Low-frequency percolation scaling for particle diffusion in electrostatic turbulence

An important point for turbulent transport consists in determining the scaling law for the diffusion coefficient D due to electrostatic turbulence as a function of the control parameter A≊E/ωB proportional to the ratio of the rms electric field to the magnetic field strength times an average frequency ω. It is well known that for weak amplitudes or large frequencies, the reduced diffusion coefficient D≊D/ω≊${\mathit{A}}^{\gamma }$ has a quasilinearlike (or gyro-Bohm-like) scaling (γ=2), while for large amplitudes or small frequencies it has been traditionally believed that the scaling is Bohm-like (γ=1). Only recently a percolation critical exponent (γ=7/10) has been predicted by Isichenko. The aim of this work consists of testing this prediction for a given realistic model. This problem is studied here by direct simulation of particle trajectories. Guiding center diffusion in a spectrum of electrostatic turbulence is computed for test particles in a model spectrum, by means of a new parallelized code R A D I G U E T 2 described here. The spectrum involves only one frequency ω but a large number of ran- domly phased electrostatic plane waves, propagating isotropically in the plane perpendicular to the confining strong magnetic field. This ensures chaotic trajectories. This set of waves represents standing waves. Their amplitudes depend on wavelength in order to reproduce the ${\mathit{k}}^{\mathrm{-}3}$ domain of the observed spectrum in tokamaks. The results indicate a continuous transition for large amplitudes toward a value of γ=0.704±0.030 which is compatible with the Isichenko percolation prediction. © 1996 The American Physical Society.