Flow generation driven by magnetic perturbations in a toroidal plasmaIntrinsic Flow from

Magnetic-Fluctuation-Driven Kinetic Stress in a Magnetically-Confined Toroal Plasma

Weixing Ding (丁卫星）

in collaboration with

D. Brower, L. Lin, W.F. Bergerson, A. Almagri, B. Chapman, G. Fiksel, D.J. Den Hartog, J.S. Sarff and the MST Group

Department of Physics & Astronomy, University of California Los Angeles Department of Physics, University of Wisconsin, Madison

Sixth US-PRC Workshop, San Diego, CA

MST Reversed-Field Pinch (RFP) is toroidal configuration with relatively weak toroidal magnetic field BT ( i.e., BT ~ Bp)

Madison Symmetric Torus - MST

For plasma w/o current profile control

R0 = 1.5 m, a = 0.51 m, Ip ~400 kA

ne ~ 1019 m-3 ,Te~Ti~400eV€

β≥6%

Intrinsic Flow: self-generated during plasma discharge in the core

604020

0

3025201510Time [ms]

(d) Flow [km/s]

400

200

0

Edge mode [G] (c)

20

10

0

Core mode [G] (b)

400200

0806040200

time [ms]

(a)

b: (m,n)=(1,6)

Ohmic discharge

b: (m,n)=(0,1)

Ip

Parallel Flow Spatial Profile on MST

-40

-20

0

20

40

V//

[km/s]

1.00.80.60.40.20.0r/a

Parallel Flow Profile

€

V// =

r V •

r B

B

parallel flow reverses direction at r/a~0.5r/a~0.6

(Flow profile is obtained by Rutherford scattering, mode velocity and edge probe )

Magnetic fluctuations play important role in RFP Plasmas

0.30

0.20

0.10

0.00

-0.10

-0.20

q

0.50.40.30.20.10.0

ρ ( )m

t=-0.25 ms

1/6 1/7 1/8

1/9

(0,1)

€

q =r

R

BT

BP

Te ~ Ti ~ 400 eV

dominant, core resonant modes m=1, n=6,7,8,9,…

m/n

r (m)

Tearing modes and broadband magnetic turbulence- island overlap leads to stochastic field

80

60

40

20

0

P(f) [Gs

2

/kHz]

806040200f [kHz]

standard 400ka ppcd 400ka

magnetic turbulence

Tearing Modes

noise

€

br∫ dl

Multiple Fluctuation-Induced Effects on Flow

Parallel momentum components

Reynolds stress

Maxwell Stress

Momentum Change

Kinetic stress

€

ρ∂∂t

< V// >=<δJ × δB >// −ρ < δr

V • ∇δr

V >// −∇ •< δp//δbr >

B0

r e r + μ∇2 r

V

damping

Without External Momentum Sources, fluctuation-induced torques play most important role in flow generation and flow damping.

Kinetic stress （动力胁强）

Momentum flux in radial direction due to particles free streaming along fluctuating magnetic field lines:

€

p// = p0 // +δp//

r b =

r B

B=

r b 0 +δ

r b

€

r b =

r B

B

€

p// = T//δn + noδT//

€

Π=T//< δnδbr >

B+ n

< δT//δbr >

B= Πn + ΠT

€

Π=<p//r b •

r e r >

€

Π=<p//δbr >

B

Multi-measurements enable us to determine the kinetic stress

Laser (differential) interferometer ( )

€

T//i Rutherford Scattering (bulk deuterium ions), CHERS (impurity)

Thomson scattering€

br(r) Laser Faraday rotation

€

n δn

€

∇ne

Motional Stark effect

€

B0

€

ρ∂∂t

< V// > ⇔ −∇ • Πnv e r = −∇ • T//

< δnδbr >

B0

⎡

⎣ ⎢

⎤

⎦ ⎥v e r

€

T//e

Investigate balance between kinetic stress and inertial term - simple momentum balance

FIR Laser Polarimeter-Interferometer System

MST

11 chords, x ~ 8 cm, phase ~ 0.05 deg. degree, time response ~ 1 s

€

φ ~ ndl∫ + δndl∫

Ψ ~ nr B • d

r l + nδ

r b • d

r l + δn

r B • d

r l ∫∫∫

Interferometer density fluctuations

Faraday rotation magnetic field

fluctuations

Ding, Brower, et al., PRL(2003),(2004),(2009), RSI(2004),(2008)

32+8 magnetic coils toroidal-poloidal array (m,n)+

2-D Space-Time Image of Fluctuationsusing combined interferometry and Faraday polarimetry

€

φ∝ n dl∫

€

ψ ∝ nr B o • d

r l ∫ + no δ

r b • d

r l ∫

2R

€

−∇• Πn =

−∇ • T//i< δnδbr >

B0

⎡

⎣ ⎢

⎤

⎦ ⎥

(1.6) mode density and magnetic fluctuation spatial profile

2.5

2.0

1.5

1.0

0.5

0.01.00.50.0

[ / ]r a

60

40

20

0

40

20

0

-20

1.00.50.0[ / ]r a

brbp

1.0x10-1

0.5

0.00.40.0-0.4

[m]

Exp fit

1.0

0.5

0.00.40.20.0-0.2-0.4

[ ]m

Exp fit

Faraday fluctuations Inversion: parameterized fitting

Density fluctuations

€

ψ

Kinetic Stress Profile (away from sawtooth crash)

kinetic stress has same sign, spatial distribution as flow profile, independent of flow.

€

−∇• Πn =

−∇ • T//i< δnδbr >

B0

⎡

⎣ ⎢

⎤

⎦ ⎥

(m,n)=1,6-15€

ρV// /Δt ≈ −0.20 N/m3

r/a=0.2

Measurements of Intrinsic Flow and Kinetic Stress during Enhanced Confinement (PPCD)

Intrinsic flow and Kinetic stress track changes in fluctuation amplitudes

Intrinsic Flow

Kinetic stress

-0.2-0.10.00.10.2

1.00.80.60.40.20.0r/a

(c)

40302010

025201510

(a)

8

6

4

2

025201510

[ms]

2.0

1.5

1.0

0.5

0.0

(b)

Flow correlates with density and magnetic fluctuations

t=15-20 ms

€

−∇• Πn = −∇ • T//i< δnδbr >

B0

⎡

⎣ ⎢

⎤

⎦ ⎥

During PPCD, RFP has tokamak-like confinement

PPCD

€

τm ≈ 20 ms

€

n

Advanced Faraday Rotation System on C-Mod

By Irby, Peng. Bergenson, Brower,Ding et al

Resistive Ballooning

Tearing

Time [s]

€

˜ ψ

Faraday Rotation Fluctuations are measured on C-Mod, providing new opportunity to study flow in Tokamaks

Time (sec)

Radial Magnetic Fluctuations on EAST and HL-2A

Both EAST and HL-2A in China have developed Faraday rotation measurements with radial access, which allows direct measurement of radial magnetic fluctuations.

€

ψ = nr B 0 • d

r r ∫ + no δbrdr∫

To investigate the role of fast particle modes on plasma rotation.

Summary

• Kinetic stress, the correlated product between density fluctuations and magnetic fluctuations, acts to drive plasma flow

• Kinetic stress is consistent with observed flow generation - spatial distribution, direction and amplitude of force

• In PPCD plasmas with good (tokamak-like) confinement,

(1) core flow is reduced and momentum confinement increases when density and magnetic fluctuations are suppressed

(2) flow dynamics likely governed by additional effects (es turbulence) in addition to magnetic fluctuation driven kinetic stress .