Abstract
Exponential energy growth in a rectangular billiard with an oscillating bar has been clearly demonstrated earlier. Using the log-normal approximation, analytical estimates for the energy growth rate have also been provided. However, these analytical estimates are valid only when the amplitude of oscillation of the bar is small. In this paper, for larger oscillation amplitude, the log-normal approximation is numerically shown to be invalid and analytical estimates are obtained for the true energy growth rate in the case of very large particle velocities or small bar length. It is also shown that when everything else remains constant, the length of the bar which gives rise to maximum energy growth rate decreases as the oscillation amplitude increases and the true value of this maximizing length is also smaller than what is predicted by the log-normal approximation. Thus, the rectangular Fermi accelerator forms a very good example of a contemporary research problem where the limitations of the log-normal approximation can be easily appreciated.
Published Version
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