Nonlinear Guiding Center Theory of Perpendicular Diffusion: Derivation from the Newton‐Lorentz Equation

Abstract

We revisit the problem of charged-particle scattering in the direction perpendicular to a mean magnetic field. By combining the well-established nonlinear guiding center theory with the Newton-Lorentz equation, we derive an integral equation for perpendicular scattering without the assumption that charged particles follow magnetic field lines. A comparison with solar wind observations is also presented.

Compound perpendicular transport of charged particles with drift, advection, wave propagation effects, and an arbitrary turbulence spectrum

“…1 The mean free path obtained in the current article in the limit t → ∞ for electrons (dotted line) and protons (solid line). For comparison we have also shown the results for electrons (dashed line) and protons (dash-dotted line) obtained by Shalchi and Dosch (2008). The latter result was obtained by combining the nonlinear guiding center theory with the Newton-Lorentz equation…”

“…1. For comparison we have also shown the results obtained in Shalchi and Dosch (2008) to explore the relevance of our new results. The latter results were obtained by combining the nonlinear guiding center theory with the Newton-Lorentz equation.…”

“…Different theories have been developed in the past for computing the parameter κ add . Shalchi and Dosch (2008), for instance, have developed an approach based on the Newton-Lorentz equation to take into account that charged particles can be scattered away from a single field line. According to (29) we find subdiffusion with ( x) 2 P ∼ √ t for early times and normal (Markovian) diffusion for later times ( x) 2 P ∼ t).…”

“…This effect could be important. Shalchi and Dosch (2008) combined the nonlinear guiding center theory with the Newton-Lorentz equation to take into account this effect. Although, the nonlinear guiding center theory is based on several ad hoc assumptions (e.g., exponential velocity correlation functions) and is, therefore, not very systematic, this theory agrees very well with several solar wind observations.…”

“…For instance, the effect that particles can be scattered away from a single field line was taken into account (see Shalchi and Dosch 2008) as well as advection and particle drift (see Webb et al 2008), and wave propagation effects (see Shalchi et al 2007). …”