München 2019 – wissenschaftliches Programm

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P: Fachverband Plasmaphysik

P 5: Helmholtz Graduate School I

P 5.5: Vortrag

Montag, 18. März 2019, 15:45–16:10, HS 21

Relaxation to magnetohydrodynamics equilibria via collision brackets — •Camilla Bressan1,2, Michael Kraus1,2, Philip James Morrison3, and Omar Maj1,21Max Planck Institute for Plasma Physics, Garching, Germany — 2Technische Universität München, Zentrum Mathematik, Garching, Germany — 3The University of Texas at Austin, Physics Department and Institute for Fusion Studies, USA

It is well known that three-dimensional Magnetohydrodynamic (3D MHD) equilibrium equation has multiple solutions. In order to select a unique solution, existing numerical approaches either constrain suitable plasma parameters or relax an initial condition by means of suitable relaxation terms added to ideal MHD equations (relaxation methods). Concerning in particular the latter approach, ideas and results from Geometric Mechanics have been successfully applied to select a unique solution of the equilibrium problem which is consistent with external constrained profiles. The method presented fits into the framework of metriplectic dynamics, developed by Morrison ([Morrison, 1984, Phys. Lett. A, 100, 423-7], [Morrison, 1986, Physica D, 18, 410-9]), in which energy-preserving dynamics is combined with entropy dissipation. Convergence to the desired equilibrium state compatible with experimental data can be investigated by techniques similar to the Boltzmann’s H-theorem [Lenard, 1960, Ann. of Phys., 3, 390-400]. Relevant applications of the new approach are presented: the vorticity form of the 2D Euler equations, the Grad- Shafranov equation, Taylor-relaxed states (3D Beltrami fields).

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