Frequency multiplication with toroidal mode number of kink/fishbone modes on a static HL-2A-like tokamak

TL;DR

This study uses hybrid kinetic-MHD simulations to explore how energetic particles influence the frequency and mode number of kink/fishbone modes on a static HL-2A-like tokamak, revealing a linear frequency multiplication with mode number n.

Contribution

It demonstrates that energetic particles cause frequency multiplication of kink/fishbone modes, with frequency proportional to n, even without plasma rotation, and analyzes mode growth rate dependencies.

Findings

Frequency increases linearly with EP pressure and mode number n.

Higher-n modes become dominant as EP pressure increases.

Frequency multiplication persists despite variations in q0.

Abstract

In the presence of energetic particles (EPs), the Long-Lived Mode (LLM) frequency multiplication with n = 1,2,3 or higher is often observed on HL-2A, where n is the toroidal mode number. Hybrid kinetic-MHD model simulations of the energetic particle (EP) driven kink/fishbone modes on a static HL-2A-like tokamak using NIMROD code find that, when the background plasma pressure is relatively high, and the EP pressure and the beam energy are relatively low, the mode frequency increases almost linearly with EP pressure, and the frequency is proportional to n ("frequency multiplication"), even in absence of any equilibrium plasma rotation. In addition, the frequency multiplication persists as the safety factor at magnetic axis q0 varies. In absence of EPs, the growth rate of the 1/1 mode is the largest; however, as the EP pressure increases, the growth rate of 2/2 modes or 3/3 modes becomes dominant, suggesting that the higher-n modes are more vulnerable to EPs. These results may shed light on the understanding about the toroidal mode number dependence of kink/fishbone modes in the advanced scenarios of tokamaks with weak or reversed central magnetic shear.