Energetic-particle-induced electromagnetic geodesic acoustic mode in tokamak plasmas

Energetic-particle-induced kinetic electromagnetic geodesic acoustic modes (EKEGAMs) are numerically studied in low β (=plasma pressure/magnetic pressure) tokamak plasmas. The parallel component of the perturbed vector potential is considered along with the electrostatic potential perturbation. The effects of finite Larmor radius and finite orbit width of the bulk and energetic ions as well as electron parallel dynamics are all taken into account in the dispersion relation. Systematic harmonic and ordering analysis are performed for frequency and growth rate spectra of the EKEGAMs, assuming (kρi)∼q−3∼β≪1, where q, k, and ρi are the safety factor, radial component of the EKEGAMs wave vector, and the Larmor radius of the ions, respectively. It is found that there exist critical βh/βi values, which depend, in particular, on pitch angle of energetic ions and safety factor, for the mode to be driven unstable. The EKEGAMs may also be unstable for pitch angle λ0B<0.4 in certain parameter regions. Finite β effect of the bulk ions is shown to have damping effect on the EKEGAMs. Modes with higher radial wave vectors have higher growth rates. The damping from electron dynamics is found decreasing with decrease of the temperature ratio Te/Ti. The modes are easily to be driven unstable in low safety factor q region and high temperature ratio Th/Ti region. The harmonic features of the EKEGAMs are discussed as well