Probability distribution functions for intermittent scrape-off layer plasma fluctuations

TL;DR

This paper develops a stochastic model for plasma fluctuations in the scrape-off layer, exploring how different amplitude distributions affect statistical properties and proposing a parameter estimation method based on the empirical distribution function.

Contribution

It introduces a flexible amplitude distribution in the model and presents a new parameter estimation approach using the empirical distribution function.

Findings

Changing amplitude distributions impacts the moments and probability density functions.

The proposed parameter estimation method is effective on synthetic data.

The model helps describe intermittent plasma fluctuations in magnetized boundary regions.

Abstract

A stochastic model for intermittent fluctuations in the scrape-off layer of magnetically confined plasmas has been constructed based on a super-position of uncorrelated pulses arriving according to a Poisson process. In the most common applications of the model, the pulse amplitudes are assumed exponentially distributed, supported by conditional averaging of large-amplitude fluctuations in experimental measurement data. This basic assumption has two potential limitations. First, statistical analysis of measurement data using conditional averaging only reveals the tail of the amplitude distribution to be exponentially distributed. Second, exponentially distributed amplitudes leads to a positive definite signal which cannot capture fluctuations in for example electric potential and radial velocity. Assuming pulse amplitudes which are not positive definite often make finding a closed form for the probability density function difficult, even if the characteristic function remains relatively simple. Thus estimating model parameters requires an approach based on the characteristic function, not the probability density function. In this contribution, the effect of changing the amplitude distribution on the moments, probability density function and characteristic function of the process is investigated and a parameter estimation method using the empirical distribution function is presented and tested on synthetically generated data. This proves valuable for describing intermittent fluctuations in the boundary region of magnetized plasmas.