Abstract
Paraxial optics of charged particles in solenoid magnets with axisymmetric field is considered. Analytic and symplectic transverse maps for charged particle motion through solenoids with 3D magnetic fields have been derived. The formula for transverse maps contains both linear and nonlinear effects caused by entrance and exit fringe fields of the solenoid. The explicit transfer map can be used for applications of accelerator physics that use solenoid magnets.
Highlights
We derived an analytic nonlinear-linear transverse map for single charged particle dynamics through solenoid magnets in a paraxial approximation
Precise linear and nonlinear beam dynamics calculations are performed by using numerical simulations of particles in given 3D fields [9,10]
The solution has been represented in the form of transfer maps widely used in accelerator physics
Summary
We derived an analytic nonlinear-linear transverse map for single charged particle dynamics through solenoid magnets in a paraxial approximation. For calculation of single particle dynamics in solenoids, the most commonly used solution in the form of a transfer map can be found, for example in [1]. This transfer map is a good linear approximation of beam dynamics but it considers only the linear effects and does not take into account the detailed distribution of 3D magnetic field in the solenoid. In this paper we derive an analytic nonlinear transfer map for beam dynamics in solenoids directly from Newton’s force equation for charged particle motion in a 3D magnetic field. The solution has been represented in the form of transfer maps widely used in accelerator physics
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