WEIGHTINESS OF THE DISPERSIVE RATE IN STOCHASTIC ACCELERATION PROCESSES

We present analytical solutions to the transport of the accelerated pa rticles that are valid over the entire energy range (nonrelativistic, transrelativistic, and ultrarelativistic) for the time-dependent and e quilibrium cases. On the basis of these overall spectra, we have studi ed the relative importance of the term of average (systematic) energy increased and the term of diffusion (spread) in energy that define the evolution of accelerated particles within the frame of a simplified d iffusion-convection transport equation, when the particle distribution function N(E,t)is assumed to be independent of spatial pitch-angle di ffusion (isotropic). Since in some astrophysical works, only the term of average energy increase in the simplified transport equation in ene rgy space is considered to be leading directly to a power-lay-type spe ctrum, we have established the conditions under which such an approxim ation may be justified. The analysis is illustrated for acceleration b y two different kinds of turbulence: MHD and langmuir waves. The omiss ion of the term of energy spread leads, in general, to an important de pletion or overproduction of the accelerated particle flux that must b e seriously considered in any calculation of the flux of secondary rad iation produced by the accelerated particles. The presented analytical spectra may be of particular relevance to gamma-ray, neutron, and pio n production in solar flares as well as in other astrophysical sites