T. W. Speiser

A particle model for magnetotail neutral sheet equilibria

Previous studies of forced current sheet equilibria, that is, x-independent current sheets with a constant Bz = Bn and a constant, uniform electric field Ey (Eastwood, 1972, 1974; Hill, 1975; Francfort and Pellat, 1976; Lyons and Speiser, 1985) are numerically and analytically extended to the regime υD/υT ≲ 1 and Bn/( 4πnbυT²) ≲ 1, where υD = cEy/Bn, υT the proton thermal velocity, and nb is the value of the number density outside the current sheet (at the simulation boundary). Such equilibria may be applicable to the thin current sheets observed in the current disruption region of the magnetotail during substorm growth phase and to the magnetotail neutral sheet. It is found that the current and thickness of the forced current sheet are controlled by the motions of the individual protons. For κA ≪ 1 and υD/υT ≳ 1, we numerically verify the scaling for the current sheet half thickness, a ∼ (υD/υT)−4/3 λb (Francfort and Pellat, 1976), where λb = (mic²/4πnbe²)1/2 and κA is the value of κ = (Rmin/ρmax)1/2 in the self-consistent current sheet for protons of average energy (Rmin is the minimum field line radius of curvature and ρmax is the maximum gyroradius). The magnetic field outside the current sheet Bx0 is given by eBx0/mic = υD/λb (Hill, 1975). It is further found that if the degree of pitch angle scattering is treated as a variable parameter, there is a peak value of the current corresponding to zero isotropization of the distribution as it passes through the field reversal. The maximum reduction in the net current (or equivalently, the reduction in Bx0) due either to nonlinear particle dynamics (chaos) or to pitch angle scattering wave-particle interactions is by a factor of .This maximum reduction in the current can be achieved by particle nonlinear dynamics for values of κA near 1 in the regime υD/υT ≳ 1. Rather than an anomalous resistivity, the most important effect arising from the particle nonlinear dynamics is a catastrophic loss of equilibrium near κA = 1. This feature is due to the inability of proton trajectories with κ ≳ 1 to balance the gradient of the magnetic pressure and to set a length scale in the z direction. The signatures of this process, expressed in terms of the current sheet distribution function, the external distribution function, and the magnetic field structure, are charted. These signatures could be used to determine, through satellite observation, if the abrupt loss of equilibrium observed in our model can result in a disruption in the cross-tail current.

Ion tearing in a magnetotail configuration with an embedded thin current sheet

The ion tearing instability is investigated in a magnetotail configuration that consists of a diffuse plasma sheet current and an embedded, thin current sheet with a strong current. For historical reasons, the thin embedded current sheet will be called a {open_quotes}neutral sheet{close_quotes}, even though the normal component of the magnetic field, B{sub n}, is nonzero. In particular, the authors assume that the current within the thin current sheet is due to the acceleration of {open_quotes}Speiserlike{close_quotes} ion trajectories by a cross-tail electric field E{sub y}. It is found that the strong current within the neutral sheet is essentially unimportant to the growth rate of the tearing instability, and that the growth rate scales as ({lambda}{sub 0}/L{sub z}){sup 2}, where L{sub z} is the overall half thickness of the plasma sheet, {lambda}{sub 0} is the ion inertial length, c/{omega}{sub pi}, and {omega}{sub pi} is the ion plasma frequency at the neutral sheet edge. In the absence of the current outside the neutral sheet, current filamentation is stable. 37 refs., 3 figs.

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.

Particle chaos and pitch angle scattering

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.

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.

Observational support for the current sheet catastrophe model of substorm current disruption

It has recently been found that a one-dimensional current sheet equilibrium with a non-zero confection electric field, Ey, and a non-zero normal magnetic field component, Bn, can reach a point of catastrophe through either the reduction of the drift velocity, υD = cEy/Bn or the increase of Bn. This point of catastrophe coincides with a value of κA ≃ 0.7, where κA is the self-consistent value of κ = (Rmin/ρA max)½ corresponding to ions of average energy. (Here Rmin is the minimum field-line radius of curvature and ρA max is the maximum gyroradius for ions of average energy.) The point of catastrophe was found to be preceded by a twisting of the current sheet field-lines into the dawnward direction, i.e. by the development of a y-component of B, with odd symmetry in z, and a sign opposite Bx, where positive x is earthward, positive y is in the dawn-to-dusk direction and positive z is northward. Since the loss of the current sheet would cause the local configuration to become more dipolar, it was suggested that the catastrophic loss of the local current sheet equilibrium could correspond to local current disruption and dipolarization. In this paper, observations of some of the signatures predicted by theory are presented.

An estimation of the electric field in the magnetotail current sheet using the observed energetic ion bulk flow

It is important to know the electric field in the tail current sheet in order to understand how particles behave and how much energy is being dissipated. The electric field is also a measurement of the reconnection rate during substorms. For the CDAW-6 substorm period of March 22, 1979, we used the ion data from the medium energy particles experiment (MEPE) on the ISEE-1 satellite, and studied nine measurements of the 3D distribution function centered on the center of the current sheet. The measured distribution function was then integrated to obtain the average of bulk flow velocity in the geocentric solar ecliptic (GSE) frame. This bulk flow velocity was then broken up into its components perpendicular and parallel to the magnetic field for the nine cases. It was further assumed that the perpendicular component was due, in part, to an energy dependent drift and to an energy independent electric field drift. Using the bulk flow velocities from any two energy channels we can separate out the electric and energy dependent drifts and thus obtain electric field and energy dependent components. The two lowest energy channels (34.3 keV and 54.9 keV) give the main results, and the 80.4 keV and 118.8 keV channels are used as a cross check. We find that Ex fluctuates approximately ±5 mV/m, and Ey ± 10 mV/m, in reasonable agreement with measurements by the electric field instrument [Pedersen et al., 1985], with most of the fluctuation presumably due to the motion of the current sheet. Using current sheet oscillation theory and the central current sheet data points, we can estimate Ey in the frame of the current sheet and find a positive average Ey with a magnitude of ≈ 0.1 mV/m, which is also consistent with that expected for reconnection in this substorm time period. The Ez component has a remarkable linear correlation with Bx, with a correlation coefficient of 0.91. Assuming Bx varies linearly with z, a positive ion density of 3.14×10−20/d(Re) Coulombs/m³ is implied. Such a positive space charge near the current sheet center is expected theoretically.

Comment on ‘‘Physics of the magnetotail current sheet’’ [Phys. Fluids B 5, 2663 (1993)]

The discussion on the current sheet catastrophe2 is carried further in this comment. In particular, the choice of boundary conditions where the incoming portion of the distribution function is a drifting Maxwellian is discussed. (AIP)