Ergodic mixing for turbulent drift motion in an inhomogeneous magnetic field

Abstract

The turbulent Ex B drift of a test particle in an inhomogeneous magnetic field is not reducible to a simple diffusion, but rather leads to a biased diffusion producing an inhomogeneous density distribution (pinch effect). The statistical properties of the long-time chaotic two-dimensional drift motion of a charged particle in the magnetic field B(x,y) and the time-dependent electrostatic potential </J(x,y,t) are studied by numerical symplectic integration. For a conditionally periodic potential with two or more incommensurate frequencies, an ergodic behavior is demonstrated in which the probability density of the particle position is proportional to the magnetic field B. The accuracy of this prediction is found to be independent of the number N w of the incommensurate frequencies for N w~ 2. The relation of this result with the KOlmogorov-Arnold-Moser theory is discussed.

Turbulent transport and the plasma edge

“…The transport is certainly not governed by a standard 'Fickian' diffusive process. It can be described by an effective pinch, which may be understood by considering the continuity equation for the impurity particle density N [42,19]. Consider an inhomogeneous magnetic field BðxÞẑ:…”

Fluctuation driven transport and stationary profiles

“…a) Electronic mail: kesner@psfc.mit.edu Self-consistent estimates of transport driven by turbulence usually require computerintensive non-linear calculations. However, for broadband low frequency turbulence, a crossfield flow proportional to the fluctuation intensity can be derived following the ergodic hypothesis 1 (also known as turbulent equipartiton) when the fluctuations conserve constants of motion [2][3][4][5] . The resulting transport equations determine stationary density and pressure profiles and the direction of the associated turbulence-driven fluxes.…”

Gyrofluid potential vorticity equation and turbulent equipartion states

“…In either case, if in a bounded region the mixing time-scale is faster than other competing time-scales (e.g., collisional diffusion time-scale), the Lagrangian invariants will be uniformly distributed, a state denoted turbulent equipartition (TEP) [9,27]. A simple example is the equipartition of n/B in simplified 2D drift-fluid turbulence [28,12], which implies that the particle density profile is given by the magnetic field n ∼ B and that n is transported up-gradient by the so-called curvature pinch velocity [27]. Here, we are concerned with mixing of the Lagrangian invariants L + and L − given in equation (24).…”