Neoclassical Transport Including Collisional Nonlinearity

In the standard $\delta f$ theory of neoclassical transport, the zeroth-order (Maxwellian) solution is obtained analytically via the solution of a nonlinear equation. The first-order correction $\delta f$ is subsequently computed as the solution of a linear, inhomogeneous equation that includes the linearized Fokker-Planck collision operator. This equation admits analytic solutions only in extreme asymptotic limits (banana, plateau, Pfirsch-Schlüter), and so must be solved numerically for realistic plasma parameters. Recently, numerical codes have appeared which attempt to compute the total distribution $f$ more accurately than in the standard ordering by retaining some nonlinear terms related to finite-orbit width, while simultaneously reusing some form of the linearized collision operator. In this work we show that higher-order corrections to the distribution function may be unphysical if collisional nonlinearities are ignored.