The role of fluctuational acceleration in the generation of solar particles

Abstract

Stochastic particle acceleration is essentially a diffusion process in energy phase space. In spite of the statistical behavior of the diffusion process, there is an average energy gain tendency of deterministic nature which is usually called Systematic Acceleration. In practice only the systematic acceleration rate has been considered, ignoring effects of the diffusion process, usually identified as a fluctuational acceleration rate. However, depending on the nature of the phase velocity spectrum of the turbulence, or on competitive energy loss processes, the average systematic acceleration rate may become inefficient and even null, so that energetic particle production is due only to the energy spread effects (diffusion in energy). We calculate separately the contribution of both energy change rates, in order to evaluate the importance of particle production by each. We consider the classical Fermi process and turbulent acceleration by magnetosonic waves (for the case in which S=O in the resonance condition). The transport equation is solved analytically for the steady state and for the time-dependent situation. We find that the contribution of fluctuational acceleriltion to the source solar particle spectrum cannot be considered as mere particle flux fluctuations, but may represent an important overproduction in some cases and particle depression in others. The relevance of energy spread effects is related to the efficiency of the energy gain: the nature of the initial particle population relative to the velocity spectra of turbulence, and thus the relative proportion among the different kind of interactions of particles with acc!lerating agents. We discuss the conditions under which diffusion in energy effects should be ignored relative to the average energy gain rate. With some exceptions in the stationary case, energy spectra derived on the basis of systematic acceleration alone cannot describe the real particle flux. This must be taken into account in calculations of the flux of secondary radiation.