In this paper the classical evolution of a particle is studied which bounces back and forth in a 1D vibrating cavity such that the reflection from the wall does not change the speed of the particle. A peculiar behaviour of the particle motion can be seen where the time evolution of the motion shows superposition of linear and oscillatory behaviour. In particular, the parameter range is found in which the particle oscillates between the walls in steady state as if the wall was static and it is showed that for these parameter ranges the particle settles to this steady state for all initial conditions. It is proposed that this phenomenon can be used to bunch charged particles in short pulses where the synchronization proposed in our model should work against the space charge effect in the charged particle bunch.
Volume 94, 2019
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