For a special model, it is possible to compute the self-consistent confinement and penetration of an energetic plasma by an rf field of large amplitude for arbitrary values of the quantity $\left(\frac{v}{c}\right) \left(\frac{{\omega }_P}{\omega }\right)$, where $v$ is a characteristic electron thermal speed, ${\omega }_P$ is the plasma frequency deep in the plasma, and $\omega (<\mathrm{}{\omega }_P)$ is the rf frequency. Previous theories concerning nonlinear behavior of electromagnetic waves in plasmas have required this quantity to be small compared to unity.

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