Thesis (Ph. D.)--University of Rochester. Department of Physics and Astronomy, 2021.
Statistical mechanics governs the fundamental properties of many body systems and the corresponding velocity distributions dictates most material properties. In plasmas, a description through statistical mechanics is challenged by the fact that the movement of one electron effects many others through their Coulomb interactions, leading to collective motion. Although most of the research in plasma physics assumes equilibrium electron distribution functions, or small departures from a Maxwell-Boltzmann (Maxwellian) distribution, this is not a valid assumption in many situations. Deviations
from a Maxwellian distribution can have significant ramifications on the interpretation of diagnostic signatures, and more importantly in our ability to understand the basic nature of plasmas. Optical collective Thomson scattering provides precise density and temperature measurements in numerous plasma-physics experiments. A statistically based, quantitative analysis of the errors in the measured electron density and temperature is presented when synthetic data calculated using a non-Maxwellian electron distribution function is fit assuming a Maxwellian electron distribution [A. L. Milder et al., Phys.
Plasmas 26, 022711 (2019)]. In the specific case of super-Gaussian distributions, such analysis lead to errors of up to 50% in temperature and 30% in density. Including the proper family of non-Maxwellian electron distribution functions, as a fitting parameter, in Thomson-scattering analysis removes the model-dependent errors in the inferred parameters at minimal cost to the statistical uncertainty. This technique was used to determine the picosecond evolution of non-Maxwellian electron distribution functions in a laser-produced plasma using utrafast Thomson scattering [A. L. Milder et al., Phys.
Rev. Lett. 124, 025001 (2020)]. During the laser heating, the distribution was measured to be approximately super-Gaussian due to inverse bremsstrahlung heating. After the heating laser turned off, collisional ionization caused further modification to the distribution function while increasing electron density and decreasing temperature. Electron distribution functions were determined using Vlasov-Fokker-Planck simulations including atomic kinetics. A novel technique that encodes the electron motion to the frequency of scattered light while using collective scattering to improve the scattering efficiency at velocities where the number of electrons are limited was invented to measure non-Maxwellian electron distributions [A. L. Milder et al., in review Phys. Rev. Lett. (2021)]. This angularly resolved Thomson-scattering technique is a novel extension of Thomson scattering, enabling the measurement of the electron velocity distribution function over many orders of magnitude. Electron velocity distribution functions driven by inverse bremsstrahlung heating were measured to be super-Gaussian in the bulk (v/vth < 3) and Maxwellian in the tail (v/vth > 3) when the laser heating rate dominated over the electron-electron thermalization rate. Simulations with the particle code Quartz
showed the shape of the tail was dictated by the uniformity of the laser heating. The reduction of electrons at slow velocities resulted in a ∼ 40% measured reduction in inverse bremsstrahlung absorption. A reduced model describing the distribution function is given and used to perform a Monte Carlo analysis of the uncertainty in the measurements [A. L. Milder et al., in review Phys. Plasmas (2021)]. The electron density and temperature were determined to a precision of 12% and 21%, respectively, on average while all other parameters defining the distribution function were generally
determined to better than 20%. It was found that these uncertainties were primarily due to limited signal to noise and instrumental effects. Distribution function measurements with this level of precision were sufficient to distinguish between Maxwellian and non-Maxwellian distribution functions.
Department of Energy (DOE) - National Nuclear Security Administration under Award Number DE-NA0003856, Office of Fusion Energy Sciences under Award Number DE-SC0016253, performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344
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