Date of Award

9-2023

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Department of Mathematics and Statistics

First Advisor

Benjamin F. Akers, PhD

Abstract

The modeling, simulation, and analysis of high energy laser propagation is a research topic of significant interest to the defense community. A detailed understanding of the phenomenon of thermal blooming is crucial as it is detrimental to the propagation of lasers over long distances and in the presence of aerosols. The simulation of thermal blooming has historically relied on wave optics models and scaling laws for the fluid response to the laser. Since thermal blooming occurs in the presence of natural convection, however, there is a need for simulating this coupled fluid-beam effect using a first principles approach. In this work, we introduce a coupled method to solve the steady-state Boussinesq Navier–Stokes equations for fluid behavior with the paraxial equation for beam propagation. We introduce four distinct methods for solving the forced Boussinesq equations in stream function-vorticity variables in two dimensions: a fixed-point approach, a perturbation series expansion, a functional Pad´e approximant, and a composite Pad´e–Newton method. The fluid is coupled to the laser propagation via the refractive index. We prove both the existence of steady solutions for small laser intensities through the fixed-point method as well as the parametric analyticity of solutions in laser intensity. The steady fluid solvers are then used to simulate thermal blooming within an experimental chamber at a laser wavelength with high absorption. The results of this simulation are directly compared to experimental results, where we conclude that an off-centered beam propagating within a finite enclosure will experience horizontal asymmetries in the irradiance pattern as a result of the induced asymmetric temperature fluctuations.

AFIT Designator

AFIT-ENC-DS-23-S-003

Comments

A 12-month embargo was observed for posting this dissertation on AFIT Scholar.

Approved for public release. PA case number on file.

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