Paper detail

Acceleration in perpendicular relativistic shocks for plasmas consisting of leptons and hadrons

We investigate the acceleration of light particles in perpendicular shocks for plasmas consisting of a mixture of leptonic and hadronic particles. Starting from the full set of conservation equations for the mixed plasma constituents, we generalize the magneto-hydrodynamical jump conditions for a multi-component plasma, including information about the specific adiabatic constants for the different species. The impact of deviations from the standard model of an ideal gas is compared in theory and particle-in-cell simulations, showing that the standard-MHD model is a good approximation. The simulations of shocks in electron-positron-ion plasmas are for the first time multi-dimensional, transverse effects are small in this configuration and 1D simulations are a good representation if the initial magnetization is chosen high. 1D runs with a mass ratio of 1836 are performed, which identify the Larmor frequency ω_{ci} as the dominant frequency that determines the shock physics in mixed component plasmas. The maximum energy in the non-thermal tail of the particle spectra evolves in time according to a power-law proportional to t^αwith αin the range 1/3 < α< 1, depending on the initial parameters. A connection is made with transport theoretical models by Drury (1983) and Gargate & Spitkovsky (2011), which predict an acceleration time proportional to γand the theory for small wavelength scattering by Kirk & Reville (2010), which predicts a behavior rather as proportional to γ^2. Furthermore, we compare different magnetic field orientations with B_0 inside and out of the plane, observing qualitatively different particle spectra than in pure electron-ion shocks.