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Register a new userHelicity and alpha-effect by current-driven instabilities of helical magnetic fields
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Helical magnetic background fields with adjustable pitch angle are imposed on a conducting fluid in a differentially rotating cylindrical container. The small-scale kinetic and current helicities are calculated for various field geometries, and shown to have the opposite sign as the helicity of the large-scale field. These helicities and also the corresponding $alpha$-effect scale with the current helicity of the background field. The $alpha$-tensor is highly anisotropic as the components $alpha_{phiphi}$ and $alpha_{zz}$ have opposite signs. The amplitudes of the azimuthal $alpha$-effect computed with the cylindrical 3D MHD code are so small that the operation of an $alphaOmega$ dynamo on the basis of the current-driven, kink-type instabilities of toroidal fields is highly questionable. In any case the low value of the $alpha$-effect would lead to very long growth times of a dynamo in the radiation zone of the Sun and early-type stars of the order of mega-years.
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The constraint imposed by magnetic helicity conservation on the alpha effect is considered for both magnetically and flow dominated self-organizing plasmas. Direct numerical simulations are presented for a dominant contribution to the alpha effect, which can be cast in the functional form of a total divergence of an averaged helicity flux, called the helicity-flux-driven alpha ( H$alpha$) effect. Direct numerical simulations of the H$alpha$ effect are prese nted for two examples---the magnetically dominated toroidal plasma unstable to tearing modes, and the flow-dominated accretion disk.
Previously unobservable mirror asymmetry of the solar magnetic field -- a key ingredient of the dynamo mechanism which is believed to drive the 11-year activity cycle -- has now been measured. This was achieved through systematic monitoring of solar active regions carried out for more than 20 years at observatories in Mees, Huairou, and Mitaka. In this paper we report on detailed analysis of vector magnetic field data, obtained at Huairou Solar Observing Station in China. Electric current helicity (the product of current and magnetic field component in the same direction) was estimated from the data and a latitude-time plot of solar helicity during the last two solar cycles has been produced. We find that like sunspots helicity patterns propagate equatorwards but unlike sunspot polarity helicity in each solar hemisphere does not change sign from cycle to cycle - confirming the theory. There are, however, two significant time-latitudinal domains in each cycle when the sign does briefly invert. Our findings shed new light on stellar and planetary dynamos and has yet to be included in the theory.
We present nonlinear mean-field alpha-Omega dynamo simulations in spherical geometry with simplified profiles of kinematic alpha effect and shear. We take magnetic helicity evolution into account by solving a dynamical equation for the magnetic alpha effect. This gives a consistent description of the quenching mechanism in mean-field dynamo models. The main goal of this work is to explore the effects of this quenching mechanism in solar-like geometry, and in particular to investigate the role of magnetic helicity fluxes, specifically diffusive and Vishniac-Cho (VC) fluxes, at large magnetic Reynolds numbers (Rm). For models with negative radial shear or positive latitudinal shear, the magnetic alpha effect has predominantly negative (positive) sign in the northern (southern) hemisphere. In the absence of fluxes, we find that the magnetic energy follows an Rm^-1 dependence, as found in previous works. This catastrophic quenching is alleviated in models with diffusive magnetic helicity fluxes resulting in magnetic fields comparable to the equipartition value even for Rm=10^7. On the other hand, models with a shear-driven Vishniac-Cho flux show an increase of the amplitude of the magnetic field with respect to models without fluxes, but only for Rm<10^4. This is mainly a consequence of assuming a vacuum outside the Sun which cannot support a significant VC flux across the boundary. However, in contrast with the diffusive flux, the VC flux modifies the distribution of the magnetic field. In addition, if an ill-determined scaling factor in the expression for the VC flux is large enough, subcritical dynamo action is possible that is driven by the action of shear and the divergence of current helicity flux.
Potential field extrapolations are widely used as minimum-energy models for the Suns coronal magnetic field. As the reference to which other magnetic fields are compared, they have -- by any reasonable definition -- no global (signed) magnetic helicity. Here we investigate the internal topological structure that is not captured by the global helicity integral, by splitting it into individual field line helicities. These are computed using potential field extrapolations from magnetogram observations over Solar Cycle 24, as well as for a simple illustrative model of a single bipolar region in a dipolar background. We find that localised patches of field line helicity arise primarily from linking between strong active regions and their overlying field, so that the total unsigned helicity correlates with the product of photospheric and open fluxes. Within each active region, positive and negative helicity may be unbalanced, but the signed helicity is only around a tenth of the unsigned helicity. Interestingly, in Cycle 24, there is a notable peak in unsigned helicity caused by a single large active region. On average, the total unsigned helicity at the resolution considered is approximately twice the typical signed helicity of a single real active region, according to non-potential models in the literature.
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.
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