A concept for generating nuclear fusion power and converting the kinetic energy of aneutronic fusion products into electric energy is proposed, and simulations are developed to design and evaluate this concept. The presented concept is a spherical fusor consisting of linear ion acceleration channels that intersect in the sphere center, where the converging ions form a high-energy, high-density fusion core. The geometry is that of a truncated icosahedron, with each face corresponding to one end of an ion beam channel. Walls between the channels span radially from the outer fusion fuel ionization source to an inner radius delimiting the fusion core region. Voltage control is imposed along these walls to accelerate and focus the recirculating ions. The net acceleration on each side of the channel is in the direction of the center, so that the ions recirculate along the channel paths. Permanent magnets with radial polarization inside the walls help to further constrain the ion beams while also magnetizing electrons for the purpose of neutralizing the fusion core region. The natural modulation of the ion beams along with a proposed phase-locked active voltage control results in the coalescence of the ions into ``bunches'', and thus the device operates in a pulsed mode. The use of proton-boron-11 (p-11B) fuel is studied due to its terrestrial abundance and the high portion of its energy output that is in the form of charged particles.

The direct energy converter section envelopes the entire fusion device, so that each fusion fuel channel extends outward into a fusion product deceleration region. Because the fusion device operates in a pulsed mode, the fusion products will enter the energy conversion region in a pulsed manner, which is ideal for deceleration using a standing-wave direct energy converter. The charged fusion products pass through a series of mostly-transparent electrodes that are connected to one another in an oscillating circuit, timed so that the charged fusion products continuously experience an electric field opposite to the direction of their velocity. In this way the kinetic energy of the fusion products is transferred into the resonant circuit, which may then be connected to a resistive load to provide alternating-current energy at the frequency of the pulsed ion beams.

Preliminary calculations show that a one-meter fusor of the proposed design would not be able to achieve the density required for a competitive power output due to limits imposed by Coulomb collisions and space charge. Scaling laws suggest that a smaller fusor could circumvent these limitations and achieve a reasonable power output per unit volume. However, ion loss mechanisms, though mitigated by fusor design, scale unfavorably with decreasing size. Therefore, highly effective methods for mitigation of ion losses are necessary. This research seeks to evaluate the effectiveness of the proposed methods through simulation and optimization.

A two-dimensional axisymmetric particle-in-cell ion-only simulation was developed and parallelized for execution on a graphics processing unit. With fast computation times, this simulation serves as a test bed for investigating long-timescale thermalization effects as well as providing a performance output as a cost function for optimization of the electrode positions and voltage control.

An N-body ion-only simulation was developed for a fully 3D investigation of the ion dynamics in an purely electrostatic device. This simulation uses the individual time-step method, borrowed from astrophysical simulations, to accurately model close encounters between particles by slowing down the time-step only for those particles undergoing sudden high acceleration.

A two-dimensional hybrid simulation that treats electrons as a fluid and ions as particles was developed to investigate the effect of ions on an electrostatically and magnetically confined electron population. Electrons are solved for at each time-step using a steady-state iterative solver.

A one-dimensional semi-analytic simulation of the direct energy conversion section was developed to optimize electrode spacing to maximize energy conversion efficiency.

A two-dimensional axisymmetric particle-in-cell simulation coupled with a resonant circuit simulation was developed for modeling the direct energy conversion of fusion products into electric energy.

In addition to the aforementioned simulations, a significant contribution of this thesis is the creation of a new model for simulating Coulomb collisions in a non-thermal plasma that is necessary to account for both the low-angle scattering that leads to thermalization as well as high-angle scattering that leads to ion departure from beam paths, and includes the continuous transition between these two scattering modes.

The current implementation has proven problematic with regard to achieving sufficiently high core densities for fusion power generation. Major modifications of the current approach to address the space charge issues, both with regard to the electron core population and the ion population outside of the core would be necessary.