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. Menard 2, C. Zhang 5 Reconstruction of NSTX Equilibria.

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