Cross-field diffusion of charged particles and the problem of ion injection and acceleration at quasi-perpendicular shocks

It is an open question how charged particles are injected at quasiperpendic ular shocks into a first-order Fermi acceleration mechanism. Cross-field di ffusion of solar wind ions is a possible injection process. However, in a s ystem with at least one ignorable spatial dimension, charged particles movi ng in fluctuating fields are tied to the magnetic field lines. We have ther efore determined the cross-field diffusion coefficient of charged particles in self-consistently generated turbulence by three-dimensional hybrid simu lations. The initial setup consists of a homogeneous magnetic field with an isotropic core plasma plus a second, nongyrotropic ion distribution. The c ombined distributions resemble the distribution found immediately downstrea m of the quasi-perpendicular Earth bow shock: Part of the solar wind is tra nsmitted (core) and part is specularly reflected and subsequently convected downstream (nongyrotropic part). Such a particle distribution excites the Alfven ion cyclotron and mirror mode instability. The turbulence scatters t he nongyrotropic ions both parallel and perpendicular to the field. The per pendicular and the parallel diffusion coefficients have been determined for two values of the density of the nongyrotropic distributions, nb. The rati o of the two diffusion coefficients is smaller than the value predicted by hard sphere scattering theory, i.e., parallel scattering is considerably st ronger than scattering perpendicular to the field. The power in the magneti c field fluctuations in the high nb case is comparable to the power obtaine d in a two-dimensional. quasiperpendicular shock simulation immediately beh ind the shock ramp. On the basis of perpendicular scattering time it is sug gested that cross-field diffusion in the turbulent wave field generated by the specularly reflected ions is sufficient to inject and accelerate these ions effciently at quasi-perpendicular shocks.