Shock wave surfing acceleration

Dynamics of a charged relativistic particle in a uniform magnetic field and an obliquely propagating electrostatic shock wave is considered. The system is reduced to a two degrees of freedom Hamiltonian system with slow and fast variables. In this system, the phenomenon of capture into resonance can take place. Under certain condition, a captured phase point stays captured forever. This corresponds to unlimited surfing acceleration of the particle. The preprint is a more detailed version of a comment on the paper by D.Ucer and V.D.Shapiro (Phys.Rev.Lett., vol. 87, 075001, 2001), intended for the Comments section of Physical Reviews Letters.