Nonlinear Alfvén Waves in a Vlasov Plasma

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Abstract
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.

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