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

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 $K_0 J_0(\hatρ)$, where $J_0$ is the zeroth-order Bessel function and $\hatρ$ is the Larmor radius. Assuming a Maxwellian probability density function (pdf) for $\hatρ$, we compute analytically and numerically the pdf and the cumulative distribution function of the effective drift-wave perturbation amplitude $K_0 J_0(\hatρ)$. 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.