Approximation of Space Charge Effect in the Presence of Longitudinal Magnetic Fields

The space charge effect plays a significant role in the evolution of phase space during beam transport. Applying an external longitudinal magnetic field has been shown to effectively reduce beam expansion through the mechanism of beam rotation. In this article, we present a fast approximation algorithm for estimating the impact of an external magnetic field on beam expansion. The algorithm enables efficient computations and provides insights into controlling the phase space dynamics of the beam in the presence of longitudinal magnetic fields.