R. F. Martin

On the nonadiabatic precipitation of ions from the near‐Earth plasma sheet

We examine the precipitation of ions which result from nonadiabatic pitch angle scattering in the near-Earth magnetotail. We focus on dynamical situations between the adiabatic limit where the particle magnetic moment is conserved and the current sheet limit where particles experience meandering motion about the midplane. Defining the κ parameter as the square root of the minimum curvature-radius-to-maximum Larmor radius ratio, the situations we consider correspond to κ between 1 and 3. We demonstrate that throughout this range of κ values, magnetic moment variations are systematically organized into three categories: (1) at small (a few degrees) equatorial pitch angles, large magnetic moment enhancements regardless of gyration phase; (2) at large equatorial pitch angles (typically, above 30°), negligible magnetic moment changes; and (3) in between, a prominent dependence upon gyration phase with either magnetic moment enhancement or damping. We show that these three distinct regimes can be understood in terms of relative magnitude of the centrifugal force experienced by the particles with regard to that of the Lorentz force. In agreement with previous studies, we show that detrapping of plasma sheet ions due to nonadiabatic pitch angle scattering is effective throughout the 1- to 3-κ range. However, the degree of loss cone filling critically depends upon the angular characteristics of the incident population. It is significantly greater for initially isotropic populations than for initially field-aligned ones, because only particles away from the magnetic field direction experience strong damping of magnetic moment.

A simple model of magnetic moment scattering in a field reversal

We examine the nonadiabatic motion of charged particles in a field reversal using a simple centrifugal impulse model. It is shown that, though this model cannot account for long term behaviors, it accurately describes the abrupt magnetic moment change experienced by the particles between two consecutive adiabatic (magnetic moment conserving) sequences. Good agreement is obtained between analytical estimates and trajectory computations. Our analysis also suggests a new pitch angle dependent parameter to characterize the jumps in magnetic moment. Application to particle motion in a cusped field geometry demonstrates that magnetic moment damping and subsequent particle escape can be adequately modeled by means of such centrifugal impulses.

Application of the centrifugal impulse model to particle motion in the near-Earth magnetotail

Particles traveling in the geomagnetic tail do not conserve their magnetic moment (first adiabatic invariant) due to significant field variations on the length scale of their Larmor radius. We examine the possibility of describing these magnetic moment changes by the action of an impulsive centrifugal force on the timescale of the particle cyclotron turn. Trajectory calculations demonstrate that such a centrifugal impulse model adequately describes the nonadiabatic particle behavior for situations where the κ parameter (defined as the square root of the minimum curvature radius-to-maximum Larmor radius ratio) is of the order of 1 to 2. In particular, it is shown that this behavior can be organized by another parameter (referred to as κα), which is proportional to κ but depends upon the particle pitch angle, namely, one obtains: systematic magnetic moment enhancements for κα ≪ 1, large gyrophase effects with possibly prominent damping of the magnetic moment for κα ∼ 1, and nearly constant magnetic moment for κα ≫ 1. More generally, we show that the centrifugal impulse approximation applies to an intermediate orbit regime at the transition between the fully adiabatic (magnetic moment conserving) regime and that regime where particles experience meandering motions about the field minimum. It applies to ion transport in the near-Earth magnetotail where the magnetic field lines evolve from dipolar to taillike configurations and where the κ parameter nears unity. In this region of space the model predictions are in agreement with numerical results, revealing both enhanced trapping (due to magnetic moment enhancement) and possible precipitation (due to magnetic moment damping) of plasma sheet ions depending upon their pitch and phase angles.

Energetic ions as remote probes of X type neutral lines in the geomagnetic tail

Martin and Speiser (1988) have predicted ridges in the velocity space distribution function as a signature of the interaction of energetic ions with an X type neutral line in the geomagnetic tail. In this paper we study the properties of these ridges as the observation point is moved relative to the X line, as phase angle is varied, and the effect of the ridges on initial distributions with a loss cone. With the ridges, one can remotely sense not only the presence of an X line, but also, potentially, the distance from the X line, whether the observer is earthward or tailward of the X line, and the vertical position within the current sheet. For example, we find that for single particle dynamics in a current sheet with neutral line, the phase space ridge is predicted to be found throughout the current sheet if it is not destroyed by collective behavior. The ridge is predicted to be found for distributions plotted in ν⊥, ν∥ space and also in νx, νy, νz space. Additionally, valleys are found in νx, νy, νz space, which are also signatures of a neutral line, and which depend on the initial flowing distribution. An initially tailward flowing distribution causes asymmetries in distributions earthward versus tailward of the neutral line. These asymmetries are due to the fact that part of the distribution below (at smaller pitch angles than) the ridge comes from initially earthward (tailward) particles when the modeling point is earthward (tailward) of the neutral line. The accelerated beam is not predicted inside the current sheet at x = L (one separatrix distance earthward of the neutral line), but close to the sheet center a perpendicular bulk flow is predicted. Spatially, the ridge is found to move to larger pitch angles as the observation point approaches the neutral line in the plasma sheet boundary layer. As the observation point moves toward the current sheet center, the ridge stays at about the same pitch angle, but then tends to be diminished very near the center where a perpendicular bulk flow is found. Chaotic pitch angle scattering can fill even a relatively large (10°), initially empty loss cone. This loss cone filling is more complete when orbits are calculated in a thicker current sheet. Thus chaotic pitch angle scattering may be a dominant mechanism to produce nightside proton isotropy in the auroral zones, as suggested by Sergeev et al. (1983).

Neutral line chaos and phase space structure

Phase space structure and chaos near a neutral line are studied with numerical surface-of-section (SOS) techniques and analytic methods. Results are presented for a linear neutral line model with zero crosstail electric field. It was found that particle motion can be divided into three regimes dependening on the value of the conserved canonical momentum, Py, and the conserved Hamiltonian, h. The phase space structure, using Poincare SOS plots, is highly sensitive to bn = Bn/B0 variations, but not to h variations. It is verified that the slow motion preserves the action, Jz, as evaluated by Sonnerup (1971), when the period of the fast motion is smaller than the time scale of the slow motion. Results show that the phase space structure and particle chaos depend sensitively upon Py and bn, but are independent of h.

Pitch angle scattering near energy resonances in the geomagnetic tail

In sharp field reversals where the particle Larmor radius is larger than the magnetic field line curvature radius, particles may not conserve their magnetic moment (first adiabatic invariant). We examine the pitch angle scattering which affects the particles under such conditions. We show that this scattering alternatively leads to a clear three-branch pattern of magnetic moment variations or to unstructured variations. The three-branch pattern is characterized by systematic enhancements of magnetic moment at relatively small (up to ∼30°) pitch angles, negligible change at large pitch angles and, in between, either enhancement or damping depending on phase. We show that this three-branch pattern emerges near the energy resonances reported by Burkhart and Chen [1991], where particles escape after transient oscillations inside the reversal. Away from resonance, the three-branch pattern gradually expands and affects an increasing volume of the velocity space. Such a structuring of pitch angle scattering is similar to that obtained in weak field reversals (i.e., for Larmor radii comparable to the field line curvature radius), even though the particle orbits in sharp and weak reversals are significantly different. This fact allows us to extend the centrifugal impulse model developed for weak reversals to sharp ones. In this model, nonadiabatic behavior is viewed as the result of perturbation of the particle gyromotion by an impulsive centrifugal force. We demonstrate that this model reproduces essential features of the particle dynamics in sharp reversals and, in particular, the energy resonance phenomenon. We show that in a like manner to weak reversals, three-branch dynamics in sharp reversals has significant implications for particle injection into the loss cone and gyrophase bunching near the magnetotail midplane.

Centrifugally driven phase bunching and related current sheet structure in the near‐Earth magnetotail

We examine the role of centrifugal effects during nonadiabatic interactions of charged particles with the magnetotail current sheet. It is shown that when the parameter κ (defined as the square root of the minimum curvature radius- to- maximum Larmor radius) is of the order of unity, as is the case for ions traveling in the near-Earth plasma sheet, enhanced centrifugal effects lead to prominent bunching of the particles in gyration phase. As a result of this bunching effect we demonstrate that a thin current sheet develops in the vicinity of the tail midplane. When average values of the plasma density (a few tenths of ions per cubic centimeter) and temperature (several keV) in the near-Earth tail are used, the current sheet obtained has a characteristic thickness of the order of a few tenths of an Earth radius and leads to significant stretching of the local magnetic field lines. A further consequence of phase bunching is the buildup of a substantial current in the Earth-tail direction at low latitudes, which leads to field line inclination in the dawn-dusk direction. This phase bunching mechanism, which maximizes when the bulk of the ion distribution nears κ = 1, is of potential importance for the dynamics of the inner plasma sheet during the growth phase of substorms.

Gyrophase effects in the centrifugal impulse model of particle motion in the magnetotail

We investigate the dynamics of charged particles in a magnetic field reversal in the particular case where the Larmor radius is comparable to the magnetic field line curvature radius. In the current interpretation framework based upon the parameter κ (defined as the square root of the minimum curvature radius-to-maximum Larmor radius ratio), this situation corresponds to κ of the order of 1. We show that this nonadiabatic regime, which lies at the transition between adiabatic motion (κ ≫ 1) and the nonadiabatic one characterized by oscillations about the field minimum (κ < 1), results from prominent centrifugal effects in the field reversal. To model these effects, we develop a simple analytical description which is based upon an impulsive centrifugal force perturbing the particle gyromotion on the time scale of the cyclotron turn. Comparisons with numerical calculations of ion trajectories demonstrate that this centrifugal impulse model adequately describes both the magnetic moment variations and the gyrophase variations experienced by the particles. As for the magnetic moment, three distinct behaviors (negligible change, strong phase dependence with possible damping, and systematic enhancement) are identified depending upon pitch angle. As for the gyration phase, important bunching effects are obtained which are interpreted as being due to the action of the impulsive centrifugal force. These phase bunching effects are enhanced as the κ parameter approaches unity. In the limit κ ∼ 1, a strong imbalance is obtained between the two phase sectors corresponding to duskward and dawnward motions. This imbalance, which extends over a few tenths of an Earth radius in the Z direction, leads to the formation of a thin current sheet in the vicinity of the magnetotail midplane.

Bursty bulk flows, the geomagnetic tail current sheet, and substorm timing

Individual flow bursts in a bursty bulk flow event observed by the AMPTE/IRM satellite at R = (−12, −3, 1) Re, have been modelled by following large numbers of single particle orbits in a model of the geomagnetic tail current sheet containing both Bz and By components and a near-Earth neutral line. A flow burst modelled in the central plasma sheet, just after a substorm onset, implied there was a near-Earth neutral line 1 to 112 Re tailward of the satellite. An earlier flow burst at the plasma sheet edge, 1–2 minutes before the substorm onset, implied that at this earlier time the neutral line was already formed and closer to the satellite. To match the centroid of the observations, it was necessary that the source population was strongly earthward and duskward flowing, probably originating from the distant current sheet, and that there must have been a relatively large |By| component. With such a By component, it is interesting that a secondary feature of the observed distribution can also be explained qualitatively. During the time that we see the need for a strong earthward flow from a distant source, ground measurements indicate a significant increase in magnetospheric convection. A model with weak but non-reversing Bz reproduces some of the observed distribution function features, but not all of them, as well as the neutral line model.

The energetic ion signature of an O-type neutral line in the geomagnetic tail

An energetic ion signature is presented which has the potential for remote sensing of an O-type neutral line embedded in a current sheet. A source plasma with a tailward flowing Kappa distribution yields a strongly non-Kappa distribution after interacting with the neutral line: sharp jumps, or ridges, occur in the velocity space distribution function f(nu-perpendicular, nu-parallel) associated with both increases and decreases in f. The jumps occur when orbits are reversed in the x-direction: a reversal causing initially earthward particles (low probability in the source distribution) to be observed results in a decrease in f, while a reversal causing initially tailward particles to be observed produces an increase in f. The reversals, and hence the jumps, occur at approximately constant values of perpendicular velocity in both the positive nu parallel and negative nu parallel half planes. The results were obtained using single particle simulations in a fixed magnetic field model.