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The most unstable current-driven resistive modes of an axially bounded coronal loop are found in computer simulations to exhibit the spatial structure of ballooning modes. The observed modes are not confined to mode rational surfaces, but instead have broad radial extent. A theory assuming ballooning mode spatial structure predicts that a minimum current should be required for linear instability, and that, when the mode is unstable, the linear growth rate scales linearly with the resistivity below a critical resistivity, and scales as resistivity to the one-third for larger resistivities. Both predictions are borne out by simulations results. Both theory and simulation analyses of the mode suggest that the strong radial structure of the mode near the ends of the system is the primary contributing factor to the instability of the mode. A helical current sheet is formed in the nonlinear evolution of the mode near the edge of the current channel and is accompanied by a strong radial gradient in the current and partial current reversal.
Coronal magnetic fields are twisted up by motion of their footpoints in the photosphere. When the twist exceeds a critical amount, kink-ballooning instabilities occur. We study these instabilities numerically, in long, thin, axially bounded magnetic fields. Nonlinearly, the three-dimensional kinking motion compresses magnetic flux, forming a current sheet. Magnetic energy can be dissipated at a rate orders of magnitude greater than without the current sheets. The energy of footpoint motion can then go into coronal heating, via Ohmic dissipation in the current sheets.
A new simulation method is used to study the interaction of kinetic Alfvén waves and double layers in the auroral acceleration region. The simulation model is designed to clarify the confusion over the source of free energy, which was effectively imposed by boundary conditions in previous double layer simulations. The validity and characteristics of the model are discussed. Early results from the simulation show the presence of "current-driven" double layers. When an infinitely wide current channel is modeled, a parallel electric field is found to be generated to maintain a constant current through the double layers. For a finite width channel, the parallel current is observed to decay away due to an effective resistance presented by the double layers via a magnetic diffusion effect. This effective resistance is apparently reduced in the finite width channel case, possibly due to a charge-neutralizing effect of the ion polarization drift.
A time-continuous, constant-resistivity version of the fast dynamo model introduced by Bayly and Childress (1988) is studied numerically. The expected dynamo mechanism in this context is described and is shown to be operative in the simulations. Exponential growth of the fastest growing mode is observed, with the growth rate for the smallest resistivity attempted (1/Rm = 10-4) agreeing well with the Bayly-Childress model. It is argued, based on the long- and short-wavelength behaviour of the mode for different resistivities, that the growth rates obtained for the Rm=104 case should persist as Rm -> infinity.
Fast dynamo saturation is explored numerically using a simplified model. The magnetic field has many degrees of freedom and allows the generation of fine structure at large Rm. The velocity field is constrained, containing two Fourier modes and so eight degrees of freedom; the Lorentz force is projected onto these modes. Numerical simulations at varying Rm are discussed.
A plasma simulation has been developed to model interactions between inertial Alfvén waves and double layers and to investigate their relative contributions to auroral particle acceleration. We use a novel one-dimensional particle-in-cell code, with periodic boundary conditions, to model the nonlinear excitation of current-driven weak double layers via the free energy supplied by an inertial Alfvén wave. Analysis of the simulation output shows that double layers are not the agent primarily responsible for electron acceleration. Rather, the inertial Alfvén wave accelerates groups of electrons into a steepening beam as it encounters them. As the beam electrons reenter the main distribution, decelerated by anomalous resistive effects, they are replaced by electrons farther downstream. Hence, the particles do not free-stream over the length of the channel. Furthermore, this wave action persists even when the system is linearly stable to ion-acoustic modes, precluding the possibility that this behavior is brought about by the formation of ion-acoustic double layers.
Numerical simulations of the Farley-Buneman instability in 2-1/2 dimensions using particle ions and fluid electrons show the growth, saturation and nonlinear behavior of two-stream waves. This hybrid technique models the saturated state of the instability for a much longer period of time than the pure particle codes that preceded it. While focusing principally on modeling the topside E region equatorial electrojet, many of these results apply to the auroral two-stream instability as well. The following features are seen in all our hybrid simulations: (1) wave growth at an angle offset from the electron drift direction where the angle depends on the strength of the driving electric field, (2) nonlinear coupling to waves traveling perpendicular to the propagation direction of the principal two-stream waves, (3) a saturated wave phase velocity at or above the sound speed but well below the velocity predicted by linear theory and (4) phase velocities which remain almost constant as a simulated radar sweeps from a horizontal direction to nearly vertical. The nonlinear electron motion dominates the behavior of these waves. Further, these simulations indicate that ion kinetic effects are not essential for the saturation of the instability and that electron temperature effects have a minor impact on the final saturated state.
Pickup ions in a ring velocity distribution are unstable to several kinetic plasma instabilities. At the large heliocentric distances where the overall plasma beta (ratio of kinetic to magnetic energy) is dominated by the energy density of interstellar pickup ions and pickup is perpendicular to the interplanetary magnetic field, the dominant of these is the Alfvén ion cyclotron instability (AIC). We demonstrate by hybrid particle simulation that, for conditions where the solar wind beta is low, AIC driven by the pickup ions couples to the solar wind. The result is perpendicular heating, leading to an anisotropic solar wind distribution. This process may contribute to enhanced solar wind temperatures at large heliocentric distances and may allow for indirect measurement of interstellar pickup ions.
This paper proposes a possible means for ion acceleration in the topside auroral ionosphere. Specifically, it postulates that the interaction of lower hybrid waves with a small-amplitude (1 - 2 %) density cavity leads to an energy transfer to shorter-wavelength modes. Such a mechanism may help explain the transverse acceleration of positive ions observed in this region. Both analytic and computer simulation results on the growth of these slow phase velocity waves will be presented. The resulting acceleration of test particle ions is consistent with the theory of quasi-linear diffusion of the test particle distribution function. The results of the test particle simulations indicate that this effect may be strong enough to account for the observed ion acceleration. This model is consistent with the results from the Marie and TOPAZ II and III sounding rockets which indicate a strong correlation between transverse ion acceleration, depletions in the background density, and lower hybrid waves.
The Farley-Buneman instability is a collisional two-stream instability observed in the E-region ionosphere at altitudes in the range 90-120km. While linear theory predicts the dominant wavelengths, it cannot fully describe the behavior of this nonlinearly saturated instability as observed by radar and rocket measurements. This paper explores the nonlinear behavior of this phenomenon and the resulting waves through simulations and theory. Our 2D simulations model wave behavior in the plane perpendicular to the Earth's magnetic field, applying a fluid model to describe the electron dynamics and either a particle or a fluid model to describe ion behavior. The results show the growth, saturation and nonlinear behavior of the instability for a much longer period of time than was possible with the pure particle codes used in previous studies. These simulations show: (1) growth of Farley-Buneman waves, (2) the development of secondary waves which propagate along the extrema and perpendicular to the Farley-Buneman waves, (3) turning of the primary waves away from the electron drift direction, (4) a saturated wave phase velocity below the one predicted by linear theory but above the acoustic speed and (5) nonlinear electron drifting dominates the behavior of the saturated waves. This paper describes the both the simulation techniques and fundamental results. Additionally, this paper outlines a theory explaining the dominant nonlinear process seen in this instability.
The Farley-Buneman instability is a collisional two-stream instability observed in the E-region ionosphere at altitudes in the range of 95-110km. While linear theory predicts the dominant wavelengths, it cannot fully describe the behavior of this nonlinearly saturated instability as observed by radar and rocket measurements. We simulate the behavior of this instability in the plane perpendicular to the Earth's magnetic field using a 2D hybrid code which models electron dynamics as a fluid and ion dynamics with a particle-in-cell approach. The results show the growth, saturation and nonlinear behavior of the instability for a much longer period of time than was possible with the pure particle codes used in previous studies. This paper describes the spectra from these simulations and compares them to the observed spectra. Both the simulations and observations show that (1) type I spectra result from saturated two-stream waves for a broad range of zenith angles, (2) the phase-velocity of these waves is below that predicted by linear theory, (3) mode coupling leads to type II-like spectra without the presence of a plasma density gradient as often thought necessary, (4) an east-west asymmetry exists in the spectral power, (5) longer wavelengths develop due to mode coupling and (6) spectral power decreases at a rate of 0.3dB/degree of elevation angle.
Studies with a reduced-mode two-fluid model have revealed a promising candidate for the saturation mechanism of the Farley-Buneman instability in the daytime equatorial electrojet. The mechanism operates by redistributing the zero-order electron ExB flow field. Secondary waves generated nonlinearly by the instability are responsible for the flow field modification. Saturation occurs because the modified flow reduces the principal charge transport responsible for the growth of the primary wave. Two-dimensional particle simulations of the instability exhibit saturation via the same mechanism.
N. F. Otani and M. Oppenheim, Saturation of the Farley-Buneman intability via three-mode coupling, Journal of Geophysical Research 111(A3), A03302 (2006).
Characteristics of type-1 radar echoes obtained from the E region ionosphere have yet to be conclusively explained. The dynamical properties of the saturated state of the Farley-Buneman instability are widely thought responsible for these type-1 echoes. In this paper we present a different perspective and new details on a previously proposed three-wave coupling mechanism (Otani and Oppenheim, 1998) for the saturation of the Farley-Buneman instability. A novel method is presented for the analysis of general, three-wave systems with stationary, sinusoidal solutions. Computer simulations of the three-wave system produce steady states in close agreement with those obtained from the method. Despite the fact that the system only contains three modes, a number of features also agree well with observation, including density fluctuation magnitudes (|dn|/n0 = 5%), propagation speeds (clustered around the sound speed), and power falloff as a function of elevation angle. We demonstrate how the spatial distributions of the phases of the electron advection term and electron E x B velocity for the secondary modes lead to the partial cancellation of the destabilizing zero-order electron drift, thereby saturating the Farley-Buneman instability. The mechanism is consistent with the one previously advanced, which described saturation of the instability in terms of the diversion of electron flow around density peaks.
Basic plasma and fusion plasma abstracts.
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