Interaction of the electromagnetic 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 electromagnetic 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 electromagnetic 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 electromagnetic waves.