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The theory of diffusive particle acceleration explains the spectral properties of the cosmic rays below energies of approx. 10^6 GeV as produced at strong shocks in supernova remnants (SNRs). To supply the observed flux of cosmic rays, a significant fraction of the energy released by a supernova has to be transfered to cosmic rays. The key to the question of the efficiency of SNRs in producing cosmic rays is the injection process from thermal energies. A self-consistent model has to take into account the interaction of the accelerated particles with magneto-hydrodynamic waves, which generate the particle diffusion, a requisite for the acceleration process. Such a nonlinear model of the turbulent background plasma has been developed recently (Malkov, 1998, Phys. Rev. E 58, 4911). We use this model for the first numerical treatment of the gas dynamics and the diffusion-convection equation at a quasi-parallel strong shock, which incorporates a plasma-physical injection model to investigate the cosmic ray production.
The non-linear back reaction of accelerated cosmic rays at the shock fronts, leads to the formation of a smooth precursor with a length scale corresponding to the diffusive scale of the energetic particles. Past works claimed that shocklets could be
Collisionless shocks with low sonic Mach numbers, $M_{rm s} lesssim 4$, are expected to accelerate cosmic ray (CR) protons via diffusive shock acceleration (DSA) in the intracluster medium (ICM). However, observational evidence for CR protons in the
An analytic solution describing an ion-acoustic collisionless shock, self-consistently with the evolution of shock-reflected ions, is obtained. The solution extends the classic soliton solution beyond a critical Mach number, where the soliton ceases
The existence and properties of low Mach-number ($M gtrsim 1$) electrostatic collisionless shocks are investigated with a semi-analytical solution for the shock structure. We show that the properties of the shock obtained in the semi-analytical model
Particle acceleration and heating at mildly relativistic magnetized shocks in electron-ion plasma are investigated with unprecedentedly high-resolution two-dimensional particle-in-cell simulations that include ion-scale shock rippling. Electrons are