Statistical theory of intermittency in a multi-scale model of MHD and micro-turbulence

Traditionally the effects of MHD instabilities and micro-instabilities on plasma confinement are investigated separately. However, these two instabilities often occur simultaneously, with the overlap of the dynamics on a broad range of spatial scales. It is thus vital to incorporate these instabilities consistently by a proper multi-scale modeling. Furthermore, there has been an overwhelming evidence that the overall transport of heat and particles is significantly influenced by intermittency (or bursty events) caused by coherent structures. A crucial question in plasma confinement is thus the prediction of the probability distribution functions (PDFs) of the transport due to these structures and of their formation. In this paper, we investigate intermittent transport in a multi-scale model by consistently incorporating both tearing instabilities and micro-instability due to pressure gradient [1]. We first present an exact nonlinear solution in the form of a coherent structure (modon or bipolar vortex soliton). We then present a first analytical result of intermittency in our multi scale model by utilizing a novel non-perturbative method. Specifically, we compute the PDF tails of momentum flux and heat flux, by assuming that a short-lived modon is a coherent structure responsible for bursty and intermittent events, contributing to the PDF tails. The governing equations for modeling the MHD and drift wave turbulence [1] are as follows, ∂ ∂ t ∇⊥φ +[φ ,∇⊥φ ] = [ψ,∇⊥ψ]−κ1 ∂ p ∂y −ν∇⊥φ + f1, (1) ∂ p ∂ t +[φ , p] = −v⋆ ( (1−κ2) ∂φ ∂y +κ2 ∂ p ∂y )