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

Ballooning Mode in a Stochastic Magnetic Field—A Quasi-mode Model
Mingyun Cao, P.H. Diamond
University of California, San Diegoe-mail (speaker): m2cao@ucsd.edu
Resonant magnetic perturbation (RMP) is widelyadopted to generate a stochastic magnetic field tosuppress ELM. But it is also found that RMP can lead toan increase in the power threshold for L-H transition.
Therefore, good confinement must be achieved alongwith good boundary control and power handling. Giventhat peeling-ballooning mode is a quite probablemechanism of ELM, understanding how a stochastic
magnetic field affects ballooning mode is crucial for
fusion devices that employ RMP, such as ITER.
Recent experiments provide important observations
that deserve our attention. Choi et al. appliedcomplexity-entropy analysis to characterize the change
in the statistics of pedestal turbulence with RMP
switched on and off [1]. In this approach, a metric called
Jensen-Shannon complexity 𝐶JS is defined to quantify asystem’s complexity. They observed a reduction in therescaled 𝐶JS of the temperature fluctuations in the RMP
ELM suppression phase, compared to the RMP ELM
mitigation phase and natural ELM-free phase. Thisindicates that stochastic magnetic field can reduce thepredictability of plasma turbulence. In addition, an
increase in the bicoherence of the pedestal turbulence
was also observed in the RMP ELM suppression phase.
These results are very intriguing and need to beunderstood.
Due to the fact that models for ballooning mode areset up in a toroidal geometry while theories involving
RMP typically focus on resonant surfaces within acylindrical geometry, we need to reconcile these twodifferent geometries in order to develop a comprehensive
theory that includes both the ballooning mode and RMP.
Based on the resemblance between a quasi-mode in acylinder and a ballooning mode in a torus, our strategy is
to replace ballooning mode by quasi-mode first, and thenextend the results we get to ballooning mode.
In this work, a multi-scale model of quasi-mode in astatic stochastic magnetic field is presented. The
framework of this model can be summarized by theflowchart in figure 1. The lessons we learned forballooning mode in a stochastic magnetic field are:i.) To maintain ∇ ⋅ 𝑱 = 0 at all scales, the beat of thequasi-mode and stochastic magnetic field drives a
microturbulence, which could promote spectral
transfer by increasing the number of triadinteractions. This may account for the increase in thebicoherence of the pedestal turbulence reported by
Choi et al.
ii.) The microturbulence can further generate a turbulent

viscosity and a turbulent diffusivity, which damp theballooning mode growth by boosting the mixing.
N.B., as a result of the difference in mode structure,
the scaling of the turbulent viscosity/diffusivity islarger than that in our study on resistive interchange
mode [2].
iii.) The stochastic magnetic field can enhance theeffective plasma inertia and reduce the effectivedrive. This result is similar to the “magnetic brakingeffect” in Rutherford’s work on nonlinear tearing
mode [3]. But the critical magnetic island in our1/2

work is reduced by a factor (𝑘𝑦 /𝑘1𝑦 ) , which is afootprint of the multi-scale nature of our model.
Combining with ⅱ.), we can conclude that stochastic
magnetic field can slow down the mode growth.
iv.) A non-trivial correlation develops between themagnetic perturbations and the velocity fluctuations.
In other words, the microturbulence ‘locks on’ to theambient stochastic magnetic field, thus becoming
more stochastic. This theoretical prediction may
explain the reduction in the 𝐶JS of the pedestal
turbulence.
Several experiments for future investigations are also
proposed. Especially, it would be interesting to perform asimilar analysis on the velocity fluctuation data collectedfrom BES in both the RMP ELM suppression phase andthe natural ELM-free phase, not only as a complement toChoi's results, but also as a verification of our theory.
This work is supported by U.S. Dept. of Energy underAward Number DE-FG02-04ER54738.
References[1] Choi, M.J., et al., PoP, 29(12), p.122504.
[2] Cao, M. and Diamond, P.H., PPCF, 64(3), p.035016.
[3] Rutherford, P.H., PoF, 16(11), pp.1903-1908.

Figure 1. Multi-scale feedback loops of quasi-mode and microturbulence