Development and Application of Real-Time Magnetic Coordinate

Mapping System in LHD

C. Suzuki, K. Ida, Y. Suzuki, M. Yoshida, M. Emoto and M. YokoyamaNational Institute for Fusion Science

322-6 Oroshi-cho, Toki 509-5292, Japan

S12.4

Contents

Introduction Background / objectives

Equilibrium database VMEC calculations / inverse mapping User tools to access "Line-of-sight" database

Equilibrium mapping Real-time mapping to "Thomson" data Automation / viewer program

Current status Possible applications

Introduction

Background

Experimental profile data (e.g., Te /ne profile) are originally expressed in real coordinates.

It is important to map real coordinates into magnetic coordinates by specifying a proper equilibrium.

For this inverse problem, it is necessary to construct a database composed of numerous 3D equilibria in wide ranges of plasma parameters (pressure, plasma current).

Real coordinates Magnetic coordinatesequilibrium mapping

Objectives

Construction of equilibrium database Automatic generation of a new large-scale database in 7 dimensional

parameter space (Rax, Bq, gamma, p0, pf, ip, ipf) Coverage of special cases (e.g., strongly peaked pressure profiles)

Development of user-friendly tools Routines to retrieve mapping results (reff, B, etc.) by specifying the 7

parameters and real coordinates

Automatic real-time mapping Real-time mapping for all the time slices of "Thomson" data Automatic generation and registration of mapping data table for any

position-dependent diagnostics (e.g., CXS, MSE)

Equilibrium database

Database in 7 (=3+4) dimensional parameter space

7865 (=11x5x13x11) equilibria have been calculatedfor each vacuum configuration (combination of Rax, Bq, gamma).

3 parameters to specify vacuum magnetic configuration

4 parameters to specify plasma condition

Calculation sometimes does not converge specifically for extremely high beta or peculiar current profile.

description range standard value

Rax magnetic axis position 3.50 – 4.00 [m] 3.60

Bq quadruple field -50 – 200 [%] 100

gamma pitch parameter 1.129 – 1.262 1.254

description range mesh points

p0 peak beta 0 – 10 [%] 11

pf pressure peaking factor 1.41 – 5.00 5

ip toroidal current -150 – 150 [kA/T] 13

ipf current peaking factor -12.60 – 4.00 11

Equilibrium calculation and inverse mapping

Free-boundary LHD equilibria by the latest VMEC code* in the 7-dimensional parameter space

Magnetic flux through LCFS (phiedge) same as that in vacuum configuration (No specific definition of LCFS for finite beta)

Fourier coefficients automatically extrapolated up to s = 2.0

Relational database composed of equilibrium parameters including R00(0), R00(1), etc.

*S. P. Hirshman and J. C. Whitson: Phys. Fluids 26 (1983) 3553.

Original flux surface

Extrapolated (imaginary)flux surface

(R, Z, Φ)

Inverse mapping

(reff, θ, φ)

Library for database access

Library routine for the server access via PV-WAVE, C and Fortran The server program retrieve equilibrium parameters from relational database,

and run inverse mapping to retrieve output parameters for given (R, Z, Phi). Any intermediate or excess input values are allowed, and output parameters

are automatically interpolated or extrapolated.

Library (written by C)PV-WAVE

C

VMEC output filesInverse mapping solver（ written by Fortran ）

Fortran

Client domainServer domain

Relational database

Server program

Rax, Bq, gammap0, pf, ip, ipf

R, Z, Phi

reff, theta, br, bz, bphi,iota, di/ds, p, du/dv, phi

Input parameters

Output parameters

R00(0), R00(1), etc.path of VMEC output files

Line-of-sight database for real-time processing

Inverse mapping solver is not fast enough for real-time processing.

"Line-of-sight" database : pre-calculated mapping results along several lines of sights (Thomson, CXS, FIR, etc.)

Retrieve output parameters by designating name of line-of-sight

Output parameters are automatically interpolated.

start point end point

Diag. R (m) Z (m) Phi (deg.) R (m) Z (m) Phi

(deg.)# of

Points

YAG 2.300 0.000 234.0 5.300 0.000 234.0 301

CXS(ary1) 2.300 0.000 199.3 5.300 0.000 199.3 301

MSE(NB3A) 4.326 0.000 134.76 4.541 0.000 201.07 512

FIR(3669) 3.669 1.200 72.0 3.669 -1.200 72.0 121

FIR interferometerlines of sights

Equilibrium mapping

Initial

Thomson scattering mapping program (TSMAP)

Choice of an equilibrium minimizing the discrepancy between inboard and outboard sides of the electron temperature profile*

In search of best-fitted equilibrium ... Peaking factors (pf, ipf): proper initial values Plasma current (ip) : Rogowski coil data

Retrieving line-of-sight database, Search for p0 minimizing the discrepancy for each time slice

p0=0.00, pf=2.14, ip=8.0, ipf=2.00, a99= 0.629, avmec=0.637, chi=280.

Best Fit

p0=4.00, pf=2.45, ip= 8.0, ipf=2.00, a99=0.612, avmec=0.625, chi=4.188

*K. Narihara, I. Yamada, H. Hayashi, and K. Yamauchi: Rev. Sci. Instrum. 72 (2001) 1122.

inboard

outboard

Real-time mapping and automation

Real-time processing to follow the sequence (3 min. shot interval) using 2 servers and 6 virtual machines

Automatic registration of "TSMAP" results for our Kaiseki Data Server System* Mapping Results (R ↔ reff)

Additional equilibrium parameters : e.g., Wpe, R00(0) Mapped data for CXS and MSE

Development of a viewer program to display Te / ne profiles as functions of effective minor radius

*M. Emoto, S. Ohdachi, K. Watanabe, S. Sudo, and Y. Nagayama: Fusion Eng. Des. 81 (2006) 2019.

Viewer program

inboard/outboard side effective minor

radius

stored energy (diamagnetic) and electron

kinetic energy

minor radius and magnetic flux in vacuum

calibrated electron density

Current status & application

Current status of database generation

The equilibrium calculation takes about 5 days for each vacuum configuration under multi-CPU environment.

Database generation (incl. line-of-sight database) has been completed for 24 vacuum configurations. Coverage of more than 95% of the shots in the LHD experiment

Bq=100%gamma

1.129 1.151 1.174 1.197 1.208 1.254 1.259 1.262

Rax (m)

3.5 　 　 　 　 　 　 　 　

3.55 　 　 　 　 　 　 　 　

3.6 　 　 　 　 　 　 　 　

3.65 　 　 　 　 　 　 　 　

3.7 　 　 　 　 　 　 　 　

3.75 　 　 　 　 　 　 　 　

3.8 　 　 　 　 　 　 　 　

3.85 　 　 　 　 　 　 　 　

3.9 　 　 　 　 　 　 　 　

3.95 　 　 　 　 　 　 　 　

4.0 　 　 　 　 　 　 　 　

Databases for (Rax, Bq, gamma) = (3.7, 50, 1.254), (3.75, 50, 1.254), (3.7, 0, 1.254) have also been prepared.

How many percentage of shots can be mapped ?

Rax Bq gamma # of shots3.6 100 1.2538 3557

3.75 100 1.2538 10753.9 100 1.2538 482

3.53 100 1.2538 4573.6 100 1.1967 1873.8 100 1.2538 167

3.75 53 1.2538 843.55 100 1.2538 81

3.575 100 1.2538 783.61 100 1.2538 673.6 100 1.129 63

3.63 100 1.2538 563.58 100 1.2538 513.85 100 1.2538 463.66 100 1.2538 453.7 100 1.2538 44

3.65 100 1.2538 423.6 100 1.2553 413.8 100 1.1967 36

3.75 100 1.1967 363.7 100 1.1967 354 100 1.2538 17

3.59 100 1.2538 163.9 100 1.1967 14

3.75 100 1.2553 23.58 100 1.2553 23.55 100 1.2553 23.65 100 1.2553 2

3.575 100 1.2553 23.61 100 1.2553 13.9 100 1.2553 1

total 6789

14th cycle (FY2010) 14th cycle (FY2010)

13th cycle (FY2009) 15th cycle (FY2011)

Summary & application to further analysis

We have newly developed a large-scale LHD equilibrium database and user tools to retrieve the results of inverse mapping program.

We have also developed a real-time magnetic coordinate mapping system available for almost all of the LHD shots by using "Thomson" data.

Any points in real coordinates can be mapped into magnetic coordinates by specifying shot number and time. This can be applied to: Inversion of line-integrated data (e.g., spectrometer, bolometer, etc.) Simulation of millimeter wave ray tracing in a plasma

The "TSMAP" data is utilized for generation of input Te / ne profiles for transport analysis codes Evaluations of particle/heat transport, confinement, neutral beam deposition,

power balance ... (mentioned by Dr. Yokoyama on Wed. and Dr. Ida this morning)

Convergence of VMEC calculation

0 1 2 3 4 5 6 7 8 9 10

1.41

2.14

3.00

4.00

5.00

Rax = 3.75 m, Bq = 100%, gamma = 1.2538, ip = 0 kA, ipf = 2.0

■: Converged■: Converged if residual tolerance is mitigated (10-11 -> 10-8)■: No convergence / Error

p0

pf

#108200 f 204/ 292: 4.050s Rax= 3.600m Bq= 100% gamma=1.254 avac= 0.637m denl= 480.581 [a.u.] nel_fir= 4.937 nel_mmw= 9.005 [10^19 m^-2] kk= 0 k= 0 p0= 0.00 pf= 2.14 ip= 8.0 ipf= 2.00 sts= 0 err= 0 a99= 0.629 avmec= 0.637 chi= 280. kk= 0 k= 1 p0= 1.00 pf= 2.14 ip= 8.0 ipf= 2.00 sts= 0 err= 0 a99= 0.627 avmec= 0.635 chi= 184. kk= 0 k= 2 p0= 2.00 pf= 2.14 ip= 8.0 ipf= 2.00 sts= 0 err= 0 a99= 0.623 avmec= 0.631 chi= 96.0 kk= 0 k= 3 p0= 3.00 pf= 2.14 ip= 8.0 ipf= 2.00 sts= 0 err= 0 a99= 0.619 avmec= 0.628 chi= 28.3 kk= 0 k= 4 p0= 4.00 pf= 2.14 ip= 8.0 ipf= 2.00 sts= 0 err= 0 a99= 0.612 avmec= 0.626 chi= 6.41 kk= 0 k= 5 p0= 5.00 pf= 2.14 ip= 8.0 ipf= 2.00 sts= 0 err= 0 a99= 0.608 avmec= 0.625 chi= 50.6 kk= 1 k= 0 p0= 3.40 pf= 2.48 ip= 8.0 ipf= 2.00 sts= 0 err= 0 a99= 0.616 avmec= 0.626 chi= 13.9 kk= 1 k= 1 p0= 3.50 pf= 2.48 ip= 8.0 ipf= 2.00 sts= 0 err= 0 a99= 0.615 avmec= 0.626 chi= 11.6 kk= 1 k= 2 p0= 3.60 pf= 2.48 ip= 8.0 ipf= 2.00 sts= 0 err= 0 a99= 0.615 avmec= 0.625 chi= 9.07 kk= 1 k= 3 p0= 3.70 pf= 2.48 ip= 8.0 ipf= 2.00 sts= 0 err= 0 a99= 0.614 avmec= 0.625 chi= 7.10 kk= 1 k= 4 p0= 3.80 pf= 2.48 ip= 8.0 ipf= 2.00 sts= 0 err= 0 a99= 0.613 avmec= 0.625 chi= 5.38 kk= 1 k= 5 p0= 3.90 pf= 2.48 ip= 8.0 ipf= 2.00 sts= 0 err= 0 a99= 0.613 avmec= 0.625 chi= 4.20 kk= 1 k= 6 p0= 4.00 pf= 2.48 ip= 8.0 ipf= 2.00 sts= 0 err= 0 a99= 0.612 avmec= 0.625 chi= 4.06 kk= 1 k= 7 p0= 4.10 pf= 2.48 ip= 8.0 ipf= 2.00 sts= 0 err= 0 a99= 0.611 avmec= 0.624 chi= 4.80 kbest= 6 p0= 4.00 pf= 2.45 ip= 8.0 ipf= 2.00 sts= 0 err= 0 a99= 0.612 avmec= 0.625 chi= 4.188 Wpe= 9835.5 geom_center= 3.735 Rax_vmec= 3.896 nl_thomson_mid= 53.37 nl_thomson_R3579= 89.24 nl_thomson_R3669= 89.86 nl_thomson_R3759= 94.89 nl_thomson_R3849= 89.73 nl_thomson_R3939= 86.30

Example of mapping for high beta discharge

p0 coarse scan

p0 fine scan

Best fit

Fixedexperimental

valuerenew initial

valuescan by 0.1%

step χ-square error

Plasma sometimes spreads beyond VMEC boundary

p0 = 1.20, pf = 1.94, ip = 2.7, ipf = 2.00a99 = 0.544, avmec= 0.555

Rax = 3.6 m, Bq = 100%, gamma = 1.197

p0 = 1.00, pf = 2.14, ip = 0.0, ipf = 2.00

p0 = 5.00, pf = 2.14, ip = 0.0, ipf = 2.00

p0 = 5.10, pf = 2.35, ip = 28.8, ipf = 2.00a99 = 0.544, avmec= 0.552

'reff': Effective minor radius (m)'a99': Plasma minor radius defined by the region covering 99% kinetic energy (m)'p0': Central beta for the best-fitted equilibrium (%)'pf': Pressure peaking factor for the best-fitted equilibrium'ip': Plasma current per 1 Tesla measured by Rogowski coil (kA/T)'ipf': Current peaking factor (fixed at 2.0)'nl_thomson_mid': Line-integrated electron density along midplane from Thomson (arb)'nl_mmw_mid': Line-integrated electron density along midplane from MMW interferometer (e19m-2)'nl_thomson_3669': Line-integrated electron density along FIR (R3669) from Thomson (arb)'nl_fir_3669': Line-integrated electron density from FIR (R3669) (e19m-2)'nl_thomson_3579': Line-integrated electron density along FIR (R3579) from Thomson (arb)'nl_fir_3579': Line-integrated electron density from FIR (R3579) (e19m-2)'nl_thomson_3759': Line-integrated electron density along FIR (R3759) from Thomson (arb)'nl_fir_3759': Line-integrated electron density from FIR (R3759) (e19m-2)'nl_thomson_3849': Line-integrated electron density along FIR (R3849) from Thomson (arb)'nl_fir_3849': Line-integrated electron density from FIR (R3849) (e19m-2)'nl_thomson_3939': Line-integrated electron density along FIR (R3939) from Thomson (arb)'nl_fir_3939': Line-integrated electron density from FIR (R3939) (e19m-2)'chi': Best minimum mean square error of mapping'Wpe': Electron kinetic energy calculated from Thomson and best-fitted equilibrium (arb)'dVdreff': Derivative of plasma volume versus reff [dV/d(reff)] (m^2)'geom_center': Geometric center of the best-fitted equilibrium (m)'Rax_vmec': Magnetic axis position of the best-fitted equilibrium (m)'Te_median_smooth': Median smoothed electron temperature profile used for mapping (keV)'ne_median_smooth': Median smoothed electron density profile used for mapping (arb)'mask': Reserved for masking'Wp': Stored energy from diamagnetic loop (kJ)

Registered parameters

For ne calib.

Pressure / current parametersfor the best-fitted equilibrium

kineticEnergy

Geometric center / Axis position

Preset pressure/current profiles

Pressure profile

1

23

4

5

reff/a

Input/output of the library (PV-WAVE)

Library name Structure definition (vacuum magnetic field, real coordinates, output parameters)

Definition of structure array

Input parameters

Input real coordinatesoutput parameters

Library call

effective minor radius, poloidal angle, 3 components of magnetic field,rotational transform, pressure, specific volume, toroidal flux

Required time: 5 seconds per 100points Not enough for real-time process of Thomson data

Required time to process one shot

#90982 (132 frames) #90983 (132 frames)

PC1 only 188 s 188 s

PC2 only 155 s 156 s

Both (PC1, PC2) 198 s 167 s

Both (PC2, PC1) 158 s 189 s

Run multiple jobs from separate PCs at the same time

PC1: Celeron E1400 @2.00GHzPC2: Core2 Duo E7200 @2.53GHz

If we use high-spec multiple clients, real-time mapping between shot intervals may be possible.

# [Parameters]# Name = TSMAP# ShotNo = 90000# Date = '12/17/2010 11:59'# # DimNo = 2# DimName = 'Time', 'R'# DimSize = 267, 136# DimUnit = 's', 'm'# # ValNo = 33# ValName = 'Te', 'dTe', 'n_e', 'dn_e', 'laser', 'laser number', 'reff', 'a99', 'p0', 'pf', 'ip', 'ipf', 'nl_thomson_mid', ...# ValUnit = 'keV', 'keV', 'arb', 'arb', 'arb', 'arb', 'm', 'm', '%', 'arb', 'kA/T', 'arb', 'arb', ...## [Comments]# Bt = -1.4300000# Rax = 3.6000000# Bq = 100.000# Gamma = 1.2538000# phiedge = -3.28050# avac = 0.63900000# ExpDate = 20081127# Cycle = 12# density (ne) is only for very rough information# Do not use data for ne_bar < 5*1-^12cm-3# High Voltage is set at 0.90 times# Te limit = 22keV# Laser#1, #3, #5, # # [data] 0.000, 2.532, 0.016, 21.780, 0, 1, 2365, 1, 10.000, 0.000, 0.000, 0.000, -0.000, ... 0.000, 2.572, 0.090, 21.780, 2, 1, 2365, 1, -0.688, 0.000, 0.000, 0.000, -0.000, ... 0.000, 2.611, 0.000, 21.780, 0, 1, 2365, 1, -0.677, 0.000, 0.000, 0.000, -0.000, ... 0.000, 2.648, 0.008, 21.780, 0, 1, 2365, 1, -0.666, 0.000, 0.000, 0.000, -0.000, ... 0.000, 2.683, 2.646, 19.357, 0, 0, 2365, 1, -0.655, 0.000, 0.000, 0.000, -0.000, ...

Registered data format

same as Thomson data added parts

Diagnostic name: tsmap (mapped to Te profile) or tsmap_pe (mapped to pe profile)

Information on magnetic field configuration