Parametric decay of plasma waves near the upper-hybrid resonance

An intense X wave propagating perpendicularly to dc magnetic field is unstable with respect to a parametric decay into an electron Bernstein wave and a lower-hybrid wave. A modified theory of this effect is proposed that extends to the high-intensity regime, where the instability rate $γ$ ceases to be a linear function of the incident-wave amplitude. An explicit formula for $γ$ is derived and expressed in terms of cold-plasma parameters. Theory predictions are in reasonable agreement with the results of the particle-in-cell simulations presented in a separate publication.