Poisson-Vlasov : Stochastic representation and numerical codes

A stochastic representation for the solutions of the Poisson-Vlasov equation, with several charged species, is obtained. The representation involves both an exponential and a branching process and it provides an intuitive characterization of the nature of the solutions and its fluctuations. Here, the stochastic representation is also proposed as a tool for the numerical evaluation of the solutionsComment: 17 pages, 5 figure

Stochastic and Discrete Time Models of Long-Range Turbulent Transport in the Scrape-Off Layer

Two dimensional stochastic time model of scrape-off layer (SOL) turbulent transport is studied. Instability arisen in the system with respect to the stochastic perturbations of both either density or vorticity reveals itself in the strong outward bursts of particle density propagating ballistically across the SOL. The stability and possible stabilization of the cross- field turbulent system depend very much upon the reciprocal correlation time between density and vorticity fluctuations. Pdf of the particle flux for the large magnitudes of flux events can be modelled with a simple discrete time toy model of random walks concluding at a boundary. The spectra of wandering times feature the pdf of particle flux in the model and qualitatively reproduce the experimental statistics of transport events.Comment: 21 pages,11 figure