Shock Acceleration and Transport of Solar Energetic Particles in the Corona

In gradual solar energetic particle (SEP) events, the phase-space density of suprathermal seed particles plays an important role in the bootstrap acceleration of SEPs at a coronal-mass-ejection driven shock in the corona. Higher seed proton density causes more rapid resonant amplification of ambient Alfvén waves and hence faster shock acceleration of SEPs. On the other hand, SEP-driven Alfvén wave growth is slowed by higher plasma density and by the thermal damping of left-hand polarized waves at frequencies exceeding a fraction of the proton cyclotron frequency. Damping also influences the background wave distribution. Coronal magnetic field strongly influences the wave-particle interaction since its magnitude scales the resonant wavenumber and its negative parallel gradient focuses the charged particles. The solar-wind velocity and Alfvén speed, relevant to the height of shock formation, are related to the plasma density and magnetic field. Consequently, the spatial dependences of all these environmental parameters influence the coupled evolution of SEP and Alfvén wave distributions. We will present results from our models of SEP acceleration and transport combining the effects of the above physical considerations. The model results will be compared to directly observed and inferred features of SEP events (e.g. streaming-limited intensity, maximum energy, height of first solar particle release) to address the roles and relative importance of the above physical factors.