Charged particle escapes from uniformly magnetized Newtonian centers

Abstract

We analyze the motion of a charged particle orbiting a Newtonian point mass permeated by a uniform magnetic field. Specifically, we focus on studying the escapes from the system, which may be relevant to understanding astrophysical jets. We find the typical definition of escape to no longer apply in our system, and we motivate and adopt a new definition based on the limiting case of cyclotronic motion in a uniform magnetic field. With this definition of escape, we calculate the escape times of charged particles that are vertical kicked from the equator, and map out how these escape times depend on the conserved energy and angular momentum on a particular slice of phase space.