MHD Dynamos in the Lab

and

Dynamos Beyond MHD

The lab plasma dynamo does• Generate current locally • 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 steady state

(with full backreaction)

The lab plasma dynamo does NOT• Generate magnetic field from a small seed field• Increase magnetic energy (it redistributes

magnetic field)

in experiment

-0.5

0.5

1.0

1.5

2.0

V/m

0.0

0.0 0.2 0.4 0.6 0.8 1.0ρ/a

E||

ηneo J||(Zeff = 2)

€

E ≠ η j

E||

ηj||

radius

additional current drive mechanism (dynamo)

Measure quantities during discrete dynamo event

ToroidalMagneticFlux(Wb)

MST

time (ms)

The MHD Dynamo

The nonlinear dynamo

€

⟨E⟩

€

⟨ j⟩

⟨B⟩

€

⟨ ˜ v ⟩,⟨ ˜ B ⟩energysource

instability

dynamo

€

E + ˜ v × ˜ B = η jMHD

dynamo

analytical quasilinear theory, nonlinear MHD computation

tasks

• Measurements of dynamo

• Active flow drive

• Connections to more general

problem

MHD Dynamo: Status of Past Measurements

• edge measurements with probes, core with passive Doppler spectroscopy

• Important in edge and core, but not full story

time (ms)

r/a = 0.9

€

⟨ ˜ v × ˜ B ⟩

€

η⟨ j⟩− ⟨E⟩

MHD dynamo dominant at some radii, not everywhere

r/a = 0.8

Measurement of MHD dynamo

0

-10

-20

0

-20

-10

Volts m

Volts m

-0.5 0 0.5time (ms)

r/a = 0.9

r/a = 0.8

MHD Dynamo Measurements(~ 3 year project)

• Measure spatial profile of <v x B> in MST

good progress in CHERS for v - now debuting

laser Faraday rotation improving (B)motional Stark effect in several years (B)probes for edge

• Measure dynamo and helicity changes in MRX

probes

SXR imaging of dynamo instabilities

information on 3D structure of magnetic field,

collaboration with RFX team (P. Franz, P. Martin, L. Mirelli)

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

spatial resolution being improved

Active Flow Drive

• Present experiments:

• Flow drive experiments

€

j ⇒ ˜ v ⇒ B

€

v ⇒ B

Exploratory: flow drive via neutral beam injection,

inject ~ 25 keV beam of neutral atoms,

transfers momentum to plasma

Test experimental feasibility in MST

Beam installed;

momentum transfer tested in few months

If good absorption, then model with MHD computation, implement in MST and MRX

from Novosibirsk

Investigate why alpha effect (<v x B>) large in lab, small in geometrically simpler computation

Specifics of flow pattern?

dynamo effects beyond MHD

Effects from Two-Fluid Theory

parallel mean-field component,

Linear part,

Using in top eqn,

€

E + v × B −j × B

ne−∇pe

ne= ηj

€

E||+ ˜ v × ˜ B

||+

˜ j × ˜ B ||

ne= η j

||

€

˜ v −˜ j

ne≈

˜ E × B

B2 −

∇˜ p e × B

B2

€

E||+

˜ E ⊥˜ B ⊥

B2 +

(∇⊥˜ p e ) ˜ B ⊥

B2 = η j

||

MHD Hall

Pressureless MHD

diamagnetic

<E>|| + dynamo = η<j>||

Dynamo theory statusMHD QL, NL comp

€

˜ v × ˜ B

€

˜ j × ˜ B

€

˜ B ⊥∇˜ p ⊥

€

˜ B r ˜ p ||

Hall QL

Diamagnetic very little

Kinetic RR, constraints fromLandau resonances

Status of non-MHD effects

• Diamagnetic dynamo observed in edge probe measurements under some conditions

• Hall dynamo observed in MST recently

Hall dynamo measured by laser Faraday rotation

€

~ nB ⋅dl∫

(Ding, Brower, Deng)

11-chordFIR laser

rotation angle

Experimental Goal

Determine locations and conditions at which different dynamo mechanisms dominate

Experimental Plans

• Measure diamagnetic dynamo (probes in MST and MRX, explore Thomson scattering for pe)

• Measure ve x B (= v x B + j x B/ne)(explore laser Fizeau effect for ve,)

• Measure Hall dynamo with improved spatial resoluton

(Faraday rotation, MSE, probes)

Hall Dynamo Theory and Computation

• Expand quaslinear calculation to finite pressure

• Develop early nonlinear theory (Rutherford theory)

• Develop two-fluid computation for lab plasma (Nimrod)

Related work:

Two-fluid computation in a box shows Hall dynamo important under some conditions(Minnini, Gomez, Mahajan)

Ongoing

Assessment of astrophysical relevance of various dynamo effects