Search

Collisionless shocks are efficient particle accelerators. At Earth, ions with energies exceeding 100 keV are seen upstream of the bow shock when the magnetic geometry is quasi-parallel, and large-scale supernova remnant shocks can accelerate ions into cosmic rays energies. This energization is attributed to diffusive shock acceleration, however, for this process to become active the ions must first be sufficiently energized. How and where this initial acceleration takes place has been one of the key unresolved issues in shock acceleration theory. Using Cluster spacecraft observations, we study the signatures of ion reflection events in the turbulent transition layer upstream of the terrestrial bow shock, and with the support of a hybrid simulation of the shock, we show that these reflection signatures are characteristic of the first step in the ion injection process. These reflection events develop in particular in the region where the trailing edge of large-amplitude upstream waves intercept the local shock ramp and the upstream magnetic field changes from quasi-perpendicular to quasi-parallel. The dispersed ion velocity signature observed can be attributed to a rapid succession of ion reflections at this wave boundary. After the ions' initial interaction with the shock, they flow upstream along the quasi-parallel magnetic field. Each subsequent wave front in the upstream region will sweep the ions back toward the shock, where they gain energy with each transition between the upstream and the shock wave frames. Within three to five gyroperiods, some ions have gained enough parallel velocity to escape upstream, thus completing the injection process., 30 pages, 10 figures. Accepted for publication in The Astrophysical Journal

We propose a path-based framework for deriving and simplifying source-tracking information for first-order term unification in the empty theory. Such a framework is useful for diagnosing unification-based systems, including debugging of type errors in programs and the generation of success and failure proofs in logic programming. The objects of source-tracking are deductions in the logic of term unification. The semantics of deductions are paths over a unification graph whose labels form the suffix language of a semi-Dyck set. Based on this idea of unification paths, two algorithms for generating proofs are presented: the first uses context-free labeled shortest-path algorithms to generate optimal (shortest) proofs in time O(n3) for a fixed signature, where n is the number of vertices of the unification graph. The second algorithm integrates easily with standard unification algorithms, entailing an overhead of only a constant factor, but generates non-optimal proofs. These non-optimal proofs may be further simplified by group rewrite rules.