding center and radius vector and two parameters which are determined from the solution of a first‐order differential equation containing the magnetic‐field variation. One exact and two approximate constants of the motion are evaluated and discussed.

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