0 2 4 6 8 10 12 14 16-2

0

2

4x 10

-4

B

(T)

0 2 4 6 8 10 12 14 16-2

0

2

4x 10

-4

B

(T)

V3FIT Itor

= 0

Exp. t = 10. ms

0 2 4 6 8 10 12 14 16-2

0

2

4

6

x 10-4

B

(T)

0 2 4 6 8 10 12 14 16-5

0

5x 10

-4

Br (

T)

Poloidal Station #

V3FIT Itor

= 0

V3FIT Itor

= IBOOTSJ

Exp. t = 10. msExp. t = 50. ms

0 2 4 6 8 10 12 14 16-5

0

5

10x 10

-4

B

(T)

0 2 4 6 8 10 12 14 16-5

0

5x 10

-4

Br (

T)

Poloidal Station #

V3FIT Itor

= 0

V3FIT Itor

= IBOOTSJ

Exp. t = 10. msExp. t = 50. ms

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

500

1000

P (

Pa)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-50

0

50

100

(kA

/ m

2 )

JBS

. B

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.95

1

1.05

1.1

s = 2

iota

with bootstrap current (vacuum)

• The toroidal current is consistent with numerical estimates of bootstrap current• The measured magnetic diagnostic signals match predictions of V3FIT

• Comparisons with and without toroidal bootstrap current show agreement• Helical nature of Pfirsch-Schlüter current in HSX has been confirmed

• Future modeling and measurement• Temporal evolution of toroidal current will be studied – Poloidal flux diffusion• Effects of toroidal current on rotational transform will be studied• Configuration Flexibility: HSX can alter the magnetic spectrum with a set of auxiliary coils• Mirror: The helical symmetry is spoiled by introducing (n,m) = (4,0) component (and harmonics) into the magnetic spectrum, affecting the equilibrium and bootstrap currents• Well/Hill: Rotational transform profile may be raised/lowered, adjusting the location of the = 1 resonant surface

0 20 40 60 800

100

200

300

400

500

600

time (ms)

I tor

(Am

ps)

EC

H tu

rnoff

0

50

100

150

200

250

S.E

. (J

oule

s); n

e (10

11 c

m-3

)

0

50

100

150

200

250

0 10 20 30 40 50 60 700

100

200

300

400

500

600

700

800

rise

= 39.4125 ms I = 708.1735 A

t0 = 4.7003 ms

I tor

(Am

pere

s)

EC

H turn

off

T.S

. Laser

time (msec)

Itor

Measured

Central ne (line average)

Stored Energy

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

500

1000

1500

2000

2500

3000

T e (e

V)

0 100 200 300 400 500 6000

200

400

600

800

1000

Boostrap Current -- BOOTSJ (A)

I tor

Itor

@ t = ECH Off

Extrapolated ISS

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110

-3

10-2

10-1

100

101

102

* e

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1

2

3

4

5

6

7

8

9

10

n e (1

012cm

-3)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110

-2

10-1

100

101

Magnetic

Diff

usiv

ity (m2 /s

)

• The Helically Symmetric eXperiment has• Quasi-Helically Symmetric axis: (n,m)=(4,1)• No toroidal curvature

• The Pfirsch-Schlüter current • Rotates with toroidal angle• Is reduced by a factor of compared to a conventional stellarator

• The bootstrap current• Is in opposite direction than that of a tokamak• Reduces the rotational transform in HSX

• VMEC• Calculates free-boundary MHD Equilibrium • Inputs are measured Te & ne profiles and

assumed Ti & ni (Zeff ≈ 1)• BOOTSJ

• Calculates bootstrap current profile from VMEC results. Results may be input back into VMEC as toroidal current profile.

• V3FIT• Computes response function for diagnostic coils• Expected magnetic signals are computed from response functions and VMEC output

• BOOTSJ calculates the bootstrap current; Assumes LMFP regime• BOOTSJ provides an upper limit to the bootstrap current• The toroidal current rises throughout the majority of the shot

• Steady state reached only in coldest plasmas• Decaying exponential growth is observed in many cases:

projections are based this model

Measurement of the Pfirsch-Schlüter and Bootstrap Currents in HSX

HSX Magnetics and HSX Magnetics and Computational ModelingComputational Modeling

J.C. Schmitt, J.N. Talmadge, P.H. Probert, S.F. Knowlton*, D.T. AndersonHSX Plasma Laboratory, Univ. of Wisconsin – Madison, WI USA *Physics Department, Auburn Univ. – Auburn, AL USA

Summary + Future DirectionsSummary + Future Directions

Pfirsch-Schlüter CurrentPfirsch-Schlüter CurrentOperating Parameters Operating Parameters & Diagnostics& Diagnostics

Bootstrap CurrentBootstrap Current

Numerical Model and Measurement

• B0 = 1 Tesla• 50 kW ECR Heating (1st Harmonic)

• 10-chord Thomson Scattering• Te(ρ) and ne(ρ) profiles

• Rogowski coil – External • Toroidal current• Low-frequency response

• dB/dt triplet array – External• MHD and bootstrap currents• Low-frequency response• Poloidal and toroidal measurements

• The Pfirsch-Schlüter current exhibits dipole behavior and rotates with the |B| contours

Temporal Evolution of Currents in HSXTemporal Evolution of Currents in HSX

• Majority of HSX plasmas are in long mean free path (LMFP) regime• Magnetic diffusivity varies across the confinement volume

16

Poloidal Station #16

2

1

1

2

BOOTSJ: 478 A

• Diagnostic signals and toroidal current evolution• t = 10. ms: MHD equilibrium established, bootstrap current still small• t = 50. ms: ECH turn-off, bootstrap current has grown to 450 A

• The diagnostic signals agree well with the V3FIT numerical results• Toroidal current is still evolving – Radial profile information is not yet known

VMEC equilibrium, JBS=JBOOTSJ

effTe2/1* Rqvh

hee

0

||

• The bootstrap current is the upper limit for the measurements to date• Projected steady state values exceed bootstrap current estimate

• Decaying exponential growth is not appropriate for most cases – may overestimate steady state value

1/2 FP

1/6 FP

Poloidal Rotation of Null Point in Bθ

50 kW ECRH heated plasma

Profiles obtained during resonance heating location scan

TorteItI /1

3

11 mN

• Special thanks to Steve Knowlton and the V3FIT team

HSX Vacuum Vessel and Diagnostic Coils

Off-axis ECRH

Near-axis ECRH

JPS

1/2 FP

1/2 FP 1/6 FP

1/6 FP

49th Annual Meeting of the Division of Plasma Physics, November 12-16, 2007, Orlando, Florida

Offset in measured Bθ due to toroidal bootstrap current