Stochastic modelling of intermittent scrape-off layer plasma fluctuations

Abstract

In the tokamak scrape-off layer, radial motion of blob-like structures is the dominant mechanism for transport of particles and heat. Fixed point probe measurements in the Tokamak à Configuration Variable scrape-off layer reveal highly intermittent fluctuations in the ion saturation current. These measurements are well described by a shot noise process with exponential pulse shapes, exponentially distributed pulse amplitude and pulses arriving according to a Poisson process.

The statistical properties of this shot noise process is explored in this thesis. Characteristic functions and probability density functions of the shot noise process have been derived, as well as the joint probability density function between the resulting signal and its derivative. These probability density functions have then been used to derive a general model for the excess statistics of a shot noise process. This model has been explored using synthetically generated shot noise time series.

Synthetically generated shot noise time series have also been used to compare results of conditional averaging using various pulse amplitude and waiting time distributions, as well as different pulse shapes. While the pulse shape is well preserved after conditional averaging, the pulse waiting time and amplitude distributions are not.

Excess time statistics have been analyzed for the ion saturation current measured by a Langmuir probe at a fixed point in the Tokamak à Configuration Variable scrape-off layer. The general model gives a qualitatively better fit to the data from the measurements than the normal limit does. Probability density functions of the time above threshold per upcrossing have been computed, and reveal exponential tails. It is found that both the average time above threshold per upcrossing and the root mean square value of the time above threshold per upcrossing have very slow decay for large threshold values, underlining the importance of intermittent fluctuations for plasma-wall interactions for tokamak plasmas.