7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Toroidal modelling of interactions between internal kink instability andenergetic ions in HL-2M
G.Q Dong1, Y.Q. Liu2, G.Z. Hao1 and S. Wang1
1
Southwestern Institute of Physics,
2
General Atomics
e-mail (speaker): donggq@swip.ac.cn

Understanding the interaction between macroscopic
magnetohydrodynamic (MHD) instabilities and energetic
particles (EPs) remains a crucial issue for both presentand future large tokamak experiments1. In order tomaintain favorable conditions for fusion, energetic ionsneed to be confined inside the plasma for a sufficiently
long time to deposit their energy onto the backgroundthermal species. On the other hand, EPs are also known
to strongly (either stabilization or destabilization)
influence the MHD instabilities. The equilibrium
distribution of EPs, in both the configuration and particle
velocity spaces, plays an important role in this process.
The present work investigates some of theaforementioned effects, specifically (i) targeting theinternal kink instability and (ii) with application to theHL-2M device.
Besides the specific new application, this study alsopresents new physics aspects as compared to many ofprevious studies. Specifically, we consider the following.
 Non-perturbative MHD-kinetic hybrid computationof the IK instability in the presence of EPs.
 A systematic survey of kinetic contributions due tovarious EP drift resonances to the IK mode stability,
assuming a reasonably realistic equilibrium
distribution of EPs in the particle phase space(slowing down in energy and anisotropic in pitch,as shown in Fig.1) in HL-2M.
 Detailed guiding center drift orbits as traced by test
EPs in the presence of magnetic perturbations dueto the IK instability, with the overall perturbation
amplitude being scanned.
 The EP loss fraction due to the unstable IK, as wellas the strike point pattern on the limiting surface
due to lost particles, is quantified for HL-2M.
 The loss study is performed, and the results

contrasted, assuming either a static 3-D perturbation
or a sawtooth like time-varying perturbation.
Compared to the fluid model, MHD-kinetic hybrid
computations with MARS-K2 show a stabilization effecton the IK in HL-2M. An exception is the strong
fishbone-like drive to the mode by precessional drift
resonances of trapped EPs, for a weakly unstable fluid
IK in the presence of plasma flow. In addition, the transit
resonance of co-current (counter-current) passing EPs
destabilizes (stabilizes) the IK. While this resonance ofco-NBI will introduce the infernal-like3 mode structure.
These results suggest that the sawtooth behavior can becontrolled by the choosing the direction of NBI.
REORBIT module4 is utilized for the EP loss study. 3-D
perturbations due to an unstable IK affect the EP drift
orbit, confinement and loss in HL-2M, but the effect isgenerally moderate. The IK instability induced EP loss
fraction is found to be typically less than 10%, without
counting the prompt orbit loss associated with the 2-D
equilibrium field for counter-current particles. The latterreaches about 16% in HL-2M. A sawteething-liketime-varying perturbation field, produces about 30% loss
for the co-current EPs in HL-2M. The majority of lostEPs tend to strike the lower divertor region, with only asmall fraction of particles striking the low-field side
mid-plane region of the limiting surface. These should
thus be the regions of particular concern when operating
HL-2M.
References[1] T. Hender et al., Nucl. Fusion 47, S128 (2007)[2] Y.Q. Liu et al., Phys. Plasmas 15, 112503 (2008)[3] G.Q. Dong et al., Nucl. Fusion 59, 066011 (2019)[4] Y.Q. Liu et al., Nucl. Fusion 61, 106029 (2021)

FIG. 1. (a) The EP distribution in the particle pitch angle space, calculated by TRANSP and averaged over the particleenergy interval of 60-80 keV (solid line), versus that approximated by the analytic model and adopted in MARS-K
simulations in this study (dash-dotted line). (b) The analytical EP distribution along the particle energy E and theparticle pitch ζ ≡ v|| /v.