Experimental Measurements of Non-MHD Dynamo Effects

Summarized byS.C. Prager

many contributors:

J. Anderson W. Ding

D. Brower G. FikselD. Craig H. JiD. Den Hartog J. Sarff

plus most of MST group

<E>|| + dynamo = <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

Three 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

The “kinetic dynamo”radial transport of parallel current along stochastic magnetic field

for electrons, the flux of parallel momentum

or

€

Γr =r Γ || • ˆ r = Γ||

r B

B• ˆ r =

˜ Γ || ˜ B rB

€

Γr =˜ p ||e ˜ B r

B

Experimental Observations

To my knowledge,

Only in RFP(some MHD dynamo measurements in SPHEX spheromak)

Dynamo Measurements

• MHD: some detailed measurements

• Hall: some detailed measurements

• Diamagnetic: one measurement

• Kinetic: no measurements

All measurements are ongoing;

Diagnostics being expanded

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||

neo J||(Zeff = 2)

€

E ≠ η j

E||

j||

radius

additional current drive mechanism (dynamo)

Dynamo occurs in bursts

ToroidalMagneticFlux(Wb)

MST

time (ms)

MHD Dynamo

(exists, but not the whole story)

Early measurement, passive Doppler spectroscopy

(1995)

MHD dynamo in edge

€

˜ E ̃ B By Langmuir and magnetic probes

€

˜ v × ˜ B By spectroscopic and magnetic probes

Consistent with MHD dynamo

1995

Spectroscopic Probe

Fiksel,

Den Hartog

yields local flow velocity

time (ms)

r/a = 0.9

€

⟨ ˜ v × ˜ B ⟩

€

⟨ 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

Hall Dynamo

• Edge: magnetic probes

• Core: laser Faraday rotation

Fluctuation Power Spectra

B

j

Frequency (kHz)

probes at edge

Shen et al 1993

Correlation between j and B

Frequency (kHz)

phase

coherence

Result

at r/a ~ 0.9, Hall term accounts for less than 25% of the total current

-25

-20

-15

-10

-5

0

5

-1 -0.5 0 0.5 1 1.5 2

Hall dynamo (V/m)

Time from crash (ms)

Hall term is significant at r/a = 0.8 Fiksel, Almagri

ongoing

time (ms)

V/m

€

⟨ ˜ j × ˜ B ⟩ne

Core measurements of Hall Dynamo

E vector of injected laser rotates by angle

€

~ nBdl∫

Wave phase-shifted by angle

€

~ ndl∫

Can infer

€

˜ B , ˜ j

W. Ding, D. Brower, B. Deng UCLA 2003

3-Wave Polarimeter-Interferometer System

MST R0 = 1.50 ma = 0.52 mIp = 400 kAne ~ 1019 m-3

B0 ~ 4 kG

Faraday rotation/interferometer system

Faraday rotation angle: detects mean B, fluctuating B, sawteeth

6

4

2

0

-2

-4

x=-17 cm

-9

-2

6

13

21

m=1 activity

1.0

0.5

0.026.025.525.024.524.0

[ ] Time ms

external magnetic coil

Current fluctuations increase during dynamo event

120

100

80

60

40

20

-2 -1 0 1 2

Time [ms]

(1,6) mode current fluctutaion

€

˜ j T(kA/m2)

Hall dynamo large near resonant surface

Diamagnetic dynamo: significant at some conditions

Kinetic dynamo

•No direct measurement

•In ZT-40, fast electrons detected in edge may imply transport from core

Summary

• Evidence for importance of MHD and Hall dynamos

• Some indications that diamagnetic dynamo may be important

• Would not be surprised if kinetic dynamo was important. Evidence for stochastic transport of particles, energy - why not electron momentum?

• Goal: understand what mechanisms are important, under what conditions

• Possibly dynamo always relaxes plasma toward preferred MHD state - specific mechanisms vary with conditions

• Experimental dynamo program is active, with new diagnostics.