Steven T. Zalesak

Magnetic structure of overexpanding coronal mass ejections: Numerical models

Numerical simulations are presented of the evolution of overexpanding coronal mass ejections (OCMEs), which are also magnetic clouds. The OCME is assumed to arise from the evolution of a magnetic flux rope with high plasma and magnetic pressure and high plasma density near the Sun in a high-speed solar wind. It is shown that the flux rope maintains its integrity from near the Sun to ≈ 5 AU, resisting hydrodynamic forces that tend to distort it. Thus OCMEs that are magnetic clouds at large heliocentric distances should have simply evolved from near-Sun flux ropes. It is shown that an initially circular flux rope is distorted into a hemispheric shape by its interaction with solar wind plasma flows. Forward and reverse shock pairs form with the forward shock being curved while the reverse shock is straight. The magnetic field properties at large distances are shown to depend on whether the initial flux rope undergoes overexpansion. A flux rope that is convected passively in the solar wind without overexpansion will ultimately have a magnetic field profile dominated by its toroidal component, so would not be observed as a magnetic cloud. The overexpanding flux ropes modeled here maintain an approximately equal ratio of toroidal to poloidal magnetic fields. The relative initial speed of the flux rope with respect to the solar wind does not influence the large-scale magnetic properties up to 5 AU, although it does affect the detailed field topology.

Geometry of interplanetary magnetic clouds

Two dimensional magnetohydrodynamic simulations are presented of the distortion of a magnetic flux rope that is being accelerated through ambient solar wind plasma. The flux rope magnetic field has an axial component parallel to the solar wind field and an azimuthal component, which lies in the simulation plane. As the flux rope moves through the solar wind plasma, vortices form on its trailing edge and couple strongly to its interior. If the flux rope azimuthal field is weak, it deforms into an elongated banana-like shape after a few Alfven transit times. A strong azimuthal field component tends to inhibit this distortion. If the flux rope is taken to model a magnetic cloud, it is suggested that the shape of the cloud at 1 AU is determined by its distortion in the inner solar wind. Distortion timescales beyond 1 AU are estimated as many days. It is estimated that effective drag coefficients somewhat greater than unity are appropriate for modelling flux rope propagation.

Magnetohydrodynamic Simulations of Alfvénic Pulse Propagation in Solar Magnetic Flux Tubes: Two-dimensional Slab Geometries

Two-dimensional magnetohydrodynamic simulations are presented of the evolution of a nonlinear Alfven wave pulse in the region between the solar photosphere and corona. A magnetic field profile that incorporates the characteristic field spreading expected in flux tubes is used. The pulse is chosen initially to have a purely Alfvenic polarization and to extend over a limited horizontal distance. It is shown that as this pulse rises in the atmosphere, it becomes wedge-shaped. The part of the pulse at the center of the flux tube reaches the transition region first, with other parts arriving at a time that is determined by the history of the Alfven speed along the path of the wave. Since field lines that spread out from the center of the flux tube spend longer in the high-density photosphere and chromosphere, and also have a smaller total field strength, waves that travel along them will take longer to reach the corona. The nonlinearity of the Alfvenic pulse drives a plasma flow both parallel to the ambient magnetic field and in a direction normal to the field, owing to transverse modulation of the Alfvenic pulse. The pulse associated with this plasma flow is also wedge-shaped, but the actual shape is different from that of the Alfvenic pulse. Since these plasma flows are compressible, they propagate at a different characteristic speed from the Alfven waves, and so can reach the transition region either before or after the Alfven pulse, the precise result depending on the plasma parameters. As the compressible pulse moves upward, a finite-sized blob of chromospheric material is injected into the corona. The relevance of this to spicules and jets is discussed.

Simulation of the magnetosphere with a new three dimensional MHD code and adaptive mesh refinement: Preliminary results

Abstract We present the first results from a new unstructured mesh three dimensional finite element MHD code which uses dynamic solution-adaptive mesh refinement in a manner similar to our two dimensional finite element MHD code /31/. The problem being considered here is the interaction of the solar wind with the earths magnetosphere, using a three-dimensional Cartesian approximation. Our results strongly indicate that such adaptive mesh techniques have the ability to resolve structures in the three dimensional MHD flow field that would otherwise be possible only with orders of magnitude greater cost and that are most likely beyond the capability of present supercomputers.

Finite element simulation of a turbulent MHD system: comparison to a pseudo-spectral simulation

Abstract A finite element MHD algorithm is used to simulate a two-dimensional, viscous and resistive turbulent model, namely the Orszag-Tang vortex. The results are compared to a pseudo-spectral simulation of the same system reported by Dahlburg and Picone (Phys. Fluids B 1 (1989) 2153). The agreement of results from both methods supports the contention that the finite element method can appropriately simulate systems exhibiting turbulence, thus enabling the use of realistic geometries and boundary conditions, as well as adaptive refinement on simulations of turbulent systems. A short discussion on the behavior of ▿· B is presented. An inverse correlation between spatial resolution and the magnitude of ▿· B was found. The relevance of our findings to Adaptive Mesh Refinement is briefly discussed.

A particle model on an unstructured mesh

We describe a particle in the cell scheme which incorporates finite elements in space and finite difference in time to follow the trajectories of particles in their self consistent fields. As such the model exploits the power of finite element techniques to better investigate the rich physics embedded in the particle or kinetic models. A brief description of the foundations of the hybrid model of kinetic ions and mass-less fluid electrons is first presented, followed by a brief summary of linear finite elements on triangles with relevance to the particle modeling. The particle trace method on triangular elements, particle to node density assignment, node to particle response, the scheme algorithm, numerical stability, and finally tests of the code via eigenmode analysis and comparison with the analytic theory and the structured simulation results are presented. The version presented here is a 212-dimensional one.