Mechanism of Edge Localized Mode Mitigation by Resonant Magnetic Perturbations

A possible mechanism of edge localized modes (ELMs) mitigation by resonant magnetic perturbations (RMPs) is proposed based on the results of nonlinear resistive magnetohydrodynamic modeling using the jorek code, realistic JET-like plasma parameters and an RMP spectrum of JET error-field correction coils (EFCC) with a main toroidal number $n=2$ were used in the simulations. Without RMPs, a large ELM relaxation is obtained mainly due to the most unstable medium-$n$ ballooning mode. The externally imposed RMP drives nonlinearly the modes coupled to $n=2$ RMP which produce small multimode relaxations, mitigated ELMs. The modes driven by RMPs exhibit a tearinglike structure and produce additional islands. Mitigated ELMs deposit energy into the divertor mainly in the structures (“footprints”) created by $n=2$ RMPs, however, slightly modulated by other nonlinearly driven even harmonics. The divertor power flux during a ELM phase mitigated by RMPs is reduced almost by a factor of 10. The mechanism of ELM mitigation by RMPs proposed here reproduces generic features of high collisionality RMP experiments, where large ELMs are replaced by small, much more frequent ELMs or magnetic turbulence. Total ELM suppression was also demonstrated in modeling at higher RMP amplitude.

Figure 1

Magnetic energy ($\sim |{\psi }_n{|}^2$) of modes $n=2:8$ in natural and mitigated ELMs with $n=2$ RMP at 40 kAt.

Figure 2

Power to inner and outer divertor in natural and mitigated by RMPs ($n=2$, 40 kAt) ELMs.

Figure 3

Magnetic energy of modes $n=2:8$ in natural and mitigated ELMs at EFCC current scan.

Figure 4

Initial magnetic energy of even harmonics coupled to $n=2$ RMP.

Figure 5

Flux averaged edge pressure gradient before an ELM without RMP, at lower initial pressure without RMP, and at 40 and 60 kAt EFCC current.

Figure 6

The initial growth rate of $n=8$ mode in natural ELM (bold), at lower pressure gradient (dashed), with RMP at 4 kAt (dot-dashed), at 20 kAt (cross), at 40 kAt (diamonds), at 40 kAt in linear run for $n=8$ (three-dimensional equilibrium) in circles, at 60 kAt (squares).

Figure 7

Edge magnetic topology (Poincaré plot) for natural ELM due to $n=8$ mode (a), with RMP $n=2$,40 kAt (b), with mitigated by RMPs ELMs (c). Coordinates are geometrical poloidal angle and normalized poloidal flux.

Figure 8

Footprints in the outer divertor in the natural $n=8$ ELM (a), with RMP $n=2$ (40 kAt) (b), with mitigated ELMs (c). Brighter colors indicate longer connection length.

Figure 9

Magnetic energy in ELMs due to $n=6$ mode without RMP (in bold) and magnetic energy in $n=2:8$ modes in total ELM suppression regime with RMP $n=2$ at 80 kAt.