Date of Award

5-2026

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Aerospace, Physics, and Space Sciences

First Advisor

Donald C. Warren, III

Second Advisor

Ryan T. White

Third Advisor

Juan Carlos Palacios Caicedo

Fourth Advisor

Donald Platt

Abstract

Cosmic rays are a phenomenon known to humankind from the early 1900s, and yet today the details of their physical behavior are not fully settled. While the observed spectral fluxes of cosmic rays follow a power-law trend when plotted against particle energy, the exact mechanisms under which they get to such high energies are still under study. This thesis will undertake a subsection of that task, where the Monte Carlo simulation of particle accelerations is described in Warren (2015), and we aim to identify and quantify the noise inherent in such simulations. This document takes a long path through particle acceleration mechanisms, the distributions of random variables and fitting them to sample data, and identifying a goodness-of-fit metric for theoretical statistical distributions to observed data. We find that the simulations for particle fluxes mostly follow a Normal (Gaussian) distribution at a given particle Lorentz factor 𝛾, where the mean, as expected, follows a power-law trend, and the standard deviation is determined empirically. We also use the goodness-of-fit metric, namely the Bhattacharya distance, as an indicator of reliability for the distribution estimates. On the low energy (γ ≲ 10) and very high energy (γ ≳ 10⁷) ends of the spectra, where the Monte Carlo simulation procedure is not especially robust, we find that the flux samples deviate quite a bit from the theoretical Gaussian distribution, and the simple assumptions about large number statistics break down. Therefore, for the final result, we identify a section of each spectra where we can have reliable noise estimates, and provide such estimates at those sections.

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