Theoretical and Mathematical Physics

Minimal model of the Fermi acceleration

D. M. Naplekov^a, A. V. Tour^b, V. V. Yanovskii<sup>a

a</sup> Institute for Single Crystals, National Academy of Sciences of Ukraine, Kharkov
^b Center D'etude Spatiale Des Rayonnements, C.N.R.S.-U.P.S., 31028 TOULOUSE CEDEX 4, France

Abstract: A simple model of the Fermi acceleration of a particle placed between two periodically oscillating walls is considered. The motion of the walls obeys a continuous (but not smooth) law. An exact map of such a system is obtained. The existence of trajectories with an infinitely increasing velocity is shown. The main characteristics of these trajectories are discussed. The results are compared with those obtained in a high-energy approximation. The exact and approximate descriptions are found to differ qualitatively. Specifically, the trajectories with an infinitely increasing velocity are absent in the high-energy approximation.

Received: 30.06.2009

 English version: Technical Physics, 2010, 55:5, 601–612

Bibliographic databases:

•