Predicting PDF tails of flux in plasma sheath region

This letter provides the first prediction of the probability density function (PDF) of flux R in plasma sheath sheath region in magnetic fusion devices which is characterized by dynamical equations with exponential non-linearities. By using a non-perturbative statistical theory (instantons), the PDF tails of first moment are shown to be modified Gumbel distribution which represents a frequency distribution of the extreme values of the ensemble. The non-Gaussian PDF tails that are enhanced over Gaussian predictions are the result of intermittency caused by short lived coherent structures (instantons). [email protected] 1 In the edge region of magnetically confined fusion experiment the plasma exhibits large bursty fluctuations, often called intermittency [1][9]. Intermittent turbulence is characterized by patchy spatial structure that is bursty in time. The likelihood of these events are described by probability density functions (PDFs) which significantly deviate from Gaussian predictions. More specifically, exponential scalings are often observed in the PDF tails in magnetic confinement experiments [6][9], and intermittency at the edge strongly influences the overall global particle and heat transport. In particular it may for instance influence the threshold for the high confinement mode (H-mode) in tokamak experiments [10]. In the view of these experimental results, theories built on average transport coefficients and Gaussian statistics fall short in predicting vital transport processes. The high possibility of confinement degradation by intermittency strongly calls for a powerful predictive theory. The purpose of this letter is to provide the theoretical prediction for the PDF tails of flux in plasma sheath by using a non-perturbative statistical method. The basic idea is to associate the bursty event with the creation of a coherent structure (e.g. blobs, streamers etc.). The candidate that could describe the creation process is the instanton which is localized in time, existing during the formation of the coherent structure. This idea is embedded in our theoretical method the so-called instanton method which is a non-perturbative way of calculating the PDF tails [11][21]. Note that, the instanton method has been adopted from quantum field theory and then modified to classical statistical physics for Burgers turbulence [12][13] and by Kraichnan [22]. Our previous papers using this instanton method have shown that the PDF tails of momentum flux and heat flux are significantly enhanced over