Large-scale Magnetic Helicity Research Articles

Magnetic Helicity Reversal in the Corona at Small Plasma Beta

Abstract Solar and stellar dynamos shed small-scale and large-scale magnetic helicity of opposite signs. However, solar wind observations and simulations have shown that some distance above the dynamo both the small-scale and large-scale magnetic helicities have reversed signs. With realistic simulations of the solar corona above an active region now being available, we have access to the magnetic field and current density along coronal loops. We show that a sign reversal in the horizontal averages of the magnetic helicity occurs when the local maximum of the plasma beta drops below unity and the field becomes nearly fully force free. Hence, this reversal is expected to occur well within the solar corona and would not directly be accessible to in situ measurements with the Parker Solar Probe or SolarOrbiter. We also show that the reversal is associated with subtle changes in the relative dominance of structures with positive and negative magnetic helicity.

Effects of Magnetic and Kinetic Helicities on the Growth of Magnetic Fields in Laminar and Turbulent Flows by Helical Fourier Decomposition

Abstract We present a numerical and analytical study of incompressible homogeneous conducting fluids using a helical Fourier representation. We analytically study both small- and large-scale dynamo properties, as well as the inverse cascade of magnetic helicity, in the most general minimal subset of interacting velocity and magnetic fields on a closed Fourier triad. We mainly focus on the dependency of magnetic field growth as a function of the distribution of kinetic and magnetic helicities among the three interacting wavenumbers. By combining direct numerical simulations of the full magnetohydrodynamics equations with the helical Fourier decomposition, we numerically confirm that in the kinematic dynamo regime the system develops a large-scale magnetic helicity with opposite sign compared to the small-scale kinetic helicity, a sort of triad-by-triad α-effect in Fourier space. Concerning the small-scale perturbations, we predict theoretically and confirm numerically that the largest instability is achived for the magnetic component with the same helicity of the flow, in agreement with the Stretch–Twist–Fold mechanism. Vice versa, in the presence of Lorentz feedback on the velocity, we find that the inverse cascade of magnetic helicity is mostly local if magnetic and kinetic helicities have opposite signs, while it is more nonlocal and more intense if they have the same sign, as predicted by the analytical approach. Our analytical and numerical results further demonstrate the potential of the helical Fourier decomposition to elucidate the entangled dynamics of magnetic and kinetic helicities both in fully developed turbulence and in laminar flows.

Ribbons characterize magnetohydrodynamic magnetic fields better than lines: a lesson from dynamo theory

Blackman and Brandenburg argued that magnetic helicity conservation in dynamo theory can in principle be captured by diagrams of mean field dynamos when the magnetic fields are represented by ribbons or tubes, but not by lines. Here, we present such a schematic ribbon diagram for the α2 dynamo that tracks magnetic helicity and provides distinct scales of large-scale magnetic helicity, small-scale magnetic helicity, and kinetic helicity involved in the process. This also motivates our construction of a new ‘2.5 scale’ minimalist generalization of the helicity-evolving equations for the α2 dynamo that separately allows for these three distinct length-scales while keeping only two dynamical equations. We solve these equations and, as in previous studies, find that the large-scale field first grows at a rate independent of the magnetic Reynolds number RM before quenching to an RM-dependent regime. But we also show that the larger the ratio of the wavenumber where the small-scale current helicity resides to that of the forcing scale, the earlier the non-linear dynamo quenching occurs, and the weaker the large-scale field is at the turnoff from linear growth. The harmony between the theory and the schematic diagram exemplifies a general lesson that magnetic fields in magnetohydrodynamic are better visualized as two-dimensional ribbons (or pairs of lines) rather than single lines.

LARGE-SCALE MAGNETIC HELICITY FLUXES ESTIMATED FROM MDI MAGNETIC SYNOPTIC CHARTS OVER THE SOLAR CYCLE 23

To investigate the characteristics of large-scale and long-term evolution of magnetic helicity with solar cycles, we use the method of Local Correlation Tracking to estimate the magnetic helicity evolution over solar cycle 23 from 1996 to 2009 using 795 MDI magnetic synoptic charts. The main results are as follows: the hemispheric helicity rule still holds in general, i.e., the large-scale negative (positive) magnetic helicity dominates the northern (southern) hemisphere. However, the large-scale magnetic helicity fluxes show the same sign in both hemispheres around 2001 and 2005. The global, large-scale magnetic helicity flux over the solar disk changes from a negative value at the beginning of solar cycle 23 to a positive value at the end of the cycle, while the net accumulated magnetic helicity is negative in the period between 1996 and 2009.

Current helicity constraints in solar dynamo models

AbstractWe investigate to what extent the current helicity distribution observed in solar active regions is compatible with solar dynamo models. We use an advanced 2D mean-field dynamo model with dynamo action largely concentrated near the bottom of the convective zone, and dynamo saturation based on the evolution of the magnetic helicity and algebraic quenching. For comparison, we also studied a more basic 2D mean-field dynamo model with simple algebraic alpha quenching only. Using these numerical models we obtain butterfly diagrams for both the small-scale current helicity and the large-scale magnetic helicity, and compare them with the butterfly diagram for the current helicity in active regions obtained from observations. This comparison shows that the current helicity of active regions, as estimated by −A·B evaluated at the depth from which the active region arises, resembles the observational data much better than the small-scale current helicity calculated directly from the helicity evolution equation. Here B and A are respectively the dynamo generated mean magnetic field and its vector potential.

Large scale magnetic helicity fluxes estimated from MDI magnetic synoptic charts

AbstractTo investigate the characteristics of large scale and long term evolution of magnetic helicity with solar cycles, we use the method of Local Correlation Tracking (LCT) to estimate the magnetic helicity evolution over the 23rd solar cycle from 1996 to 2009 by using 795 MDI magnetic synoptic charts. The main results are: the hemispheric helicity rule still holds in general, i.e. the large-scale negative (positive) magnetic helicity dominates the northern (southern) hemisphere. However, the large scale magnetic helicity fluxes show the same sign in both hemispheres around 2001 and 2005. The global, large scale magnetic helicity flux over the solar disk changes from negative value at the beginning of the 23rd solar cycle to positive value at the end of the cycle, which also shows the similar trend from the normalized magnetic flux by using the magnetic flux. The net accumulated magnetic helicity is negative in the period between 1996 and 2009.

CURRENT HELICITY OF ACTIVE REGIONS AS A TRACER OF LARGE-SCALE SOLAR MAGNETIC HELICITY

We demonstrate that the current helicity observed in solar active regions traces the magnetic helicity of the large-scale dynamo generated field. We use an advanced 2D mean-field dynamo model with dynamo saturation based on the evolution of the magnetic helicity and algebraic quenching. For comparison, we also studied a more basic 2D mean-field dynamo model with simple algebraic alpha quenching only. Using these numerical models we obtained butterfly diagrams both for the small-scale current helicity and also for the large-scale magnetic helicity, and compared them with the butterfly diagram for the current helicity in active regions obtained from observations. This comparison shows that the current helicity of active regions, as estimated by $-{\bf A \cdot B}$ evaluated at the depth from which the active region arises, resembles the observational data much better than the small-scale current helicity calculated directly from the helicity evolution equation. Here ${\bf B}$ and ${\bf A}$ are respectively the dynamo generated mean magnetic field and its vector potential. A theoretical interpretation of these results is given.

Bihelical magnetic relaxation and large scale magnetic field growth

A unified, three-scale system of equations accommodating nonlinear velocity driven helical dynamos, as well as time-dependent relaxation of magnetically dominated unihelical or bihelical systems is derived and solved herein. When opposite magnetic helicities of equal magnitude are injected on the intermediate and small scales, the large scale magnetic helicity grows kinematically (independent of the magnetic Reynolds number) to equal that on the intermediate scale. For both free and driven relaxation large scale fields are rapidly produced. Subsequently, a dissipation-limited dynamo, driven by growth of small scale kinetic helicity, further amplifies the large scale field. The results are important for astrophysical coronae fed with bihelical structures by dynamos in their host rotators. The large scale for the rotator corresponds to the intermediate scale for the corona. That bihelical magnetic relaxation can produce global scale fields may help to explain the formation of astrophysical coronal holes and magnetohydrodynamic outflows.

Dynamical magnetic relaxation: A nonlinear magnetically driven dynamo

A nonlinear, time-dependent, magnetically driven dynamo theory that shows how magnetically dominated configurations can relax to become helical on the largest scale available is presented. Coupled time-dependent differential equations for large-scale magnetic helicity, small-scale magnetic helicity, velocity, and the electromotive force are solved. The magnetic helicity on small scales relaxes to drive significant large-scale helical field growth on dynamical (Alfvén crossing) time scales, independent of the magnitude of finite microphysical transport coefficients, after which the growing kinetic helicity slows the growth to a viscously limited pace. This magnetically driven dynamo complements the nonlinear kinetic helicity-driven dynamo; for the latter, the growing magnetic helicity fluctuations suppress, rather than drive, large-scale magnetic helicity growth. A unified set of equations accommodates both types of dynamos.

Magnetic Helicity, Dynamo Action, Reconnection, and Particle Acceleration

Blackman & Field have shown that a working α-Ω dynamo requires finite but opposite flows of small- and large-scale magnetic helicity through a body's surface. The helicity is accompanied by magnetic energy available for dissipation. The observed solar coronal nonthermal power is consistent with the derived lower limit required. This link between dynamo field generation and nonthermal emission should generally apply to stars, spiral galaxies, and accretion disks.