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We perform kinetic simulations of diffusive shock acceleration (DSA) in TypeIa supernova remnants (SNRs) expanding into a uniform interstellar medium(ISM). Bohm-like diffusion assumed, and simple models for Alfvenic drift anddissipation are adopted. Phenomenological models for thermal leakage injectionare considered as well. We find that the preshock gas temperature is theprimary parameter that governs the cosmic ray (CR) acceleration efficiency andenergy spectrum, while the CR injection rate is a secondary parameter. For SNRsin the warm ISM, if the injection fraction is larger than 10^{-4}, the DSA isefficient enough to convert more than 20 % of the SN explosion energy into CRsand the accelerated CR spectrum exhibits a concave curvature flattening toE^{-1.6}. Such a flat source spectrum near the knee energy, however, may not bereconciled with the CR spectrum observed at Earth. On the other hand, SNRs inthe hot ISM, with an injection fraction smaller than 10^{-4}, are inefficientaccelerators with less than 10 % of the explosion energy getting converted toCRs. Also the shock structure is almost test-particle like and the ensuing CRspectrum can be steeper than E^{-2}. With amplified magnetic field strength oforder of 30 microG, Alfven waves generated by the streaming instability maydrift upstream fast enough to make the modified test-particle power-law assteep as E^{-2.3}, which is more consistent with the observed CR spectrum.

Cosmic Ray Spectrum in Supernova Remnant Shocks