Focused interplanetary transport of approximately 1 MeV solar energetic protons through self-generated Alfven waves

Abstract

We present a model of the focused transport of approximately 1 MeV solar energetic protons through interplanetary Alfven waves that the protons themselves amplify or damp. It is based on the quasi-linear theory but with a phenomenological pitch angle diffusion coefficient in the 'resonance gap.' For initial Alfven wave distributions that give mean free paths greater than approximately 0.5 AU for approximately 1 MeV protons in the inner heliosphere, the model predicts greater than roughly an order of magnitude amplification (damping) in the outward (inward) propagating resonant Alfven waves at less than or approximately equal to o.3 AU heliocentric distance. As the strength of proton source is increased, the peak differential proton intensity at approximately 1 MeV at 1 AU increases to a maximum of approximately 250 particles (/(sq cm)(s)(sr)(MeV)) and then decreases slowly. It may be attenuated by a factor of 5 or more relative to the case without wave evolution, provided that the proton source is sufficiently intense that the resulting peak differential intensity of approximately 1 MeV protons at 1 AU exceeds approximately 200 particles (/(sq cm)(s)(sr)(MeV)). Therefore, in large solar proton events, (1) one may have to take into account self-amplified waves in studying solar particle propagation, (2) the number of accelerated protons escaping from a flare or interplanetary shock may have been underestimated in past studies by a significant factor, and (3) accelerated protons escaping from a traveling interplanetary shock at r less than or approximately equal to 0.3 AU should amplify the ambient hydromagnetic waves siginificantly to make the shock an efficient accelerator, even if initially the mean free path is greater than or approximately equal to 1 AU.