Theoretical analysis of particle dynamics in time-periodic systems is
of great interest in plasma physics. We have analysed this problem for
the case of both continuous and discrete systems. For the continuous
case, we have derived analytic expressions of the plasma distribution
function in Paul traps and have shown that the time averaged plasma
density is very different from that predicted by conventional
theory. For the discrete case, this problem is termed Fermi
acceleration (dynamical billiards with moving boundaries). In this
case, particles have been shown to undergo unbounded energy growth if
the frozen billiard is chaotic. We have shown that chaos is not
necessary and unbounded energy growth can be obtained with
pseudo-integrable billiards too. In fact, the energy growth in chaotic
systems is only quadratic-in-time whereas in pseudo-integrable systems
it is exponential-in-time!
