HAMILTONIAN-FORMULATION OF LOW-FREQUENCY, NONLINEAR PLASMA DYNAMICS

In this paper we present a set of equations that governs the linear and nonlinear evolution of plasma phenomena with frequencies below the ion cyclotron and the magneto-sonic and above the ion-acoustic frequencies. Finite electron mass and ion gyroradius effects are taken into account. The spatial scales of the phenomena may range from MI-ID scales down to the inertia electron skin depth. In a high-temperature plasma, this skin depth is smaller than the gyro-radius of a thermal ion. This set describes Alfven and drift vortices, magnetic islands and current sheets. These equations can be cast in (noncanonical) Hamiltonian form. It is shown that infinite sets of conserved quantities (Casimirs) exist that reduce to the Casimirs of 2-D reduced MHD in the appropriate limit. Sufficient conditions for stability are discussed on the basis of the second variation, at constant Casimirs, of the Hamiltonian functional

GENERALIZED 2-FLUID THEORY OF NONLINEAR MAGNETIC-STRUCTURES

A system of equations is introduced and discussed that describe the nonlinear dynamics of magnetic perturbations in a magnetized, high-temperature plasma. Diamagnetism, ion gyroradii effects, and finite electron mass are taken into account. These equations govern Alfven as well as electrostatic waves and vortices and describe the nonlinear evolution of reconnecting modes. Electrons are treated in a fluid model. The equation for the ion response is new and is a nonlinear generalization to all orders in the thermal ion gyroradius of the nonlinear fluid model. This system of equations conserves two fluxes that are different from, but related to, the magnetic flux. Two-dimensional equilibrium solutions in the form of stationary propagating magnetic structures are obtained with the methods introduced in the theory of vector nonlinearities in electrostatic drift vortices. In the noncollisional regimes of interest the inertia of the electrons resolves the singularity in the current density that tends to develop at magnetic separatrices. The positions of the X points of the conserved fluxes are mirror symmetric and at a distance of the order of the electron skin depth from the resonant surface. The set of equations admits an energy integral and can be cast in noncanonical Hamiltonian form. The role of the Casimir invariants, that are functions of the conserved fluxes, is investigated and the connection with ''reduced magnetohydrodynamics'' is emphasized

Generalized two-fluid theory of nonlinear magnetic structures

A system of equations is introduced and discussed that describe the nonlinear dynamics of magnetic perturbations in a magnetized, high-temperature plasma. Diamagnetism, ion gyroradii effects, and finite electron mass are taken into account. These equations govern Alfvén as well as electrostatic waves and vortices and describe the nonlinear evolution of reconnecting modes. Electrons are treated in a fluid model. The equation for the ion response is new and is a nonlinear generalization to all orders in the thermal ion gyroradius of the nonlinear fluid model. This system of equations conserves two fluxes that are different from, but related to, the magnetic flux. Two-dimensional equilibrium solutions in the form of stationary propagating magnetic structures are obtained with the methods introduced in the theory of vector nonlinearities in electrostatic drift vortices. In the noncollisional regimes of interest the inertia of the electrons resolves the singularity in the current density that tends to develop at magnetic separatrices. The positions of the X points of the conserved fluxes are mirror symmetric and at a distance of the order of the electron skin depth from the resonant surface. The set of equations admits an energy integral and can be cast in noncanonical Hamiltonian form. The role of the Casimir invariants, that are functions of the conserved fluxes, is investigated and the connection with ‘‘reduced magnetohydrodynamics’’ is emphasized

Hamiltonian vortices and reconnection in a magnetized plasma

Hamiltonian vortices and reconnection in magnetized plasmas are investigated analytically and numerically using a two-fluid model. The equations are written in the Lagrangian form of three fields that are advected with different velocities. This system can be considered as a generalization and extension of the two-dimensional Euler equation for an ordinary fluid. It is pointed out that these equations allow solutions in. the form of singular current-vortex filaments, drift-Alfven vortices and magnetic islands, and admit collisionless magnetic reconnection where magnetic flux is converted into electron momentum and ion vorticity

Electron inertia and small-scale magnetic structures in a nonuniform collisionless plasma

In collisionless plasmas, electron inertia has a strong influence on the formation of magnetic islands, through magnetic field line reconnection, and on the dynamics of coherent nonlinear structures such as magnetic vortices. We present a physical model for the nonlinear dynamics of such magnetic structures in configurations with a strong magnetic field. This model includes diamagnetic velocities and ion gyro-radius and electron inertia effects and yields the so-called Reduced MagnetoHydroDynamic (RMHD) equations in the appropriate limit. (C) 1997 COSPAR. Published by Elsevier Science Ltd

Structural control and system-level behavior of the seismic cycle at the Nankai Trough

The Nankai Trough in Southwest Japan exhibits a wide spectrum of fault slip, with long-term and short-term slow-slip events, slow and fast earthquakes, all associated with different segments down the plate interface. Frictional and viscous properties vary depending on rock type, temperature, and pressure. However, what controls the down-dip segmentation of the Nankai subduction zone megathrust and how the different domains of the subduction zone interact during the seismic cycle remains unclear. Here, we model a representative cross-section of the Nankai subduction zone offshore Shikoku Island where the frictional behavior is dictated by the structure and composition of the overriding plate. The intersections of the megathrust with the accretionary prism, arc crust, metamorphic belt, and upper mantle down to the asthenosphere constitute important domain boundaries that shape the characteristics of the seismic cycle. The mechanical interactions between neighboring fault segments and the impact from the long-term viscoelastic flow strongly modulate the recurrence pattern of earthquakes and slow-slip events. Afterslip penetrates down-dip and up-dip into slow-slip regions, leading to accelerated slow-slip cycles at depth and long-lasting creep waves in the accretionary prism. The trench-ward migrating locking boundary near the bottom of the seismogenic zone progressively increases the size of long-term slow-slip events during the interseismic period. Fault dynamics is complex and potentially tsunami-genic in the accretionary region due to low friction, off-fault deformation, and coupling with the seismogenic zone.Published versionThis study was funded by the National Science Foundation under grant no. EAR-1848192