A study of Magnetic Reconnection Brooke L. Nielsen I. Introduction The breaking and reconnecting of oppositely directed magnetic field lines in a plasma is known as magnetic reconnection. When magnetic reconnection occurs, magnetic field energy is converted into kinetic and thermal energy. In many systems this process can determine the structure and overall stability of the plasma. II. Astrophysical Significance Magnetic reconnection is an important part of several astrophysical events. In our sun, flares are believed to be powered by reconnection. Solar flares can output a large amount energy; 3x10^32 erg can be released in the largest of events. This energy, in the form of particles, can cause problems when it reaches Earth. Power grids and communications can be affected as well as putting spacecraft and satellite equipment in danger. When and where solar flares occur is not completely understood. Gaining a better understanding of solar magnetic field conditions preceding flares will help scientists to better predict flares and eventually protect the Earth from their harm. It is believed that the magnetic field, and reconnection, plays an important role in configuring the morphology of the galactic gas. Turbulence in this gas is a potential source of amplified and organized magnetic fields (the dynamo effect). In the smallest eddies magnetic energy is converted into heat and therefore dissipated. In this sense turbulence destroys magnetic fields. However, magnetic fields are observered in spiral galaxies, so the dynamo effect must be present. A current theory to explain this is the rotational motion of the gas in the galaxy gives rise to reconnection, producing closed field lines known as magnetic loops. These fields under the action of the differential rotation of the galaxy may produce the large azimuthal fields observed. The physics behind rotation of spiral galaxies is well understood whereas how the magnetic fields behave in the turbulent gas is not greatly understood. Having a better understanding of magnetic reconnection and field configurations before and after reconnection would aid in understanding this system. III. MHD, Sweet-Parker Theory and Limitations A conventional model of magnetic reconnection is the Sweet-Parker current sheet model, established in 1958. Before discussing the specifics of the Sweet-Parker model a basic property of magnetohydrodynamics (MHD) should be understood. This property is the conservation of flux, or flux freezing. This means that as the plasma flows the flux lines are carried along with the plasma as it moves. As a plasma flows, magnetic field lines can become twisted around each other or compressed together. This is a result of the conservation of flux. When oppositely directed magnetic fields are compressed toward each other, a Sweet-Parker current sheet will be formed. Plasma and magnetic flux being brought towards the sides of the sheet at a speed greater than magnetic diffusivity divided by the thickness of the current sheet will result in the sheet becoming thinner. The plasma pressure on the center of the compressing sheet causes material and magnetic flux to expel from the ends. A simple visualization for this is a half melted ice cream sandwich. Think of the ice cream as the plasma and the cookies as the current sheet. As you squeeze down on the sandwich to take a bite, melted ice cream expels from all sides of the cookie making the ice cream sandwich thinner. Magnetic reconnection occurs as the field lines pass through the center of the current sheet, connecting, and then breaking into two separate differently orientated field lines. There are several limitations to the Sweet-Parker theory. One problem with the theory is that it is based on two-dimensional flows. Much less is known about the physics behind reconnection when it is brought to three dimensions. Another limitation in conventional theory is that it is based on steady flows. In astrophysical systems, most plasma will not be steady. The last major limitation of conventional reconnection theory is the speed at which reconnection occurs. The Sweet-Parker model only takes into account slow reconnection. This means reconnection occurs on a much slower time scale. From observation of astrophysical reconnection events, like solar flares, reconnection occurs much faster than the theory accounts for. IV. Methods Using data from a 3D reconnection model, I studied the field configurations prior to and following magnetic reconnection. The model used consists of two plasmas each flowing in an opposite direction. As the flow progresses the system becomes unstable and a vortex forms. The magnetic field lines get wrapped up inside and around the vortex, ultimately ending in reconnection. The data was studied on the silicon graphics workstations using visualization software programs. The 4d2 and dx volume rendering packages allowed for viewing of the magnetic field topology in the plasma. The brick of bytes (bob) program was used to view 2D slices of the data. V. Results and Conclusion At very early times (time step 0 to around 6) the magnetic field lines were orientated across the box (along the x-axis). The magnetic pressure was lowest inside the vortex. Somewhere around time step 4 or 6, the field lines began to get wrapped up inside the vortex. The field lines during this time were mostly orientated across the box. An occasional field line appeared to be dragged down the box (along the z-axis). These field lines exited the box further down the z-axis than the other field lines at this time step. It is believed that either the plasma flow or reconnection could have caused this. The majority of time was spent in studying time steps 10-16. During these time steps reconnection was a common occurrence. In general it was found that after reconnection occurred, the field lines tended to be isolated from the original field lines and be spiraling down the box. Those that were not orientated down the box, followed a magnetic flux tube out the side of the box. The field lines were sometimes spiraled around the flux tube. It was also observed that on occasion a field line would jump from one flux tube over to another flux tube then following that one out the box. The magnetic pressure was highest on the arms of the vortex and lowest in the center. The flow of the plasma was beginning to get very complex. No time was spent studying the data after time step 16 because the flow was extremely chaotic and it was difficult to determine regions where reconnection was occurring. Previous data existed from a 2D model of the same turbulent flow. One of my objectives in viewing the data from the 3D model was to compare properties of the magnetic field around the time of reconnection. In the two-dimensional model, it appeared that magnetic loops were forming as a result of some reconnections. In the three-dimensional data I looked for this occurring but could not find any magnetic loops formed at any time step. However, when I took a particular slice of the 3D cube and viewed it, a loop appeared. In actuality this loop was a reconnected field line whose orientation was now down the box instead of the original orientation of across the box. The field line was spiraling down the box, giving it the appearance of a closed loop in 2 dimensions. This may be what was happening for all of the loops observed in the two-dimensional model. The data studied for this project proved to be a good introduction to the magnetic field configurations in a 3D flow. However, further work needs to be done before these findings can be applied to real world reconnection events. A more detailed look at higher resolution data and a study of data at finer time step granularity should follow. VI. References Battaner, E., 1996, Astrophysical Fluid Dynamics, (New York: Cambridge University Press). Biskamp, D., 1994, Magnetic Reconnection, Phys. Rev. Lett. 237, 179-247. Priest, E. R., 1996, Solar and Astrophysical Magnetohydrodynamic flows, ed. by K.C. Tsinganos (Netherlands: Kluwer Academic Publishers), 151. Priest, E. R., 1984, Solar Magneto-hydrodynamics, ed. by Dordecht (Boston: D. Reidel Pub. Co.).