; Fryer, Christopher L.
; Li, Hui] Los Alamos Natl Lab, Los Alamos, NM 87545 USA
; [Fan, Zhong-Hui
; Wang, Jian-Min] Chinese Acad Sci, Inst High Energy Phys, Beijing 100049, Peoples R China
; [Fan, Zhong-Hui] Yunnan Univ, Dept Phys, Kunming 650091, Yunnan, Peoples R China
; [Fryer, Christopher L.] Univ Arizona, Dept Phys, Tucson, AZ 85721 USA
; [Wang, Jian-Min] Chinese Acad Sci, Theoret Phys Ctr Sci Facil, Beijing 100864, Peoples R China
We study the stochastic electron acceleration by fast-mode waves in the turbulent downstream of weakly magnetized collisionless astrophysical shocks. The acceleration is most efficient in a dissipative layer, and the model characteristics are determined by the shock speed, density, magnetic field, and turbulence decay length. The model explains observations of shell-type supernova remnants RX J1713.7-3946 and J0852.0-4622 and can be tested by observations in hard X-rays with the HXMT and NuSTAR or gamma-rays with GLAST.