Magnetic Mirror Force Research Articles

A New Kinetic Model for Time‐Dependent Polar Plasma Outflow: Initial Results

We have developed a new time‐dependent kinetic plasma outflow model which uses a kinetic description of the parallel motions of the ion guiding centers, while assuming the electrons are a massless neutralizing fluid (i.e., Boltzmann distributed). The ions, O+ and H+, are followed as individual particles which respond to the gravitational, magnetic mirror and ambipolar electric forces as they move in one dimension along a magnetic flux tube. We show results for a case where the electron temperature in the flux tube is raised from a value near the ion temperature (3000° K) to a value of 10,000° K. The outflowing hydrogen is little affected by the change, but the barrier to the outflow of oxygen ions is greatly reduced with the result that an enhanced outflow of O+ ions travels up the flux tube. As the oxygen ions adjust to the higher electron temperature the flux of oxygen ions at the lower end of the flux tube increases very rapidly compared to the more gradual increase at the upper end. Also, an enhanced oxygen parallel temperature peak travels up the flux tube, increasing in magnitude as it goes. It travels at a speed significantly higher than the oxygen ion acoustic speed (found with Te = 10,000° K).

Kinetic modeling of the Saturn ring‐ionosphere plasma environment

A time independent kinetic plasma model has been developed for studying the plasma conditions on magnetic field lines linking the Saturnian ionosphere and rings. The model includes the gravitational, magnetic mirror, centripetal, and ambipolar electric forces. It includes the effect of the mixing of two plasma populations, a warm electron and water‐derived ion (O+, OH+, or H2O+) plasma coming from the rings, and a cool electron and hydrogen ion plasma coming from the ionosphere. Results of the model suggest that the dominant ion near the C ring will be H+ with densities ≥1.0 cm−3. For most of the B ring, the Cassini division, and the A ring the dominant ion will be the water‐derived ion, with densities as high as 50 cm−3, depending on the plasma flux from the rings. The flux of water‐derived ions from the rings to the ionosphere (at 2500 km) may be as high as 5×107 cm−2 s−1 for regions of the ionosphere magnetically connected to the outer B ring, independent of the peak ionosphere plasma density. The model results also suggest that the outflow of hydrogen from the ionosphere to the rings may be shut off for field lines passing through the outer B ring and A ring. This is due to the ambipolar electric field set up by the warm ring plasma trapped near the ring plane by the centripetal force.

Nonlinear Landau damping of weakly dispersive circularly polarized MHD waves

The combined effect of modulational instability and nonlinear Landau damping on a circularly polarized MHD wave is studied. When the wave gets modulated, the magnetic mirror force as well as the parallel electric field associated with the modulations, transfer energy to the charged particles with velocity near the Alfvén velocity, to cause a nonlinear Landau damping. Our mathematical model is a DNLS equation extended with a nonlocal term representing the resonant particles. This irreversible model allows a conservation law which in a slowly varying wave train limit corresponds to conservation of wave action. In addition to the modulational instability already known from the DNLS model, the Landau damping term introduces a modulational instability in the wave number range where the wave would otherwise be stable. We present numerical studies of the development of the instabilities and the subsequent wave damping in both ranges. One of our principal findings is that the wave frequency decreases in the same proportion as the energy density. This can be understood in terms of the conservation of action law.

Auroral arc formation: Kinetic and MHD effects

Recent observations by the Dynamics Explorer satellites indicate that auroral field lines are not equipotentials. The field-aligned “conductivity” is the same for up and downgoing currents and of the order of several 10−8 to several 10−9 Ω−1m−2. This is not in agreement with models based on the resistance provided by the magnetic mirror force alone. It is suggested that the resistivity is due to damping of kinetic shear-Alfven wave packets. This damping may be nonlinear in nature or Landau damping. We briefly review the properties of kinetic Alfven waves.

Trapping of ion conics by downward parallel electric fields

Several examples of upflowing field‐aligned electrons at altitudes between 1000 and 15000 km at high latitudes have been reported recently. The velocity‐space distributions of these electrons suggest that they were accelerated out of the ionosphere by downward parallel electric fields, and parallel potential drops of a few tens to a few hundred volts over the altitude range 1000–6000 km are implied. The electron beams are associated with ion conics. Data from electrostatic analyzers onboard the S3‐3 satellite show that ion conics can be trapped at low altitudes by the downward electric field. Evidence for the parallel electric field is obtained not only from observations of upflowing electron beams but also from observations of retardation of downflowing electrons and local acceleration of downflowing ions. The inferred parallel electric fields have magnitudes large enough to locally balance the magnetic mirror force on perpendicular ion conics in the few hundred electron volt energy range. This electrostatic trapping has important consequences for wave heating of ion conics since it extends the residence time of ions in the heating region. It is demonstrated that this multipass heating mechanism leads to perpendicular ion heating far in excess of that predicted by present theories of ion conic heating.

Energization of ions in the auroral plasma by broadband waves: Generation of ion conics

The ion conics provide an important mechanism for the transportation of ionospheric ions to the magnetosphere. The conics are generated by a transverse acceleration of the ions and by the subsequent upward repulsion by the magnetic mirror force. Here, the acceleration of ions by a broadband lower hybrid (LH) wave is considered. Since the broadband waves have a finite correlation time, the heating occurs even in the absence of a resonance between the ions and the waves. The LH waves excited by precipitating energetic electrons in the auroral ionosphere have characteristics such that ambient cold ions (<1 eV) cannot resonate with the waves. Thus the nonresonant heating mechanism discussed here may play a direct role in generating ion conics with energies of about a few hundred electron volts at altitudes below the auroral acceleration region where the lower hybrid waves have been observed. The nonresonant mechanism may also act to preheat the ions so that the resonant heating can follow. The extent of the energy gain of H+ ranges from a few electron volts to a few keV as the turbulence noise level varies from 10−9 to 10−6 V² m−2 s−1. The heavy ion gains comparably less energy. The calculations were done for turbulence regions that were both extended and limited in distance, the latter being particularly relevant to the generation of conics with very sharp pitch angle distributions.

Power spectral signatures of interplanetary corotating and transient flows

Recent studies of the time behavior of the galactic cosmic ray intensity have concluded that long term decreases in the intensity are generally associated with systems of interplanetary flows that contain flare‐generated shock waves, magnetic clouds, and other transient phenomena. In this paper the magnetic field power spectral signatures of such flow systems are compared to power spectra obtained during times when the solar wind is dominated by stable corotating streams that do not usually produce long‐lived reductions in the cosmic ray intensity. We find that the spectral signatures of these two types of regimes (transient and corotating) are distinct. However, the distinguishing features are not the same throughout the heliosphere. The transient flows at 1 AU tend to have smaller correlation lengths and larger magnetic helicity scale lengths than do the corotating flows. In data collected beyond 1 AU, the primary differences are in the power spectra of the magnitude of the magnetic field rather than in the power in the field components. Consequently, decreases in cosmic ray intensity are very likely due to magnetic mirror forces and gradient drifts rather than to pitch angle scattering.

The inner edge of Saturn's B ring

The sharp, 90‐km wide transition from an optical depth of 0.2 in the C ring to 1 in the B ring begins at 91,970 km from Saturn's center. This radius is found to be almost exactly at the inward stability limit of charged particles launched in the ring plane at the local Kepler velocity, provided these particles have large charge to mass ratio. The zonal harmonic models of Saturn's magnetic field from the Voyager data and the gravitational field model from Pioneer data are essential to get the very close agreement between theory and observation. The theoretical stability limits are 91,973±145 km from Voyager 1 magnetic field data and 91,991±145 km from Voyager 2 magnetic data. The zonal harmonic magnetic field lines are not perpendicular to the ring plane. Therefore, in addition to the magnetic mirror, gravitational, and centrigual forces, an unknown force must be postulated to produce equilibrium in the ring plane and make the stability calculation meaningful.

Ion distribution effects of turbulence on a kinetic auroral arc model

We extend an earlier plasma‐kinetic model of an inverted V auroral arc structure to include, in a phenomenological way, the effects of electrostatic turbulence with k∥/k⊥ ≪ 1. In the absence of turbulence, a parallel potential drop is supported by magnetic mirror forces and charge quasi‐neutrality, with energetic auroral ions penetrating to low altitudes; relative to the electrons, the ions' pitch angle distribution is skewed toward smaller pitch angles. The electrons energized by the potential drop form a current that excites electrostatic turbulence; we consider the specific case of the ion cyclotron mode. The turbulence heats the ions in T⊥ only, thus tending to reduce the differential pitch angle anisotropy between electrons and ions, which in turn reduces the potential drop—an effect of opposite sign to that associated with anomalous resistivity. In equilibrium the plasma is marginally stable, with growth rates and diffusion constants some 2 orders of magnitude below naive estimates. The conventional anomalous resistivity contribution to the potential drop is very small, because anomalous‐resistivity processes are far too dissipative to be powered by auroral particles; this is why growth rates and diffusion constants are so small. Under certain circumstances equilibrium may be impossible and relaxation oscillations set in; the time scale for such pulsating auroras is the ion transit time of 6–10 s.

Mechanism of parallel electric fields inferred from observations

An analysis of satellite data from regions of upward Birkeland (magnetic‐field‐aligned) current shows that the typical magnetic‐field‐aligned potential drop in the auroral zone is no larger than required to provide direct acceleration of magnetospheric electrons by the field‐aligned electric field against the upward magnetic mirror force to produce the observed upward Birkeland current. A model of simple electrostatic acceleration without anomalous resistivity predicts observable relations between parallel current and parallel potential drop and between energy deposition and parallel potential drop. The temperature, density, and species of the unaccelerated charge carriers are the relevant parameters of the model.Simultaneous measurements of electron precipitation and ion drift velocities on the satellites Atmosphere Explorer C and D were used to test these relations. In a steady state the divergence of ionospheric currents must be compensated by Birkeland currents. The model current‐voltage relation was applied to predict the densities of the primary charge carriers (i.e., plasma sheet electrons above the acceleration region for upward currents). In cases involving thin arc structures, where the reliable estimation of the divergence of ionospheric current is difficult and the steady‐state assumption may not apply, the precipitating energy flux versus voltage relation was used instead to predict the densities of the unaccelerated plasma sheet electrons. Within the experimental uncertainties, reasonable agreement is found between these predicted densities and those inferred directly from the simultaneous data of the Low‐Energy Electron Experiment. These results are interpreted as indicating that anomalous resistivity is not important in determining the magnitude of the field‐aligned potential drop in the auroral zone.

Latitudinal oscillations of plasma within the Io torus

We calculate the equilibrium latitude and the period of oscillations about this equilibrium latitude for plasma in a centrifugally dominated tilted dipole magnetic field representing Jupiter's inner magnetosphere. For a hot plasma the equilibrium latitude is the magnetic equator; for a cold plasma it is the centrifugal equator; for a warm plasma it is somewhere in between. In the small‐tilt‐angle approximation, the latitudinal oscillation period of a cold particle in the centrifugal potential field is P0=PJ/31/2, where PJ is the rotation period of Jupiter. For a warm plasma the magnetic mirror force causes the bounce period to be decreased slightly. These results are applicable to the plasma injected by Io to form the torus of plasma surrounding Jupiter. We adopt an illustrative model in which atoms are sputtered from the Jupiter‐facing hemisphere of Io and escape Io's gravity to be subsequently ionized some distance from Io. Ionization generally does not take place at the equilibrium latitude, and the resulting latitudinal oscillations provide an explanation for the irregularities in electron concentration within the torus, as reported by the radio astronomy experiment aboard Voyager 1.

Electrostatic model of a quiet auroral arc

Given auroral electron and ion distribution functions as observed with satellites in inverted V events, we construct a self‐consistent electrostatic field distribution (both parallel and perpendicular to the earth's magnetic field). This field distribution is determined by (1) magnetic mirror forces which cause charge separation for species with different pitch angle distributions; (2) Poisson's equation, which gives the electric field in terms of the charge separation; (3) the ionospheric physics of charge and current conservation, coupled with precipitation sources and recombination losses; and (4) particle distribution functions specified at the equator (and for thermal and backscattered plasma, at the ionosphere). We assume that equatorial particle distribution functions depend on L only through the dependence of the electrostatic potential on L; an assumed factorized form for the potential allows this L dependence to be simply parameterized. These ingredients combine to yield a self‐consistent latitudinal scale length of some tens of kilometers, typical for quiet arcs. A variety of particle and field data at and below S3‐3 altitude are fit semiquantitatively with the model. We do not consider in this paper physical processes which act in the equatorial magnetosphere, although they could well be connected to the processes we do consider through some sort of feedback.

Generation mechanisms for magnetic-field-aligned electric fields in the magnetosphere.

Magnetic-field-aligned electric fields in the magnetosphere can be generated in several different ways.Current driven wave instabilities can lead to either anomalous resistivity or electric double layers. Both can support potential drops of many kilovolts. In the former case this requires wave turbulence extended over large distances, because observed wave amplitudes allow only moderate field strength. In the latter case the voltage drop is concentrated to one or more (perhaps numerous) thin regions, sometimes referred to as electrostatic shocks, each of the order of several tens of Debye lengths thick. Once established, such layers may exist with or without substantial wave turbulence. It has also been proposed that wave-particle interaction may establish a collisionless version of the thermoelectric effect. In the hot magnetospheric plasma potential drops can be created as a consequence of the magnetic mirror force. In a magnetically trapped plasma this, in principle, requires no current, although some leakage current is expected. The mirror effect has its most dramatic impact in regions of upward Birkeland currents, where it limits the current density to moderate levels unless large voltages are applied (many times the voltage-equivalent of the thermal energy of the magnetospheric plasma). The distribution of this voltage depends critically on the distribution functions of the plasma particles involved, and it may well degenerate into electric double layers.Observational data now available indicate that more than one of the mechanisms mentioned are operative in the magnetosphere but it is not yet possible to evaluate their relative importance.