Current-driven discharges in theCompact Toroidal Hybrid (CTH)
experiment
S. Knowlton, G. Hartwell, J. Hanson, J. Peterson, B. Stevenson
Auburn University, Auburn, Alabama

OUTLINE:•Overview of the CTH experiment•Validation of vacuum configuration; correction of magnetic fielderrors•

Initial studies of behavior associated with plasma current

Joint 17th International Toki Conference (ITC) on Physics of Flows and Turbulence in Plasmas and 16th
International Stellarator/Heliotron Workshop (ISHW) 2007

Research areas of CTH experiment•Current-driven instabilities/ avoidance of disruptions instellarators- NCSX and, to lesser extent, QPS, will rely on bootstrap current to provide
rotational transform for optimization of configuration- Bootstrap current influences high-β stellarator equilibria in present
experiments− previous results from JIPPT-2, W7-A, W7-AS with large fraction of ohmictransform in low shear stellarators•

Determination of experimental magnetic equilibrium in 3-D
plasma- Test V3FIT 3-D equilibrium reconstruction with diagnostic data=> status of V3FIT; poster by Hanson et al., this workshop•Role of magnetic islands in highly variable transform profiles- Minimize resonant field errors at rational surfaces by design and activecorrection

CTH: l / M = 2 / 5 torsatron
5 field periods; circular Inconel
vacuum vessel
Ro = 0.75 m, R/<a> ≥ 4Bo ≤ 0.7 T
Ip ≤ 40 kA; Δι ≤0.5
Pin= 12 kW ECRH @18GHz
B0 => 0.64 T (1st harmonic)
60 kW OH
Vacuum ι(a): 0.05 – 0.6
Discharge duration: 0.5 s
w/ OH: 0.1 s<ne> = 0.2 - 1 x 1019 m-3

Single-channel, radial pathinterferometer

CTH configuration designed for flexibility• Main vertical field coil in series
with l / M = 2/5 HF field winding•

Torsatron HF coil decoupledfrom ohmic flux with externaldecoupler

CTH configuration designed for flexibility• Trim vertical field with ohmic
decoupler
Decoupler overcompensatesohmic flux to provide programmed
vertical field for equilibrium withplasma current

ΔIHF/IHF < 1%

ΔITVF/ITVF ~10%=> ΔR ≤ 1 cm
during OH pulse

CTH configuration designed for flexibility• Main vertical field coil in series
with l / M = 2/5 HF field winding• Trim vertical field with ohmic
decoupler• Toroidal field coils for variationof rotational transformITF = 0.34 IHF
ITF = 0.3 IHF
ITF = 0.2 IHF
ITF = 0.1 IHF
ITF = 0.0 IHF

CTH configuration designed for flexibility
Main vertical field coil in series withl / M = 2/5 HF field winding
Trim vertical field with ohmic
decoupler
Toroidal field coils for variation ofrotational transform

rotational transform

Shaping (quadrupole) coils forshear variation; also has ohmic
decoupler
TF=0, SVF=0

0.4
0.35

TF=0.13, SVF=00.3
0.25

TF=0.26, SVF=00.2

TF=0.13, SVF=-.161

0.15
0.1
00.05

0.1
0.15
average radius (m)

0.2

0.25

TF=.13, SVF=-.322

CTH configuration designed for flexibility
Main vertical field coil in series withl / M = 2/5 HF field winding
Trim vertical field with ohmic
decoupler
Toroidal field coils for variation ofrotational transform
Shaping (quadrupole) coils forshear variation; also with ohmic
decoupler
Ohmic coil stack powered bycapacitor banks

CTH configuration designed for flexibility
Main vertical field coil in series withl / M = 2/5 HF field winding
Trim vertical field with ohmic
decoupler
Toroidal field coils for variation ofrotational transform
Shaping (quadrupole) coils forshear variation; also with ohmic
decoupler
Ohmic coil stack powered bycapacitor banks
15 Error correction coils mounted
on ports
Circular vacuum vessel

Additional PF coils for vertical
positioning if necessary

CTH exhibits good vacuum flux surfaces
Low aspect ratio configuration achieved at rotational transform (ιedge ≤ 0.2)

0.20

MA Experimental

0.15

MA Design0.10

MA Optimized
0.05
Z (m)

1/14
0.00

1/11

-0.05

1/9-0.10

1/7
Optimized-0.15

Design-0.20
0.58

Composite photo of measured flux surfaces

0.63

0.68

0.73
R (m)

0.78

0.83

0.88

Comparison with of original coil model withexperiment.

Field-mapping of magnetic axis applied tocorrection of coil positions
Magnetic Axis Position

0.040

0.3

0.035
0.030

0.1

0.025

0.00.020
Z (m)

Z (m)

0.2

0.45 0.55 0.65 0.75 0.85 0.95 1.05
-0.1
R (m)

Experiment
IFT Design ModelIFT Constructed Model
Post-SVD Model
HF = 300 A

0.015-0.20.010-0.30.005• Magnetic axis location varied withTVF• Field-mapped at 2 toroidal locations• Model coil parameters varied in IFTline-following program• Least-squares fit SVD analysis using
measured axis position and transformTVF = 56 A

TVF = 44 A
TVF = 30 A

0.000
-0.005-0.0100.700 0.725 0.750 0.775 0.800 0.825 0.850 0.875
R (m)Required corrections to coil model are minor
Optimization of HF/VF coils includes BEXT,poloidal coil positions andradii, helical coil winding law
Helical coil winding law
φ= 2/5 θ + α1 cos θ + β1 sin θ + α2 cos 2θ + β2 sin 2θ + ...
rCOIL = r0 + a1 cos θ + b1 sin θ + ...
r0(m)a1(m) b1(m) α1
β1
α2
Design:After analysis:00
0−0.25200.0012 -0.001 0.0005 −0.2522

SOS comparison(Exp vs. Pre-SVD)

0.3
0.2

0.2

0.1

0.1

0.0

0.0

-0.1

-0.1

-0.2

-0.2

-0.3
0.45

0.55

0.65

R (m)
0.75 0.85

0.95

1.05

0 0.0520
0.0 0.0530

SOS comparison(Exp vs. Post-SVD)

0.3

Z (m)

Z (m)

0.385
0.3826β2-0.3
0.45

ExperimentmodelR (m)
0.55

0.65

0.75

0.85

0.95

1.05

Magnetic islands on rational surfaces
With auxiliary TF coils,vacuum rotational transform can be raised to ι(a) ≤ 0.6
ι= 1/3, 2/5, 1/2 rational surfaces exhibit islands at low fields for field mapping.

Island width vs magnetic field6

B ~ 0.06 T

island widthLower Left5

island width Right

Island width (cm)island width Upper Leftaverage experimental

4fit
32
1

Island width "mn #00200400

1 B˜ mnm% $ B( I )600

8001000

1200

HF current (Amps)!

X-point

O-point

n/m = 1/3 static magnetic island

Island size decreases with increasing field• Observed islands at low mapping currents
only partly due to winding errors• Projects to island width ≤ 2 cm at operating
currents of 5 kA (B= 0.5 - 0.7 T)

Island reduced by application of primary & secondary
corrections
true error fieldcorrecting fieldmeasured error field! =m" # n$resultant

Fix Stellarator procedure (Hanson)• Determine phase of island O or X-points
ψ= (mθf - nφf) in flux coordinates.
• Compute correction field of opposite
phase; generate vector of N elements
N = no. of independent correction coils• Complete minimization by applying
additional correction orthogonal to originalvector.

n = 1 correction applied with 5 coils

Ohmic currents induced in ECRH target
plasmas• Ohmic heating pulse
applied to ECRH plasmas
at fundamental resonant
field of B0 = 0.64 T.
• Density increases withohmic current• Discharges with ιtot(a) > 0.7
obtained with iVAC(a) ~ 0.2

Current-driven plasmas show hesitations
during current rise
• Hesitations occur at/near
rational values of edgetransform.

Plasma current for 2 different vacuum transforms- Vacuum rotational transform variedwith auxiliary toroidal field coils.

• Some unstable behavior
observed during main phase ofohmic discharge• Current relaxations with bursty
precursor MHD oscillations often
occur

Data represent plasma current values at hesitations• May be associated with internal n/m =1/3, 1/2 islands, possible nonmonotonic transform profiles- address in future with shaping ofvacuum shear.
• Despite unstable behavior, nocomplete current collapse observed

Ip (kA)

30

ιVAC(a) =0.12

20
10ιVAC(a) =0.22

00.1

0.2

0.3

0.4

net edge transform

0.5

0.6

Current-rise hesitations observed onmagnetic and other diagnostics•8-segment poloidal Rogowski coil showsslight outward shift of current centroid
during hesitation, suggesting narrowing ofcurrent profile when rational surface incontact with edge.
• V3FIT used in predictive mode to model
magnetic diagnostic responses from VMEC
equilibrium; from relative measurements
estimate outward shift of 5 mm duringhesitation• Further calibration work of diagnostics
required for reconstruction•

In contrast to later part of discharge, nobursty MHD activity observed during
current rise hesitations•Decreases in line-averaged density andcore SXR emission during hesitations
For progress on V3FIT reconstruction, see poster
by Hanson et al, Wednesday afternoon

Horizontally-viewing SXR profile during
current rise
• Soft X-ray profiles typicallydecrease during current
hesitations.

ι = 1/3
ι = 1/4

ι = 2/7

CENTRAL CHORD• In early hesitations, decrease
first evident in edge chords• For later hesitations,decrease first evident incentral chord and propagatesto edge in ~ 80 µs

EDGECHORD

Discussion• Expect profiles to evolvefrom positive (stellarator)
shear through doublevalued to negative as
ohmic current profile
peaks on resistive timescale.
4 msec time scaleconsistent with assumed<Te> ~ 100 eV, Zeff ~2• Early behavior (t< 4 ms)
consistent with positiveshear profiles• Hypothesis: island at edge
rational surface causing
narrowing of current
channel, density drop.
Recovery occurs as
rational surface moves
inwardModel transform profiles during current-rise

14.8 kA

Peaked profile+4.5 msflat profiles

7.9 kA

Increasing Ip

0 kA+2.3 msvacuum

Presently testing applying n = 1 perturbation witherror correction coils to determine effect of variable
static island on current-rise behavior

Concluding remarks• Field-mapping results used to adjust model of equilibrium coils- SVD fitting procedure indicates deviations of up to 1.5 mm in helical coil radius, 1mm-scale deviations in other winding law parameters, and external fields of ≤ 2gauss.
- Similar procedures performed on other coil sets

• Low order islands observed in vacuum configuration corrected- Experiments applying static n = 1 perturbation of variable amplitude to plasma
discharges are underway.

• Hesitations in current-rise and density decreases associated withrational values of edge transform.
- Otherwise, current-rise plasmas are stable while transform profile remains
monotonic.
- -will vary vacuum shear in further studies.

Field-mapping set-up on CTH

φ = 36˚

ZnO phosphor-coated wire mesh w/ LED’sat edge for alignment

φ = 252˚

Entire set-up (gun, screen,camera) rotated toroidally by two
field periods to test for n=1 shifts
in equilibrium.
Movable phosphor-coated wand

Unstable behavior following current rise
• Plasma current shows
relaxation-type behavior• Bursty MHD oscillations onpartial Rogowski loops• Soft X-ray emission increases
after relaxation- Runaway generation• Disruptive spikes on loop
voltage• Drop in stored energy following
relaxation