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

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

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: m. Rotation period 10 8 years Magnetic fields: 3 Gauss (horizontal cmpnt) Turbulence driven by supernovae explosions Classical - dynamo

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

Evidence for dynamo effects in astrophysics Geodynamo Example of system where dynamo must operate Turbulence driven by (compositional?) convection. Strong rotation Moderate R m 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

Dynamo Effects in Laboratory Plasmas

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)

Evidence of field generation Cowlings Theorem Toroidal flux generation Ohms law

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

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

in experiment E || j || radius additional current drive mechanism (dynamo)

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

Large and small scale dynamos Assume that velocity is characterized by typical scale Small scale dynamo Generation on scales o Competition between line stretching and enhanced diffusion Dynamo generates B 2 but not B 2 Large scale dynamo Generation on scales o 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

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? /o/o 1 B 2 kinematic models nonlinear models Large-scale dynamos Small-scale dynamos

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 P m Large-scale dynamos Saturation of turbulent transport α-effect (strong-weak) β-effect (strong-weak) Role of shear Role of boundary conditions

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

Proposed research Basic phenomena: LSD Establish existence of inverse cascades in high Rm systems 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

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

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

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

time (ms) r/a = 0.9 MHD dynamo dominant at some radii, not everywhere r/a = 0.8 Measurement of MHD dynamo Volts m Volts m time (ms) r/a = 0.9 r/a = 0.8

Hall dynamo: a two-fluid effect MHD dynamo Hall dynamo Two fluid effects also alter the dynamo

From quasilinear theory for tearing mode dynamo distance from resonant surface dede s Mirnov

Time Evolution of Current Density Fluctuation Ding et al

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

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

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

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

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

Measure dynamo mechanisms directly MHD Hall Diamagnetic Kinetic Also measure and

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

Active Spectroscopy

3-Wave Polarimeter-Interferometer System MST R 0 = 1.50 m a = 0.52 m I p = 400 kA n e ~ m -3 B 0 ~ 4 kG Faraday rotation/interferometer system

Spectroscopic probe

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)

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

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

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

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

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

Effects beyond MHD in astrophysics

Important physical parameters: ion skin depth ion sound gyroradius MHD reconnection layer width Hall dynamo important if d i >> d R or s >> d R satisfied in lab

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

Plans: Computation of disk flux conversion disk arcadespheromak Proceed with Nimrod

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