Cosmic Ray Spectrum in Supernova Remnant Shocks

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We performed kinetic simulations of diffusive shock acceleration in Type Ia supernova remnants (SNRs) expanding into a uniform interstellar medium (ISM). The preshock gas temperature is the primary parameter that governs the cosmic ray (CR) acceleration, while magnetic field strength and CR injection rate are secondary parameters. SNRs in the hot ISM, with an injection fraction smaller than 10⁻⁴, are inefficient accelerators with less than 10 % energy getting converted to CRs. The shock structure is almost test-particle like and the ensuing CR spectrum can be steeper than E⁻². Although the particles can be accelerated to the knee energy of 10¹⁵.⁵Z eV with amplified magnetic fields in the precursor, Alfv'enic drift of scattering centers softens the source spectrum as steep as E⁻².¹ and reduces the CR acceleration efficiency.