Theoretical analysis of the offset-pole periodic cusped permanent magnetic fields

Abstract

The magnetic field excited by the offset-pole periodic cusped permanent magnet （OPPCPM） used for focusing the sheet electron beam has been approximately expressed in two different forms for the convenience of future numerical calculation and theoretical analysis, respectively. Firstly, the surface-current-sheet model has been used to approximate the OPPCPM, and an accurate expression has been obtained using Biot-Savart law. This expression would rather be applied to numerical calculation than theoretical analysis because of the complication. The optimization of entrance taper of the OPPCPM has been performed as an example of application of the expression, implying the high efficiency of the calculation brought by the expression. Secondly, to obtain simple expression of the magnetic field for the convenience of future theoretical analysis, the OPPCPM field has been divided into two parts: the periodic cusped magnetic （PCM） field component and the side-focusing magnetic field component. The expressions of the PCM field component have been obtained using the method of undetermined coefficient, while the expressions of the other one have been obtained using two-magnetic-charge-sheet model. The results are useful to study the transportation of the sheet electron beam in the offset-pole PCM field.