Nonlinear absorption in a gas of ions subjected to a magnetic field

A solution is obtained of the problem of interaction of a standing electromagnetic wave with a gas of ions in an inhomogeneous magnetic field. The cases when the Larmor radius of the ions is much smaller and much larger than the transverse size of the wave beam are considered. The width of a nonlinear resonance is found for these cases. It is shown that an inhomogeneity of the magnetic field gives rise to a new effect which can be described as the coherence length for the interaction of ions with an electromagnetic wave.