Steady-State Solutions in Nonlinear Diffusive Shock Acceleration

Abstract

Stationary solutions to the equations of non-linear diffusive shock acceleration play a fundamental role in the theory of cosmic-ray acceleration. Their existence usually requires that a fraction of the accelerated particles be allowed to escape from the system. Because the scattering mean-free-path is thought to be an increasing function of energy, this condition is conventionally implemented as an upper cut-off in energy space -- particles are then permitted to escape from any part of the system, once their energy exceeds this limit. However, because accelerated particles are responsible for substantial amplification of the ambient magnetic field in a region upstream of the shock front, we examine an alternative approach in which particles escape over a spatial boundary. We use a simple iterative scheme that constructs stationary numerical solutions to the coupled kinetic and hydrodynamic equations. For parameters appropriate for supernova remnants, we find stationary solutions with efficient acceleration when the escape boundary is placed at the point where growth and advection of strongly driven non-resonant waves are in balance. We also present the energy dependence of the distribution function close to the energy where it cuts off - a diagnostic that is in principle accessible to observation.

accepted for publication in ApJ

References in corpus (13)

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• Particle Spectra from Acceleration at Forward and Reverse Shocks of Young Type Ia Supernova Remnants
• Comparison of Different Methods for Nonlinear Diffusive Shock Acceleration
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• Non-linear model of particle acceleration at colliding shock flows
• Probing Nearby CR Accelerators and ISM Turbulence with Milagro Hot Spots
• Time-Dependent Escape of Cosmic Rays from Supernova Remnants, and their Interaction with Dense Media
• A critical shock Mach number for particle acceleration in the absence of pre-existing cosmic rays: $M=\sqrt{5}$
• The Fermi Bubbles as a Scaled-up Version of Supernova Remnants
• Kinetic simulations of turbulent magnetic-field growth by streaming cosmic rays
• Particle acceleration and magnetic field amplification in massive young stellar object jets
• Non-linear diffusion of cosmic rays escaping from supernova remnants: Cold partially neutral atomic and molecular phases
• Synchrotron X-ray diagnostics of cutoff shape of nonthermal electron spectrum at young supernova remnants
• Cosmic-ray current-driven instabilities -- revisiting environmental conditions
• The maximum energy of shock-accelerated electrons in a microturbulent magnetic field
• Origin of Spectral Hardening of Secondary Cosmic-Ray Nuclei
• Stability of Cosmic Ray Modified Shocks: Two-Fluid Approach
• Time-dependent treatment of cosmic-ray spectral steepening due to turbulence driving
• Spectrally resolved cosmic rays: II -- Momentum-dependent cosmic ray diffusion drives powerful galactic winds