  Fast collisionless shocks in cosmic plasmas convert their kinetic energy flow
into the hot downstream thermal plasma with a substantial fraction of energy
going into a broad spectrum of superthermal charged particles and magnetic
fluctuations. The superthermal particles can penetrate into the shock upstream
region producing an extended shock precursor. The cold upstream plasma flow is
decelerated by the force provided by the superthermal particle pressure
gradient. In high Mach number collisionless shocks, efficient particle
acceleration is likely coupled with turbulent magnetic field amplification
(MFA) generated by the anisotropic distribution of accelerated particles. This
anisotropy is determined by the fast particle transport making the problem
strongly nonlinear and multi-scale. Here, we present a nonlinear Monte Carlo
model of collisionless shock structure with super-diffusive propagation of
high-energy Fermi accelerated particles coupled to particle acceleration and
MFA which affords a consistent description of strong shocks. A distinctive
feature of the Monte Carlo technique is that it includes the full angular
anisotropy of the particle distribution at all precursor positions. The model
reveals that the super-diffusive transport of energetic particles (i.e.,
Levy-walk propagation) generates a strong quadruple anisotropy in the precursor
particle distribution. The resultant pressure anisotropy of the high-energy
particles produces a non-resonant mirror-type instability which amplifies
compressible wave modes with wavelengths longer than the gyroradii of the
highest energy protons produced by the shock.
