Richard E. Denton

Geospace Environmental Modeling (GEM) Magnetic Reconnection Challenge

The Geospace Environmental Modeling (GEM) Reconnection Challenge project is presented and the important results, which are presented in a series of companion papers, are summarized. Magnetic reconnection is studied in a simple Harris sheet configuration with a specified set of initial conditions, including a finite amplitude, magnetic island perturbation to trigger the dynamics. The evolution of the system is explored with a broad variety of codes, ranging from fully electromagnetic particle in cell (PIC) codes to conventional resistive magnetohydrodynamic (MHD) codes, and the results are compared. The goal is to identify the essential physics which is required to model collisionless magnetic reconnection. All models that include the Hall effect in the generalized Ohms law produce essentially indistinguishable rates of reconnection, corresponding to nearly Alfvenic inflow velocities. Thus the rate of reconnection is insensitive to the specific mechanism which breaks the frozen-in condition, whether resistivity, electron inertia, or electron thermal motion. The reconnection rate in the conventional resistive MHD model, in contrast, is dramatically smaller unless a large localized or current dependent resistivity is used. The Hall term brings the dynamics of whistler waves into the system. The quadratic dispersion property of whistlers (higher phase speed at smaller spatial scales) is the key to understanding these results. The implications of these results for trying to model the global dynamics of the magnetosphere are discussed.

Alfvénic collisionless magnetic reconnection and the Hall term

The Geospace Environment Modeling (GEM) Challenge Harris current sheet problem is simulated in 2 1/2 dimensions using full particle, hybrid, and Hall MHD simulations. The same gross reconnection rate is found in all of the simulations independent of the type of code used, as long as the Hall term is included. In addition, the reconnection rate is independent of the mechanism which breaks the frozen-in flux condition, whether it is electron inertia or grid scale diffusion. The insensitivity to the mechanism which breaks the frozen-in condition is a consequence of whistler waves, which control the plasma dynamics at the small scales where the ions become unmagnetized. The dispersive character of whistlers, in which the phase velocity increases with decreasing scale size, allows the flux of electrons flowing away from the dissipation region to remain finite even as the strength of the dissipation approaches zero. As a consequence, the throttling of the reconnection process as a result of the small scale size of the dissipation region, which occurs in the magnetohydrodynamic model, iio longer takes place. The important consequence is that the minimum physical model necessary to produce physically correct reconnection rates is a Hall MHD description which includes the Hall term in Ohms law. A density depletion layer, which lies just downstream from the magnetic separatrix, is identified and linked to the strong in-plane Hall currents which characterize kinetic models of magnetic reconnection.

Structure of the dissipation region during collisionless magnetic reconnection

Collisionless magnetic reconnection is studied using a 2 1/2-dimensional hybrid code including Hall dynamics and electron inertia. The simulations reveal that the dissipation region develops a two-scale structure: an inner electron region and an outer ion region. Close to the X line is a region with a scale of c/ωpe, the electron collisionless skin depth, where the electron flows completely dominate those of the ions and the frozen-in magnetic flux constraint is broken. Outside of this region and encompassing the rest of the dissipation region, which scales like c/ωpi, the ion inertial length, is the Hall region where the electrons are frozen-in to the magnetic field but the ions are not, allowing the two species to flow at different velocities. The decoupling of electron and ion motion in the dissipation region has important implications for the rate of magnetic reconnection in collisionless plasma: the ions are not constrained to flow through the very narrow region where the frozen-in constraint is broken so that ion flux into the dissipation region is large. For the simulations which have been completed to date, the resulting rate of reconnection is a substantial fraction of the Alfven velocity and is controlled by the ions, not the electrons. The dynamics of the ions is found to be inherently nonfluid-like, with multiple ion beams present both at the X line and at the downstream boundary between the inflow and outflow plasma. The reconnection rate is only slightly affected by the temperature of the inflowing ions and in particular the structure of the dissipation region is controlled by the ion inertial length c/ωpi and not the ion Larmor radius based on the incoming ion temperature.

Magnetic spectral signatures in the Earth's magnetosheath and plasma depletion layer

Correlations between plasma properties and magnetic fluctuations in the subsolar magnetosheath downstream of a quasi-perpendicular shock have been found and indicate that mirror and ion cyclotronlike fluctuations correlate with the magnetosheath proper and plasma depletion layer, respectively (Anderson and Fuselier, 1993). We explore the entire range of magnetic spectral signatures observed from the AMPTE/CCE spacecraft in the magnetosheath downstream of a quasi-perpendicular shock. The magnetic spectral signatures typically progress from predominantly compressional fluctuations, δB∥/δB⊥ ≈ 3, with F/Fp <0.2 ( F and Fp are the wave frequency and proton gyrofrequency, respectively) to predominantly transverse fluctuations, δB∥/δB⊥ ≈ 0.3, extending up to Fp. The compressional fluctuations are characterized by anticorrelation between the field magnitude and electron density, ne, and by a small compressibility, Ce ≡ (δne/ne)2(B/δB∥)2 ≈ 0.13, indicative of mirror waves. The spectral characteristics of the transverse fluctuations are in agreement with predictions of linear Vlasov theory for the H+ and He2+ cyclotron modes. The power spectra and local plasma parameters are found to vary in concert: mirror waves occur for β∥p (β∥p ≡ 2µ0npkT∥p/B2) ≈ 2, Ap ≡ T⊥p/T⊥ - 1 ≈ 0.4, whereas cyclotron waves occur for β∥p ≈ 0.2 and Ap ≈ 2. The transition from mirror to cyclotron modes is predicted by linear theory. The spectral characteristics overlap for intermediate plasma parameters. The plasma observations are described by Ap = 0.85β∥p−0.48 with a log regression coefficient of −0.74. This inverse Ap - β∥p correlation corresponds closely to the isocontours of maximum ion anisotropy instability growth, γm/Ω = 0.01, for the mirror and cyclotron modes. The agreement of observed properties and predictions of local theory suggests that the spectral signatures reflect the local plasma environment and that the anisotropy instabilities regulate Ap. We suggest that the spectral characteristics may provide a useful basis for ordering observations in the magnetosheath and that the Ap - β ∥p inverse correlation may be used as a beta-dependent upper limit on the proton anisotropy to represent kinetic effects.

Transition to whistler mediated magnetic reconnection

The transition in the magnetic reconnection rate from the resistive magnetohydrodynamic (MHD) regime where the Alfven wave controls reconnection to a regime in which the ions become unmagnetized and the whistler wave mediates reconnection is explored with 2-D hybrid simulations. In the whistler regime the electrons carry the currents while the ions provide a neutralizing background. A simple physical picture is presented illustrating the role of the whistler in driving reconnection and the rate of whistler mediated reconnection is calculated analytically. The development of an out-of-plane component of the magnetic field is an observable signature of whistler driven reconnection.

The scaling of collisionless, magnetic reconnection for large systems

Hybrid simulations with electron inertia, along with analytic scaling arguments, are presented which demon- strate that magnetic reconnection remains Alfv6nic in a col- lisionless system even as the macroscopic scale length of the system becomes very large. This fast reconnection is facil- itated by the whistler physics present near the x-line. The reconnection rate is found to be a universal constant corre- sponding to an inflow velocity towards the x-line of around 0.1 CA.

Observational test of local proton cyclotron instability in the Earth's magnetosphere

We present a study of the proton cyclotron instability in the Earths outer magnetosphere, L > 7, using Active Magnetosphere Particle Tracer Explorers/Charge Composition Explorer (AMPTE/CCE) magnetic field, ion, and plasma wave data. The analysis addresses the energy of protons that generate the waves, the ability of linear theory to predict both instability and stability, comparison of the predicted wave properties with the observed wave polarization and frequency, and the temperature anisotropy/parallel beta relation. The data were obtained during 24 intervals of electromagnetic ion cyclotron (EMIC) wave activity (active) and 24 intervals from orbits without EMIC waves (quiet). This is the same set of events used by Anderson and Fuselier [1994]. The active events are drawn from noon and dawn local times for which the wave properties are significantly different. For instability analysis, magnetospheric hot proton distributions required the use of multiple populations to analytically represent the data. Cyclotron waves are expected to limit the proton temperature anisotropy, Ap = T⊥p/T‖p − 1, according to Ap < aβ‖pc with a ∼ 1 and c ∼ 0.5, where T⊥p, T‖p, and β‖p are the perpendicular and parallel proton temperatures and the proton parallel beta, respectively. During cyclotron wave events, Ap should be close to aβ‖pc whereas in the absence of waves Ap should be below aβ‖pc. The active dawn cases yielded instability in 9 of 12 cases using the measured plasma data with an average growth rate γ/Ωp = 0.025 and followed the relation Ap = 0.85β‖p−0.52. The active noon events gave instability in 10 of 12 cases, but only when an additional ∼2 cm−3 cold plasma was assumed. The noon wave events fell well below the dawn events in Ap-β‖p space, slightly above the Ap = 0.2β‖p−0.5 curve. The lower Ap limit for the noon cases is attributed to the presence of unmeasured cold plasma. The quiet events were all stable even for additional assumed cold ion densities of up to 10 cm−3, the upper limit implied by the plasma wave data. The quiet events gave Ap < 0.2β‖p−0.5. At noon, the unstable component has T⊥p ∼ 20 keV and Ap ∼0.8. At dawn the unstable component has T⊥p ∼ 4 keV and Ap ∼ 2.3. Observed wave frequencies agree with the frequencies of positive growth, and the difference in frequency between noon and dawn is attributable to the combined effects of the different hot proton T⊥p and Ap and the inferred higher cold plasma density at noon. The dawn events had significant growth for highly oblique waves, suggesting that the linear polarization of the dawn waves may be due to domination of the wave spectrum by waves generated with oblique wave vectors.

The proton cyclotron instability and the anisotropy/β inverse correlation

Spacecraft observations in the strongly compressed subsolar magnetosheath show an inverse correlation between the proton temperature anisotropy (T{sub {perpendicular}p}/T{sub {parallel}p} > 1 where {perpendicular} and {parallel} denote directions perpendicular and parallel to the background magnetic field) and the parallel proton {beta}({beta}{sub {parallel}p}). This manuscript uses one-dimensional hybrid simulations of the proton cyclotron anisotropy instability in homogeneous electron-proton plasmas to study this correlation which may represent a limited closure relation for fluid theories of anisotropic space plasmas. The emphasis is on driven simulations which increase the temperature anisotropy by periodically reducing the magnetic-field-aligned velocities of the protons. The late-time states from ensembles of both initial value and driven simulations yield very similar expressions for the proton anisotropy/{beta}{sub {parallel}p} inverse correlation, and provide a basis for explaining differences between sheath observations from different spacecraft. The driven simulations also yield expressions for the maximum instability growth rate and the fluctuating field energy as functions of {beta}{sub {parallel}p} and a parameter characterizing the anisotropy driver. 50 refs., 5 figs.

Bounded anisotropy fluid model for ion temperatures

A bounded anisotropy fluid model is developed which describes the temperature evolution of a collisionless plasma including the effect of pitch angle scattering due to ion cyclotron waves. The model equations accurately describe the proton temperature evolution in the plasma depletion layer, a magnetosheath regime of decreasing plasma density near the magnetopause. As in double adiabatic theory, changes in T⊥ are driven by changes in flux tube area A (∝ 1/B), while changes in T∥ are driven by changes in field line scale length L. In the bounded anisotropy model, if the proton temperature ratio T⊥/T∥ rises above the value 1 + 0.85 β∥p−0.48 (Anderson et al., 1994), where β∥p is the proton parallel beta, energy is transferred from the perpendicular to parallel temperature until this equation is satisfied. This energy exchange represents the effect of ion cyclotron wave pitch angle scattering, which keeps the plasma state near to marginal stability. Equations of the same form, employing bounded anisotropy expressions appropriate to different species, are also applied to He2+ and to electrons. These equations well describe the evolution of the He2+ but do not describe the evolution of the electron temperature, apparently due to the high electron thermal conduction which the model does not include. These results indicate that an energy exchange term may be incorporated into anisotropic fluid equations to simulate the effect of ion cyclotron wave pitch angle scattering in global fluid equations.

Inverse correlations between the ion temperature anisotropy and plasma beta in the Earth's quasi‐parallel magnetosheath

Average proton parameters in the magnetosheath downstream from the quasi-perpendicular shock (the quasi-perpendicular magnetosheath) for high solar wind dynamic pressure conditions are observed to vary continuously from high-beta, low-temperature anisotropy to low-beta, high-temperature anisotropy. Observations and theory have shown that this inverse correlation is a direct consequence of pitch angle scattering by electromagnetic ion cyclotron (EMIC) waves, which regulate the anisotropy, restoring the plasma toward marginal stability. Although the previously documented spectral characteristics of EMIC waves are not evident downstream of the quasi-parallel bow shock, the inverse anisotropy-beta relation found in the quasi-perpendicular magnetosheath also holds in the quasi-parallel magnetosheath. This indicates that the EMIC instability regulates the ion anisotropy regardless of the shock geometry.