Interaction of the electro-magnetic precursor from a relativistic shock with the upstream flow. I. Synchrotron absorption of strong electromagnetic waves

This paper is the first in the series of papers aiming to study interaction of the electro-magnetic precursor waves generated at the front of a relativistic shock with the upstream flow. It is motivated by a simple consideration showing that the absorption of such an electro-magnetic precursor could yield an efficient transformation of the kinetic energy of the upstream flow to the energy of accelerated particles. Taking into account that the precursor is a strong wave, in which electrons oscillate with relativistic velocities, the standard plasma-radiation interaction processes should be reconsidered. In this paper, I calculate the synchrotron absorption of strong electro-magnetic waves.