New possibilities for the mathematical modeling of turbulent transport processes in plasma

Abstract

Measurements in the LHD, L2-M, and TJ-II stellarators show that plasma density fluctuations have non-Gaussian distributions with heavy tails and sharper vertices. Non-Gaussian probability densities of stochastic plasma processes indicate non-Brownian character of the motion (diffusion) of particles. The role of rare events related to stochastic plasma processes with larger spatial and temporal scale becomes important. It is shown that the first-order differences of fluctuation samples are stochastic and their probability distribution is a mixture of Gaussians with different scales. Subordinated Lèvy process can be used to describe the turbulent transport process.

The evolution of probability characteristics of low-frequency plasma turbulence

“…The distribution density of the particle flow probability [14] in ion acoustic tur bulence is also different from the Gaussian one and, based on the limit theorems for doubly stochastic compound Poisson processes (compound Cox processes), it can be represented by a shift scale mixture of normal distributions [6]. It was shown in [15] that each component in the distribution of the ion flow cor responds to one of the turbulence forming processes. We did not manage to separate the probabilities of the initial fluctuations (plasma density or potential) in the mixture.…”

Self‐Similarity of Fluctuation Particle Fluxes in the Plasma Edge of the Stellarator L‐2M

“…One of these methods is described in works [5,6]. In these works shift-scaling mixtures of Gaussian distributions were applied for approximation of empirical PDFs.…”

“…First, in works [1][2][3][4][5][6] it is established, that probability density function (PDF) of amplitudes of fluctuations don't described by Gauss distribution. Empirical PDFs have heavy tails and sharp peaks.…”

On the investigation of plasma turbulence by the analysis of the spectra

“…Сильная структурная турбулентность описывается математической моделью неоднородного случайного блуждания с непрерывным временем -дважды стохастическим пуассоновским процессом, иначе называемым обобщенным процессом Кокса (см. работу [Skvortsova, Korolev et al, 2005]). На следующем этапе исследований (см., например, работу ) необходимо перейти к анализу спектров, поскольку именно спектр дает возможность определить тип неустойчивости, механизм формирования турбулентности, доли ионно-звуковых солитонов и дрейфовых вихрей и т. д. Однако ранее идентификация спектра не могла быть проведена, потому что при известном числе процессов форма гармоник в амплитудном спектре осталась неизвестной.…”