Asymptotic behavior of guiding-center diffusion in a model of electrostatic turbulence.

Abstract

To compare with computer simulations of the diffusion of a test guiding center in a given electrostatic turbulence, a nonlinear theory is applied to the ``randomly phased waves'' model, with a single frequency \ensuremath{\omega} and an arbitrary wave number spectrum. The asymptotic behavior of the diffusion coefficient D is determined in both limits of large and small turbulence amplitude a. For a\ensuremath{\rightarrow}\ensuremath{\infty}, the classical ``frozen turbulence'' scaling D\ensuremath{\propto}a is found. For a\ensuremath{\rightarrow}0, an unusual quadratic scaling is obtained: for all isotropic models, D goes to the same limit (\ensuremath{\surd}2 /\ensuremath{\omega})${\mathit{a}}^{2}$. This behavior originates in the ``two scales'' character of this asymptotic problem. It is examined in detail on a simple form of the equation where the exact asymptotic solutions are obtained.