Effects of collisions on the nonlinear particle dynamics in the magnetotail

Abstract

The effects of collisional processes on the nonlinear particle dynamics in the magnetotail are considered. A simple collision operator is developed to model the effects of pitch‐angle and energy scattering. It is found that the phase space partition persists for up to moderate scattering amplitudes in pitch‐angle and energy, and that certain distribution function features are robust even in the presence of large amplitude collisions. It is shown that if the collisions are due to short scale length electrostatic fields, excessively large field amplitudes are required to significantly alter the phase space structures and the resulting distribution function features.

Self‐consistent current sheet structures in the quiet‐time magnetotail

“…(5) The inclusion of small to moderate noise levels has little effect on the equilibrium profiles. This is consistent with Holland and Chen [ 1991 ] who demonstrated that small to moderate amplitude collisions do not significantly modify the phase space partitions and thus the relative populations of transient and stochastic orbits in a given input distribution.…”

“…This is particularly important in the regime of vo << Vth where glitches in the magnetic field are amplified in subsequent iterations by ion dinmagnetism. We also include small-amplitude low-frequency pitch-angle scattering using a collision operator [Holland and Chen, 1991 ], which allows orbits to populate the integrable regions of phase space. A practical benefit is that inclusion of scattering increases the rate of convergence to self-consistent equilibria.…”

The effects of low frequency waves on ion trajectories in the Earth's magnetotail

“…As discussed above, the previous study [Holland and Chen, 1991] which modeled the effects of waves on the structure of the ion trajectories in the Earth's magnetotail, concluded that waves with reasonable amplitudes do not strongly modify the observed non-adiabatic features. Since our studies indicate that realistic waves can dramatically change the individual ion trajectories, we will briefly discuss the differences Although we have only described changes in individual trajectories, a more formal argument which indicates that changes in the phase space structures should be expected when waves are added to the system is the following: The system studied by Chen and Palmadesso [1986] and Holland and Chen [1991] has two degrees of freedom and the Hamiltonian is constant.…”

“…As discussed above, the previous study [Holland and Chen, 1991] which modeled the effects of waves on the structure of the ion trajectories in the Earth's magnetotail, concluded that waves with reasonable amplitudes do not strongly modify the observed non-adiabatic features. Since our studies indicate that realistic waves can dramatically change the individual ion trajectories, we will briefly discuss the differences Kamey [1978] found that, for a wave field with a given k (perpendicular to the background magnetic field B0), gyrofrequency, fl, and amplitude, E, significant heating and stochastic behavior occurred when ot=(kE)/(•o• 1.…”

“…OneHolland and Chen [1991] examined the effects of waves on particle wave: (c) x-z plane; (d) x-y plane.trajectories in a modified Harris magnetic field by including fields which include a broad speclxum of waves based on the characteristics of the waves observed on ISEE-1 and Geotail. initial pitch angle of 10 ø.…”