Large scale magnetic fields and Dynamo theory. Roman Shcherbakov, Turbulence Discussion Group 14 Apr 2008

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1 Large scale magnetic fields and Dynamo theory Roman Shcherbakov, Turbulence Discussion Group 14 Apr 2008

2 The Earth Mainly dipolar magnetic field Would decay in 20kyr if not regenerated Declination of the dipole axis 11.5 (at present) Strength B= G (at present) Field reversal interchange of North/South poles, last ~ yr Field excursion decrease of B to 0-20% of normal, last ~3000yr-0.03Myr There are successful simulations: Glatzmaier, Roberts Buffett, 1999 Nature 401, 861

3 The Sun Strong non-dipolar magnetic field Typical field strength B~1G, up to 1000G in active regions Field reversal 22-year cycle, sunspots 11- year cycle (7-15 years for period) Has irregular outflows driven partially by magnetic reconnections Differential rotation 25 days (equator) vs 35 days (pole) The_Magnetic_Fields_of_Planets_an d_stars_999.html Models only with fitted parameters explain observations

4 Coronal mass ejections Credit: SOHO Consortium, ESA, NASA Fan 2001, ApJ, 554, L111 May be the constituent part of dynamo sstechnology/technology/techn ovel_shock_ html

5 Energy sources The Earth and planets Radioactive decay Latent heat & light constituents release inner core freezing Precessionally driven flows Tidal heating Convection The Sun and stars Induced flows Nuclear burning Dynamical interactions in binaries Primordial magnetic field

6 Convection in rotating medium Rotation decreases convective efficiency Back-reaction of convection accelerates rotation Differential rotation Dynamo action

7 Timescales and their ratios Reynolds number Onset of turbulence Prandtl number (magnetic) Dominance of current dissipation Ekman number Rayleigh number Rossby number Size of the boundary layer Onset of convection Regime and efficiency of dynamo

8 Large scale of small scale? The Sun Large scale Large scale or small scale? Small scale

9 Axisymmetric or 3D? The Earth Credit & Copyright: Gary A. Glatzmaier (UCSC)

10 Theory of Dynamo Twisting and folding Force-free regime +diffusion Usually neglected (Differential) rotation kinetic helicity current helicity cross-helicity

11 Kinematic α-effect Yoshizawa, 2003 u α kin u ω Then two possibilities: repeat along horizontal axis shear along horizontal axis dynamo dynamo

12 Kinematic α²-dynamo u u

13 Kinematic and dynamic αω dynamo Brandenburg, Subramanian, 2005 Strong back-reaction of the magnetic field inhibits dynamo

14 Saturation of dynamos Brandenburg, Subramanian, 2005, p.122 C D CD growth of large-scale field on Ohmic timescale (if no shocks) D quasi force-free state B²>>b²

15 Large-scale magnetic field growth Brandenburg, Subramanian, 2005, p.108 Inverse cascade of magnetic helicity P. 108 forcing scale <u ω> 0 on average over large scale => symmetry breaking

16 Force-free states Formation of a star Braithwaite, Spruit 2004 field decay weak rotation

17 Effect of open boundaries =Re Pm α effect is NOT inhibited for open boundaries, unbalanced outflow of current helicity Sun? Accretion disks?

18 Accretion disk dynamo MRI represents Ω-effect Outflows, convection Velocity in vertical direction => α-effect Inverse cascade of magnetic helicity+ advection of field Balbus, Hawley, 2003 Large-scale field generation Model with minimum dynamo action, dynamics, evolution of α, β, γ Solution of the problem?

19 Discussion & Conclusions Behavior of dynamical systems strongly depends on nonlinear terms => proper non-linear model is essential In particular, solutions with outflows/stratification and vertical structure (for disks) have finite α => large-scale field generation Proper treatment of boundary conditions and helicity outflows is essential Shearing box simulations may not represent the global solution One model should be made for accretion & the Sun/Earth, it is easier to test the model on the Sun/Earth

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21 Convection+rotation=>tons of fun

22 Reversals

23 Butterfly

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