Analysis of fishbone instability excited by trapped energetic electrons on HL-2A tokamak

A generalized dispersion relation for fishbone instability is obtained by considering Gaussian distributions of spatial density and pitch angle of energetic electrons (EEs). The fishbone modes excited by trapped EEs are analysed in detail based on the HL-2A tokamak electron cyclotron resonant heating (ECRH) experiment. Numerical results show that the calculated time evolution of the mode real frequency is in reasonable agreement with the observations in ECRH experiment. Density gradient of the EEs plays an important role in excitation of the modes via resonant interaction between the modes and EEs. The modes are excited at the positions of maximum EE density gradient. The frequency of the mode in the case of on-axis heating is higher than that in the case of off-axis heating. The background plasma tends to prohibit excitation of the fishbone instabilities. The numerical results show that there is a cut-off background plasma density (or background plasma-beta) for the fishbone instabilities. In addition, the toroidal magnetic field B-t has to be higher than a critical value in order to excite the mode, and the real frequency of the modes decreases with increasing B-t.