# TRR 181 Seminar "Remarkable preservation of topological structure in extended magnetofluid models.""

The TRR 181 seminar is held every two weeks in the semester and as announced during semester break. The locations of the seminar changes between the three TRR181 locations, but is broadcastet online for all members of the TRR.

The TRR 181 seminar is held by **Prof. Phil Morrison (University of Texas in Austin)** on

### Remarkable preservation of topological structure in extended magnetofluid models

at University of Bremen, MZH 1090, on January 17 at 4.15 pm.

**Abstract**

Extended magnetohydrodynamics (XMHD) is a generalization of magnetohydrodynamics (MHD) that describes features of both astrophysical and laboratory plasmas. Like MHD it is a system of partial differential equations, but altered by possessing a complicated Ohms law that includes the physics of Hall drift and electron inertia. Although of practical importance, XMHD has generally not been perceived to possess the beautiful topological structure known for MHD. However, considerable progress made by me and coauthors [1, 2, 3, 4, 5, 6, 7] has revealed that XMHD indeed possesses rich structure. In particular, XMHD is a Hamiltonian theory, yielding Hamiltonian reductions for models that neglect Hall physics and/or electron inertia. In [1] it was shown that XMHD and the specific reductions conserve energy when dissipation is neglected, despite these versions often not appearing in text books. Using the conserved energy of [1], a generalization of the Hamiltonian structure introduced by me and John Greene (1980) was recently given in Abdelhamid et al. (2015). Considerable simplification of this structure was found in [2] by a remarkable set of transformations that map the Poisson bracket for XMHD into the simplest normal form. The transformations lead to special variables that reveal the existence of two frozen fluxes (Lie dragged 2-forms) and generalizations of the magnetic and cross helicities. Consequently, analyses of various kinds of energy stability [3] and results of so-called topological fluid mechanics and plasma reconnection (viewed as subdisciplines of the Hamiltonian theory) can be effected. For example, the topological structure of the velocity and magnetic fields can be categorized by means of Jones polynomials and related theories pertaining to knots [4]. Further understanding of these new Hamiltonian structures and invariants is achieved by constructing an action principle in terms of Lagrangian variables [5], whence the Poisson brackets can be derived. Generalizations that include gyroviscosity [6] and fully relativistically covariant [7] descriptions have also been found.

References:

[1] K. Kimura and P. J. Morrison, Phys. Plasmas 21, 082101 (2014).

[2] M. Lingam, P. J. Morrison, and G. Miloshevich, Phys. Plasmas 22, 072111 (2015).

[3] T. Andreussi, P. J. Morrison, and F. Pegoraro, Phys. Plasmas 19, 052102 (2012): Phys. Plasmas

20, 092104 (2013); erratum, Phys. Plasmas 22, 039903 (2015).

[4] M. Lingam, G. Miloshevich, and P. J. Morrison, arXiv:1602.00128 [physics.plasm-ph] (2016).

[5] I. Keramidas Charidakos, M. Lingam, P. J. Morrison, R. L. White, and A. Wurm, Phys.

Plasmas 21, 092118 (2014); E. C. DAvignon, P. J. Morrison, and M. Lingam, arXiv:1512.00942

[physics.plasm-ph] (2015).

[6] P. J. Morrison, M. Lingam, and R. Acevedo, Phys. Plasmas 21, 082102 (2014).

[7] E. DAvignon, P. J. Morrison, and F. Pegoraro, Physical Review D 91, 084050 (2015).