Escape time distributions of charged particles from uniformly magnetized Newtonian centers

Abstract

We statistically characterize the escaping trajectories of charged particles orbiting a uniformly magnetized Newtonian center. Specifically, we calculate the probability distribution a trajectory escapes for a given amount of time. It is done for a set of trajectories with varying initial conditions along the equatorial plane. We found three defining characteristics for a set of initial conditions with the same constants of motion. First, are the high proportion of trajectories that escape without returning to the system's equatorial plane. Second, are the conditional time gap in the distribution, in which there are a relatively few escaping trajectories in those times. Third, for higher escape times, the distribution decreases in a power-law manner. The gap is shown to be between the escaping trajectories that escape without returning to the equatorial plane, and the trajectories which passes through the plane once trajectories. The existence of the gap is shown to be related to the time it takes for the pass-1 trajectories to return to the equatorial plane. Lastly, the power-law exponents for the long term escape time distributions are computed for a set of constants of motion, and is shown to be dependent upon the size of the escape channel.