Calculation of non-uniform solenoids for focusing and acceleration of charged particles

Abstract

In this work the more complex problem is solved by means of using Tikhonov′s regularization method: the sections parameters of a specific kind are calculated. These can be for example a winding thickness, length or a section internal radius etc., i.e. the values of magnetic field intensity are depending, generally speaking, in the nonlinear way. The method described here is illustrated by solving the problem in case of defining the winding thickness for a solenoid with rectangular cross-sections.