Chaotic diffusion across a magnetic field in a model of electrostatic turbulent plasma

Abstract

We have investigated the particle-guiding center motion (across a strong magnetic field) caused by a time-dependent electrostatic field. Two different nonlinear Hamiltonian systems of 1.5 degrees of freedom have been used. The Hamiltonian is proportional to the electrostatic potential, which is defined through its spatial Fourier spectrum in two dimensions. A $k^{\mathrm{-}3}$ power-law spectrum (k is the wave vector) and random-phase shifts have been chosen to model the spatial dependence of the electrostatic drift-wave turbulence observed in several tokamaks. The equations of motion have been solved numerically. When the average electric field amplitude is larger than a threshold value, the particle trajectories become chaotic at large scale and a diffusion across the magnetic field sets in. The diffusion coefficient D has been measured for different values of the average electric field amplitude A. The classical (quasilinear) scaling has been found at small A, D∝$A^2$, while a transition to the Bohm scaling is found at higher amplitudes, D∝A. A recently proposed theoretical treatment of the same problem has been applied to our models and the theoretical predictions have been compared to the results of numerical simulations. For relative diffusion, the theoretical prediction of the so-called ‘‘clump effect’’ has been well confirmed by numerical simulations. Theory and simulation are in qualitative agreement for the dependence of D on A, but some quantitative discrepancies exist; their nature is discussed.