Theory of Pedestal Micro-turbulence with RMP-induced stochasticity

In this work, we present a detailed analytic theory of an electrostatic resistive interchange mode in an extrinsic, static, and ambient stochastic magnetic field [1]. Unlike previous works pursing and developing the hyper-resistivity idea [2], this work addresses issues such as effect of stochasticity on mode structure and maintains the quasi-neutrality of the system at all orders. It is found that the beat of small-scale magnetic perturbations and large-scale cell drives small-scale convective cells, i.e., micro-turbulence, which makes the dynamics of this model intrinsically multi-scale and accounts for the appearance of small-scale structures in simulations by Beyer et al [3]. The micro-turbulence can react on the large-scale cell via an effective turbulent viscosity and turbulent diffusivity (computed by closure), as well as electrostatic scattering, thus forming a feedback loop. We find that velocity fluctuations ‘lock on’ to the stochastic field and explicitly calculate the correlation between electrostatic turbulence and ambient magnetic perturbations. Recent experimental results reported by Choi et al [4] indicate that the effect of stochasticity on pedestal turbulence is to reduce its Jensen-Shannon complexity and predictability—i.e. the distribution of turbulence becomes more random compared with the natural ELM free case [4]. This nontrivial correlation could be a possible cause for this phenomenon. In addition, stochastic magnetic perturbations produce a magnetic braking effect, which resembles the nonlinear force identified by Rutherford [5]. Thus, the net effect of stochastic magnetic field is to reduce the amplification of vorticity.