Stochastic Acceleration of Energetic Particles in the Heliosphere

In this paper we assess possible roles of stochastic acceleration by random electric field and plasma motion in the production and transport of energetic particles in the heliosphere. Stochastic acceleration can occur in the presence of multiple small-scale magnetohydrodynamic waves propagating in different directions. Usually, this type of stochastic acceleration is closely related to particle pitch angle scattering or parallel diffusion. Given the values of the parallel diffusion coefficient inferred from the observations of cosmic ray modulation or other energetic particle phenomena in the heliosphere, stochastic acceleration by small-scale waves is much slower than acceleration by shock waves and it is also much slower than adiabatic cooling by the expansion of the solar wind; thus it is considered as inefficient for producing heliospheric energetic particles or for the modulation of cosmic rays. Another type of stochastic acceleration occurs when particles go through random compressions or expansions due to large-scale plasma motion. This acceleration mechanism could be very fast when the correlation time of the fluctuations in plasma compression is short compared to the diffusion time. Particle acceleration by an ensemble of small shock waves or intermittent long wavelength compressible turbulence belongs to this category. It tends to establish an asymptotic p−3 universal distribution function quickly if there is no or little large-scale adiabatic cooling. Such a particle distribution will contain an infinite amount of pressure. Back reaction from the pressure is expected to modify the amplitude of plasma waves to an equilibrium state. At that point, the pressure of accelerated particles must remain finite and the accelerated particles could approach a p−5 distribution function.