@article{ellison_double_2004, title={Diffusive shock acceleration in unmodified relativistic, oblique shocks}, volume={22}, ISSN={["1873-2852"]}, DOI={10.1016/j.astropartphys.2004.08.005}, abstractNote={We present results from a fully relativistic Monte Carlo simulation of diffusive shock acceleration (DSA) in unmodified shocks. The computer code uses a single algorithmic sequence to smoothly span the range from non-relativistic speeds to fully relativistic shocks of arbitrary obliquity, providing a powerful consistency check. While known results are obtained for non-relativistic and ultra-relativistic parallel shocks, new results are presented for the less explored trans-relativistic regime and for oblique, fully relativistic shocks. We find, for a wide trans-relativistic range extending to shock Lorentz factors >30, that the particle spectrum produced by DSA varies strongly from the canonical f(p) ∝ p−4.23 spectrum known to result in ultra-relativistic shocks. Trans-relativistic shocks may play an important role in γ-ray bursts and other sources and most relativistic shocks will be highly oblique.}, number={3-4}, journal={ASTROPARTICLE PHYSICS}, author={Ellison, DC and Double, GP}, year={2004}, month={Nov}, pages={323–338} }
 @article{double_baring_jones_ellison_2004, title={Magnetohydrodynamic jump conditions for oblique relativistic shocks with gyrotropic pressure}, volume={600}, ISSN={["0004-637X"]}, DOI={10.1086/379702}, abstractNote={Shock jump conditions, i.e., the specification of the downstream parameters of the gas in terms of the upstream parameters, are obtained for steady state, plane shocks with oblique magnetic fields and arbitrary flow speeds. This is done by combining the continuity of particle number flux and the electromagnetic boundary conditions at the shock with the magnetohydrodynamic conservation laws derived from the stress-energy tensor. For ultrarelativistic and nonrelativistic shocks, the jump conditions may be solved analytically. For mildly relativistic shocks, analytic solutions are obtained for isotropic pressure using an approximation for the adiabatic index that is valid in high sonic Mach number cases. Examples assuming isotropic pressure illustrate how the shock compression ratio depends on the shock speed and obliquity. In the more general case of gyrotropic pressure, the jump conditions cannot be solved analytically without additional assumptions, and the effects of gyrotropic pressure are investigated by parameterizing the distribution of pressure parallel and perpendicular to the magnetic field. Our numerical solutions reveal that relatively small departures from isotropy (e.g., ~20%) produce significant changes in the shock compression ratio, r, at all shock Lorentz factors, including ultrarelativistic ones, where an analytic solution with gyrotropic pressure is obtained. In particular, either dynamically important fields or significant pressure anisotropies can incur marked departures from the canonical gas dynamic value of r = 3 for a shocked ultrarelativistic flow, and this may impact models of particle acceleration in gamma-ray bursts and other environments in which relativistic shocks are inferred. The jump conditions presented apply directly to test-particle acceleration and will facilitate future self-consistent numerical modeling of particle acceleration at oblique, relativistic shocks; such models include the modification of the fluid velocity profile due to the contribution of energetic particles to the momentum and energy fluxes.}, number={1}, journal={ASTROPHYSICAL JOURNAL}, author={Double, GP and Baring, MG and Jones, FC and Ellison, DC}, year={2004}, month={Jan}, pages={485–500} }
 @article{ellison_double_2002, title={Nonlinear particle acceleration in relativistic shocks}, volume={18}, ISSN={["0927-6505"]}, DOI={10.1016/S0927-6505(02)00142-1}, abstractNote={Monte Carlo techniques are used to model nonlinear particle acceleration in parallel collisionless shocks of various speeds, including mildly relativistic ones. When the acceleration is efficient, the backreaction of accelerated particles modifies the shock structure and causes the compression ratio, r, to increase above test-particle values. Modified shocks with Lorentz factors less than about 3 can have compression ratios considerably greater than 3 and the momentum distribution of energetic particles no longer follows a power law relation. These results may be important for the interpretation of gamma-ray bursts if mildly relativistic internal and/or afterglow shocks play an important role accelerating particles that produce the observed radiation. For shock Lorentz factors greater than about 10, r approaches 3 and the so-called `universal' test-particle result of N(E) proportional to E^{-2.3} is obtained for sufficiently energetic particles. In all cases, the absolute normalization of the particle distribution follows directly from our model assumptions and is explicitly determined.}, number={3}, journal={ASTROPARTICLE PHYSICS}, author={Ellison, DC and Double, GP}, year={2002}, month={Dec}, pages={213–228} }