Topological constraints on magnetic field relaxation

Magnetic field relaxation is determined by both the field's geometry and its topology. For relaxation processes, however, it turns out that its topology is a much more stringent constraint. As quantifier for the topology we use magnetic helicity and test whether it is a stronger condition than the linking of field lines. Further, we search for evidence of other topological invariants, which give rise to further restrictions in the field's relaxation. We find that magnetic helicity is the sole determinant in most cases. Nevertheless, we see evidence for restrictions not captured through magnetic helicity.Comment: 5 pages, 5 figures, proceedings of IAU Symp. 294, Solar and Astrophysical Dynamos and Magnetic Activit

Topological constraints in magnetic field relaxation

Stability and reconnection of magnetic fields play a fundamental role in natural and man-made plasma. In these applications the field's topology determines the stability of the magnetic field. Here I will describe the importance of one topology quantifier, the magnetic helicity, which impedes any free decay of the magnetic energy. Further constraints come from the fixed point index which hinders the field to relax into the Taylor state.Comment: 5 pages, 7 figures, proceedings of "Knotted, Linked and Tangled Flux in Quantum and Classical Systems

Magnetic helicity fluxes and their effect on stellar dynamos

Magnetic helicity fluxes in turbulently driven alpha^2 dynamos are studied to demonstrate their ability to alleviate catastrophic quenching. A one-dimensional mean-field formalism is used to achieve magnetic Reynolds numbers of the order of 10^5. We study both diffusive magnetic helicity fluxes through the mid-plane as well as those resulting from the recently proposed alternate dynamic quenching formalism. By adding shear we make a parameter scan for the critical values of the shear and forcing parameters for which dynamo action occurs. For this $\alpha\Omega$ dynamo we find that the preferred mode is antisymmetric about the mid-plane. This is also verified in 3-D direct numerical simulations.Comment: 5 pages, 6 figures, proceedings of IAU Symp. 286, Comparative Magnetic Minima: characterizing quiet times in the Sun and star

Decay of helical and non-helical magnetic knots

We present calculations of the relaxation of magnetic field structures that have the shape of particular knots and links. A set of helical magnetic flux configurations is considered, which we call $n$-foil knots of which the trefoil knot is the most primitive member. We also consider two nonhelical knots; namely, the Borromean rings as well as a single interlocked flux rope that also serves as the logo of the Inter-University Centre for Astronomy and Astrophysics in Pune, India. The field decay characteristics of both configurations is investigated and compared with previous calculations of helical and nonhelical triple-ring configurations. Unlike earlier nonhelical configurations, the present ones cannot trivially be reduced via flux annihilation to a single ring. For the $n$-foil knots the decay is described by power laws that range form $t^{-2/3}$ to $t^{-1/3}$, which can be as slow as the $t^{-1/3}$ behavior for helical triple-ring structures that were seen in earlier work. The two nonhelical configurations decay like $t^{-1}$, which is somewhat slower than the previously obtained $t^{-3/2}$ behavior in the decay of interlocked rings with zero magnetic helicity. We attribute the difference to the creation of local structures that contain magnetic helicity which inhibits the field decay due to the existence of a lower bound imposed by the realizability condition. We show that net magnetic helicity can be produced resistively as a result of a slight imbalance between mutually canceling helical pieces as they are being driven apart. We speculate that higher order topological invariants beyond magnetic helicity may also be responsible for slowing down the decay of the two more complicated nonhelical structures mentioned above.Comment: 11 pages, 27 figures, submitted to Phys. Rev.

Influence of Magnetic Helicity in MHD

Observations have shown that the Sun's magnetic field has helical structures. The helicity content in magnetic field configurations is a crucial constraint on the dynamical evolution of the system. Since helicity is connected with the number of links we investigate configurations with interlocked magnetic flux rings and one with unlinked rings. It turns out that it is not the linking of the tubes which affects the magnetic field decay, but the content of magnetic helicity.Comment: 2 pages, 3 figures, proceedings of IAU Symp. 271, Astrophysical Dynamics: from Stars to Galaxies, ed. N. Brummell and A.S. Brun, CU

Magnetic field decay of three interlocked flux rings with zero linking number

The resistive decay of chains of three interlocked magnetic flux rings is considered. Depending on the relative orientation of the magnetic field in the three rings, the late-time decay can be either fast or slow. Thus, the qualitative degree of tangledness is less important than the actual value of the linking number or, equivalently, the net magnetic helicity. Our results do not suggest that invariants of higher order than that of the magnetic helicity need to be considered to characterize the decay of the field.Comment: 7 pages, 10 figure

Magnetic helicity transport in the advective gauge family

Magnetic helicity fluxes are investigated in a family of gauges in which the contribution from ideal magnetohydrodynamics takes the form of a purely advective flux. Numerical simulations of magnetohydrodynamic turbulence in this advective gauge family exhibit instabilities triggered by the build-up of unphysical irrotational contributions to the magnetic vector potential. As a remedy, the vector potential is evolved in a numerically well behaved gauge, from which the advective vector potential is obtained by a gauge transformation. In the kinematic regime, the magnetic helicity density evolves similarly to a passive scalar when resistivity is small and turbulent mixing is mild, i.e. when the fluid Reynolds number is not too large. In the dynamical regime, resistive contributions to the magnetic helicity flux in the advective gauge are found to be significant owing to the development of small length scales in the irrotational part of the magnetic vector potential.Comment: 11 pages, 10 figures, submitted to Physics of Plasma

Stabilizing Effect of Magnetic Helicity on Magnetic Cavities in the Intergalactic Medium

We investigate the effect of magnetic helicity on the stability of buoyant magnetic cavities as found in the intergalactic medium. In these cavities we insert helical magnetic fields and test whether or not helicity can increase their stability to shredding through the Kelvin–Helmholtz instability and, with that, their lifetime. This is compared to the case of an external vertical magnetic field that is known to reduce the growth rate of the Kelvin–Helmholtz instability. By comparing a low-helicity configuration with a high-helicity one with the same magnetic energy, we find that an internal helical magnetic field stabilizes the cavity. This effect increases as we increase the helicity content. Stabilizing the cavity with an external magnetic field requires instead a significantly stronger field at higher magnetic energy. We conclude that the presence of helical magnetic fields is a viable mechanism to explain the stability of intergalactic cavities on timescales longer than 100 Myr