Nonlinear Alfvén Waves in a Vlasov Plasma

Stationary solutions to the nonlinear Vlasov—Boltzmann equations are considered which represent one-dimensional electromagnetic waves in a hot magnetoplasma. These solutions appear in arbitrary reference frames as circularly polarized, sinusoidal waves of unlimited amplitude, i.e., as nonlinear Alfvén waves.

Solutions are found implicitly by deriving a set of integral dispersion relations which link the wave characteristics with the particle distribution functions. A physical discussion is given of the way in which the Alfvén waves can trap particles, and it is shown that the presence of ``cyclotron-trapped'' particles introduces a boundary condition which no set of isotropic distribution functions can satisfy.

An application of these solutions to theories of very low frequency emissions is briefly discussed. ©1965 The American Institute of Physics