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Pfeiffer Holman 2023

This repository contains archived results from research conducted by Brady Pfeiffer in Spring/Summer 2023.

Project Summary

My research was conducted with George Fox University professor of physics Bob Hamilton. While I was taking one of his courses, Dr. Hamilton reached out and asked if I would be interested in conducting research with him. Together we applied to receive funding from a university sponsored grant. Our general research area, space physics, is of growing interest to industry due to increased commercial investment in orbital infrastructure and a renewed focus on space exploration. This was an amazing opportunity to learn things that made my head spin and gain research experience while getting to connect with a welcoming professor.

Space Physics Background

Radiation from nonlinear magnetohydrodynamic (MHD) waves and shocks can impact satellites, crewed spacecraft, and infrastructure like power grids and pipelines by accelerating charged particles and inducing currents. Improved knowledge of these phenomena is vital for accurate space weather predictions, benefiting industry in cost-effective risk mitigation for personnel and infrastructure.

MHD Waves and Nonlinearity

My research focused on MHD applied to the solar wind. MHD combines the Navier-Stokes and Maxwell's equations to study magnetized conducting fluids. It involves three wave types driven by thermal and magnetic pressure gradients: the slow and fast magnetoacoustic waves, and the Alfvén wave. When a parameter known as the plasma's 'beta' is less than 1, the Alfvén and fast wave speeds coincide. For low beta values, waves at up to 20 degrees from the background magnetic field are termed 'quasiparallel.' In such cases, MHD equations simplify, leading to the derivative nonlinear Schrödinger (DNLS) equation, which can be solved using the inverse scattering transformation (IST). The IST reveals that the DNLS can be represented as a finite number of 'solitons.'

Project Description

This project expanded on Dr. Hamilton's extensive numerical studies on the dynamics of nonlinear MHD waves. It connected numerical study and analytical study of the following effects: dissipation, nonlinear Landau damping, and interactions with fast and intermediate shocks. The majority of the numerical analysis focused on collecting eigenvalue data, and comparing that data with analytical results obtained by the Adiabatic theory.


This repository contains the code and archived results from research conducted by Brady Pfeiffer in Spring/Summer 2023.






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