Electromagnetic effect on geodesic acoustic mode with adiabatic electrons

Abstract

The geodesic acoustic mode (GAM) is analytically investigated by taking into account the finite-orbit-width (FOW) resonance effect to the second order and the finite β effect. The general dispersion relation is derived from the gyro-kinetic equations in the presence of nonzero δA∥, the parallel component of the perturbed magnetic vector potential. Transparent and concise expressions for the GAM frequency and Landau damping rate in the presence of the second order FOW effect and finite β effect are first presented. It is clearly shown that the m = ±2 harmonics dominant δA∥ and the kinetic expression of δA∥ have the same form as the fluid one. For the real frequency, the electromagnetic effect introduces a term on the order of q2β, which is comparable to the second order electrostatic terms, namely, the terms introduced by the second order FOW resonance effect. While for the collisionless damping rate, δA∥ does not directly introduce β–dependent terms, but affects the damping rate via modifying the real frequency. Besides, our analytical result shows good agreement with the numerical examinations.

Gyrokinetic investigations of the electromagnetic geodesic acoustic mode

“…In addition, β can also decrease the frequency and damping rate of GAM, particularly in the large q region, and the effect of β on frequency is less than its effect on the damping rate. This is also consistent with previous results [26,33].…”

“…potential of the GAM are the m = 1 and m = 2 components. This is, however, different from the previous analytical results in the small orbit width limit where the m = 2 component is one order of amplitude larger than the m = 1 component [25][26][27]33]. The detailed comparison between the simulation results and the analytical results, and some discussions, will be given in section 3.…”

“…In addition, the plasma's toroidal rotation [30], radial equilibrium electric field [31] and shaping effects [32] also have a significant influence on the magnetic components of the GAM. Lately, Huang et al [33] studied the electromagnetic GAM under the adiabatic electron condition, and obtained results similar to [26], that the m = 2 magnetic component is dominant. There is a lot of analytical research on electromagnetic GAMs.…”

“…The amplitudes of various poloidal magnetic components of GAMs depend on many parameters [25][26][27]33], such as the ratio of plasma pressure to magnetic pressure β, the safety factor q, the normalized radial wave number kρ i and so on. The dependence of the relative amplitude of a poloidal component on β is shown in figure 8.…”

“…The linear characteristics of electromagnetic GAMs have been analytically investigated in the limit of small orbit width by several authors [25][26][27][28][29][30][31][32][33]. One aspect of concern is the poloidal mode number of the perturbed magnetic component.…”