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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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simulations showing large scale fields
Simulations showing large-scale fields

Helical turbulence (By)

Helical shear flow turb.

Convection with shear

Magneto-rotational Inst.

Käpyla et al (2008)

low pr m dynamos
Low PrM dynamos

Sun PrM=n/h=10-5

Schekochihin

et al (2005)

Here: non-helically

forced turbulence

k

Helical turbulence

upcoming dynamo effort in stockholm
Upcoming dynamo effort in Stockholm

Soon hiring:

  • 4 students
  • 3 post-docs
  • 1 assistant professor
  • Long-term visitors
calculate full a ij and h ij tensors
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 a ij and h ij tensors1
Calculate full aij and hij tensors

Original equation (uncurled)

Mean-field equation

fluctuations

Response to arbitrary mean fields

test fields
Test fields

Example:

validation roberts flow
Validation: Roberts flow

SOCA

SOCA result

normalize

non helical with rotation
Non-helical with rotation

Rotational quenching, finite d>0 for W>0

shear turbulence
Shear turbulence

Growth rate

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

fluctuations of a ij and h ij
Fluctuations of aij and hij

Incoherent a effect

(Vishniac & Brandenburg 1997,

Sokoloff 1997, Silantev 2000,

Proctor 2007)

from linear to nonlinear
From linear to nonlinear

Use vector potential

Mean and fluctuating

U enter separately

nonlinear a ij and h ij tensors
Nonlinear aij and hij tensors

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

Expect:

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

r m dependence for b b eq
Rm dependence for B~Beq
  • l is small  consistency
  • a1 and a2 tend to cancel
  • making a small
  • h2 small
earlier results on h t quenching
Earlier results on ht quenching

Yousef et al.

(2003, A&A)

nonlinear a ij and h ij tensors1
Nonlinear aij and hij tensors

Another consistency check:

passive vector equation

solar paradigm shifts
Solar paradigm shifts
  • 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
i is magnetic buoyancy a problem
(i) Is magnetic buoyancy a problem?

Stratified dynamo simulation in 1990

Expected strong buoyancy losses,

but no: downward pumping

Tobias et al. (2001)

ii before helioseismology
(ii) Before helioseismology
  • 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)

revisit paradigm shifts
Revisit paradigm shifts
  • 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
conclusion
Conclusion
  • 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

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