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Galactic cosmic rays are widely believed to be accelerated in expanding shock waves initiated by supernova explosions. The theory of diffusive shock acceleration of cosmic rays is now well established, but two fundamental questions remain…
We review the main observational and theoretical facts about acceleration of Galactic cosmic rays in supernova remnants, discussing the arguments in favor and against a connection between cosmic rays and supernova remnants, the so-called…
We evaluate the current status of supernova remnants as the sources of Galactic cosmic rays. We summarize observations of supernova remnants, covering the whole electromagnetic spectrum and describe what these obser- vations tell us about…
Context: Multiwavelength observations of supernova remnants can be explained within the framework of the diffusive shock acceleration theory, which allows effective conversion of the explosion energy into cosmic rays. Although the models of…
Particle acceleration in the dynamically evolving environment of Supernova Remnants is discussed in the framework of a genuinely time-dependent nonlinear theory, assuming spherical symmetry. As a consequence the dependence of injection on…
The instability in the cosmic-ray precursor of a supernova shock moving in interstellar medium is studied. The level of magnetohydrodynamic turbulence in this region determines the maximum energy of particles accelerated by the diffusive…
The escape of charged particles accelerated by diffusive shock acceleration from supernova remnants is shown to be a more complex process than normally appreciated. Using a box model it is shown that the high-energy end of the spectrum can…
A concise and critical review of Balmer-dominated shocks (BDSs) is presented, summarizing the state of theory and observations, including models with/without shock precursors and their synergy with atomic physics. Observations of BDSs in…
Diffusive shock acceleration is considered as the main mechanism for particle energization in supernova remnants, as well as in other classes of sources. The existence of some remnants that show a bilateral morphology in the X-rays and…
Galactic cosmic rays are believed to be accelerated at supernova remnants via diffusive shock acceleration. Though this mechanism gives fairly robust predictions for the spectrum of particles accelerated at the shock, the spectrum of the…
In this review we discuss some observational aspects and theoretical models of astrophysical collisionless shocks in partly ionized plasma with the presence of non-thermal components. A specific feature of fast strong collisionless shocks…
Supernova remnants (SNRs) are believed to accelerate particles up to high energies through the mechanism of diffusive shock acceleration (DSA). Except for direct plasma simulations, all modeling efforts must rely on a given form of the…
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 (SNR's). To supply the observed flux of cosmic rays, a…
Recent precise measurements of cosmic ray (CR) spectra show that the energy distribution of protons is softer than those of heavier nuclei, and there are spectral hardenings for all nuclear compositions above $\sim$200 GV. Models proposed…
We review the basic features of particle acceleration theory around collisionless shocks in supernova remnants (SNRs). We show how non linear effects induced by the back reaction of accelerated particles onto the shock dynamics are of…
Shocks of supernova remnants (SNRs) accelerate charged particles up to 100 TeV range via diffusive shock acceleration (DSA) mechanism. It is believed that shocks of SNRs are the main contributors to the pool of Galactic cosmic rays,…
These notes present the fundamentals of Fermi acceleration at shocks, with a special attention to the role that supernova remnants have in producing Galactic cosmic rays. Then, the recent discoveries in the theory of diffusive shock…
Collisionless shocks, that is shocks mediated by electromagnetic processes, are customary in space physics and in astrophysics. They are to be found in a great variety of objects and environments: magnetospheric and heliospheric shocks,…
A rapidly growing amount of evidences, mostly coming from the recent gamma-ray observations of Galactic supernova remnants (SNRs), is seriously challenging our understanding of how particles are accelerated at fast shocks. The cosmic-ray…
In this work we investigate particle acceleration in supernova remnant shocks within a semi-analytical formalism which self-consistently accounts for particle acceleration, amplification of the magnetic field via streaming instability and…