Plans for Dynamo Research

1. Plans for Dynamo Research Presented by F. Cattaneo, S. Prager

2. Outline • Evidence for dynamo effects in astrophysics in the lab • Nonlinear Features of the dynamo status and plans • Dynamo Effects Beyond MHD status and plans

3. Evidence for dynamo effects in astrophysics • IGM • Typical size: 30 kpc wide, 300 kpc long • Magnetic fields: 0.5 – 5  Gauss • Dynamo action in disk around central SMBH • Galaxy • Typical size: 1020 m. Rotation period 108 years • Magnetic fields: 3  Gauss (horizontal cmpnt) • Turbulence driven by supernovae explosions • Classical - dynamo

4. Evidence for dynamo effects in astrophysics • Accretion disks • Turbulence driven by MRI • Magnetic field necessary to drive MRI, self consistently generated by dynamo action • Late-type stars (Sun) • Magnetic activity extremely well documented • Turbulence driven by convection. • Activity cycles • “Mounder minima” • Classical - dynamo for large-scale field • Evidence for small scale dynamo action

5. Evidence for dynamo effects in “astrophysics” • Geodynamo • Example of system where dynamo must operate • Turbulence driven by (compositional?) convection. Strong rotation • Moderate Rm • Dipolar field exhibits reversals • Laboratory experiments • Plasma devices (more about it presently) • Liquid metal experiments • Experiments with highly constrained geometries have achieved dynamo action • Experiments with “open” geometries hopefully will achieve dynamo action soon

6. Dynamo Effects in Laboratory Plasmas

7. The lab plasma dynamo does • Generate current locally • Convert poloidal magnetic flux to toroidal flux (and the inverse) • Increase toroidal magnetic flux • Conserve magnetic helicity • Act through alpha and other effects • Arise from fluctuations superposed on the mean field • Achieve a nonlinearly saturated state with (with self-generated ) The lab plasma dynamo does NOT • Generate magnetic field from a small seed field • Increase magnetic energy (it redistributes magnetic field) †

8. Evidence of field generation • Cowling’s Theorem • Toroidal flux generation • Ohm’s law

9. Cowling’s theorem applied to the RFP A time-independent, cylindrically symmetric plasma cannot contain a reversed magnetic field Bz Proof: assume Bz is reversed. at the radius where Bz = 0 r Thus, magnetic flux decays within reversal surface, in constrast to experiment

10. Toroidal magnetic flux increases(in discrete dynamo events) Toroidal Magnetic Flux (Wb) MST time (ms)

11. in experiment E|| j|| radius additional current drive mechanism (dynamo)

12. Linear and nonlinear dynamos • Kinematic regime • Weak initial field • Lorentz force negligible • Seek “exponentially” growing solutions of the induction equation • Linear eigenvalue problem • Nonlinear regime • Lorentz force dynamically important • Dynamo saturation and stationary MHD state • Self consistent solution of velocity and magnetic field • Nonlinear initial value problem

13. Large and small scale dynamos • Assume that velocity is characterized by typical scale ℓ • Small scale dynamo • Generation on scales  ℓo • Competition between line stretching and enhanced diffusion • Dynamo generatesB2 but not B2 • Large scale dynamo • Generation on scales ℓo • Lack of reflectional symmetry important (helicity) • Inverse cascades (magnetic helicity, energy, etc.) • Mean field theory and transport • Average induction α-effect • Average diffusion β-effect • Average advection γ-effect

14. From kinematic to nonlinear dynamos • Most astrophysical situations: • Dynamos operate in nonlinear regime • Magnetic fields are in equipartition with velocity on integral scales • Rotation is present and important What are the dynamo saturation mechanisms that leads to observed field stregths? ℓ/ℓo Large-scale dynamos 1 kinematic models nonlinear models B2 Small-scale dynamos

15. How do dynamos saturate? • Small-scale dynamos • What happens to lagrangian properties of flow? • What is the structure of resulting MHD turbulence? • Dependence of dynamo fields on Pm • Large-scale dynamos • Saturation of turbulent transport • α-effect (strong-weak) • β-effect (strong-weak) • Role of shear • Role of boundary conditions

16. Proposed research • Basic phenomena: SSD • Study development and properties of stationary MHD turbulence state generated and sustained by dynamo action (Turbulence effort) • Eulerian properties • Lagrangian properties • Study dependence of final state with magnetic Prandtl number. • Requirements: • Existing codes • Manpower

17. Proposed research • Basic phenomena: LSD • Establish existence of inverse cascades in high Rmsystems • Establish conditions for strong satruration of α-effect • Boundary terms (helicity flux) • Time dependence • Relation between DN simulations results and RFP experiments • Conditions for strong satruration of β-effect • Role of shear • Role of magnetic helicity • Requirements: • Some modifications of existing codes • Formulation of sensible “model problems” • Manpower

18. Proposed research • Specific models: • The solar dynamo: Develop a self consistent model capable of reproducing basic observed properties • Cyclic activity • Realistic distribution of angular velocity in the CZ • Thin tachocline • Correct migration pattern of magnetic activity • Requirements: • New code must be developed • Spherical geometry • Incompressible/anelastic • Spatial adaptivity • Major effort in Sub-Grid-Scale modeling • Better understanding of angular momentum transport (angular momentum effort) • Manpower

19. Dynamo Effects Beyond MHD • In the lab strong indications of importance, a rich, relatively unexplored topic • In astrophysics general importance not established, possibly only some “special cases,” depends on scope of “dynamo physics”

20. Dynamo Effects Beyond MHD • Hall dynamo • Diamagnetic dynamo • Kinetic dynamo (current transport)

21. Measurement of MHD dynamo 0 Volts m -10 r/a = 0.9 r/a = 0.9 -20 Volts m 0 -10 r/a = 0.8 r/a = 0.8 -20 time (ms) -0.5 0 0.5 time (ms) MHD dynamo dominant at some radii, not everywhere

22. Hall dynamo: a two-fluid effect MHD dynamo Hall dynamo Two fluid effects also alter the <v x B> dynamo

23. From quasilinear theory for tearing mode dynamo Mirnov de s distance from resonant surface

24. Time Evolution of Current Density Fluctuation Ding et al

25. Hall term is significant at r/a = 0.8 V/m Fiksel, Almagri time (ms)

26. The diamagnetic dynamo parallel component of mean-fields, or, writing yields MHD dynamo diamagnetic dynamo

27. Measurement of diamagnetic dynamo Ji et al TPE-1RM20 RFP Different dynamo mechanisms dominate in different parameter regimes

28. Kinetic Dynamo Radial transport of parallel current (electron momentum) by particle motion along stochastic magnetic field not yet measured

29. Ready for a comprehensive study via • Experiment (MST, some SSPX, possibly MRX) • Analytic theory (quasilinear, early nonlinear stage) • Computation (NIMROD)

30. Measure dynamo mechanisms directly • MHD • Hall • Diamagnetic • Kinetic • Also measure <E> and <j>

31. Measurement Techniques In the hot core passive spectroscopy, active spectroscopy (charge exchange recombination spectroscopy) Laser Faraday rotation Motional Stark effect In the cool edge Insertable probes: magnetic, Langmuir (E), spectroscopic

32. Active Spectroscopy

33. 3-Wave Polarimeter-Interferometer System Faraday rotation/interferometer system MST R0 = 1.50 m a = 0.52 m Ip = 400 kA ne ~ 1019 m-3 B0 ~ 4 kG

34. Spectroscopic probe

35. Plannned measurements MHD Dynamo Edge:upgrade spectroscopy probe (6 months) Core: CHERS - operation in 1 year for V fluctuations physics in 2 years Hall Dynamo Edge: probe measurements in 1 year Core: improve FIR - 1 year MSE - design spec for mag fluctuations - 6 months first operation ~ 1.5 years Study spectral properties (nonlinear coupling)

36. Diamagnetic dynamo edge: probes to reversal surface ~ 1.5 years Core: need new ideas for pe fluctuations (fast Thomson) Kinetic dynamo Need ideas for pe|| fluctuations

37. Two-Fluid Dynamo Theory • Quasilinear theory with p (one year) • Early nonlinear stage (1 - 2 years)

38. Two-Fluid Computation Nimrod: well-suited to experiment, two-fluid operation in ~ 1 year, physics results in 2 - 3 years

39. In ~ 3 years,expect major advance in understanding two-fluid dynamos in the lab

40. Flow-driven dynamo • Drive flow with neutral beam injection or biased probes (in MST, MRX) • Establish NBI feasibility for MST (expt) and MRX (calculation) - 6 months

41. Effects beyond MHD in astrophysics

42. Important physical parameters: ion skin depth ion sound gyroradius MHD reconnection layer width Hall dynamo important if di>> dR or s >> dR satisfied in lab

43. Venues in astrophysics with Hall effects • Extra-galactic radio lobes • flux conversion dynamo in relaxing plasmas • Black hole accretion disks • MRI dynamo, flux conversion • Protostellar disks • Weakly ionized, charged dust • Neutron star, white dwarf crusts • ions immobilized

44. Plans: Computation of disk flux conversion disk arcade spheromak Proceed with Nimrod

45. Plans:more completely assess prospects of non-MHD effects in astrophysical dynamo physicsthen, construct work plan or de-emphasize (~ 4 months)