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# Magnetic Helicity Fluxes and their Effect on the Solar Dynamo

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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 $10^{5}$. 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 equatorial plane. This is also verified in 3-D direct numerical simulations.

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### Magnetic Helicity Fluxes and their Effect on the Solar Dynamo

1. 1. Magnetic Helicity Fluxes and their Effect on the Solar Dynamo Simon Candelaresi
2. 2. Magnetic helicity fluxesAim: Study the role of magnetic helicity in dynamical quenching.Method: 1d mean-field dynamo with helical forcingMean-field decomposition:Induction equation:Electromotive force: effect: 2
3. 3. Magnetic helicity fluxes advective: diffusion 3
4. 4. Magnetic helicity fluxes Solve equations for one hemisphere. Impose (anti)symmetric field at the equator.vertical field perfect conductor(open boundaries) (closed boundaries)increasing upwardwind Fickian diffusionsymmetric field antisymmetric field 4
5. 5. Magnetic helicity fluxesopen boundary closed boundary VS.symmetric antisymmetricwind 5
6. 6. Adding shear Critical values for the forcing and the shearing amplitudeShearingvelocity field:
7. 7. Full domain Imposed parity in the hemispheric model is artificial. Include both hemispheres. Nz S Preferred antisymmetric mode?
8. 8. Parity changeLook at the parity of the magnetic field Random initial field Symmetric initial field The antisymmetric solution seems to be the preferred one.
9. 9. Parity change Random initial field Symmetric initial fieldMFDNS
10. 10. Conclusions● Advective magnetic helicity fluxes can alleviate catastrophic quenching.● Diffusive magnetic helicity fluxes can alleviate catastrophic quenching.● Symmetric mode is unstable.● The antisymmetric mode seems to be the preferred one.● Check the growth rate of the modes. 10
11. 11. ReferencesBrandenburg et al. 2009 Axel Brandenburg, Simon Candelaresi and Piyali Chatterjee. Small-scale magnetic helicity losses from a mean-field dynamo. Mon. Not. Roy. Astron. Soc., 398:1414-1422, September 2009.Candelaresi et al. 201? Simon Candelaresi and Axel Brandenburg, Bifurcation behavior of dynamically quenched dynamos. www.nordita.org/~iomsn 11