“The Analytic Connection Between the Magnetic and the Non-magnetic Compton Scattering Relativistic Cross Sections”
Zach Doctor, Mentor Peter Gonthier

This research investigates the analytical relationship between the magnetic, relativistic Compton scattering cross section derived from Quantum Electrodynamics principles and the non-magnetic, relativistic Klein-Nishina cross section. Both cross sections are the lowest-order solutions of the Dirac equation that exhibit polarization and spin dependence. In a separate study, we developed concise analytics describing the polarization-dependent and spin-averaged cross section of Compton scattering in strong magnetic fields. Both cross sections display distinctly different kinematic behaviors, particularly in intense magnetic field environments within the magnetospheres of highly magnetic neutron stars known as magnetars. In these contexts, quantized states known as Landau states play a crucial role in characterizing the perpendicular energies relative to the magnetic field. While the initial electron or positron is in the ground state and at rest, the final state can be excited to a maximum Landau state dependent on the incident photon energy and magnetic field. Therefore, the comparison requires summing all contributing final Landau states and averaging over spin states. Our previous work established a numerical equivalence between these two cross sections, highlighting the potential for an underlying analytical connection. The primary objective of this research is to lay the groundwork for a comprehensive article intended to be submitted to a peer-reviewed journal.
 
“An Examination of Nonlinear Collisionless Magnetic Reconnection through Eigenmode Decomposition”
Nathan Stolnicki, Mentor Zach Williams

Plasma, commonly referred to as the fourth state of matter, is a hot, electrically charged gas that is prone to various instabilities. These instabilities are responsible for coronal mass ejections, solar flares, as well as degrading confinement in fusion reactions. This work examines the nonlinear evolution of collisionless magnetic reconnection as brought about by the tearing instability. Simulations are performed using the Dedalus code to model magnetic reconnection through a linear eigenmode decomposition. Stable mode dynamics are observed to play a significant role in the nonlinear evolution of reconnection, with contributions from a linearly damped mode comparable to the dominant unstable mode at the same spatial scale. The participation and necessity of the stable mode in nonlinear reconnection activity are highlighted.