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We present a nonlinear Monte Carlo model of efficient diffusive shockacceleration (DSA) where the magnetic turbulence responsible for particlediffusion is calculated self-consistently from the resonant cosmic-ray (CR)streaming instability, together with non-resonant short- and long-wavelengthCR-current-driven instabilities. We include the backpressure from CRsinteracting with the strongly amplified magnetic turbulence which deceleratesand heats the super-alfvenic flow in the extended shock precursor. Uniquely, inour plane-parallel, steady-state, multi-scale model, the full range ofparticles, from thermal (~eV) injected at the viscous subshock, to the escapeof the highest energy CRs (~PeV) from the shock precursor, are calculatedconsistently with the shock structure, precursor heating, magnetic fieldamplification (MFA), and scattering center drift relative to the backgroundplasma. In addition, we show how the cascade of turbulence to shorterwavelengths influences the total shock compression, the downstream protontemperature, the magnetic fluctuation spectra, and accelerated particlespectra. A parameter survey is included where we vary shock parameters, themode of magnetic turbulence generation, and turbulence cascading. From oursurvey results, we obtain scaling relations for the maximum particle momentumand amplified magnetic field as functions of shock speed, ambient density, andshock size.

Magnetic field amplification in nonlinear diffusive shock acceleration including resonant and non-resonant cosmic-ray driven instabilities