Diffusion of charged particles in tokamak-like stochastic magnetic and electric fields

Abstract

In this paper the diffusion of guiding centers induced by stochastic magnetic and electric field fluctuations, with both time and space dependence, is analyzed for the case of tokamak plasmas. General experimental results on tokamak fluctuations are used to derive guidingcenter equations that properly describe the particle motion. These equations assume uniform average magnetic and electric fields with random stationary Gaussian fluctuations that constitute a homogeneous and cylindrically symmetric turbulence. By applying Novikov's theorem, a Fokker-Planck equation for the probability distribution function is derived and an expression for the guiding-center diffusion coefficient is obtained. This coefficient not only contains the standard terms due to the stochastic wandering of the magnetic lines and the stochastic electric drift, but also new terms due to the stochastic curvature and VB drifts. The form of these terms is shown explicitly in terms of the correlation functions of the fields.

Lagrangian coherent structures and plasma transport processes

“…Although this is a restrictive assumption that neglects among other effects the drift caused by (fluctuating) transverse electric fields, particle trapping along field lines, etc., it has a paradigmatic role since it makes it possible to relate in a simple way barriers in the electron transport with LCS in the magnetic configuration. A more precise formulation of the (self-consistent) relationship between electron particle and heat transport and magnetic fluctuations can be found in Coronado & Akcasu (1992), White & Wu (1992), Beyer et al (2002), Kasilov et al (2002) and Hatch et al (2012) and for space plasmas in Matthaeus (2003) and references therein.…”

Diffusion of stochastic magnetic field lines with average poloidal magnetic component

“…In this subsection we present some results concerning the influence of the aforementioned parameters (L ¹ ) K K 1, , av on the diffusion coefficients (see figures [19][20][21][22][23][24].…”

“…[17] and [18]). We also note here some early works on the shearless slab model such as [19] and [20]. The DCT method was used in many situations to calculate the diffusion coefficients even if Kubo numbers are relatively high and the numerical calculation sometime fails.…”

Stochastic modelling of turbulence and anomalous transport in plasmas

“…Here the fields E(r, t) and B(r, t) and the acceleration a c [v(t), t] representing the effect of collisions are random quantities (for an illustration of this problem, see e.g. Coronado et al 1992;Hannibal 1993;Vanden Eijnden 1997 a).…”