Date of Award

Spring 2018

Project Type


Program or Major


Degree Name

Doctor of Philosophy

First Advisor

Martin A. Lee

Second Advisor

Benjamin D. G. Chandran

Third Advisor

Karsten Pohl


Solar energetic particles (SEPs) are high-energy ions and electrons originating at or near the Sun. The energies of these particles extend from solar wind energies up to ∼10 GeV for ions and ∼100 MeV for electrons. This dissertation employs primarily analytical tools to accomplish three research tasks related to the propagation of SEPs from the lower solar corona to 1 AU: (1) developing a transport model based on the focused transport equation to illustrate and predict the spatial and pitch-angle distribution of the nearly scatter-free beam-like protons observed during the onset phase of the so-called ground level events; (2) constructing an analytical theory for the formation of the double-power-law proton differential fluence spectra observed in the largest SEP events; (3) investigating the validity of the test particle approach to SEP transport in the interplanetary medium including Alfvenic wave excitation by the streaming protons. These three tasks feature and illuminate three fundamental characteristics of large “gradual” SEP events: the large anisotropy of the high energy beam at the onset of events that have good magnetic connection between observers and source region at the Sun; the double-power law energy spectrum characterizing these events; and the substantial excitation of solar wind Alfvenic turbulence at cyclotron resonant frequencies.

In task 1, by solving the focused transport equation at small pitch angles with a constant focusing length and a constant pitch angle diffusion coefficient, we successfully account for the evolution of the beam-like protons in interplanetary space with stochastic pitch-angle scattering and adiabatic focusing. We attribute for the first time the observed Reid-Axford profile to the effect of nearly scatter-free interplanetary transport of SEPs rather than to the SEP injection process near the Sun. In task 2, through the convolution of the derived Green’s function of the stationary energetic-particle transport equation with a power-law SEP source spectrum injected near the Sun, presumably generated by shock acceleration, we naturally reproduce the double-power-law feature characteristic of proton differential fluence spectra observed in the largest SEP events and, for the first time, interpret it as a result of convection and adiabatic cooling in the divergent solar wind rather than the acceleration mechanism in the low corona. In task 3, to address the question of how “large” an event should be so that the passage of the streaming protons is enough to noticeably amplify the interplanetary hydromagnetic waves at their cyclotron resonant wavelengths, we employ a diffusive transport model and examines the wave growth arising from the first-order anisotropy of SEPs. We, for the first time, relate the wave growth with proton differential fluence and derive the characteristic differential fluence magnitude 6.3*10^6 cm^-2sr^-1MeV^-1 at 10 MeV/nuc. If is below this value, the test-particle theory is a valid description of SEP transport at and above 10 MeV/nuc; above this fluence wave excitation is important in modifying the time-profile of the event.