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Magnetic helicityconservation and fluxes in
astrophysical dynamosSimon Candelaresi
Axel Brandenburg
NORDITA
Helical Dynamos
2
kinetic helicity helical magnetic fields
effect growth of large-scale fields
Closed alpha^2 Dynamo
forcing functionMomentum equation:
Helical forcing on scale
Helical motions
Helical magnetic field
normalized helicities
3
(Frisch et. al. 1975, Seehafer 1996)
resistive growth for large-scale field (Brandenburg, Subramanian 2005)
Predictions from the General Theory
6
mean-field interpretation
Saturation magnetic field strength:
(Blackman, Brandenburg 2002)
normalized kinetic helicity
For the man magnetic field to grow:
What Pietarila Graham Finds
7
(Pietarila Graham, et. al. 2012)
Fit formula:
MFT prediction
Parameters: and
Reproduction of the Predictions
9
Consider the resistive phase well after the kinematic phase.
forcing function
triply periodic BC magnetic helicity is conserved
helical forcing helical motions
helical magnetic field (Beltrami field)
Parameters: and
resistive growth:
Saturation Magnetic Field
10(Candelaresi, Brandenburg 2012)
Saturation Magnetic Field
11
(Blackman, Brandenburg 2002)Prediction:
(Candelaresi, Brandenburg 2012)
Saturation Magnetic Field
12
Predictions:
NB:
High
Match their parameters.
No change in for high .
is underestimated for high due to viscous losses.
13
(Candelaresi, Brandenburg 2012)
(Pietarila Graham, et. al. 2012)
Magnetic Helicity Fluxes
14
Mean-field induction equation:
Electromotive force (EMF):
Induction equation:
(Pouquet et al. 1976)
Moffatt, H. K., 1978, Krause and Raedler, 1980
mean-field considerations
diffusion
Magnetic Helicity Fluxes
advective:
I)
II)
III)
Helical forcing profile:
1D mean-field in z
15(Brandenburg, et al., 2009)
symmetric
wind
antisymmetric
open boundary closed boundaryVS.
Magnetic Helicity Fluxes
16
Summary
● MF prediction reproduced in DNS.
● Discrepancy of (Graham) due to SSD contamination.
● Magnetic helicity fluxes alleviate catastrophic alpha quenching.
17
U. Frisch, A. Pouquet, J. Leorat, and A. Mazure.Possibility of an inverse cascade of magnetic helicity in magnetohydrodynamic turbulence.Journal of Fluid Mechanics, 68:769, 1975.
Frisch et al., 1975
References
H. K. Moffatt.Magnetic field generation in electrically conducting fluids.Camb. Univ. Press, 1978.
Moffatt, 1978
N. Seehafer.Nature of the α effect in magnetohydrodynamics.Phys. Rev. E, 53:1283, 1996.
Seehafer, 1996
18
A. Brandenburg and K. Subramanian.Astrophysical magnetic fields and nonlinear dynamo theoryPhys. Rep. 417:1, 2005.
Brandenburg, Subramanian, 2005
F. Krause and K.-H. Raedler.Mean-field magnetohydrodynamics and dynamo theory.1980.
Krause, Raedler, 1980
References
www.nordita.org/~iomsn
Pouquet, A., Frisch, U., and Leorat, J.,Strong MHD helical turbulence and the nonlinear dynamo effect.Journal of Fluid Mechanics, 77:321, 1976.
Pouquet et al., 1976
E. G. Blackman and A. Brandenburg.Dynamic nonlinearity in large-scale dynamos with shear.Astrophys. J., 579:359, 2002.
Blackman, Brandenburg, 2002
J. Pietarila Graham, E. G. Blackman, P. D.Mininni, and A. Pouquet.Not much helicity is needed to drive large-scale dynamos.Phys. Rev. E, 85:066406, 2012.
Pietarila Graham, et al., 2012
19
A. Brandenburg, S. Candelaresi and P. ChatterjeeSmall-scale magnetic helicity losses from a mean-field dynamo.Mon. Not. Roy. Astron. Soc., 398:1414, 2009.
Brandenburg, et al., 2009
S. Candelaresi and A. BrandenburgHow much helicity is needed to drive large-scale dynamos?ArXiv:1208.4529, 2012.
Candelaresi, Brandenburg, 2012
20
ABC-Flow Forcing
Forcing:
no dominant mode
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