Relativistic waves raised by explosions in space as sources of ultra-high-energy cosmic rays

The paper discusses the possibility of particle acceleration up to high energies in relativistic waves generated by various explosive processes in the interstellar medium. We propose to use the surfatron mechanism of acceleration (surfing) of charged particles trapped in the front of relativistic waves as a generator of high-energy cosmic rays (CRs). Conditions under which surfing in the waves under consideration can be made are studied thoroughly. Ultra-high-energy CRs (up to 10²⁰ eV) are shown to be obtained due to the surfing in relativistic plane and spherical waves. Surfing is supposed to take place in nonlinear Langmuir waves excited by powerful electromagnetic radiation or relativistic beams of charged particles, as well as in strong shock waves generated by relativistic jets or spherical formations that expand fast (fireballs).