NSTX S. A. Sabbagh 1, M.G. Bell 2, R.E. Bell 2, L. L. Lao 3, B.P. LeBlanc 2, F.M. Levinton 4, J.E....
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Transcript of NSTX S. A. Sabbagh 1, M.G. Bell 2, R.E. Bell 2, L. L. Lao 3, B.P. LeBlanc 2, F.M. Levinton 4, J.E....
NSTX
S. A. Sabbagh1, M.G. Bell2, R.E. Bell2, L. L. Lao3, B.P. LeBlanc2, F.M. Levinton4, J.E. Menard2 , C. Zhang5
Reconstruction of NSTX Equilibria including MSE data
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
1Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY2Plasma Physics Laboratory, Princeton University, Princeton, NJ3General Atomics, San Diego, CA4Nova Photonics, Inc., Princeton, NJ 5Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, China
17th NSTX Program Advisory Committee MeetingJanuary 20 - 21, 2005
Princeton Plasma Physics Laboratory
NSTX
• Approach “Best” model
• for a given physics model / data set, reliably fit all data within error
• improved physics/data set reduces artificial constraint
“Rapid” reconstruction
• between-shots
• find one constraint set for a given (data,model)
“Levels” of reconstruction
• based on available data
• seamlessly switch levels during shot if needed data
phys
ics
mod
el
basic advancedmagnetics
kineticprofiles
rotationprofile
B pitchangleprofile
Motional Stark Effect data is a natural addition to NSTX EFIT reconstructions
rotating plasma
3-D effects
vessel currents
plasma current
vacuum
NSTX
MSE can be included in all levels of EFIT
• NSTX EFIT “Levels” Level 1: external magnetics data alone Level 2: partial kinetic profile data added Level 3: toroidal rotation added
• Statistics on MSE fits so far: Four channels span typical magnetic axis position; 0.3 degree error MSE data for 58 shots available on data tree All 58 shots reconstructed with NSTX EFIT and written to NSTX
database
• More than 7,500 equilibria available to the group
• More than 11,000 equilibria run in MSE testing so far
fittedparameters
artificialconstraints
4 strong
10 3 weak
20 none
NSTX
• Physics constraints Data points Internal magnetic field pitch angle (MSE) 4 Plasma rotational pressure (CHERS) 51 Flux surfaces are electron temperature isotherms 20
• Te = Te((R)|z=0) directly from Thomson data - rapid analysis required to insure self-consistent solution with toroidal rotation
Plasma kinetic pressure
• Ion pressure (CHERS)
51
• Electron pressure (Thomson)
20
External magnetics / plasma current 119 Plasma diamagnetism 1 Vacuum vessel current (includes “3-D” vessel effects) 25 Shaping coil / TF currents 9
MSE data adds further constraint to present rotating, high ST equilibrium reconstructions
Total (per time point)
300
NSTX
B field pitch angle profile added to reconstruction
Pki
netic
(kP
a)P
dyna
mic (
kPa)
10
20
30
0
2
3
4
5
6
Poloidal flux and pressure
-2
-1
1
2
0
Z(m
)
0.5 2.01.0 1.5R(m)
2.01.5R(m)
0 1.0 2.00.5 1.5R(m)
isotherm constraint
(mWb/rad*10)
-6
-4
-2
2
0
magnetic axis
0.0
114444t=0.257s
1
0 1.00.5
magnetic axis
0
0.96 1.081.00 1.04R(m)
-0.2
0.2
0.0
Pitch angle (rad) vs. R
MSE data
peak pressure
NSTX
Fits with / without MSE confirm high results
• Few % change in stored energy
• Fits without MSE give good q0 values “calibrated” constraint
set (using sawtooth onset, rational surface position from USXR in selected shots)
can now use MSE for “calibration”
• Correlation with crossing q0 = 1 and collapse0.00 0.10 0.20 0.30 0.40
t(s)
050
100150200
01234012340.90
0.951.001.051.100
102030400.00.51.01.52.0
Shot 114465
Ip (MA)
t (%)
Raxis
(m)
q0
qmin
2
MSE data available
solid (red) – with MSEdashed (black) – w/o MSE
Partial kinetic fits114465
MSE data starts
NSTX
Fitted pitch angle evolution follows MSE dataP
itch
an
gle
(ra
d)
Pitc
h a
ngl
e (
rad
)R = 0.975 m R = 1.107 m
R = 1.059 m R = 1.10 m
114465
0.0 0.2 0.4 0.6t(s)
0.6
0.4
0.2
0.0
-0.2
0.80.6
0.4
0.2
0.0
-0.2
0.6
0.4
0.2
0.0
-0.2
0.8
0.6
0.4
0.2
0.0
-0.2
0.8
0.0 0.2 0.4 0.6t(s)
0.0 0.2 0.4 0.6t(s)
0.0 0.2 0.4 0.6t(s)
Fit Fit
FitFit
NSTX
MSE finds q0 ~ 1 in plasmas with sawteeth
• External magnetics-only fit has q0 = 1.1
• Partial kinetic fit does not give q0 ~ 1 at low stored energy MSE required to find
reasonable q0
0.00 0.20 0.40 0.60 0.80t(s)
050
100150200
01234012340
50100150200
02468
0.000.100.200.300.400.50
Shot 113983
Ip (MA)
t (%)
USXR(arb)
q0
qmin
2
solid (red) – with MSEdashed (black) – w/o MSE
113983
MSE data available
Partial kinetic fits
NSTX
MSE fits indicate shear reversal in some equilibria
• Shear reversal not seen in reconstruction for this shot without MSE
• Shear reversal not apparent in li evolution
• Collapse in when q0 = 2, qmin = 1.5
Shot 114140
0.00 0.05 0.10 0.15 0.20 0.25 0.30t(s)
050
100150200
012340.0
0.20.40.60.81.00
51015200.00.20.40.60.81.0
Ip (MA)
t (%)
li
q0
qmin
2
q
MSE data available
114140
2.01.5
NBI (4 MW)
NSTX
CY05 MSE channels will provide additional q constraint
114140t = 0.208 s
span of present MSE data Pitch angle (rad) vs. R
q
0.0 0.5 1.0 1.5R(m)
• Present MSE measurements do not span qmin position in shear reversed equilibrium
0
1
2
3
4
1.00 1.04 1.08
R(m)
MSE data
EFIT reconstruction
0.96-0.6
-0.4
-0.2
0.0
0.2
0.4
planned channels
NSTX
Diagnostic input / code interaction continues to expand
• Add new MSE channels 8 channels start of FY05 run Up to 14 channels by end of FY05 run
• Include computed fast-ion profiles directly from TRANSP Understand possible role of MHD on fast-ion diffusion/loss Include beam pressure anisotropy and flow of fast ions
• Use EFIT to help benchmark other reconstruction codes LRDFIT: time-evolved circuit model of vessel included in fit
• Reconstruction of 20kA PF-only start-up plasmas
ESC: reconstruction version built around fixed-boundary code
• Used on JET for current holes, being developed for CDX-U (LTX)
NSTX
NSTX EFIT with MSE is ready for the 2005 run
• Pre-run testing / analysis Greater basis function flexibility, constraint optimization Radial electric field correction to MSE data (using toroidal flow) Further consistency checks with other diagnostics More tests of rotating equilibria – comparison to static case Physics analysis
• effects of reversed shear• low-order rational surfaces and collapse
• Between-shots EFIT reconstructions with MSE will improve analysis including present control room MHD stability calculations
NSTX
Supporting slides follow
NSTX
Expanded magnetics set reproduces 3-D eddy currents as axisymmetric currents during OH ramp
VALEN(J. Bialek)
plate eddy currents
1
3
24
1
3
2
4
1050
-5-10
8
4
0
-4
I v(k
A)
I v(k
A)
1050
-5-10
1050
-5-10
0.0 t(s)1.0 0.0 1.0t(s)
• Black points: plate current approximated from Vloop sensors
• Solid lines: EFIT reconstructed plate currents using all magnetics data Fitted currents match 3-D eddy
currents as a 2-D analog
NSTX
External magnetics data allow basic reconstruction
• Over 60 attempted variations to find model
• Profile constraints: p’(0) = 0, (ff’)’(1) = 0 constraints reproduce q0 = 1
appearance, rational surface position from USXR
allows finite edge current (to model current transients)
• 4 profile variables (1 p’, 3 ff’; 2nd order polynomial in p’, 3rd order in ff’)
• Goodness of fit 2 ~ 70 over majority of pulse for 108 measurements
0.2t(s)
0.0 0.4 0.6 0.8
Ip (MA)
t (%)
li
2
100
0
0.8
0.4
0.0
210
1.0
0.0
2010
0
1.0
0.0
112783
(PNBI = 7 MW)
t = 20<p> / B02
NSTX
“Partial kinetic” prescription reduces artificial constraint• Over 110 attempted model variations used to find model
• 10 profile variables (5 p’, 5 ff’); allows finite edge current
• External magnetics plus 20 Thomson scattering Pe points to constrain P profile shape
Ptot = Pe + “Pi” + “Pfast”; errors summed in quadrature (large total error)
• Diamagnetic flux to constrain stored energy Greater freedom in ff’ basis function for good fit over full
discharge evolution and for various shots
• Weak constraints on p’(0), ff’(0) yield “reasonable” q(0)
112783 t = 0.445s
0.0 1.0 2.00.5 1.5R(m)
60
40
20
0
Pto
t(kP
a)
0.5 2.01.0 1.5R(m)
0.0
-2
-1
1
2
0
Z(m
)
112783 t = 0.445s
“partial kinetic”assigned error
NSTX
NSTX EFIT* alterations required for low A geometry• Uniform discretization of
elements at low aspect ratio
• Vessel currents required Lower A components have lower
resistance Total vessel currents ~ 0.3 MA;
plasma current ~ 1.0 MA Vessel / plates broken into 30
groups (poloidally) Wall currents determined by local
loop voltage data (9 loops) Vessel element resistances
matched against independent model of vacuum field shots
• Stabilizing plates / divertor plates included (~5 kA) plate currents not well-diagnosed
*S.A. Sabbagh, et al., Nucl. Fus. 41 (2001) 1601.
fluxloops /voltagemonitors
pickupcoils
0.5 2.01.0 1.5 R(m)0.0
-2
-1
1
2
0
Z(m
)
stabilizingplates
initialdiagnostics
NSTX
Expanded magnetics to yield more accurate X-point and plate currents
• Significant upgrade to magnetics set 57 pickup coils vs. 23 25 local loop voltage data vs. 9
for wall current distribution Compensation for stray field
from TF leads
• Stabilizing plates / divertor plates currents now better resolved
newpickupcoils(tangentialand normal)
0.5 2.01.0 1.5 R(m)0.0
-2
-1
1
2
0
Z(m
)
CY 2004diagnostics
NSTX
Pure toroidal flow allows a tractable equilibrium solution
• Solve , , R components of equilibrium equation MHD: v v = JxB – p ; = mass density
• f() = RBt
• R 2Pd(,R)/R = p’(,R)|; Pd (,R)2()R2/2 (Bernoulli eq.)
• * = -0R2p’(,R)|R - 02ff’()/(42) (G.S. analog)
Pure toroidal rotation and T = T() yields simple solution for p
• p(,R) = p0() exp (mfluid 2()(R2 – Rt2)/2T())
• Constraints for fit EFIT reconstructs two new flux functions: Pw(), P0()
• Pw() () Rt22()/2; P0() defined so that:
• p(,R) = P0() exp (Pw()/P0() (R2 – Rt2)/ Rt
2)
Standard input: Pw(), P0() from approximation or transport code New approach:
• Solve for Pw(), P0() in terms of measured P(,R)|z=0, Pd(,R)|z=0