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# The Test-field Method - PowerPoint PPT Presentation

The Test-field Method. Output so far. Simulations showing large-scale fields. Helical turbulence ( B y ). Helical shear flow turb. Convection with shear. Magneto-rotational Inst. K äpyla et al (2008). Low Pr M dynamos. Sun Pr M = n/h =10 -5. Schekochihin et al (2005).

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## PowerPoint Slideshow about 'The Test-field Method' - taya

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### The Test-field Method

Helical turbulence (By)

Helical shear flow turb.

Convection with shear

Magneto-rotational Inst.

Käpyla et al (2008)

Low PrM dynamos

Sun PrM=n/h=10-5

Schekochihin

et al (2005)

Here: non-helically

forced turbulence

k

Helical turbulence

Soon hiring:

• 4 students

• 3 post-docs

• 1 assistant professor

• Long-term visitors

Calculate full aij and hij tensors

turbulent emf

• Correlation method

• MRI accretion discs (Brandenburg & Sokoloff 2002)

• Galactic turbulence (Kowal et al. 2005, 2006)

• Test field method

• Stationary geodynamo (Schrinner et al. 2005, 2007)

• Shear flow turbulence (Brandenburg 2005)

a effect and turbulent

aagnetic diffusivity

Calculate full aij and hij tensors

Original equation (uncurled)

Mean-field equation

fluctuations

Response to arbitrary mean fields

Example:

SOCA

SOCA result

normalize

Kinematic a and ht independent of Rm (2…200)

Sur et al. (2008, MNRAS)

Rotational quenching, finite d>0 for W>0

Growth rate

Use S<0, so need negative h*21 for dynamo

Fluctuations of aij and hij

Incoherent a effect

(Vishniac & Brandenburg 1997,

Sokoloff 1997, Silantev 2000,

Proctor 2007)

Use vector potential

Mean and fluctuating

U enter separately

Nonlinear aij and hij tensors

Consistency check: consider steady state to avoid da/dt terms

Expect:

l=0 (within error bars)  consistency check!

Rm dependence for B~Beq

• l is small  consistency

• a1 and a2 tend to cancel

• making a small

• h2 small

Earlier results on ht quenching

Yousef et al.

(2003, A&A)

Nonlinear aij and hij tensors

Another consistency check:

passive vector equation

• 1980: magnetic buoyancy (Spiegel & Weiss) overshoot layer dynamos

• 1985: helioseismology: dW/dr > 0  dynamo dilema, flux transport dynamos

• 1992: catastrophic a-quenching a~Rm-1(Vainshtein & Cattaneo) Parker’s interface dynamo  Backcock-Leighton mechanism

Stratified dynamo simulation in 1990

Expected strong buoyancy losses,

but no: downward pumping

Tobias et al. (2001)

• Angular velocity (at 4o latitude):

• very young spots: 473 nHz

• oldest spots: 462 nHz

• Surface plasma: 452 nHz

• Conclusion back then:

• Sun spins faster in deaper convection zone

• Solar dynamo works with dW/dr<0: equatorward migr

Benevolenskaya et al. (1998)

Thompson et al. (2003)

Yoshimura (1975)

• 1980: magnetic buoyancy  counteracted by pumping

• 1985: helioseismology: dW/dr > 0  negative gradient in near-surface shear layer

• 1992: catastrophic a-quenching  overcome by helicity fluxes  in the Sun: by coronal mass ejections

• 11 yr cycle

• Dyamo (SS vs LS)

• Problems

• a-quenching

• slow saturation

• Solution

• Modern a-effect theory

• j.b contribution

• Magnetic helicity fluxes

• Location of dynamo

• Distrubtion, shaped by

• near-surface shear

1046 Mx2/cycle