Calculation of resonant transport coefficients from mappings

Abstract

For a two-degree-of-freedom dynamical system in which the dynamics depends on a parameter μ, the effect of an externally imposed random variation (e.g., collisions) of μ is considered. In particular, mapping equations in conjunction with particle conservation are used to directly derive transport coefficients. The analytic method and nature of the results depend on a stochasticity parameter K which describes the nonlinearity of the collision-free dynamics and a collisionality parameter σ. For large K or σ, Rechester, Rosenbluth, and White’s method of diagrams in Fourier space is used to calculate stochastic diffusion. For small K and moderate σ(≳K3/2), an expansion in powers of K is used to solve the map equations and thus obtain plateau transport coefficients. For small K and small σ, an expansion in powers of σ leads to banana transport coefficients. The results are applied to the calculation of radial resonant transport coefficients for tandem mirrors; the plateau and banana particle and energy fluxes are equivalent to those previously obtained from drift-kinetic theory, and the stochastic fluxes, not directly calculable in the drift-kinetic approach, are given explicitly.