22P130-P
Development of Real-Time Magnetic Coordinate Mapping System in LHD
LHDにおける磁気座標リアルタイムマッピングシステムの構築	 
Chihiro Suzuki, Katsumi Ida, Yasuhiro Suzuki, Masanobu Yoshida and Masahiko Emoto
鈴木千尋, 居田克巳，鈴木康浩，吉田正信，江本雅彦
National Institute for Fusion Science322-6 Oroshi-cho, Toki 509-5292, Japan
核融合科学研究所 〒509-5292	  土岐市下石町322-6
We have newly constructed a large-scale equilibrium database and a magnetic coordinate mapping system
for the Large Helical Device (LHD) experiment. Once the parameters designating vacuum magneticconfiguration and pressure/current and their peaking factors are given, results of inverse mapping between
real and magnetic coordinates as well as additional equilibrium parameters can be retrieved from the dataserver. Additional database composed of pre-calculated mapping results along several lines of sights forfrequently used diagnostics has been prepared to accelerate mapping procedure. Real-time mapping anddisplay of electron temperature/density profiles as functions of effective minor radius are thus realized andutilized for further transport analyses.

1. Introduction
Because raw experimental data of position
dependent quantities such as electron temperatureare expressed in real coordinates, it is importantfor further analyses to map real coordinates onto
magneticcoordinates
byspecifying
anappropriate equilibrium. In the Large HelicalDevice (LHD) experiment, it is reasonable tochoose
anequilibrium
minimizing
thediscrepancy between inboard and outboard sidesof the electron temperature profile because
reliable Thomson scattering diagnostic data areavailable with high spatial resolution [1]. In orderto solve this inverse problem, it is necessary toconstruct a database composed of a lot of
three-dimensional equilibria beforehand.
In this work we have newly developed alarge-scale database composed of many LHD
equilibria under wide ranges of pressure andplasma current and their profiles, which can cover
special conditions such as strongly peakedpressure profiles often observed in high density
discharges. Additional tools for more efficient
data handling and processing have also beendeveloped to achieve automated real-time
mapping into magnetic coordinates for all thetime frames of Thomson scattering data.
2. Equilibrium Database
In LHD, vacuum magnetic configuration isdesignated by three parameters: magnetic axis
position (Rax), quadruple magnetic field (Bq) andpitch parameter (γ). We have calculated thefree-boundary LHD equilibria by the latest VMEC
code [2] in the parameter space shown in Table I,

which generates more than 7000 equilibria for eachvacuum configuration. This process takes about 5days for each vacuum configuration undermulti-CPU environment.
Then a library routine for the database access has
been developed to run an inverse mapping programon a server and get equilibrium parameters such aseffective minor radius, components of magnetic
field, etc. by giving real cylindrical coordinates (R,Z, Φ), and seven input parameters specifying anequilibrium: Rax, Bq, γ, p0 (central beta), pf(pressure peaking factor), ip (plasma current) andipf (current peaking factor). In this routine, any
values are allowed as an input and the output
parameters are automatically interpolated when thegiven values are intermediate in the parameter
space mesh, and extrapolated when the given real
coordinates are outside of the calculation boundary.
Table I. Parameter ranges in the database for central beta(p0), pressure peaking factor (pf), plasma current (ip)and current peaking factor (ipf).

p0pfipipf	  	  Range	  	  Mesh points	  0–10%
11	  1.41–5.00
5	  -150–150 kA/T
13	  -12.60–4.00
11

3. Line-of-Sight Database
Because the inverse mapping program is not fastenough for real-time processing of all the timeframes of Thomson scattering data, we have also
prepared "Line-of-sight database" which tabulatespre-calculated results of the mapping along severalfrequently used lines of sights (Thomson, Charge
Exchange Spectroscopy, Interferometer, etc.) for all
the mesh points of input parameters. A function toretrieve the output parameters by designating thename of the line of sight was added to the library toachieve real-time mapping.
4. Real-time Mapping and Viewer
In the procedure to search the best-fitted
equilibrium parameters from the experimental dataof Thomson scattering, pf and ipf are assumed to beappropriate initial values and Rogowski coil data isused for ip. By reading the line-of-sight database,error between inboard and outboard sides of theelectron temperature profile is calculated withscanning p0 step by step for each time frame. This
procedure is repeated until the minimum error isobtained to determine the best-fitted equilibrium
parameters. The other parameters such as electron
kinetic energy, magnetic axis position, etc. arecalculated at the same time. Once all the frames areprocessed, the results are automatically registeredas an analyzed data for the Kaiseki Data Server
System [3] with a diagnostic name "tsmap".
We have also developed a viewer program todisplay electron temperature/density profiles asfunctions of effective minor radius. A screenshot ofthe viewer program is shown in Fig. 1, where
absolute electron density is automatically calibratedusing interferometer data, and time evolutions ofseveral parameters (p0, pf, magnetic axis position,electron kinetic energy) for the best-fitted
equilibrium are also displayed.
Database generation including the line-of-sightdatabase has been completed for 23 vacuum
configurations, which results in coverage of morethan 90% of the shots in the LHD experiment. The"tsmap" data are useful specifically for furtherstudies on particle/heat transport and neutral beam
deposition based on experimental profiles.
Acknowledgments
The authors acknowledge all the members ofLHD experiment group for their assistance.
References[1] K. Narihara, I. Yamada, H. Hayashi, and K.
Yamauchi: Rev. Sci. Instrum. 72 (2001) 1122.
[2] S. P. Hirshman and J. C. Whitson: Phys. Fluids 26(1983) 3553.
[3] M. Emoto, S. Ohdachi, K. Watanabe, S. Sudo, and Y.
Nagayama: Fusion Eng. Des. 81 (2006) 2019.

Fig.1. Screenshot of the "tsmap" viewer program.