On electromagnetic perturbations of geodesic acoustic modes in anisotropic tokamak plasmas

Electromagnetic geodesic acoustic modes are analytically investigated in tokamak plasmas with anisotropy, utilizing gyro-kinetic equations and a rigorously self-consistent anisotropic distribution. When including first-order finite-orbit-width effects and first-order finite-Larmor-radius effects, it is proven that the anisotropy with an arbitrary strength does not induce the m=+/- 1 harmonics of A & Vert;, where m and A & Vert; denote the poloidal wavenumber and the parallel component of the perturbed magnetic vector potential, respectively. The rigorously self-consistent anisotropy introduces an equilibrium electrostatic field with poloidally asymmetric structure, and consequently induces an additional E -> xB -> drift term within the gyro-kinetic equation. This equilibrium electrostatic field inhibits the anisotropy from generating non-zero m=+/- 1 harmonics of A & Vert;. Indeed we demonstrate that introducing anisotropy self-consistently into the equilibrium quantitatively influences m=+/- 1,+/- 2 harmonics of the perturbed electrostatic potential, but only the m=+/- 2 harmonics of A & Vert;.