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### Variational method for estimating nonlinear acceleration of collisionless magnetic reconnection

Hirota, M; Morrison, PJ; Ishii, Y; Yagi, M; Aiba, N *(Japan Atomic Energy Agency & University of Texas at Austin)*

Friday 27 July 2012, 10:10-10:30

Seminar Room 1, Newton Institute

#### Abstract

Magnetic reconnection in collisionless plasma is studied by applying a technique that utilizes variational principle. Following the fact that a model of collisionless (namely, dissipationless) plasma constitutes a Hamiltonian system, the corresponding variational principle is formulated, where the displacement field of fluid elements is the dynamical variable to be varied. The effect of so-called "electron inertia" is a singular perturbation that modifies the topological invariant of plasma and, hence, allows magnetic reconnection to occur without any dissipation mechanism. If the potential energy of this variational principle decreases for some displacement field (under the modified topological constraint), such the fluid motion turns out to grow with the release of free energy. A rather simple fluid motion is enough to prove the occurrence of spontaneous magnetic reconnection. Decrease of potential energy in the nonlinear regime (where the magnetic island is larger than the width of boundary layer) is found to be steeper than in the linear regime, resulting in acceleration of the reconnection.

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