Fast-particle acceleration at a spherical shock front

A mechanism of particle acceleration at a shock front is discussed, in which preshock scattering of the particles is taken into account. The nonsteady momentum distribution function is detemined for a particular law of shock motion, R proportional t/sup 1/2/. The sphericity of the shock front will have little influence on the index in the universal power-law accelerated-particle spectrum, provided μ/sub asterisk/-1equivalent3[kappa-cur1+kappa-curγ/(γ -1)]/RR<<1 (kappa-cur1, kappa-cur are the diffusion coefficients inside and outside the envelope; γ is the ratio of the shock velocity to the postshock gas velocity). In this event the peak particle momentum will grow with time as proughly-equalp0(t/t0)*/2γ. The possibilities for cosmic ray acceleration in supernova envelopes are examined