Study of fishbone instabilities induced by energetic particles in tokamak plasmas

Abstract

Fishbone instabilities, driven by trapped and barely passing energetic particles (EPs), including electrons and ions (EEs or EIs), are numerically studied with the spatial distribution of EPs taken into account. The dispersion relations of the modes are derived for slowing-down and Maxwellian models of EP energy distribution. It is found that the modes with frequency comparable to the toroidal precession frequency ω d of EPs are resonantly excited. Electron and ion fishbone modes share the same growth rates and real frequencies but rotate in opposite directions. The frequency of the modes is found to be higher in the case of near-axis heating than that of off-axis heating. The fishbone instabilities can only be excited by barely trapped or barely passing and deeply trapped particles in positive and negative spatial density gradient regions, respectively. In addition, the most interesting feature of the fishbone modes induced by barely passing particles is that there exists a second stable regime in the higher β h (pressure of EPs/toroidal magnetic pressure) region, and the modes exist in the range of β th1 < β h < β th2 (β th is threshold or critical beta of EPs) only. The results are well confirmed with Nyquist technology. The possible physical mechanism for the existence of the second stable regime is discussed.

Kinetic effects of trapped energetic particles on stability of external kink modes with a resistive wall

“…The characteristic of this narrow stable window is similar to the second stable region of the classical fishbone mode. 36 The critical value for the onset of the second FLM branch, for a 0 B 0 ¼ 1:18, is about 0.04, much smaller than that needed for the FLM branch with X pf ;c > 1. With increasing the pitch angle (a 0 B 0 ¼ 1:21), the two FLM branches merge into one instability, with the initial real frequency X pf ;c ð¼ 1Þ.…”

Discrete Alfv&eacute;n eigenmodes under the condition &lt;_ufe:lines-br xmlns:_ufe=&quot;http://www.arbortext.com/namespace/Styler/UserFormattingElements&quot; xml:base=&quot;-7mm&quot;&gt; &lt;/_ufe:lines-br&gt;of bootstrap current in EAST

“…理论上还发现了一种离散阿尔芬本 征模式αTAE [5] ( q Reactor)装置中 [13] . 自举电流因为不需要外部驱动, 只 [14,15] . [16,17] 和(s,α)平衡模型 [18] (s 19] 如下:…”

Non-resonant fishbone-like modes in tokamak plasmas with reversed magnetic shear

“…A pressure profile of ( ) ( ) = − p r p r 1 0 2 and = C 0.175 for the reversed magnetic shear configurations [23,30]. Considering a slowing-down beam distribution [2,5], the function ( ) [31], where n 0 is the peak value of n h at the peak location = r r b , and σ is the width of the beam distribution.…”