Relativistically strong electromagnetic waves in magnetised plasmas

Using a two-fluid approach, we consider the properties of relativistically nonlinear (arbitrary

), circularly polarised electromagnetic waves propagating along a magnetic field in electron–ion and pair plasmas. Dispersion relations depend on how wave intensity scales with frequency, e.g.

a 0 left parenthesis omega right parenthesis a 0 ( ω ) $a_0 (\omega )$

. For superluminal branches, the nonlinear effects reduce the cutoff frequency, while the general form of the dispersion relations

omega left parenthesis k right parenthesis ω ( k ) $\omega (k)$

remains similar to the linear case. For subluminal waves, whistlers and Alfvén, a new effect appears: dispersion curves effectively terminate at finite

omega Superscript asterisk Baseline minus k Superscript asterisk ω ∗ − k ∗ $\omega ^\ast {-} k^\ast$

, where the group velocity becomes zero. Qualitatively, subluminal modes with fluctuating electric field larger than the guide field,

upper E Subscript w Baseline left parenthesis omega right parenthesis greater than or slanted equals upper B 0 E w ( ω ) ⩾ B 0 $E_w (\omega ) \geqslant B_0$

, cannot propagate. In extended systems, e.g. within magnetospheres of neutron stars, this leads to opening of the magnetosphere by a strong wave.