## Dissertations

2018

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Mechanical and Aerospace Engineering

#### Committee Chair

Jason T. Cassibry

George H. Miley

#### Committee Member

William Seidler, II

Gabe Xu

Gary P. Zank

#### Subject(s)

Nuclear fusion., Pinch effect (Physics), Plasma (Ionized gases), Stopping power (Nuclear physics)

#### Abstract

The objective of this dissertation is to explore the theoretical feasibility and technical potential of achieving thermonuclear ignition in a z-pinch plasma using a deuterium-lithium (D$^{6}$Li) fuel mixture at approximately solid density or higher. In this context, ignition occurs when a fusion plasma produces enough energy to sustain itself without auxiliary heating by external sources. The question of whether it is even possible to successfully ignite D$^{6}$Li targets to achieve a net positive energy gain finds a possible answer in two critical factors: (1) the high dependence of fusion reactivity on the density of the fuel, and (2) the physics of burn wave propagation through the target. The latter of these two factors is governed by the plasma stopping power, which is in turn heavily influenced by the density of the plasma. Ignition and high positive gain are greatly facilitated by localized (i.e. short) penetration depths of the fusion products into the surrounding cold fuel layer. In this study, a recently formulated model of plasma stopping power is integrated into a Smoothed Particle Hydrodynamics (SPH) code called SPFMax in order to examine the behavior of burning fusion plasmas. The results show that the density of the fuel does indeed prove to be a heavy influence on the penetration depth. Further, the conditions for which ignition will occur turn out to be more feasible than expected due to this high dependence of fusion reactivity on fuel density and the charge number (Z = 3) of fully ionized lithium. It is found that a central hotspot with a temperature of 40 keV between sections of colder fuel at 1 keV temperature will launch a burn wave in dense D$^{6}$Li. The ratio between the hotspot density and that of the exterior fuel ($\rho_{hs}/\rho_{ext}$) is also found to be a significant figure of merit in z-pinch target design. Additionally, simulations using initial conditions equivalent to the output of the Charger-1 pulsed power facility at 15 and 30 percent efficiency are used to predict the possible neutron yield that can be expected from a D$^{6}$Li pinch experiment using Charger-1 as the driver. The predicted yields are found to agree with a recent scaling model that was formulated based on combined data from multiple experiments. The principle conclusion of this study is that thermonuclear ignition in a solid density D$^{6}$Li z-pinch plasma appears to be achievable in a parameter space that is accessible with current pulse power technology.

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