Higher branches of the dispersion relation for perpendicular magnetosonic waves in relativistic anisotropic plasmas

Dispersion relations are calculated and solved for frequencies near the first two harmonics (Ω/Ω₊ = 2, 3) of perpendicular magnetosonic waves in relativistic anisotropic plasmas. In this, wavelengths larger than the ion Larmor radius and large plasma frequency (Ω²_p, Ω²₊) are assumed. It is found that, even for Tψ T the plasma is stable. This result has application to the steady-state, spherically symmetrical, expanding, solar-wind plasma.