NSTX ACS APS 2004
Resistive Wall Mode Stabilization of High- NSTX Plasmas
Supported by
Columbia UComp-X
General AtomicsINEL
Johns Hopkins ULANLLLNL
LodestarMIT
Nova PhotonicsNYU
ORNLPPPL
PSISNL
UC DavisUC Irvine
UCLAUCSD
U MarylandU New Mexico
U RochesterU Washington
U WisconsinCulham Sci Ctr
Hiroshima UHIST
Kyushu Tokai UNiigata U
Tsukuba UU Tokyo
JAERIIoffe Inst
TRINITIKBSI
KAISTENEA, Frascati
CEA, CadaracheIPP, Jülich
IPP, GarchingU Quebec
46th Annual Meeting of Division of Plasma PhysicsAmerican Physical Society
November 15-19, 2004Savannah, GA
A.C. Sontag1, S. A. Sabbagh1, J.M. Bialek1, D.A. Gates2, A. H. Glasser3, B.P. LeBlanc2, J.E. Menard2, W. Zhu1, M.G. Bell2, R. E. Bell2, A. Bondeson4, J.D. Callen5, M.S. Chu6, C.C. Hegna5, S. M. Kaye2, L. L. Lao6, Y. Liu4, R. Maingi7, D. Mueller2, K.C. Shaing5, D. Stutman8, K. Tritz8
1Department of Applied Physics, Columbia University2Plasma Physics Laboratory, Princeton University3Los Alamos National Laboratory4Institute for Electromagnetic Field Theory, Chalmers U., Goteborg, Sweden5University of Wisconsin - Madison6General Atomics7Oak Ridge National Laboratory8Johns Hopkins University
NSTX ACS APS 2004
Understanding of -Limiting Instabilities Necessary for Sustained High- Operation
• Motivation Recent machine upgrades have extended performance further into
the high- long-pulse regime Several instabilities can limit performance in this regime Resistive wall mode (RWM) can limit high- operations at low
plasma rotation and low-q
• Outline RWM identification at high- and low aspect ratio RWM rotation damping and critical rotation frequency Beta limiting mechanisms in wall stabilized regime Resonant field amplification using initial RWM stabilization coil
NSTX ACS APS 2004
NSTX Facility Equipped to Study RWM Physics at Low Aspect Ratio
NSTX ParametersIp
BT
R0
A
PNBI
1.5 MA 0.6 T0.86 m>1.27
2.67 MW
• New Capabilities: RWM sensors Initial stabilization coils
• Theory Ideal MHD stability – DCON (Glasser) Drift kinetic theory (Bondeson – Chu) RWM growth rate – VALEN (Bialek –
Boozer )
Initial RWM stabilization coilsSensors
Passive plates
NSTX ACS APS 2004
Long-Pulse High- Correlated with High Toroidal Rotation
• NSTX extending performance to higher-IN
t = 39% N = 6.8 achieved lower-q more susceptible
to RWM
Tor
oida
l (
%)
IN Ip/aBT (MA/m-T)
0 2 4 6 80
10
20
30
40
50N = 6
5
4
3
2
Shot 112546
t
N
DCONn = 1
I p (
MA
)
0.4
0.8
PN
BI (M
W)2
46
time (s)0 0.2 0.4 0.6 0.8 1.0 1.2
51015
t (
%)
Ip
PNBI
246
N
Ft (
kHz)
5
15
25 R = 1.3 mW
(ar
b.)
0
-20
-40
• Long-pulse, high-N requires wall stabilization
no-wallideal-wall
NSTX ACS APS 2004
RWM Can Limit at Low-q
• RWM is external kink modified by presence of resistive wall
• RWM Characteristics: slow growth: ~ 1/wall
slow rotation: fRWM ~ 1/wall
strong rotation damping stabilized by rotation & dissipation
• High toroidal rotation passively stabilizes RWM at higher-q
• Other modes can saturate before RWM is destabilized
Shot 114147
0.2
0.4
0.6
0.8
1.0
1.2
0
4
-4
I p (
MA
)
no-wallideal-wall
Ip
N
0
2
4
6
1
3
5
N
0.00 0.05 0.10 0.15 0.20 0.25 0.30time (s)
0.25 0.26 0.27time (s)
Bp
(Gau
ss)
0
2040
60locked n = 1 frominternal sensors
wallstabilized
DCON n = 1
W (
arb.
)
wall ~ 5 ms)
RWM
NSTX ACS APS 2004
Visible Image & Theory Show Mode Structure
• Toroidal asymmetry observed on visible camera images during RWM
• DCON computed B structure EFIT reconstruction of experimental
equilibrium includes sum of n=1-3 components scaled to measured amplitudes and
phases
Before RWM activity
RWM with Bp = 92 G Theoretical B (x10) with n=1-3 (DCON)
(interior view)(exterior view)
114147t = 0.268s
114147t = 0.250s
NSTX ACS APS 2004
Internal Sensor Array Used for RWM Detection• Internal toroidal arrays of Bz and Br
sensors installed 5 kHz digitization rate instrumented to detect n = 1 - 3
• Measured coil currents used for background subtraction ~2 Gauss noise level achieved allows real time mode detection
• SVD mode detection is robust
CL
Br
Shot 114150
BzI p
(M
A)
0.40.81.2
10
20
10
20
10
20
B (
Gau
ss)
lower Bpupper Bp
external Br
0.25 0.26 0.27 0.28 0.29 0.30time (s)
2
4
6
NIp
N
n=1
n=2
n=3
Passive Stabilizing Plate•See poster JP1.005 (S.A. Sabbagh - Wed. Afternoon)
NSTX ACS APS 2004
SXR Measurement Shows RWM Toroidal Asymmetry
• Experiment / theory show RWM not edge localized Supported by
measured Te
Bay G array (0 deg)Bay J array (90 deg)
114024, t=0.273sN = 5
0.27 0.28 0.29
8
4
0
time (s)
Inte
nsity
(ar
b)
0.0 0.5 1.0 1.5 2.0R(m)
2
1
0
-1
-2
Z(m
)
USXR separated by 90 degrees toroidally
6
2
2
1
00.0 0.2 0.4 0.6 0.8 1.0
DCON n = 1 modedecomposition
n
(arb
)
m=34
56
m=2
m=1
Te During RWM
1139240.26s - 0.277s
T
e (k
eV)
0.0 0.4 0.8 1.2
R (m)
0.0
0.1
0.2
0.3
RWM growth
n = 0.4
NSTX ACS APS 2004
RWM Rotation Damping Differs from Other Modes
• RWM damping is global 1/1 mode not present
• Edge rotation does not go to zero consistent with neoclassical
toroidal viscosity (NTV)
• 1/1 causes core damping leads to ‘rigid rotor’ plasma
core
• momentum transfer across rational surface at R = 1.3 m
RWM Core 1/1
€
Torque NTV ~ δB2Ti0.5
Ft (
kHz)
Radius (cm)90 100 110 120 130 140
10
0
20
30
40
Ft (
kHz)
10
0
20
30
40
150
50
Radius (cm)90 100 110 120 130 140 150
Time (s)0.2250.2350.255
Time (s)0.4150.4250.4350.445
NSTX ACS APS 2004
Neoclassical Toroidal Viscosity Theory Matches Measured Damping Profile
• Damping due to NTV only
• B magnitude and profile from measured Te
• No low frequency islands during this period
• Damping due to NTV and JB torques
• B magnitude and profile from measured SXR emission
core 1/1 modeRWM
*See talk CO3.008 by W. Zhu for more detail- Monday Afternoon, Room 204/205 SCC
113924
Td
(N m
-2)
0.40.30.20.10.0
-0.1-0.2
t = 0.276s
TNTV
theory3.0
2.0
1.0
0.0
1.61.41.21.00.8
TNTV+JxB
theory
measuredTd
(N m
-2)
R (m)
-R2(d/dt)
-R2(d/dt)measured
0.8 1.0 1.2 1.4 1.6R (m)
NSTX ACS APS 2004
Experiment Supports 1/q2 Scaling of Critical Rotation Frequency
• Scaling from two stability classes: stabilized no RWM for t >>
wall when N > N no-wall
not stabilized collapse after a few wall when N > N no-wall
• Bondeson-Chu drift-kinetic model* agrees with observed scaling trapped particle effects weaken
stabilizing ion Landau damping toroidal inertia enhancement
becomes more important Alfven continuum damping
gives:
€
crit ≡ωt
ωA
=14q2 q
t(q
)/
A
0.0
0.1
0.2
0.3
0.4
0.5
1 2 3 4 5
*Phys. Plasmas 3 (1996) 3013
not stabilized1/4q2stabilized
t/A(q,t) profiles
NSTX ACS APS 2004
High- Discharges Below crit(q) Can Suffer Collapse
• RWM growth when: rotation below crit inside q = 2
when N exceeds no-wall limit example - shot 114147:
• exceeds no-wall limit at ~ 0.2s
• RWM collapse at ~0.265 s
• Edge and low-order rational surfaces not stabilized
• Observed in all RWM shots
t(q
)/
A
0.0
0.1
0.2
0.3
1 2 3 4q
0.40.81.2
I p (
MA
)
Shot 114147
246
N
204060
Bp
(G)
0.20 0.22 0.24 0.26 0.28time (s)
0.21 s0.22 s0.23 s0.24 s0.25 s
n = 1
Ip
N
NSTX ACS APS 2004
Global Mode Limits at Highest N
• Collapse observed at highest N on many shots
• Mode involves both core and edge Coincident D spike and neutron collapse
• Rotation collapse is global but brief not associated with rotating MHD
Shot 112794
0.0 0.2 0.4 0.6 0.8time (s)
D
neu
tro
ns/1
012
0
2
4
6
200
400600
24
6
NF
t (kH
z)
5
15
25 R = 1.3mFt (
kHz)
neutronsD
0
10
20
30
40
50
1.0 1.2 1.4 1.6R (m)
Time (s)0.4850.4950.5050.515
NSTX ACS APS 2004
Growth Rate During Collapse Approaches Ideal
• early phase growth ~ 5 ms from RWM sensors
• later growth ~ 670 s from Mirnovs
• VALEN growth = 530 s
B (
Gauss
) Odd-n0.2-40 kHz
2468
Bp
(Gau
ss)
LowerArrayn = 1
0.45 0.46 0.47 0.48
-505
• Consistent with external to internal kink transition DCON shows kink becomes more
internal wall stabilization less effective
• VALEN shows mode growth rate approaching ideal
N
4
6
8Shot 112785
0.30 0.35 0.40 0.45 0.50time (s)
W
0-10
(s
-1)
-20
50010001500
ideal-wallno-wall
NSTX ACS APS 2004
Collapse Restores Stability, Triggers Rotating Mode
• collapse removes unstable drive
• Rotation profile moves toward stability N > N no-wall before and after
collapse
• Relatively low amplitude Bp < 10 Gauss Bp > 30 Gauss during typical
RWM
• n = 1 triggered by collapse pure n = 2, n = 3 modes
triggered in similar discharges
n = 1 2 3
F (
kHz)
20
40
60
80
time (s)0.35 0.450.30 0.500
0.40
Magnetic PickupMode Spectrum
NSTX ACS APS 2004
Resonant Field Amplification by Stable RWM Observed
• Single RWM coil pair available for CY 04 run 180 degree separation
• Resonant field amplification (RFA) when N > N no-wall
amplification of external perturbations by stable RWM
predicted by theory*
Shot 113955
0.20 0.24 0.28 0.32time (s)
0.2
0.6
1.0
2
4
6
N
I p (
MA
)
Ip
N
W (
arb.
)
0
4
-4
-8
5
10
15B
p (G
auss
)
ideal-wallno-wall
coil on
DCONn = 1
n = 1plasma
response
*Boozer, A.H., Phys. Rev. Lett., 86 5059 (2001)
NSTX ACS APS 2004
RWM Coil Used to Study RFA Characteristics
• RFA amplitude increases with N
similar to DIII-D
• RFA decay after coil pulse gives negative mode growth rate ~3 ms decay time observed ~ wall
• Full coil set will enable more detailed study of RWM rotating error field odd and even n harmonics
0.24 0.26 0.28 0.30
4 5 6
0.1
0.2
0.3
0.4
0.5
0.6
1
2
3
4
5
6
4.5 5.50.0
0
time (s)
N
RF
AB
p (G
auss
)
no-walllimit
decayperiod
Active Coil On
n = 1
NSTX ACS APS 2004
Understanding Key RWM Physics Important for Sustained High- Operation in NSTX
• Control system improvements allow access to high-IN & high- regime t = 39%, N = 6.8 early H-mode gives routine access to long-pulse
• n = 1 - 3 RWM measured
• Rotation damping consistent with neoclassical toroidal viscosity model
• Rotation data indicate crit ~ A/q2
• Global mode with growth rate >> 1/wall observed to limit highest N plasmas
• Initial resonant field amplification results consistent with DIII-D observations
• Preparation for RFA suppression and active feedback stabilization of RWM is underway