Magnetic helicity: why is it so important and how to get rid of it

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Magnetic helicitywhy is it so important and how
to get rid of it

• Axel Brandenburg (Nordita, Copenhagen)
• Kandaswamy Subramanian (Pune)

Brandenburg (2001, ApJ 550, 824 2005, ApJ 625,
539) Brandenburg Subramanian (2005, Phys. Rep.,
astro-ph/0405052)
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Magnetic helicity
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Magnetic helicity conservation
How J diverges as h?0
Ideal limit and ideal case similar!
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Inverse cascade of magnetic helicity
Pouquet, Frisch, Leorat (1976)
and
Initial components fully helical
and
? k is forced to the left
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Production of LS helicity
forcing produces
and
But no net helicity production
therefore
? alpha effect
Yousef Brandenburg AA 407, 7 (2003)
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LS dynamos

• Difference to SS dynamos
• Field at scale of turbulence
• The small PrM problem
• Mechanisms for producing LS fields
• Field at scale larger than that of turbulence
• Alpha effect (requires helicity)
• Shear-current of WxJ effect
• Others incoherent alpha, Vishniac-Cho effect,
  perhaps other effects

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Cartesian box MHD equations
Magn. Vector potential
Induction Equation
Momentum and Continuity eqns
Viscous force
forcing function
(eigenfunction of curl)
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(i) Small scale dynamos
Small PrM stars and discs around NSs and YSOs
Schekochihin et al (2005) ApJ 625, 115L
k
Here non-helically forced turbulence
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256 processor run at 10243 at PrM1
-3/2 slope?
Haugen et al. (2003, ApJ 597, L141)
Result not peaked at resistive scale ? Kolmogov
scaling!
instead kpeakRm,crit1/2 kf 6kf
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(ii) Large scale dynamos 2 different geometries
(a) Periodic box, no shear
(b) open box, w/ shear

• Helically forced turbulence (cyclonic events)
• Small large scale field grows exponentially
• Past saturation slow evolution
• ? Explained by magnetic helicity equation

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Scale separation inverse cascade
Position of the peak compatible with
Decomposition in terms of Chandrasekhar-Kendall-Wa
leffe functions
No inverse cascade in kinematic regime
LS field force-free Beltrami
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Time dependence slow saturation
Brandenburg (2001, ApJ 550, 824)
Position of the peak compatible with
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Connection with a effect writhe with internal
twist as by-product
a effect produces helical field
W
clockwise tilt (right handed)
? left handed internal twist
both for thermal/magnetic buoyancy
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Revised nonlinear dynamo theory(originally due
to Kleeorin Ruzmaikin 1982)
Two-scale assumption
Dynamical quenching
Kleeorin Ruzmaikin (1982)
(? selective decay)
Steady limit ? algebraic quenching
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Dynamo growth saturation
Significant field already after kinematic growth
phase
followed by slow resistive adjustment
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Large scale vs small scale losses
Diffusive large scale losses ? lower saturation
level Brandenburg Dobler (2001 AA 369, 329)
Periodic box
with LS losses
Small scale losses (artificial) ? higher
saturation level ? still slow time scale
Numerical experiment remove field for kgt4 every
1-3 turnover times (Brandenburg et al. 2002, AN
323 99)
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Current helicity flux

• Advantage over magnetic helicity
• ltj.bgt is what enters a effect
• Can define helicity density

Rm also in the numerator
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Significance of shear

• a ? transport of helicity in k-space
• Shear ? transport of helicity in x-space
• Mediating helicity escape (? plasmoids)
• Mediating turbulent helicity flux

Expression for current helicity flux (first
order smoothing, tau approximation)
Schnack et al.
Vishniac Cho (2001, ApJ 550, 752) Subramanian
Brandenburg (2004, PRL 93, 20500)
Expected to be finite on when there is shear
Arlt Brandenburg (2001, AA 380, 359)
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(ii) Forced LS dynamo with no stratification
azimuthally averaged
no helicity, e.g.
Rogachevskii Kleeorin (2003, 2004)
geometry here relevant to the sun
neg helicity (northern hem.)
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Conclusions

• Shearflow turbulence likely to produce LS field
• even w/o stratification (WxJ effect, similar to
  Rädlers WxJ effect)
• Stratification can lead to a effect
• modify WxJ effect
• but also instability of its own
• SS dynamo not obvious at small Pm
• Application to the sun?
• distributed dynamo ? can produce bipolar regions
• a perhaps not so important?
• solution to quenching problem? No aM even from
  WxJ effect

1046 Mx2/cycle