Relativistic kinetic theory of the large-amplitude transverse Alfvén wave

It is shown that the relativistic Vlasov-Maxwell equations admit a solution very much like the transverse Alfvén wave of magnetohydrodynamic theory. This wave propagates as a plane electromagnetic wave of arbitrary amplitude, is noncompressive, is associated with fluctuations in direction (but not magnitude) of magnetic field, is characterized by a non-linear ‘dispersion relation’, and reduces in the limit of small amplitude to the transverse Alfvén mode of linearized plasma wave theory. The dispersion relation yields a criterion for the firehose instability which turns out to be the same as that derived from linearized theory.