Acceleration of suprathermal particles by compressional plasma wave trains in the solar wind
This paper presents a calculation of particle acceleration by an idealized compressional plasma wave train. In this model, suprathermal particles, such as pickup ions, are continuously injected into a wave train consisting of a series of compression or rarefaction regions. The momentum distribution of particles will become broader and broader as they go through the wave train, which is very similar to diffusion in momentum space. The acceleration process is very fast: it does not take too many wave cycles even with a small compression amplitude to reach an asymptotic steady state momentum distribution. In the absence of large-scale adiabatic cooling, the asymptotic distribution is flat below the initial injection momentum, and above the injection momentum, it is proportional to a power law distribution with the slope of -3. This distribution appears to be independent of any model parameters in this acceleration mechanism. If there is a prevailing large-scale adiabatic cooling by the expanding solar wind, the asymptotic steady state distribution remains to be flat below the injection momentum and it is a power law distribution but with a steeper slope above the injection momentum. The acceleration process alone does not automatically guarantee a p-5 power law. However, since the process can quickly build up pressure from the accelerated particles, it is expected that the amplitude of compressional plasma wave will be reduced. In the final state after nonlinear wave-particle interactions, the distribution of accelerated particles and plasma wave must achieve a balance between large-scale adiabatic cooling and the acceleration by compressional plasma waves. The particle distribution at the equilibrium will settle with a p-5 distribution given that the initial solar wind pressure is much larger than the initial pressure of newly injected particles.