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. www.nordita.org/~iomsn/

1. Magnetic Helicity Fluxes
and their Effect on the
Solar Dynamo
Simon Candelaresi

2. Magnetic helicity fluxes
Aim: Study the role of magnetic helicity in dynamical quenching.
Method: 1d mean-field dynamo with helical forcing
Mean-field decomposition:
Induction equation:
Electromotive force:
effect:
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3. Magnetic helicity fluxes
advective: diffusion
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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 upward
wind
Fickian diffusion
symmetric field antisymmetric field
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5. Magnetic helicity fluxes
open boundary closed boundary
VS.
symmetric antisymmetric
wind
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6. Adding shear
Critical values for the forcing
and the shearing amplitude
Shearing
velocity field:

7. Full domain
Imposed parity in the hemispheric model is artificial.
Include both hemispheres.
N
z
S
Preferred antisymmetric mode?

8. Parity change
Look at the parity of the magnetic field
Random initial field Symmetric initial field
The antisymmetric solution seems to be the preferred one.

9. Parity change
Random initial field Symmetric initial field
MF
DNS

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.
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11. References
Brandenburg 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
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