Gyrokinetic theory of low-frequency electromagnetic waves in finite-<i>?</i> anisotropic plasmas

We present a gyrokinetic theory for the electromagnetic waves and instabilities with frequencies much lower than ion cyclotron frequency in finite-$\beta$ anisotropic uniform plasmas. Here, $\beta$ is ratio between plasma magnetic pressures. Kinetic effects due to both finite Larmor radii wave-particle resonances are fully kept analysis. Corresponding linear dispersion relation wave polarizations, valid general value perpendicular wavelength, then specifically derived bi-Maxwellian plasma. Analytic expressions criteria of kinetic firehose mirror also given. The mode frequency, stability, polarization broad spectrum normal modes investigated numerically systematic study over set parameters. Our clearly demonstrates that, radius effect, ion-sound wave, mode, shear Alfven intrinsically coupled.