Analyzing the Effect of Energy Anisotropy on Electromagnetic Ordinary Mode and Purely Transverse Extraordinary Mode

Abstract

The effects of energy anisotropy has been analysed for the Ordinary mode (O-mode) and the purely transverse Extraordinary mode (X-mode). By using kinetic theory, the general dispersion relations for O-mode and X-mode have been derived. The stability condition and growth rates have been calculated with the help of energy anisotropy, magnetic field to density ratio \(\left(\Omega_{0} / \omega_{p}\right)\) and the plasma beta \(\beta_{\|}\) . The stability of the said modes and the growth rates showt the dependenace of stability on plasma beta  \(\beta_{\|}\) and energy anisotropy \(T_{\perp} / T_{\|}\). The marginal threshold plasma beta and energy anisotropy  \(T_{\perp} / T_{\|}\) The marginal threshold O-mode, the dependance of oscillatory and purely growing mode on energy anisotropy are totally opposite to each other.
On the other hand, the X-mode satisfies the instability condition according to difference of geometry with the O-Mode. These modes are important for spherical tokamaks, their coupling leads the generation of the Bernstein mode, which causes the heating effects.