Computer Science – Numerical Analysis
Scientific paper
May 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994apj...426..327l&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 426, no. 1, p. 327-333
Computer Science
Numerical Analysis
19
Astronomical Models, Computerized Simulation, Electron Transfer, Electrons, Numerical Analysis, Particle Acceleration, Protons, Shock Waves, Mach Number, Supernova Remnants, Whistlers, X Ray Sources
Scientific paper
We present results of numerical simulations of electron injection and acceleration at nonlinear high Mach number shocks. The electrons are assumed to be heated at the thermal subshock to an energy Einj, which is treated as a free parameter, above which they are injected by self-generated whistlers to momentum mp x VA. This injection mechanism requires Mach numbers greater than (43/(beta-))(((k Te)/(Einj))1/2), where Te and beta - are the upstream electron temperature and plasma beta parameter. Above mp x VA electrons are trapped in the shock by Alfven waves. In the proton precursor region the Alfven waves are assumed to be generated by protons accelerated at the shock, and have nonlinear intensities. Below GeV, however, electrons of a given rigidity propagate faster than protons with a similar rigidity and therefore diffuse to regions ahead of the proton precursor. In those regions the Alfven waves are generated by the electrons themselves. The diffusion coefficient appears to increase with decreasing acceleration efficiency. As a result, the number of electrons accelerated to energies GeV and above and, hence, the electron to proton ratio, depend only weakly on the extent of electron heating at the subshock. The negative feedback also renders the electron spectra insensitive to shock compression ratio and smoothing length scale. The estimated e/p ratio at GeV is between approximately 1%-10%.
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