Influence of adiabatic response of passing energetic ions on high-frequency fishbone

Adiabatic response effects on high-frequency fishbone instability driven by passing energetic ions are studied. With finite orbit width effects, the adiabatic contribution $\delta W_{\mathrm{hf}}$ is derived analytically for purely passing energetic ions. By approximating the adiabatic contribution to the first order of the reverse aspect ratio $\epsilon ,$ we derive one of its analytic expressions, which is expected to be more accurate than that in a previous work (Graves J P 2004 Phys. Rev. Lett. 92 185003). For high-frequency fishbone instability, nonadiabatic response is usually dominant over adiabatic response, but under certain circumstances the latter plays an important role, comparable to the former. With a more generalized distribution function by introducing Gaussian-type factors representing their pitch and radial dependences and using a slowing-down equilibrium distribution for the energy of energetic ions, numerical analysis indicates that the adiabatic contribution is conducive to stabilization of the mode and causes a decrease in mode frequency. In addition, we find that the adiabatic contribution has a weak stabilizing effect on the fishbone instability when the finite orbit width effect is taken into account. We further analyze the dependence of the adiabatic contribution on the characteristic parameters of the distribution function. When the neutral beam has either a larger deviation from the plasma axis or a larger radial profile, the adiabatic contribution has a more evident effect on the fishbone instability. When the neutral beam has a relatively small critical energy, the adiabatic contribution has a greater effect on the mode instability.