Electron acceleration to non-thermal , ultra-relativistic energies ( \sim 10 - 100 TeV ) is revealed by radio and X-ray observations of shocks in young supernova remnants ( SNRs ) .
The diffusive shock acceleration ( DSA ) mechanism is usually invoked to explain this acceleration , but the way in which electrons are initially energized or ‘ injected ’ into this acceleration process starting from thermal energies is an unresolved problem .
In this paper we study the initial acceleration of electrons in non-relativistic shocks from first principles , using two- and three-dimensional particle-in-cell ( PIC ) plasma simulations .
We systematically explore the space of shock parameters ( the Alfvénic Mach number , M _ { A } , the shock velocity , v _ { sh } , the angle between the upstream magnetic field and the shock normal , \theta _ { Bn } , and the ion to electron mass ratio , m _ { i } / m _ { e } ) .
We find that significant non-thermal acceleration occurs due to the growth of oblique whistler waves in the foot of quasi-perpendicular shocks .
This acceleration strongly depends on using fairly large numerical mass ratios , m _ { i } / m _ { e } , which may explain why it had not been observed in previous PIC simulations of this problem .
The obtained electron energy distributions show power law tails with spectral indices up to \alpha \sim 3 - 4 .
The maximum energies of the accelerated particles are consistent with the electron Larmor radii being comparable to that of the ions , indicating potential injection into the subsequent DSA process .
This injection mechanism , however , requires the shock waves to have fairly low Alfénic Mach numbers , M _ { A } \lesssim 20 , which is consistent with the theoretical conditions for the growth of whistler waves in the shock foot ( M _ { A } \lesssim ( m _ { i } / m _ { e } ) ^ { 1 / 2 } ) .
Thus , if the whistler mechanism is the only robust electron injection process at work in SNR shocks , then SNRs that display non-thermal emission must have significantly amplified upstream magnetic fields .
Such field amplification is likely achieved by the escaping cosmic rays , so electron and proton acceleration in SNR shocks must be interconnected .