Self-Organizing Knotted Magnetic Structures in Plasma

Abstract

We perform full-magnetohydrodynamics simulations on various initially helical configurations and show that they reconfigure into a state where the magnetic field lines span nested toroidal surfaces. This relaxed configuration is not a Taylor state, as is often assumed for relaxing plasma, but a state where the Lorentz force is balanced by the hydrostatic pressure, which is lowest on the central ring of the nested tori. Furthermore, the structure is characterized by a spatially slowly varying rotational transform, which leads to the formation of a few magnetic islands at rational surfaces. We then obtain analytic expressions that approximate the global structure of the quasistable linked and knotted plasma configurations that emerge, using maps from S 3 to S 2 of which the Hopf fibration is a special case. The knotted plasma configurations have a highly localized magnetic energy density and retain their structure on time scales much longer than the Alfvénic time scale.

Variational formulation of relaxed and multi-region relaxed magnetohydrodynamics

“…On this time scale, the system self-organizes into multiple Taylor states in disjoint subregions Ω i with non-disjoint boundaries ∂Ω i (geometrically fixed on this time scale due to plasma inertia) supporting current sheets on their common interfaces Γ i,j (recent simulations by Smiet et al (2015) give some support for this scenario). The tangential-B boundary condition, (1.1) is satisfied on both sides of these interfaces, but in general B suffers a tangential discontinuity across them.…”

Spin-Orbital Momentum Decomposition and Helicity Exchange in a Set of Non-Null Knotted Electromagnetic Fields

“…That duality, termed "electromagnetic democracy" [10], has been central in the work of knotted field configurations [5,[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. Related field configurations have also appeared in plasma physics [27][28][29][30], optics [31][32][33][34][35], classical field theory [36], quantum physics [37,38], various states of matter [39][40][41][42][43] and twistors [44,45].…”

Magnetic surface topology in decaying plasma knots

“…This type of MHD equilibrium, where the fluid velocity is parallel to the field and equal to the local Alfvén speed, was shown by Chandrasekhar to be stable [19], even in specific cases in the presence of dissipative forces [20]. Quasi stable self-organizing magnetic fields with similar magnetic topology to Kamchatnov's field (but different flow) have recently been demonstrated to occur in full-MHD simulations [12]. Here the final configuration is not a Taylor state, which is consistent with recent findings in [21].…”

“…It is remarkable how abstract topological concepts are directly relevant to many branches of science. A prime example is the Hopf map [1], a non-trivial topological structure that has found applications in liquid crystals [2], molecular biology [3], superconductors [4], superfluids [5], Bose-Einstein condensates [6,7], ferromagnets [8], optics [9][10][11], and plasma physics [12,13]. This article deals with topological aspects of novel persistent plasma configurations that emerge from decaying plasma torus knots.…”