Using a two-fluid approach, we consider the properties of relativistically nonlinear (arbitrary a₀), circularly polarized electromagnetic waves propagating along magnetic field in electron-ion and pair plasmas. Dispersion relations depend on how wave intensity scales with frequency, a₀ (ω). For superluminal branches, the nonlinear effects reduce the cut-off frequency, while the general form of the dispersion relations ω (k) remains similar to the linear case. For subluminal waves, whistlers and Alfven, a new effect appears: dispersion curves effectively terminate at finite ω^ - k^ due to current starvation. Qualitatively, subluminal modes with fluctuating electric field larger than the guide field, Ew (ω) B₀, cannot propagate.
Maxim Lyutikov (Sun,) studied this question.