nstx the resistive wall mode and beta limits in nstx s. a. sabbagh 1, j. bialek 1, r. e. bell 2, a....
TRANSCRIPT
NSTX
The Resistive Wall Mode and Beta Limits in NSTX
S. A. Sabbagh1, J. Bialek1, R. E. Bell2, A. H. Glasser3, B. LeBlanc2, J.E. Menard2, F. Paoletti1, M. Bell2, T. Biewer2, R. Fitzpatrick4, E. Fredrickson2,
A. M. Garofalo1, D.A. Gates2, S. M. Kaye2, L. L. Lao5, R. Maingi6, D. Mueller2, G. A. Navratil1, M. Ono2, Y.-K. M. Peng6, D. Stutman7, W. Zhu1,
and the NSTX Research Team
1Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, USA
2Plasma Physics Laboratory, Princeton University, Princeton, NJ, USA3Los Alamos National Laboratory, Los Alamos, NM, USA4University of Texas at Austin, Austin, TX, USA5General Atomics, San Diego, CA, USA6Oak Ridge National Laboratory, Oak Ridge, TN, USA7Johns Hopkins University, Baltimore, MD, USA
44th Annual Meeting of the APS Division of Plasma Physics
Orlando, Florida - November 11th, 2002
NSTX
NSTX is operating at sufficiently high beta to study passive wall stabilization
• Operation in wall-stabilized, high beta regime
• Resistive wall mode (RWM) and rotation damping
• Physical mechanisms for higher N and longer pulse
NSTX
NSTX is equipped to study passive stabilization
Machine
Aspect ratio ≥ 1.27
Elongation ≤ 2.5Triangularity ≤ 0.8Plasma Current ≤ 1.5 MAToroidal Field ≤ 0.6 TNBI ≤ 7 MW
Stabilizing plates
Analysis
EFIT – equilibrium reconstruction
DCON – ideal MHD stability
(control room analysis)VALEN – RWM growth rate
NSTX
0
1
2
3
4
5
6
7
8
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6li
N
Plasma operation now in wall-stabilized space
EFIT0
1
2
3
4
5
6
7
8
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6li
N
2001 Data
N = 6 i
Wall stabilized
Nomin
al “n
o-wal
l lim
it”
2002 Data
EFIT
4 l i
6 l i
8 l i
10 l i
• Normalized beta, N = 6.5, with N/li = 9.5; N up to 35% over N no-wall
• Toroidal beta has reached 35% (t = 20<p> / B02 )
Design target
NSTX
Maximum N strongly depends on pressure peaking
0
1
2
3
4
5
6
7
8
1 2 3 4 5Fp
N
• Fp = p(0) / <p>
• P profile from EFIT using Pe, diamagnetic loop, magnetics
• Time-dependent calculations required to evaluate stability limits and mode structure
NSTX
Operational improvements yield higher, sustained N
• n=1 error field reduced by an order of magnitude in 2002
• H-mode pressure profile broadening raises N limit
• qmin > 1 maintained (EFIT qmin without MSE)
2001 (High error field) 2002 (Reduced error field)
t(s)
RWM
H-mode
qmin
Fp
N
Br
n=1(G)
0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3 0.4 0.50
10
123
345
246
2
n = 1 no-wall unstable(DCON)
n = 1 unstable(with-wall) (no-wall)
n = 1 unstable106165
107636Locked modedetector
3.5 wall (VALEN)
NSTX
Rotation damping rate larger when N > N no-wall
• Rotation damping rate is ~ 6 times larger when N > N no-wall
ToroidalRotationF(kHz)
N
Br
n=1(G)
0
2.0
2
4
6
1.0
t(s)0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3 0.4 0.5
2468
10
108197 107994
Locked modedetector
F (q = 2)F (R = 1.35m)
n = 1 no-wallunstable
RWM No RWM
n = 1,2 rotating modes
F (q = 2)F (R = 1.35m)
3.5 wall
(VALEN)
n = 1 rotating mode
NSTX
Two stages of rotation damping during RWM
• Initial stage: Global, non-resonant rotation damping
• Final stage: Local rotation damping at resonant surfaces appears as rotation slows
• Analogous to rotation dynamics in induced error field experiments E. Lazzaro, et al., Physics of Plasmas 9 (2002) 3906. (JET)
NSTX
-5
0
5
10
15
20
25
0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
-20
-15
-10
-5
0
5
0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5R(m)
-20
-15
-10
-5
0
5
0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
Rotation damping during RWM is rapid and global
• Field ripple damping by neoclassical toroidal viscosity ~ Br2Ti0.5
candidate for observed damping profile during RWM
R (m)
F
(kH
z)F
(k
Hz)
0.43 s
1079940.27 s0.29 s
0.31 s
0.33 s
0.35 s0.37 s
0.39 s
n = 1, 2 rotating modesF
(k
Hz)
F
(kH
z)
108197
0.29 s
0.31 s
0.33 s
0.31 s
0.33 s
RWM
R (m)
0.41 s
0.45 s
0.43 s
0.27 s0.29 s
0.31 s
0.33 s
0.35 s0.37 s
0.39 s0.41 s
0.45 s
0
5
10
15
20
25
30
0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
NSTX
Core rotation damping decreases with increasing q
• Largest rotation damping (dF/dt = -600 kHz/s) at Bt < 0.4T, qmin < 2 Factor of 8 times larger than damping from n=2 island alone
• When qmin ~ 2 damping rate is reduced and F is maintained longer
• Consistent with theory linking rotation damping to low order rational surfaces
0
5
10
15
20
25
30
35
0 0.1 0.2 0.3 0.4 0.5 0.6t (s)
rota
tion
freq
uenc
y (k
Hz)
108195 Bt=0.34T108197 Bt=0.39T108189 Bt=0.44T108420 Bt=0.44T
qmin
1.41.71.92.1
1.4 1.7 1.92.1qmin
EFIT qmin without MSE
Ip = 0.8 MA
NSTX
Plasma stabilized above no-wall N limit for 18 wall
0
1
2
3
4
5
6
7
8
0.0 0.2 0.4 0.6 0.8
N
108420
Ip = 0.8 MA
-15
-10
-5
0
5
0.0 0.2 0.4 0.6 0.8t (s)
W(arb)
DCON
n = 1 with-wall
n = 1 no-wall
VALEN mode growth time = 15 ms
VALEN mode growth time = 0.03 – 0.05 ms
• Plasma approaches with-wall N limit VALEN growth rate
becoming Alfvénic
• F(0) increases as N >> N no-wall
• Passive stabilizer loses effectiveness at maximum N
Neutrons collapse with N - suggests internal mode
• TRANSP indicates higher Fp
Computed N limits conservative
30 kHz
F(0)
5MW NBI
N > no-wall limit
qmin > 2
NSTX
Research on passive stabilization and high N rotation damping physics has begun
• Passive stabilization above ideal no-wall N limit by up to 35% Improvement in plasmas with highest N up to 6.5; N/li = 9.5
• The N limit increases with decreasing pressure profile peaking
• Rotation damping at N > N no-wall has two stages Global, non-resonant damping Local, resonant field damping during final stage
• Rotation damping rate substantially decreases as q increases
• Passive stabilization becomes less effective at highest N
• Active feedback design shows sustained N/N wall = 94% possible See Bialek, et al., GP1.107 Tuesday
For more RWM detail, see NSTX poster session (Tuesday)
NSTX
Other presentations on NSTX beta limits, RWM, and mode stabilization
• High toroidal beta plasmas Gates, et al., BI1.001 Monday
• High poloidal beta plasmas Menard, et al., CO1.002 Monday
• Resistive wall modes Zhu, et al., GP1.106 Tuesday
(Sabbagh for) Paoletti, et al., GP1.105 Tuesday
• RWM active feedback design Bialek, et al., GP1.107 Tuesday
PresentationSubject
NSTX
Active stabilization might sustain 94% of with-wall limit
• System with ex-vessel control coils can reach 72% of N wall
• System with control coils among passive plates can only reach 50% of N wall
VALEN model of NSTX(cutaway view)
7.57.06.56.05.55.010- 1
100
101
102
103
104
105
figure B3 active feedback in NSTXData from "NSTX.04.2002"
beta normal
grow
thrate
(1/s
)G
row
th r
ate
(s-1)
N
5.510-1
5.0 6.0 6.5 7.0 7.5
100
101
102
103
104
105
Passive
With-wall limit(N wall)
0.1 1.0
figure B1''10/09/02 16:27:06 EST artemis executable: xvps6
VALEN model figure B1''
X
Y
Z Modeled active feedback coils
In-vessel control coils
Activegain (V/G)
Bialek, et al., GP1.107 Tuesday
NSTX
Te perturbation measured during RWM
• No low frequency (< 80 kHz) rotating modes observed during measured Te
• Te displacement precedes n=2 rotating mode
t = 0.293 s
t = 0.310 s
0.2 0.4 0.6 0.8 1.0 1.2 1.40.0
0.5
1.0
1.5
Te
(keV
)
R (m)
109030
Thomson scattering (LeBlanc)0.26 0.30 0.34
Fre
quen
cy (
kHz)
20
0
40
60
80
100
t(s)
1 2 3 4mode number
t = 0.293 s t = 0.31 s
N246
0.0 0.1 0.2 0.3 0.4
2
1
0
t(s)
Br
n=1(G)
Locked modedetector
N > no wall limit
NSTX
N limit now insensitive to plasma proximity to wall
• At high N ~ 5, external modes are well-coupled to passive stabilizing plates, independent of gap Confirmed by ideal
MHD stability calculations
• Higher error field (2001 data) may have also lowered limit for smaller outer gap
See W. Zhu, et al., GP1.106 Tuesday
2002 data (H-mode)2001 data (L-mode)0.0
1.0
2.0
3.0
4.0
5.0
6.0
0.0 2.5 5.0 7.5 10.0plasma outer gap (cm)
N a
t fa
st c
olla
pse
NSTX
Rotation damping strongest where mode amplitude largest
• Field ripple damping by neoclassical parallel viscosity ~ Br2Ti0.5
possible candidate for observed damping profile
q=2 q=3 ........
0.28
0.20
0.12
0.04
0.00
Aco
sine
0.0 0.5 1.0r/a
m=1
m=3
m=2
0.08
0.16
0.24
Naxis edge
Mode decompositionToroidal rotation evolution
106165
axis edge
t = 0.15 s
t = 0.17 s
t = 0.19 s
(a
rb)
t = 0.192 s
R (cm)100 120 140 160
F
(kH
z)
25
20
15
10
5
0
NSTX
Mode intensifies in divertor region at highest N
N = 5.1
VALEN / DCON computed n = 1 external mode currents
N = 7.1
• Increased p drive more significant in producing higher growth rate