Macroscopic Stability Research on NSTX – Macroscopic Stability Research on NSTX – Results and Theory InteractionResults and Theory InteractionS.A. Sabbagh1, S.P. Gerhardt2, R.E. Bell2, J.W. Berkery1, R.
Betti3, J.M. Bialek1, J. Breslau2, R. Buttery4, L. Delgado-Aparicio5, D.A. Gates2, B. Hu3, R. LaHaye4, J-K. Park2, J.E.
Menard2, H. Reimerdes1, K.C. Shaing5, K. Tritz6, and the NSTX Research Team
1Department of Applied Physics, Columbia University, New York, NY2Plasma Physics Laboratory, Princeton University, Princeton, NJ
3University of Rochester, Rochester, NY4General Atomics, San Diego, CA
5University of Wisconsin, Madison, WI 6Johns Hopkins University, Baltimore, MD
PPPL MHD Science Focus Group MeetingJanuary 6th, 2010
PPPL
College W&MColorado Sch MinesColumbia UComp-XGeneral AtomicsINELJohns Hopkins ULANLLLNLLodestarMITNova PhotonicsNew York UOld Dominion UORNLPPPLPSIPrinceton UPurdue USandia NLThink Tank, Inc.UC DavisUC IrvineUCLAUCSDU ColoradoU MarylandU RochesterU WashingtonU Wisconsin
Culham Sci CtrU St. Andrews
York UChubu UFukui U
Hiroshima UHyogo UKyoto U
Kyushu UKyushu Tokai U
NIFSNiigata UU Tokyo
JAEAHebrew UIoffe Inst
RRC Kurchatov InstTRINITI
KBSIKAIST
POSTECHASIPP
ENEA, FrascatiCEA, Cadarache
IPP, JülichIPP, Garching
ASCR, Czech RepU Quebec
NSTXNSTX Supported by
v1.0
NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 2January 6th, 2010
NSTX Macrostability Research is Addressing Topics Needed to Maintain Long-Pulse, High Performance ST
Motivation / Goals (e.g. from recent ReNeW process) Maintenance of high N with sufficient physics understanding allows
confident extrapolation to ST applications (Hybrid, CTF, DEMO) Sustain target N of ST applications with margin to reduce risk
Physics studied in NSTX to best ensure steady-state ST operation Locked mode behavior at low to moderate N < N
no-wall
Ability of plasma rotational stabilization to maintain high N
Possibility of multiple RWMs that can affect active control Physics of 3D fields to control plasma rotation profile (for greater
stability, confinement) NTM onset and marginal island width for stabilization Multiple scalable control systems to maintain <N>pulse
Successful connections being made to theory – continue/expand interaction…
NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 3January 6th, 2010
NSTX Macrostability Research – Topics Covered in Talk
Error fields (n = 1 and n = 3)
Resistive wall modes
Non-resonant magnetic braking physics
NTM threshold physics
Improving <N>pulse with n = 1 and N feedback
NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 4January 6th, 2010
n = 1 error field threshold for mode locking decreased as βN increased n = 1 rotating modes sometimes observed, study limited to static modes IPEC resonant field joins linear ne correlation from low-β to increased-β
Ideal plasma amplification of applied resonant field restores linear correlation of mode locking threshold with density
Lower-β locked later
(w/ larger RWM currents)
XP903:
J.-K. Park
Ide
al
Pla
sm
a A
mp
lifi
ca
tio
n
Higher-β locked earlier
(w/ smaller RWM currents)
vacuum
IPEC
NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 5January 6th, 2010
Optimal n=3 Error Field Correction Determined vs. IP, BT
2009
2009
2009
“optimal” n = 3 error field correction attained by maximizing angular momentum, scanning Ip, Bt, elongation
n = 3 error field consistent with known equilibrium field coil distortion scales with equilibrium field coil current field phase and amplitude of correction is consistent with that expected from
coil distortion n = 3 error field correction routinely used to maximize plasma
performance in conjunction with n = 1 RWM feedback control NTV theoretical analysis performed by J-K Park for these cases
XP902: S. Gerhardt
NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 6January 6th, 2010
NSTX Macrostability Research – Topics Covered in Talk
Error fields (n = 1 and n = 3)
Resistive wall modes
Non-resonant magnetic braking physics
NTM threshold physics
Improving <N>pulse with n = 1 and N feedback
NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 7January 6th, 2010
ˆˆ2
3ˆˆ2
5**
deiil
iW
EeffbD
ETN
K
Resistive wall modes can terminate NSTX plasmas at intermediate plasma rotation levels without active control (no simple, scalar crit)
Kinetic modification to ideal MHD growth rate
Trapped and circulating ions, trapped electrons
Alfven dissipation at rational surfaces Stability depends on
Integrated profile: resonances in WK (e.g. ion precession drift)
Particle collisionalityTrapped ion component of WK (plasma integral)
Energy integral
Kb
Kw WW
WW
collisionality
profile (enters through ExB frequency)
Hu and Betti, Phys. Rev. Lett 93 (2004) 105002.
precession drift bounce
Modification of Ideal Stability by Kinetic theory (MISK code) investigated to explain experimental RWM stabilization
NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 8January 6th, 2010
0.00 0.01 0.02 0.03 0.04Re(WK)
0.00
0.01
0.02
0.03
Im(
WK)
φ/φexpφ/φexpφ/φexpφ/φexpφ/φexpφ/φexpφ/φexpφ/φexpφ/φexpφ/φexpw
0.0
-0.2
-0.4
-0.60.20.40.60.81.01.2
80
60
40
20
0
[kH
z]
1.00.80.60.40.20.0
/a
/exp
= 0.2
exp
/exp
= 2.0
Kinetic modifications show decrease in RWM stability at relatively high V
Marginally stable experimental plasma reconstruction, rotation profile
exp
Variation of away from marginal profile increases stability
Unstable region at low Role of energetic particles now
under investigation (Berkery, et al.)
Theoretical variation of
Marginally stable
experimentalprofile
121083
RWM stability vs. V (contours of w)
/a
/exp
2.0
1.0
0.2
/
2 (
kHz)
Im(
WK)
Re(WK)
/exp
w
experiment
2.0
1.0
0.2
unstable
/exp
J.W. Berkery
NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 9January 6th, 2010 9
Channel of “Weak Rotation” for RWM passive stabilization observed in MISK calculations for NSTX; altered by plasma collisionality
Stabilization from precession drift resonance at low rotation and bounce resonance at high rotation
Stability dependence on collisionality key for ST fusion burn devices
w contours vs. ν and NSTX 121083
unstable
Marginal stability
experiment
J.W. Berkery (APS DPP 2009 invited talk; PRL accepted)
NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 10January 6th, 2010
High N shots exhibit low frequency mode activity in magnetic and kinetic diagnostics
0
20
40
nano
amps
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amps
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amps
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nano
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0.4 0.6 0.8 1.0 1.2seconds
0
400
800
nano
amps
133775Shots:
133775
0.80.4 0.6 1.0 1.2t(s)
Multi-energy SXR data shows ~ 30 Hz mode activity
02
03
04
05
06
08
10
14
edge
core
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4
8
-
0
200
ampe
res
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km/s
ec
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1.5
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a
0.0010
0.0030
0.0050
Tesl
a
0 0.2 0.4 0.6 0.8 1.0 1.2seconds
-40
0
40
nano
amps
133775Shots:
N
2
4
8
133775
0.80.4 0.6 1.0 1.2t(s)
0.20.0
IRWM-6 (kA)
0.2
0
048 /ch-18
(kHz)
Bpun=1(G)
BNn=1(G)
Ip = 0.8 MA
ME
-SX
Rlo
w-2
3050
10
0.5
1.5
Soft X-ray measurements show low frequency mode activity is global
Mode activity in RWM frequency range coincident in magnetics, SXR
n = 1 RWM feedback on
0
40
040
0100
0
200
0200
0200
0
400
0400
(arb
)
XP935: S.A. Sabbagh
When unstable, growing n = 1 RWM appears to be independent of ~30 Hz activity
NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 11January 6th, 2010
RWM multimode response theoretically expected to be significant at high N based on ideal MHD theory
Boozer multimode criterion for n = 1 met at high N
|W| smallest for 2nd n = 1 eigenfunction Ratio of |W| for 3rd vs. 1st least stable mode sometimes also > 1
N
(PoP 10 (2003) 1458.)
012345678
0.0 0.2 0.4 0.6 0.8 1.0 1.2
-20-10
01020
0.0 0.2 0.4 0.6 0.8 1.0 1.2
133775
mode 3
mode 1
mode 2
t(s)
W(arb)
no-wall stability DCON
0.2 0.80.4 0.60.0 1.0 1.2
-20
-10
0
10
0
2
4
6
0.0 0.2 0.4 0.6 0.8 1.0 1.2
|W|ratio
0
2
4
mode 1/mode 3
mode 1/mode 2
n = 1multimode
period
t = 0.655s
mode 1
mode 2
2.01.00.0 R(m)
1.0
-1.0
Z(m
)
2.0
0.0
-2.0
DCON BN
mode 3
(deg) 1800
BN(a
rb)
mode 1
mode 2
mode 3
133775
XP935: S.A. Sabbagh
NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 12January 6th, 2010
Multi-mode VALEN code (RWM control) testing successfully on high N NSTX plasmas
mmVALEN to be used to examine response of 2nd mode to n = 1 feedback, error field and compare to experiment
RWM growth time vs. betaN 133775 - mmVALEN
0.000
0.005
0.010
0.015
0.020
0.025
5.0 5.5 6.0 6.5 7.0
NM
od
e g
row
th t
ime
(s)
N
Growth rate vs. # of modes – mmVALEN
133775
t = 0.655s
116 DCON modes
76 DCON modes
Typical growth
times (experiment)
J. Bialek
NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 13January 6th, 2010
NSTX Macrostability Research – Topics Covered in Talk
Error fields (n = 1 and n = 3)
Resistive wall modes
Non-resonant magnetic braking physics
NTM threshold physics
Improving <N>pulse with n = 1 and N feedback
NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 14January 6th, 2010
100 110 120 130 140 150r (cm)
-20
0
20
40
60
80
nq
E [kH
z], i/
[kH
z],1
/2
ti [
kH
z]
0123456
0
200
400
600
800
05
10152025
0
5
10
15
20
0.5 0.55 0.60 0.65 0.70 0.75 0.80 0.85sec
02468
10
Stronger braking with constant n = 3 applied field as E reduced – accessing superbanana plateau NTV regime
XP933: S.A. Sabbagh
133367
t = 0.815 s
i = 1
nqE
i/(kH
z)
Torque not 1/(non-resonant) NTV in “1/ regime” (|nqE| < i/ and *i < 1) Stronger braking expected when E ~ 0 (superbanana plateau) (K.C. Shaing et al., PPFC 51
(2009)) – theoretical analysis continues (Sabbagh)
E ~ 0
/
2 (
kHz)
20
15
10
5
0
1.0 1.1 1.2 1.3 1.4 1.5R(m)
t(s)
0.795
0.805
0.815
N
4
Ic (kA)
2
/ch-5 (kHz)
/ch-12 (kHz)
/ch-18 (kHz)
core
mid
outer
6
0
0.4
0.020
100
20
10
0
8
400.5 0.6 0.7 0.8
Faster braking with Constant N, applied n = 3 field No mode activity
t (s) 40
0
Broad, near zero
WITHOUT rational surface locking
n = 3 braking
80
NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 15January 6th, 2010
NSTX Macrostability Research – Topics Covered in Talk
Error fields (n = 1 and n = 3)
Resistive wall modes
Non-resonant magnetic braking physics
NTM threshold physics
Improving <N>pulse with n = 1 and N feedback
NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 16January 6th, 2010
Consistent pre-2009 DIII–D/NSTX results on m/n = 2/1 NTM marginal island width for stability; good restabilization data sets in 2009
Wmarg/0.5i ratio ~ 2 in tokamaks
AUG, DIII-D, JET data for 3/2 mode
First results show Wmarg/0.5i also ~ 2 for NSTX (2/1 mode) (!)
NSTX XP914: R. LaHaye
Pre-2009 2009 data
Status: DIII-D Used gas puff to stay in H-mode 5 good 2/1 (and 2 good 3/1) cases
Status: NSTX Achieved a reproducible onset condition
using modest Li evaporation 8 good cases (2009)
NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 17January 6th, 2010
Required (missing) bootstrap drive for NTM onset better correlated with rotation shear than rotation magnitude
Rotation variation via n = 1 or 3 applied field
Operational space fully spanned up to locked mode limits
No measureable trend vs. rotation
Weak positive correlation with normalized rotation shear
Lowest/highest thresholds at low/high rotation shear
2d fit vs rotation & rotation shear offers little improvement
Consistent with prior results (S.P. Gerhardt, et al., 2008)
0L
qj
BS
,Sau
ter/B
0
Lqj
BS
,Sau
ter/B
(dF/dr) ALS
F2/1 Hz
XP915: R. Buttery
NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 18January 6th, 2010
NSTX Macrostability Research – Topics Covered in Talk
Error fields (n = 1 and n = 3)
Resistive wall modes
Non-resonant magnetic braking physics
NTM threshold physics
Improving <N>pulse with n = 1 and N feedback
NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 19January 6th, 2010
Successful N feedback at varied plasma rotation levels
Prelude to control Reduced by
n = 3 braking does not defeat FB control
Increased PNBI needed at lower
Steady N established over long pulse independent of
over a large range
0
2
4
6
-
0
2.0
4.0
6.0
MW
-600
-200
200
600
ampe
res
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12
km/s
ec
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20
km/s
ec
0 0.2 0.4 0.6 0.8 1.0 1.2Seconds
-10
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10
Gau
ss
135468135513
Shots:
135468135513
0.80.4 0.6 1.0 1.2t(s)
0.20.0
N
24
6
I RW
M-6 (
kA) 0.6
0
246
-0.6
PN
BI (
MW
)
/ c
h-1
8
(kH
z)
/ c
h-5
(kH
z)
48
10
20
10
n = 3 error correctingphasing
n = 3 brakingphasing
n = 1 feedback
XP934: S.A. SabbaghS.A. Sabbagh, S. Gerhardt, D. Mastrovito, D. Gates
0
NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 20January 6th, 2010
NSTX Macrostability Research – Interaction with Theory
Error fields (n = 1 and n = 3) IPEC used successful to support experiment; continue IPEC development,
including interface of ideal plasma response to other analyses (Park, Boozer) Resistive wall modes
MISK development continues (CU, U. Rochester, PPPL), present focus on energetic particle description, comparison to experiment (Berkery, et al.)
Multi-mode RWM analysis with new mmVALEN code (Bialek, Boozer), comparison to experiment (Sabbagh)
Non-resonant magnetic braking physics Continued development of MHD models (CU, PPPL, UW), working from Shaing
model (Sabbagh), Park/Boozer model (Park), etc. (e.g. Cole, et al.) Work aimed for comparison to particle codes (GTC-Neo (Wang), FORTEC-3D
(Satake)) should continue NTM threshold physics
Mostly empirical, or simple MRE assumptions to date, largest gap in theory support here (linear – computation of ’ (PEST 3), non-linear codes ?)
Improving <N>pulse with n = 1 and N feedback, general RMPs Multi-faceted, including beta, rotation control (Gerhardt, Koleman), RWM
control optimization (Hopkins, et al.), ideal, RWM, NTM, ELM stability theory
NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 21January 6th, 2010
Backup Slides
NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 22January 6th, 2010
NSTX Macrostability Research in 2009 is Addressing Topics Furthering Steady Operation of High Performance Plasmas
Ideal plasma amplification of applied n = 1 resonant field (IPEC) joins linear density scaling of mode locking threshold from low to moderate-β
Optimal n=3 error field correction determined vs. IP, BT
RWM instability, observed at intermediate plasma rotation, correlates with kinetic stability theory; role of energetic particles under study
Low frequency ~ O(1/wall) mode activity at high N being investigated as potential driven RWM
Theory shows multi-mode RWM response may be important at high N; multi-mode VALEN code now passing initial tests
Strong non-resonant braking observed NTV braking observed from all i/nqE(R) variations made; apparent transitions in NTV at low
Expanded NTM onset experiments continue to find best correlation between NTM onset drive and flow shear
Successful NBI power limitation via new N feedback control system; initial success in regulation of N at varied plasma rotation levels
NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 23January 6th, 2010
0
0.4
0.8
ampe
res
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ampe
res
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8
km/se
c
0
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30
km/se
c
2
6
Tesl
a
0.0010
0.0030
0.0050
Tesl
a
0 0.2 0.4 0.6 0.8Seconds
0.0002
0.0006
0.0010
Tesl
a
133467Shots:
When unstable, observed growing n = 1 RWM appears to be independent of the driven, ~30 Hz activity
Unstable RWM is locked; driven mode co-rotating at low frequency Unstable RWM grows (magnetics); low frequency mode appears steady in SXR
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0.6 0.65 0.70 0.75 0.80 0.85seconds
200
600
1000na
noam
ps
133467Shots:
02
03
04
06
08
10
14
high-f mode
core133467
edge
N4
0.40.8
IRWM-6 (kA)
0.2
2
10
84
/ch-18 (kHz)
Bpun=1(G)
BNn=1(G)
3050
10
200
IP (MA)
/ch-5 (kHz)
6
2
-0.2-0.6
6
2
6
100
BRun=1(G)
133467
0.20.0 0.4t(s)
0.8t(s)
0.6 0.650.6 0.7 0.80.75 0.85
N46
2BN
n=1(G)26
ME
-SX
Rlo
w
unstable RWMn = 3 braking
unstable RWM
NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 24January 6th, 2010
Multi-mode VALEN code (RWM control) testing successfully on ITER Scenario 4 cases (reversed shear)
At highest N, n =1 and 2 are unstable
N
Number of modes (VALEN)
Gro
wth
rat
e (1
/s)
Growth time vs. betaN - ITER Scen 4
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
2 2.5 3 3.5 4
Mo
de
gro
wth
tim
e (s
)
single-mode
matched to N
wall
multi-mode
VALEN
(converged)
DCON W shows several modes with high response Three n = 1 modes at high N
Two n = 2 modes at high N
n = 1
J. Bialek
NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 25January 6th, 2010
Illustration of Bn() on plasma surface from mmVALEN for ITER Scenario 4, N = 3.92
n = 1 eigenfunctions shown
multi mode response (incl. wall), total Bn
Bn from wall, plasma
Bn from wall alone
toroidal
toroidal
po
loid
alpo
loid
al
outboard
inboard
inboardoutboard
inboard
inboard
J. Bialek
NSTXNSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.) 26January 6th, 2010
Illustration of Bn() on plasma surface from mmVALEN for NSTX shot 133775 (t=0.655s)
single mode response, total Bn
multi mode response, total Bn
Bn from wall, multi mode response
Bn from wall, multi mode response
toroidal
toroidal
toroidal
po
loid
al
po
loid
alp
olo
idal
J. Bialek
outboard
inboard
inboard
outboard
inboard
inboard
outboard
inboard
inboard
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