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Abstract The observed energy spectra of accelerated particles at interplanetary shocks often do not match the diffusive shock acceleration (DSA) theory predictions. In some cases, the particle flux forms a plateau over a wide range of energies, extendingupstream of the shockfor up to seven fluxe-folds before submerging into the background spectrum. Remarkably, at and downstream of the shock we have studied in detail, the flux falls off in energy asϵ⁻¹, consistent with the DSA prediction for a strong shock. The upstream plateau suggests a particle transport mechanism different from those traditionally employed in DSA models. We show that a standard (linear) DSA solution based on a widely accepted diffusive particle transport with an underlying resonant wave–particle interaction is inconsistent with the plateau in the particle flux. To resolve this contradiction, we modify the DSA theory in two ways. First, we include a dependence of the particle diffusivityκon the particle fluxF(nonlinear particle transport). Second, we invoke short-scale magnetic perturbations that are self-consistently generated by, but not resonant with, accelerated particles. They lead to the particle diffusivity increasing with the particle energy as ∝ϵ^3/2that simultaneously decreases with the particle flux as 1/F. The combination of these two trends results in the flat spectrum upstream. We speculate that nonmonotonic spatial variations of the upstream spectrum, apart from being time-dependent, may also result from non-DSA acceleration mechanisms at work upstream, such as stochastic Fermi or magnetic pumping acceleration. 

Abstract Recent precise measurements of primary and secondary cosmic-ray (CR) species in the teravolt rigidity domain have unveiled a bump in their spectra, located between 0.5 and 50 TV. We argue that a local shock may generate such a bump by increasing the rigidity of the preexisting CRs below 50 TV by a mere factor of ∼1.5. Reaccelerated particles below ∼0.5 TV are convected with the interstellar medium flow and do not reach the Sun, thus creating the bump. This single universal process is responsible for the observed spectra of all CR species in the rigidity range below 100 TV. We propose that one viable shock candidate is the Epsilon Eridani star at 3.2 pc from the Sun, which is well aligned with the direction of the local magnetic field. Other shocks, such as old supernova shells, may produce a similar effect. We provide a simple formula, Equation (9), that reproduces the spectra of all CR species with only two nonadjustable shock parameters, uniquely derived from the proton data. We show how our formalism predicts helium and carbon spectra and the B/C ratio. 

Recent measurements of primary and secondary CR spectra, their arrival directions, and our improved knowledge of the magnetic field geometry around the heliosphere allow us to set a bound on the distance beyond which a puzzling 10-TeV ‘‘bump” and certain related spectral features cannot originate. The sharpness of the spectral breaks associated with the bump, the abrupt change of the CR intensity across the local magnetic equator (90 pitch angle), and the similarity between the primary and secondary CR spectral pat- terns point to a local reacceleration of the bump particles out of the background CRs. We argue that, owing to a steep preexisting CR spectrum, a nearby shock may generate such a bump by boosting particle rigidity by a mere factor of 1.5 in the range below 50 TV. Reaccelerated particles below 0.5 TV are convected with the interstellar medium flow and do not reach the Sun. The particles above this rigidity then form the bump. This single universal process is responsible for the observed spectral features of all CR nuclei, primary and secondary, in the rigidity range below 100 TV. We propose that one viable candidate is the system of shocks associated with Eridani star at 3.2 pc of the Sun, which is well aligned with the direction of the local magnetic field. Other shocks, such as old supernova shells, may produce a similar effect. We provide a simple formula that reproduces the spectra of all CR species with only three parameters uniquely derived from the CR proton data. We show how our formalism predicts helium, boron, carbon, oxygen, and iron spectra, for which accurate data in GV-TV range exist. Our model thus unifies all the CR spectral features observed below 50 TV.