Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)



Committee Chair

Vladimir Florinski

Committee Member

Gary Zank

Committee Member

Jakobus le Roux

Committee Member

Ming Sun

Committee Member

Babak Shotorban


Voyager Project., Cosmic rays., Astrophysics., Space probes.


Interstellar neutral atoms entering the heliosphere could become ionized by photo-ionization or charge exchange with solar-wind ions. These newly created ions are picked up by the solar wind and carried to the termination shock (TS) where they are believed to be accelerated by the diffusive shock acceleration process to high energies (~1-100 MeV n$^{-1}$). The accelerated ions are known as anomalous cosmic rays (ACRs). When NASA's space probe, textit{Voyager 1} crossed the TS in 2004, the measured ACR spectra did not match the theoretical prediction of a continuous power law, and the source of the high-energy ACRs was not observed. However, over the next few years, in the declining phase of the solar cycle, the spectra began to evolve into the expected power-law profile. The model developed here is based on the suggestion that ACRs are still accelerated at the shock, but away from the Voyager crossing points. First, we study ACR acceleration using a three-dimensional, non-spherical model of the heliosphere that is axisymmetric with respect to the interstellar flow direction. A semi-analytic model of the plasma and magnetic field backgrounds is developed to permit an investigation over a wide range of parameters under controlled conditions. The model is applied to helium ACRs, whose phase-space trajectories are stochastically integrated backward in time until a pre-specified, low-energy boundary of 0.5 MeV n$^{-1}$, is reached. Next, we propose that the solar cycle had an important effect on the evolving of the spectra in the heliosheath. To investigate this, a magnetohydrodynamic background model with stationary solar-wind inner boundary conditions was used to model the transport of helium and oxygen ions. In addition, we developed a charge consistent stochastic model to simulate multiply charged oxygen ACRs. It is shown that the spectral evolution of ACRs in the heliosheath at textit{Voyager 1} could be explained by combining intermediate-energy particles arriving from the heliotail-facing part of the TS, an increase in the source strength, and an enhancement in diffusion as a result of a decrease of the turbulent correlation length in the declining phase of the solar cycle. Drift effects seem to have had a smaller effect on the evolution of the spectra. Additionally, we found that the spectrum of heavy ACRs ions, such as oxygen, may be dominated by multiply charged ions at some characteristic energy that depends on the diffusion coefficient.



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