Stochastic modelling of blob-like plasma filaments and flattened profiles in the scrape-off layer

A stochastic model for a super-position of uncorrelated pulses with a random distribution of and correlations between amplitudes 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-dependent with a power law dependence on the instantaneous amplitudes, as suggested by blob velocity scaling theories. In accordance with experimental measurements, the blob amplitudes are taken to be exponentially distributed.

As a consequence of linear damping and time-dependent velocities, it is demonstrated that blob structures stagnate during their radial motion. This makes the average pulse waiting time increase radially outwards in the scrape-off layer of magnetically confined plasmas. In the case that blob velocities are proportional to their amplitudes, the radial profile of the mean value of the process is the same as for the case when all pulses have the same, time-independent velocity. The profile e-folding length is then given by the product of the average pulse velocity and the parallel transit time, explaining the flattened profiles in the far scrape-off layer. The average pulse amplitude as well as velocity are the same at all radial positions. Moreover, the relative fluctuation level is high with fast and large-amplitude pulses dominating the process, which further enhances plasma-surface interactions.