A statistical study of gyro-averaging effects in a reduced model of drift-wave transport

Abstract

A statistical study of finite Larmor radius (FLR) effects on transport driven by electrostatic drift-waves is presented. The study is based on a reduced discrete Hamiltonian dynamical system known as the gyro-averaged standard map (GSM). In this system, FLR effects are incorporated through the gyro-averaging of a simplified weak-turbulence model of electrostatic fluctuations. Formally, the GSM is a modified version of the standard map in which the perturbation amplitude, $K_0$, becomes $K_0{J}_0(\hat{\rho })$, where $J_0$ is the zeroth-order Bessel function and $\hat{\rho }$ is the Larmor radius. Assuming a Maxwellian probability density function (pdf) for $\hat{\rho }$, we compute analytically and numerically the pdf and the cumulative distribution function of the effective drift-wave perturbation amplitude $K_0{J}_0(\hat{\rho })$. Using these results we compute the probability of loss of confinement (i.e., global chaos), $P_c$, and the probability of trapping in the main drift-wave resonance, $P_t$. It is shown that $P_c$ provides an upper bound for the escape rate, and that $P_t$ provides a good estimate of the particle trapping rate. The analytical results are compared with direct numerical Monte-Carlo simulations of particle transport.