The toroidicity-induced Alfven eigenmode (TAE) excited by energetic (fast) ions was first simulated using the GTC code for HL-2A experiments. The simulation results indicate that the fraction of energetic ions is about 3% in the experiments. The critical density of energetic ions to excite the TAE mode is around 0.023, which is in good agreement with the theoretical expectation of 0.026. The real frequency of TAE with toroidal mode number n = 3 is around 211 kHz and is inversely proportional to the square root of electron density, which is quantitatively in agreement with the experimental observation (Ding et al 2013 Nucl. Fusion53 043015). The frequency is in resonance with the summations of toroidal precession frequency and transit frequency of passing energetic ions, indicating that resonance with passing energetic ions is dominant for the excitation of the modes in the experiment. It is also checked by the phase space structures of (strength of energetic particle distribution function) that the TAE modes are mainly induced by passing energetic ions in HL-2A. The growth rates of TAE modes increase with fast ion density and its gradient. In addition, lower n TAE modes, such as n = 1 can also be driven by energetic ions when off-axis heating with higher beam energy is employed in the experiment. The width of radial mode structures for lower n modes is usually wider than those for higher n modes. The perpendicular wave vector of the modes and Larmor radius of ions satisfy the relation . Finally, the polarization of the mode shows that the perturbed parallel electric field is much smaller than the electrostatic parallel electric field.
Experiments on excitation of Alfvén eigenmodes by alpha-particles with bump-on-tail distribution in JET DTE2 plasmas