In order for diffusive shock acceleration (DSA) to accelerate particles to high energies, the energetic particles must be able to interact with magnetic turbulence over a broad wavelength range. The weakly anisotropic distribution of accelerated particles, i.e. cosmic rays (CRs), is believed capable of producing this turbulence in a symbiotic relationship where the magnetic turbulence required to accelerate the CRs is created by the accelerated CRs themselves. In efficient DSA, this wave–particle interaction can be strongly non‐linear where CRs modify the plasma flow and the specific mechanisms of magnetic field amplification. Resonant interactions have long been known to amplify magnetic fluctuations on the scale of the CR gyroradius, and Bell showed that the CR current can efficiently amplify magnetic fluctuations with scales smaller than the CR gyroradius. Here, we show with a multiscale, quasi‐linear analysis that the presence of turbulence with scales shorter than the CR gyroradius enhances the growth of modes with scales longer than the gyroradius, at least for particular polarizations. We use a mean‐field approach to average the equation of motion and the induction equation over the ensemble of magnetic field oscillations accounting for the anisotropy of relativistic particles on the background plasma. We derive the response of the magnetized CR current on magnetic field fluctuations and show that, in the presence of short‐scale, Bell‐type turbulence, long‐wavelength modes are amplified. The polarization, helicity and angular dependence of the growth rates are calculated for obliquely propagating modes for wavelengths both below and above the CR mean free path. The long‐wavelength growth rates we estimate for typical supernova remnant parameters are sufficiently fast to suggest a fundamental increase in the maximum CR energy that a given shock can produce.

We present a nonlinear Monte Carlo model of efficient diffusive shock acceleration (DSA) where the magnetic turbulence responsible for particle diffusion is calculated self-consistently from the resonant cosmic-ray (CR) streaming instability, together with non-resonant short-and long-wavelength CR-current-driven instabilities. We include the backpressure from CRs interacting with the strongly amplified magnetic turbulence which decelerates and heats the super-alfvénic flow in the extended shock precursor. Uniquely, in our plane-parallel, steady-state, multi-scale model, the full range of particles, from thermal (∼ eV) injected at the viscous subshock, to the escape of the highest energy CRs (∼ PeV) from the shock precursor, are calculated consistently with the shock structure, precursor heating, magnetic field amplification (MFA), and scattering center drift relative to the background plasma. In addition, we show how the cascade of turbulence to shorter wavelengths influences the total shock compression, the downstream proton temperature, the magnetic fluctuation spectra, and accelerated particle spectra. A parameter survey is included where we vary shock parameters, the mode of magnetic turbulence generation, and turbulence cascading. From our survey results, we obtain scaling relations for the maximum particle momentum and amplified magnetic field as functions of shock speed, ambient density, and shock size.

Energetic nonthermal particles (cosmic rays, CRs) are accelerated in supernova remnants, relativistic jets and other astrophysical objects. The CR energy density is typically comparable with that of the thermal components and magnetic fields. In this review we discuss mechanisms of magnetic field amplification due to instabilities induced by CRs. We derive CR kinetic and magnetohydrodynamic equations that govern cosmic plasma systems comprising the thermal background plasma, comic rays and fluctuating magnetic fields to study CR-driven instabilities. Both resonant and non-resonant instabilities are reviewed, including the Bell short-wavelength instability, and the firehose instability. Special attention is paid to the longwavelength instabilities driven by the CR current and pressure gradient. The helicity production by the CR current-driven instabilities is discussed in connection with the dynamo mechanisms of cosmic magnetic field amplification.

Starburst regions with multiple powerful winds of young massive stars and supernova remnants (SNRs) are favorable sites for high-energy cosmic ray (CR) acceleration. A supernova (SN) shock colliding with a fast wind from a compact cluster of young stars allows the acceleration of protons to energies well above the standard limits of diffusive shock acceleration in an isolated SN. The proton spectrum in such a wind-SN pevatron accelerator is hard with a large flux in the high-energy-end of the spectrum producing copious γ-rays and neutrinos in inelastic nuclear collisions. We argue that SN shocks in the Westerlund 1 (Wd1) cluster in the Milky Way may accelerate protons to > ∼ 40 PeV. Once accelerated, these CRs will diffuse into surrounding dense clouds and produce neutrinos with fluxes sufficient to explain a fraction of the events detected by IceCube from the inner Galaxy.Since the most likely high-energy neutrino producing mechanisms are the inelastic p−nuclei and p − γ collisions of protons, where the reaction kinematics result in the energy of the neutrinos to be ∼ 0.05 that of the protons, the energy of the parent protons should exceed 4 · 10 16 eV to explain the IceCube observations. The γ-rays produced in these reactions have ∼ 0.1 of the proton energy (e.g., Halzen 2013). Furthermore, the proton accelerators must be very efficient to produce the high-energy neutrino flux of νFν ≈ 10 −8 GeV cm −2 s −1 sr −1 per flavor in the 0.1-1 PeV range detected by IceCube.Neutrinos from photo-meson p − γ interactions in compact particle accelerators, like the cores of active galactic nuc 0000 RAS arXiv:1507.04018v2 [astro-ph.HE] 12 Sep 2015

We give a brief review of the origin and acceleration of cosmic rays (CRs), emphasizing the production of CRs at different stages of supernova evolution by the first-order Fermi shock acceleration mechanism. We suggest that supernovae with trans-relativistic outflows, despite being rather rare, may accelerate CRs to energies above 10 18 eV over the first year of their evolution. Supernovae in young compact clusters of massive stars, and interaction powered superluminous supernovae, may accelerate CRs well above the PeV regime. We discuss the acceleration of the bulk of the galactic CRs in isolated supernova remnants and re-acceleration of escaped CRs by the multiple shocks present in superbubbles produced by associations of OB stars. The effects of magnetic field amplification by CR driven instabilities, as well as superdiffusive CR transport, are discussed for nonthermal radiation produced by nonlinear shocks of all speeds including trans-relativistic ones.