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Fast collisionless shocks in cosmic plasmas convert their kinetic energy flowinto the hot downstream thermal plasma with a substantial fraction of energygoing into a broad spectrum of superthermal charged particles and magneticfluctuations. The superthermal particles can penetrate into the shock upstreamregion producing an extended shock precursor. The cold upstream plasma flow isdecelerated by the force provided by the superthermal particle pressuregradient. In high Mach number collisionless shocks, efficient particleacceleration is likely coupled with turbulent magnetic field amplification(MFA) generated by the anisotropic distribution of accelerated particles. Thisanisotropy is determined by the fast particle transport making the problemstrongly nonlinear and multi-scale. Here, we present a nonlinear Monte Carlomodel of collisionless shock structure with super-diffusive propagation ofhigh-energy Fermi accelerated particles coupled to particle acceleration andMFA which affords a consistent description of strong shocks. A distinctivefeature of the Monte Carlo technique is that it includes the full angularanisotropy of the particle distribution at all precursor positions. The modelreveals that the super-diffusive transport of energetic particles (i.e.,Levy-walk propagation) generates a strong quadruple anisotropy in the precursorparticle distribution. The resultant pressure anisotropy of the high-energyparticles produces a non-resonant mirror-type instability which amplifiescompressible wave modes with wavelengths longer than the gyroradii of thehighest energy protons produced by the shock.

A nonlinear Monte Carlo model of super-diffusive shock acceleration with magnetic field amplification