Stochastic modeling of blob-like plasma filaments in the scrape-off layer: Theoretical foundation

Abstract

A stochastic model for a superposition of uncorrelated pulses with a random distribution of amplitudes, sizes, and velocities is presented. The pulses are assumed to move radially with fixed shape and amplitudes decaying exponentially in time due to linear damping. The pulse velocities are taken to be time-independent but randomly distributed. The implications of a distribution of pulse amplitudes, sizes, and velocities are investigated. Closed-form expressions for the cumulants and probability density functions for the process are derived in the case of exponential pulses and a discrete uniform distribution of pulse velocities. The results describe many features of the boundary region of magnetically confined plasmas, such as high average particle densities, broad and flat radial profiles, and intermittent large-amplitude fluctuations. The stochastic model elucidates how these phenomena are related to the statistical properties of blob-like structures. In particular, the presence of fast pulses generally leads to flattened far scrape-off layer profiles and enhanced intermittency, which amplifies plasma–wall interactions.

Strongly intermittent far scrape-off layer fluctuations in Alcator C-Mod plasmas close to the empirical discharge density limit

“…In addition, investigations are also underway on how SOL profiles change with the Greenwald fraction, other plasma parameters, and confinement modes. This would use an extended version of the stochastic model recently developed by the UiT group that includes the radial position and the parallel drainage time [93].…”

“…The experimental measurement data reported in the following reveal a bi-exponential distribution of pulse amplitudes and waiting times. Such a bi-exponential pulse amplitude distribution follows from the assumption of a discrete uniform distribution of pulse velocities [93]. The bi-exponential amplitude distribution is mathematically described as…”

“…The average amplitude is given by ⟨A⟩ = q⟨A < ⟩ + (1 − q)⟨A > ⟩. It is assumed that the amplitudes of these fluctuations correlate with the velocity, where larger-amplitude fluctuations are impacted the least by parallel drainage to the sheaths compared to smalleramplitude fluctuations [93]. Consequently, the tail of the signal amplitude distribution is predominantly influenced by the contribution of large-amplitude fluctuations.…”