Physics of relativistic collisionless shocks. III. The suprathermal particles

In this third paper of a series, we discuss the physics of the population of accelerated particles in the precursor of an unmagnetized, relativistic collisionless pair shock. In particular, we provide a theoretical estimate of their scattering length l(scatt)(p) in the self-generated electromagnetic turbulence, as well as an estimate of their distribution function. We obtain l(scatt)(p) approximate to gamma(p)epsilon(-1)(B) (p/gamma(infinity)mc)(2)c/omega(p), with p the particle momentum in the rest frame of the shock front, epsilon(B) the strength parameter of the microturbulence, gamma(p) the Lorentz factor of the background plasma relative to the shock front, and gamma(infinity) its asymptotic value outside the precursor. We compare this scattering length to large-scale PIC simulations and find good agreement for the various dependencies.