title: Nonlinear dispersion of stationary waves in collisionless plasmas.
abstract: A nonlinear dispersion of a general stationary wave in collisionless plasma is obtained in a nondifferential form expressed in terms of a single-particle oscillation-center Hamiltonian. For electrostatic oscillations in nonmagnetized plasma, considered as a paradigmatic example, the linear dielectric function is generalized, and the trapped particle contribution to the wave frequency shift Δω is found analytically as a function of the wave amplitude a. Smooth distributions yield Δω ∼ a(1/2), as usual. However, beamlike distributions of trapped electrons result in different power laws, or even a logarithmic nonlinearity, which are derived as asymptotic limits of the same dispersion relation.
authors.affiliation: Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: I Y
authors.initials: IY
authors.lastname: Dodin
authors.forename: N J
authors.initials: NJ
authors.lastname: Fisch