Memory-like effects and kinematics of trajectories in Cyclotron motion

Abstract

We investigate the collective dynamics of a bundle of charged particles undergoing cyclotron motion in a uniform magnetic field when subjected to a short-duration electric pulse. Using the geometric framework based on the evolution of trajectory congruences, we analyze how the pulse affects the expansion, shear, and rotation of a small family of trajectories. We show that the geometric imprint persists after the pulse has vanished, manifesting as a memory of the transient perturbation. Unlike gravitational memory effects, this does not manifest itself in focusing behaviour of the trajectories, and instead implies a restructuring of the shear component before and after the pulse. We offer direct analytic and regression based arguments for the same.