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Constraints on the Evolution of Plasma Currents and on Magnetic Reconnection
| Author: | Boozer A.H. |
| Coauthor: | |
| Institution : | Columbia University |
| Abstract text: | The parallel current distribution, j||/B, can be rapidly flattened by a Taylor relaxation, which means magnetic surfaces are destroyed. However if magnetic surfaces exist, the evolution of the parallel current distribution is heavily constrained by Maxwell’s equations. A magnetic surface always has the topology of a torus and can be identified as it evolves by the enclosed toroidal magnetic flux. Maxwell’s equations imply the time derivative of the poloidal flux, which is magnetic flux through the hole of the torus, is the loop voltage. The loop voltage is an integral over the magnetic surface of the electric field dotted with the magnetic field. When surfaces exist the evolution of the poloidal flux profile is determined by the parallel component of Ohm’s law, which means the evolution is slow. For a simple Ohm’s law, the parallel current is dissipated due to the parallel resistivity.
The distinction between magnetic reconnection in toroidal and space plasmas will also be discussed. Magnetic reconnection is impossible if the evolution of the magnetic field gives an electric field that can be balanced along the magnetic field by the gradient of a potential. In toroidal plasmas a solution for the potential can fail to exist on rational surfaces where field lines close on themselves. In space plasmas, the primary effect causing reconnection is apparently the size of the Lyapunov length, which is the distance along a field line over which the separation between neighboring field lines exponentiates. If the Lyapunov length becomes sufficiently short, a well-behaved potential does not exist and reconnection occurs.
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