New mechanism of particle acceleration and relativistic analog of the Fermi–Ulam model

An investigation is made of a relativistic analog of the Fermi–Ulam model in which a relativistic particle moves vertically and freely between parallel horizontal infinitely heavy walls that move in the vertical direction in accordance with a periodic law, the particle interacting with the walls in a collision in accordance with the law of elastic impact. The possibility of unlimited growth of the energy of the particle is proved; specifically, unbounded growth of the energy is realized for all initial data in some open set, and the asymptotic behavior of such growth is found.