Pulse-induced memory-like effect in cyclotron motion?

We study how a charged particle moving in a uniform magnetic field along its standard circular path (cyclotron motion) reacts to a short-duration, homogeneous, uniform electric field pulse injected in the plane perpendicular to the magnetic field. A `permanent' change in the radius of the initial circle and a shift of its centre is noted at later times, after the pulse is switched off. The velocity vector (components and magnitude) undergoes a change too, akin to a `velocity kick'. The cause behind this permanent change appears to be linked to the difference between the vector potentials before and after the duration of the electric pulse. Further, we show how such vector potentials in the past and future are related through a gauge transformation. In summary, our results suggest a pulse-induced `electromagnetic memory-like effect', which is not quite a `wave memory', but, nevertheless, has similar features within a simple, non-relativistic context.