P. L. Pritchett

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.

Three‐dimensional stability of thin quasi‐neutral current sheets

In a thin current sheet (ρi0/L ≲ 1, where ρi0 is the ion gyroradius in the lobe field and L is the current sheet half thickness) of the generalized Harris type, the relative ion-electron cross-field drift is comparable to the ion thermal velocity. The three-dimensional stability properties of such a thin current sheet are investigated by means of nonlocal two-fluid theory and two-dimensional and three-dimensional full particle simulations. As was suggested originally by Zhu et al. [1992], the drift kink mode is found to be of critical importance. For the simple case of no initial Bz field, the fluid theory demonstrates that the drift kink mode is a non-MHD mode with a polarization structure such that E1y is an antisymmetric function of z while E1z is a symmetric function with E1z(0) ≠ 0. Two-dimensional (y,z) particle simulations indicate that the nonlinear behavior of this mode is dominated by long-wavelength modes with kyL ∼ 1 and frequency ωr ∼ Ωi0, where Ωi0 is the ion gyrofrequency in the lobe field. Three-dimensional particle simulations performed on a massively parallel computer show that while the growth rates for the drift kink mode are reduced by the finite Bz, they can still be appreciable (γ/Ωi0 ≲ 0.05–0.10). The kyL ∼ 1 drift kink modes are always the first to grow in the simulations; subsequently, tearing-like modes with a dominant kx wave vector also become unstable. Implications of these results for the triggering of substorms are discussed.

Collisionless reconnection in two‐dimensional magnetotail equilibria

A two-dimensional (x, z) particle simulation model based on the Darwin approximation to Maxwells equations is developed for studying collisionless reconnection in the magnetotail. The particles and fields are initialized in accord with a general equilibrium configuration which includes a pressure gradient along the tail axis and tail flaring. The model is used to investigate a number of theoretical issues regarding the spontaneous ion tearing instability under the assumption that the electron dynamics are unimportant. It is demonstrated both numerically and analytically that in a thin current sheet with ρ i0 ∼ λ (ρ i0 is the ion Larmor radius based on the lobe field and λ is the characteristic thickness of the current sheet) the growth rates in the absence of a normal field component are much smaller than expected based upon the analytic theory for a thick sheet (ρi0 ≪ λ). For such a thin current sheet the presence of a normal field Bz on axis of even a few percent strongly inhibits the growth of the instability. This result is not altered by the addition of a constant By component smaller than the lobe field. It is demonstrated further that the transition to stability occurs when the cyclotron frequency based on Bz equals the growth rate of the Bz = 0 tearing mode. This requires typically a normal field of the order of 6% of the lobe field. If a sufficiently large external perturbation of the lobe magnetic field reduces the normal field on axis below the stabilization threshold over a significant fraction of a tearing mode wavelength, then one can recover the rapid instability of the one-dimensional neutral sheet.

Coalescence of magnetic islands

A detailed numerical analysis has been conducted of the instability described by Finn and Kaw in which parallel currents in neighboring islands tend to coalesce into larger units. The existence of this coalescence instability in the ideal magnetohydrodynamic limit is confirmed, but no evidence is found for a threshold in island width. The linear growth rates are found to be rapid compared with those for purely resistive processes, and the linear mode structure has only a weak dependence on resistivity. In the nonlinear regime, saturation of the mode in the ideal case is observed due to flux piling up at the X point, while in the nonideal case the merging process is observed to proceed to completetion.

Relativistic electron production during guide field magnetic reconnection

[1] The production of relativistic electrons during guide field magnetic reconnection is investigated with two-dimensional particle-in-cell simulations. The acceleration mechanism is found to consist of two important elements. The parallel electric field that exists in the low-density cavities along two of the separatrices leads to the production of a cold electron beam. This beam is funneled into the near vicinity (of the order of a few ion inertia lengths) of the X line where the electrons are further accelerated by the parallel electric field to form the relativistic portion of the electron spectrum. This combined process is more efficient than for undriven magnetic reconnection without a guide field and produces a harder spectrum. Secondary islands which can appear as transient structures during the guide field reconnection process do not appear to play an important role in the production of the relativistic electrons.

Convection and the formation of thin current sheets in the near‐Earth plasma sheet

Particle simulations are used to investigate plasma sheet convection in a realistic near-Earth magnetic field model including dipolelike and taillike regions. Convection leads to the formation of a thin current region characterized by a strong electrostatic potential and a depressed equatorial magnetic field component in which the cross tail current is carried predominantly by the electrons as a result of their E x B and diamagnetic drifts. Implications for the thin current sheets observed in the near-Earth magnetotail during substorm growth phase are discussed. 18 refs., 4 figs.

Linear analysis of the double-tearing mode

The linear behavior of the double‐tearing mode is investigated within the framework of magnetohydrodynamics. A two‐space‐scale analysis in which resistive solutions valid near the rational surfaces are joined to ideal solutions outside these regions is performed and used to derive the dispersion relation for the mode. If the separation of the rational surfaces at x=±xs is sufficiently small [xs/a<(kya)−7/9S−1/9], the growth rate is predicted to scale as S−1/3, and the structure of the mode proves to be essentially identical with that of the m=1 tearing mode in cylindrical geometry. With increasing separation, the mode makes a transition to the S−3/5 scaling and structure of the standard tearing mode. These predictions are confirmed by direct numerical solution of the magnetohydrodynamic equations, and the S−1/3 scaling is shown to be correlated with violations of the constant‐ψ approximation. Possible physical implications of the double‐tearing mode are discussed.

Onset and saturation of guide-field magnetic reconnection

The onset and saturation of collisionless magnetic reconnection in the presence of a guide field are investigated using two-dimensional particle-in-cell simulations in which the reconnection evolves out of the initial thermal noise in the current sheet and in which the resolution is sufficient to resolve the electron singular layer. The simulations show that reconnection does not abate when the island width exceeds either the electron singular layer or the initial current sheet width. Instead, reconnection proceeds through an explosive stage which appears to be limited only by the spatial size of the system. The guide-field reconnection dynamics is dominated by the formation of an asymmetric configuration with a deep density cavity along one pair of separatrix arms. In this cavity an electron beam feature is formed which excites the Buneman instability. Near the X line the reconnection electric field is supported by a combination of quasiviscous and bulk inertia effects for the electrons. Around the islan...

Free energy sources and frequency bandwidth for the auroral kilometric radiation

Electron distributions obtained in the source regions of auroral kilometric radiation (AKR) by the Fast Auroral SnapshoT (FAST) satellite have revealed several free energy sources with positive gradients with respect to v⊥ superimposed on a broad plateau with a radius close to the primary incident electron acceleration energy and covering pitch angles from near field-aligned all the way to the (upgoing) loss cone. Two-dimensional electromagnetic particle simulations are used to demonstrate that such a distribution arises as a quasi-steady feature of a process in which the increase of the perpendicular velocity of the electrons as they propagate into a region of increasing magnetic field strength is balanced by the diffusion to lower v⊥ caused by the electron-cyclotron maser instability. The maser radiation is emitted nearly perpendicular to the ambient magnetic field at frequencies between the relativistic and nonrelativistic cyclotron frequencies. In these circumstances, the entire primary auroral electron distribution can contribute to the resonant wave-particle interaction, leading to electric field intensities of the order of 500 mV/m. In contrast, a pure loss cone distribution is shown to produce much weaker electric fields, leads to emission at angles ≥ 10° away from perpendicular, and cannot produce the broad plateau observed in the electron distribution. The simulations and linear theory indicate that the maser instability in a uniform system produces an intrinsic bandwidth of the order of a few tenths of 1% of the cyclotron frequency (∼0.5-1.0 kHz in the AKR source region). Any narrower spectra would appear to require some nonuniform or time-dependent feature in the source region.

Electron‐cyclotron maser instability in relativistic plasmas

The electron‐cyclotron maser instability is studied for the case of an anisotropic electron velocity distribution in the regime where the relativistic corrections to the wave dispersion are significant. Solution of the linear dispersion relation reveals that when the plasma frequency–gyrofrequency ratio ωpe/Ωe<vte/c, the instability is localized just below k⊥c/Ωe=1. The growth rate is then strongly peaked for emission at 90° to the magnetic field and is considerably larger than would be the case if the cold‐plasma dispersion theory were valid. These features are confirmed by electromagnetic particle simulations. The simulations also show that saturation results from perpendicular diffusion in velocity space and that the saturation level increases as ωpe/Ωe is decreased. A quasilinear analysis predicts that the saturation level scales as (Ωe/ωpe)2 ωmaxI, where ωmaxI is the maximum linear growth rate. Applications of the maser instability to the generation of the Earth’s auroral kilometric radiation are dis...