2005/09/08 by Mikhail Malkov, M. A. Malkov, P. H. Diamond
Physics and Astronomy · #Acceleration #Astrophysics #Astrophysics and Cosmic Phenomena #Classical mechanics #Computational physics #Cosmic ray #Gamma-ray bursts and supernovae #Instability #Mechanics #Momentum (technical analysis) #Oblique shock #Particle acceleration #Physics #Shock (circulatory) #Shock wave #Solar and Space Plasma Dynamics #astro-ph
paper · pdf · doi:10.1086/500445
published as Astrophys.J.642:244-259,2006 · aastex, 13 eps figures
arxiv created 2005/09/08 · openalex publication_date 2006/04/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We suggest a physical mechanism whereby the acceleration time of cosmic rays (CRs) by shock waves can be significantly reduced. This creates the possibility of particle acceleration beyond the knee energy at ~10 15 eV. The acceleration results from a nonlinear modification of the flow ahead of the shock supported by particles already accelerated to the knee momentum at p ~ p * . The particles gain energy by bouncing off converging magnetic irregularities frozen into the flow in the shock precursor and not so much by recrossing the shock itself . The acceleration rate is thus determined by the gradient of the flow velocity and turns out to be formally independent of the particle mean free path (mfp). The velocity gradient is, in turn, set by the knee particles at p ~ p * as having the dominant contribution to the CR pressure. Since it is independent of the mfp, the acceleration rate of particles above the knee does not decrease with energy, unlike in the linear acceleration regime. The reason for the knee formation at p ~ p * is that particles with p > p * are effectively confined to the shock precursor only while they are within limited domains in the momentum space, while other particles fall into "loss islands," similar to the "loss cone" of magnetic traps. This structure of the momentum space is due to the character of the scattering magnetic irregularities. They are formed by a train of shock waves that naturally emerge either from unstably growing and steepening magnetosonic waves or as a result of acoustic instability of the CR precursor (CRP). These losses steepen the spectrum above the knee, which also prevents the shock width from increasing with the maximum particle energy.