Modeling the APLE injector solenoid magnetic field with the Biot-Savart law

Abstract

The APLE (Average Power Laser Experiment) photoinjector uses four cavities to accelerate electrons to 5 MeV. A solenoid placed between the first two cavities focuses the low energy (1.2-MeV) electron beam. Once the beam profile at the photocathode is determined, the beam transport and the beam quality of the injector depend on the detailed field profile of the solenoid. Previous study showed that the stacked current loops with a canted common axis could not describe the measured magnetic field profile. In this paper, we modeled the fields accurately by integrating the fields from each section of the solenoid using the Biot-Savart law. By comparing the measured profiles with the calculated profiles of transverse magnetic fields on the beam axis z, we determined the angle of the solenoid axis by a best match of transverse field components. We then implemented the Biot-Savart algorithm in the particle simulation code PARMELA and calculated beam qualities at optimized injector conditions. This study shows that the transverse fields calculated from the Biot-Savart law for a canted solenoid can describe the asymmetric profiles. Also the degree of sensitivity to the transverse field from the misaligned solenoid was revealed through the calculations.