Particle chaos and pitch angle scattering

Abstract

One of the most important quantities that can be obtained through test particle calculations is the pitch angle scattering of particles by interaction with current sheet magnetic fields. Pitch angle scattering is a factor that helps determine the dawn‐to‐dusk current, controls particle energization, and it has also been used as a remote probe of the current sheet structure. Previous studies have interpreted their results under the expectation that randomization will be greatest when the ratio of the two timescales of motion (gyration parallel to and perpendicular to the current sheet) is closest to one. In a simple parabolic current sheet, the ratio of timescales is proportional to κ, where κ = (Rc/ρz)1/2, Rc is the field line radius of curvature at the current sheet midplane and ρz is the gyroradius at the current sheet midplane. Recently, the average exponential divergence rate (AEDR) has been calculated for particle motion in a hyperbolic current sheet (Chen, 1992). It is claimed that this AEDR measures the degree of chaos and therefore may be thought to measure the randomization. In contrast to previous expectations, the AEDR is not maximized when κ ∼ 1 but instead increases with decreasing κ. Also contrary to previous expectations, the AEDR is dependent upon the parameter bz. In response to the challenge to previous expectations that has been raised by this calculation of the AEDR, we have investigated the dependence of a measure of particle pitch angle scattering on both the parameters κ and bz. We find that, as was previously expected, particle pitch angle scattering is maximized near κ = 1 provided that κ/bz > 1. In the opposite regime, κ/bz < 1, we find that particle pitch angle scattering is still largest when the two timescales are equal, but the ratio of the timescales is proportional to bz. In this second regime, particle pitch angle scattering is not due to randomization, but is instead due to a systematic pitch angle change. This result shows that particle pitch angle scattering need not be due to randomization and indicates how a measure of pitch angle scattering can exhibit a different behavior than a measure of chaos.