Growth rate maps in the -space for magnetic fields of various strength.
(a) Natural modes of the cold plasma and several beam modes for and oblique wave propagation (the angle between and is 10°); (b) lines of mode intersections in the -space (dash lines) superimposed on the instability map. Small circles at the two figures denote corresponding waves.
(a) Exact and hydrodynamic [Eq. (3)] growth rates as functions of for purely longitudinal wave propagation. (b) Exact and hydrodynamic [Eqs. (4) and (5)] growth rates, maximized in , as functions of the wave propagation angle for the modes and at .
Effect of the magnetic field on the angular dependence of the maximum growth rate (determined by either or mode): (a) hydrodynamic approximation and (b) exact solution of Eq. (1).
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