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[摘要]：A nonlinear dispersion of a general stationary wave in collisionless plasma is obtained in a non-differential 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 Delta omega is found analytically as a function of the wave amplitude a. Smooth distributions yield Delta omega similar to 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. |
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