Exact Nonlinear Evolution of Alfvén Modes in the Guiding-Center Model

Alfvén waves parallel to a uniform magnetic field in a uniform but anisotropic plasma are studied in the Chew-Goldberger-Low and guiding-center models. Exact solutions are found in the stable and unstable cases. When the plasma is stable, an arbitrarily large constant amplitude perturbation perpendicular to the uniform field can propagate without distortion parallel to the uniform field. The exact nonlinear behavior of an unstable circularly polarized Alfvén mode is obtained: growth of a finite perturbation is quenched in a finite time, and decay begins immediately.