C. E. Rasmussen

A two-dimensional model of the plasmasphere : refilling time constants

Abstract A two-dimensional model of the plasmasphere has been developed to study the temporal evolution of plasma density in the equatorial plane of the magnetosphere. This model includes the supply and loss of hydrogen ions due to ionosphere-magneto-sphere coupling as well as the effects of E × B convection. A parametric model describing the required coupling fluxes has been developed which utilizes empirical models of the neutral atmosphere, the ionosphere and the saturated plasmasphere. The plasmaspheric model has been used to examine the time it takes for the plasmasphere to refill after it has been depleted by a magnetic storm. The time it takes for the plasmasphere to reach 90% of its equilibrium level ranges from 3 days at L = 3 during solar minimum to as high as 100 days at L = 5 during solar maximum. Refilling is also dependent on the month of the year, with refilling requiring a longer period of time at solar maximum during June than during December for L > 3.2.

Decay of equatorial ring current ions and associated aeronomical consequences

The decay of the major ion species which constitute the ring current is studied by solving the time evolution of their distribution functions during the recovery phase of a moderate geomagnetic storm. In this work, only equatorially mirroring particles are considered. Particles are assumed to move subject to E×B and gradient drifts. They also experience losses along their drift paths. Two loss mechanisms are considered: charge exchange with neutral hydrogen atoms and Coulomb collisions with thermal plasma in the plasmasphere. Thermal plasma densities are calculated with a plasmaspheric model employing a time-dependent convection electric field model. The drift-loss model successfully reproduces a number of important and observable features in the distribution function. Charge exchange is found to be the major loss mechanism for the ring current ions; however the important effects of Coulomb collisions on both the ring current and thermal populations are also presented. The model predicts the formation of a low-energy (< 500 eV) ion population as a result of energy degradation caused by Coulomb collisions of the ring current ions with the plasmaspheric electrons; this population may be one source of the low-energy ions observed during active and quiet periods in the inner magnetosphere. The energy transferred to plasmaspheric electrons through Coulomb collisions with ring current ions is believed to be the energy source for the electron temperature enhancement and the associated 6300 A (stable auroral red [SAR] arc) emission in the subauroral region. The calculated energy-deposition rate is sufficient to produce a subauroral electron temperature enhancement and SAR arc emissions that are consistent with observations of these quantities during moderate magnetic activity levels.

Equatorial density depletions observed at 840 km during the great magnetic storm of March 1989

Early on March 14, 1989, a thermal plasma probe on the Defense Meteorological Satellite Program (DMSP) F9 spacecraft detected extensive and dramatic decreases in the ion density at 840 km, near 2130 LT, during two consecutive transequatorial passes over South America. The order of magnitude decreases in the ion density extended more than 4000 km along the satellite track. The depletions were accompanied by upward and westward plasma drifts, both in excess of 100 m/s. Their onsets and terminations were marked by extremely sharp density gradients. DMSP F9 observed no similar depletions over the Atlantic during preceding orbits. A partial depletion was detected over the eastern Pacific during the following orbit. The DMSP F9 ground track passed slightly west of a Brazilian total electron content (TEC) station and two Brazilian ionosondes during the first depletion encounter. The TEC fell far below normal during the night of March 13–14. The ionosonde measurements indicate that, in the hour after sunset, before DMSP passed through the depletions, the F2 layer rose rapidly and disappeared, but at the time of the first depletion encounter, hmF2 was decreasing over one of the stations. The DMSP F8 satellite, which orbits in the dawn-dusk meridian, made related measurements on March 13 and 14. Crossing the equator at dust on March 13, at the same longitude where DMSP F9 encountered the first depletion, DMSP F8 detected upward and westward drifts, but it measured extremely large rather then depleted ion densities. During two dawn passes over the eastern Pacific on March 14, DMSP F8 observed depletions somewhat similar to those detected by DMSP F9. Large westward drifts accompanied the depletions detected by DMSP F8. It is quite probable that the morningside depletions detected on March 14 are remnants of those detected earlier by DMSP F9 in the evening sector. We develop a phenomenological model reconciling DMSP F8, F9, and ground-based measurements. Our calculations show that rapid upward drifts sustained for several hours can produce depletions in the equatorial ion density with sharp gradients at their high-latitude boundaries, consistent with the data. We discuss possible contributing mechanisms for generating these upward drifts. These include direct penetration of the magnetospheric electric field to low latitudes, the electric fields generated by the disturbance dynamo, and the effects of conductivity gradients near the dusk terminator and the South Atlantic anomaly.

A bounce-averaged kinetic model of the ring current ion population

A bounce-averaged ring current kinetic model for arbitrary pitch angle, including losses due to charge exchange and Coulomb collisions along ion drift paths, is developed and solved numerically. Results from simplified model runs, intended to illustrate the effects of adiabatic drifts and collisional losses on the proton population, are presented. The processes of i) particle acceleration under the conditions of time-independent magnetospheric electric fields; ii) a predominant loss of particles with small pitch angles due to charge exchange; and iii) a buildup of a low-energy population caused by the Coulomb drag energy degradation, are discussed. The terrestrial ring current is associated with the motion of energetic charged particles, governed not only by the magnetospheric convection and corotation electric fields, but also by the gradient and curvature of the geomagnetic field. The trajectories of these particles have been studied during different magnetospheric conditions using adiabatic drift theory (e.g. Ejiri, 1978; Takahashi and Iyemori, 1989). Such investigations are very useful in order to explain not only the process of formation of the storm-time ring current, but also some features in the measured energy spectra of the ring current ion species like dips in different local time sectors (Mcllwain, 1972) and nose events (Ejiri et al., 1980). The local time variations of the ring current particle distributions caused by changes in the magnetospheric electric fields have also been modeled. Thus, tracing equatorially mirroring protons, Chen et al. (1994) found that convective transport has a predominant role for the storm-time enhancements in the phase space densities for energies between 30 - 160 keV at L=2.5 - 5. Kistler et al. ( 1989) and Fok et al. (1993) investigated the decay of the ring current in simple models of magnetic storms, considering drift paths of equatorially mirroring ions and different loss mechanisms along them. In this way, the former found that charge exchange is the most important loss process for the ring current population, while the latter demonstrated that Coulomb collisions between ring current ions and thermal plasma in the plasmasphere have also non negligible effects. In the present study we take these investigations further by considering nonequatorially mirroring particles. We solve the bounce-averaged kinetic equation for arbitrary pitch angle, including losses due to charge exchange and Coulomb drag. We

Interaction of ring current and radiation belt protons with ducted plasmaspheric hiss: 1. Diffusion coefficients and timescales

Protons that are converted into the inner magnetosphere in response to enhanced magnetic activity can resonate with ducted plasmaspheric hiss in the outer plasmasphere via an anomalous Doppler-shifted cyclotron resonance. Plasmaspheric hiss is a right-hand-polarized electromagnetic emission that is observed to fill the plasmasphere on a routine basis. When plasmaspheric hiss is confined within field-aligned ducts or guided along density gradients, wave normal angles remain largely below 45°. This allows resonant interactions with ions at typical ring current and radiation belt energies to take place. Such field-aligned ducts have been observed both within the plasmasphere (Kozyra et al., 1987a; Koons, 1989) and in regions outside of the plasmasphere (Chan and Holzer, 1976). Wave intensities are estimated using statistical information from studies of detached plasma regions (Chan et al., 1974). Diffusion coefficients are presented for a range of L shells and proton energies for a fixed wave distribution. Harmonic resonances in the range n = ±100 are considered in order to include interactions between hiss at 100 Hz to 2 kHz frequencies, and protons in the energy range between ∼10 keV and 1000 keV. Diffusion timescales are estimated to be of the order or tens of days and comparable to or shorter than lifetimes for Coulomb decay and charge exchange losses over most of the energy and spatial ranges of interest.

Transport of gyration-dominated space plasmas of thermal origin: 1. Generalized transport equations

Grads 20-moment set of transport equations has been examined in the limit of strong external magnetic fields. In this approximation, transport perpendicular to field lines is assumed to follow E×B convection paths, and the original 20-moment set of equations reduces to a set of six partial differential equations. This simplified set of equations describes the transport of mass and parallel momentum as well as the transport of parallel and perpendicular energy and heat flow in the magnetic field direction. However, since convection perpendicular to field lines is consistently carried throughout the derivation of the reduced 20-moment set, the transport of mass, momentum, energy, and heat flow perpendicular to the magnetic field is also explicitly maintained in this formulation. The effect of collisions was calculated assuming a modified relaxation model. Wave speeds and normal modes of the simplified set of equations were examined for an ion and electron gas. It was found that four of the 10 normal modes are electron thermal-heat waves which approximately decouple from the six ion waves in the system. When low-frequency waves are considered (slow-wave approximation), this allows the electron energy and heat flow equations to be solved separately from the ion equations and in a time-independent fashion. When this was done, it was found that under certain conditions these equations predict an infinite electron perpendicular temperature, Te⊥, in the collisionless regime. This occurs whenever Te⊥ is greater than the parallel temperature, Te∥ at any point along collisionless and diverging magnetic field lines. This nonphysical result calls into question the validity of generalized transport equations in the collisionless regime whenever Te⊥ is greater than Te∥. However, when applied appropriately, the significantly simplified set of equations derived here are well suited for application to a large variety of problems in planetary ionospheres and magnetospheres. We have also demonstrated that the heat flow must be limited to values smaller than the pressure times the thermal speed or otherwise the fundamental assumptions of the 20-moment truncation are violated. The double adiabatic approximation for hypersonic situations in the presence of heat flow was also examined.

Plasma transport in the equatorial ionosphere during the Great Magnetic Storm of March 1989

We have modeled plasma transport in the low-latitude and equatorial ionosphere during the great magnetic storm of March 1989. Our goal was to provide a consistent explanation for the DMSP (Defense Meteorological Satellite Program) observations of dramatic decreases in ion density and rapid ion drifts in the low latitude ionosphere over South America during the storm. The modeling effort supports the hypothesis that abnormally large upward drifts lifted F region plasma above the satellites altitude and created the density depletions observed by DMSP. Modeled O+ densities at the satellites altitude have a strong qualitative resemblance to DMSP observations. Both the model and the observations indicate a deep density trough with extremely sharp boundaries surrounding the equator. The widths of both the modeled and the observed equatorial troughs increase with time. Vertical ion drifts predicted by the model also have been compared with DMSP measurements. Like the observed vertical drifts, the modeled drifts reversed sign near the trough boundaries. The modeled vertical drifts are of the same order and direction as the vertical component of E × B convection near the equator, but of opposite direction (downward) near the trough boundaries and outside of the trough.

Kinetic simulation of plasma flows in the inner magnetosphere

A one-dimensional hybrid particle code is used to study the interactions between upflowing thermal ions from conjugate ionospheres. The simulation model allows for multiple species, convection of plasmaspheric flux tubes, and Coulomb self-collisions which conserve momentum and energy locally. The model incorporates a variable-flux boundary condition where the flux, at the boundaries, approaches zero as the plasmasphere fills and equilibrium conditions are reached. The effects of two important processes on plasmaspheric refilling have been considered. The first includes convection of the plasmaspheric flux tube. The second is the interaction of ionospheric thermal plasma and particle injection from an external source. Particle injection seems to play an important role in the evolution of the total particle distribution on the early timescales (t 8 days) the thermal plasma from the ionosphere dominates the particle distribution.

Anisotropic ion heating and parallel O+ acceleration in regions of rapid E × B convection

Since the discovery of O[sup +] ions in the magnetosphere a great deal of interest has been placed on understanding the ionospheric souces of these ions. The classical polar wind is not likely to be a major contributor of O[sup +] ions to the magnetosphere, because the thermal energy of these ions is insufficient for a significant fraction of them to escape the gravitational attraction of Earth. A numerical solution to the 20-moment set of transport equations has been found in order to study subauroral ionospheric outflows during periods of enhanced perpendicular ion drifts. The numerical model solves the time-dependent O[sup +] density, momentum, and both the parallel and perpendicular energy and heat flow equations in the 200-6,000 km altitude range. Assuming perpendicular drifts of 3 km/s relative to the neutral atmosphere, the authors have found that anisotropic heating of O[sup +] (a result of ion-neutral collisions) leads to a temperature anisotropy, with perpendicular temperatures exceeding 8,000 K and parallel temperatures greater than 5,000 K (near 200 km altitude). Above approximately 2,000 km, transport processes dominate the effects of collisions and wavelike oscillations in O[sup +] velocity, temperature and heat flux were noted.

Interaction of ring current and radiation belt protons with ducted plasmaspheric hiss: 2. Time evolution of the distribution function

The evolution of the bounce-averaged ring current/radiation belt proton distribution is simulated during resonant interactions with ducted plasmaspheric hiss. The plasmaspheric hiss is assumed to be generated by ring current electrons and to be damped by the energetic protons. Thus energy is transferred between energetic electrons and protons using the plasmaspheric hiss as a mediary. The problem is not solved self-consistently. During the simulation period, interactions with ring current electrons (not represented in the model) are assumed to maintain the wave amplitudes in the presence of damping by the energetic protons, allowing the wave spectrum to be held fixed. Diffusion coefficients in pitch angle, cross pitch angle/energy, and energy were previously calculated by Kozyra et al. (1994) and are adopted for the present study. The simulation treats the energy range, E ≥ 80 keV, within which the wave diffusion operates on a shorter timescale than other proton loss processes (i.e., Coulomb drag and charge exchange). These other loss processes are not included in the simulation. An interesting result of the simulation is that energy diffusion maximizes at moderate pitch angles near the edge of the atmospheric loss cone. Over the simulation period, diffusion in energy creates an order of magnitude enhancement in the bounce-averaged proton distribution function at moderate pitch angles. The loss cone is nearly empty because scattering of particles at small pitch angles is weak. The bounce-averaged flux distribution, mapped to ionospheric heights, results in elevated locally mirroring proton fluxes. OGO 5 observed order of magnitude enhancements in locally mirroring energetic protons at altitudes between 350 and 1300 km and invariant latitudes between 50° and 60° (Lundblad and Soraas, 1978). The proton distributions were highly anisotropic in pitch angle with nearly empty loss cones. The similarity between the observed distributions and those resulting from this simulation raises the possibility that interactions with plasmaspheric hiss play a role in forming and maintaining the characteristic zones of anisotropic proton precipitation in the subauroral ionosphere. Further assessment of the importance of this process depends on knowledge of the distribution in space and time of ducted plasmaspheric hiss in the inner magnetosphere.