Dynamics of Ultrarelativistic Charged Particles With Strong Radiation Reaction

Abstract

High-energy emission from pulsars suggests the presence of charged particles travelling atnearly the speed of light. Starting from the 1980s, it has been suggested that ultra-relativistic charged particles with strong radiation reaction tend to follow certain directions fixed by the local electromagnetic field. These special directions are called “principal null directions” (PNDs) in the relativity literature. Since it is the velocity, rather than the acceleration, that is determined by the fields, this behavior was later referred to as “Aristotelian” dynamics. In this work, we studied this phenomenon in detail and presented the first rigorous derivation of this behavior from the fundamental dynamical equations—the Landau-Lifshitz equations. We derived specific conditions on the fields required for charged particles to enter into an Aristotelian equilibrium, in which the energy of the particle remains constant and it follows the PND to leading order. We showed that the sub-leading behavior is a small drift velocity, also determined by the local fields, that takes particles from one PND to another. Furthermore, we studied the timescales and properties of particles entering into equilibrium. It was shown that the equilibrium is linearly stable, and oscillations can occur around the equilibrium. Lastly, we presented the first comprehensive numerical simulations of the Landau-Lifshitz equations for particles in this Aristotelian regime. We demonstrated agreement between our numerical results and our analytical predictions. This thesis provides a solid foundation for using the Aristotelian approximation to study ultrarelativistic charged particles in pulsar magnetospheres.