23P031-P
Optimization Study of Heliotron J Magnetic Configuration using
particles orbit analysis
粒子軌道解析を用いたヘリオトロンJ磁場配位の最適化
Yuichi Isoe1) . Yuji Nakamura1) , Satoshi Yamamoto2)a)
礒江 祐一. a)中村 祐司 , b)山本 聡
1)

Graduate School of Energy Science,Kyoto University, Gokasho, Uji 611-0011, Japan
京都大学大学院エネルギー科学研究科 〒611-0011 宇治市五ヶ庄
2)Institute of Advanced Energy ,Kyoto University, Gokasho, Uji 611-0011, Japan京都大学エネルギー理工学研究所 〒611-0011 宇治市五ヶ庄

The straight part of Heliotron J has a small magnetic gradient, so we can control neoclassical transport bylocalizing particles there. Heliotron J has good accessibility because of a 1-pole helical coil , but has
magnetic harmonics by the restriction of the helical coil. We think that we can improve about confinementof plasma. So in this study, we try to improve orbit confinement about Heliotron J by analyzing particle
orbit , loss rate and loss time using STELLOPT, which is nonlinear optimization method.

1. Introduction
Helical plasma including heliotron and stellarator
can confine steady state plasma in principle because
their three-dimensional magnetic field for plasmaconfinement is mainly produced by external coils.
However, magnetic field intensity change
intricately because Helical magnetic field has noaxial symmetry, and the complex nature ofthree-dimensional would lead to degradation ofplasma confinement and optimization aiming at
improvement of neoclassical and anomaloustransport, and MHD stability is needed.
Optimization has been studied for a new helicaldevice design. But it is difficult to change the coilconfiguration, once the device is completed. So thisstudy is proceeding with finding a more optimal
magnetic configuration which include additional
trim coils based on the Heliotron J.
2. Optimized the value of J invariants and Bmin
In order to improve the magnetic configuration ofHeliotron J, we try to optimize it using stellarator
optimizer “STELLOPT” [1]. In the previous
optimization with regard to good particle
confinement, we measured and optimized thevalues of both second adiabatic invariants J and Bminimum(Bmin),which indicate the orbit of helicallytrapped particle. Figure 1 shows the Bmin contour ofoptimized configuration by STELLOPT. It shows
the concentric circle contour, which well aligned
the magnetic surface. However, Bmin contour do notcontinue around the  ~ 0 (deg) where magnetic
field tend to be modulated by high magnetic
harmonics of Fourier component with small
amplitude because magnetic field intensity is weakand constant. Figure 2 shows the orbit of particle,
which moving at the optimized magnetic
configuration. The particle moved along themagnetic surface at first, but it escaped to theoutside of plasma .Figure 3 are the contour ofmagnetic field strength, and show that J invariants
optimized configuration cannot confine the trapped
particles because of unclosed Bmin contour, whichcoincide with the approximative trajectory oftrapped particles.

Fig.1. Bmin contour of optimized configuration.

Fig.2. The orbit of particle, which moving at theoptimized magnetic configuration.

(the sum of which characterizes the entire set oftarget values). The goal of the code is to minimize
the total chi-squared value.
The algorithm for STELLOPT is quite
conceptually simple. First a VMEC equilibria isfound. Using this equilibria as input, various utility
codes are run. These utility codes provide
STELLOPT with equilibria values to compare
against target values. The STELLOPT code thenenters it's main minimization loop. Here all freeparameters are varied and VMEC is run for eachvaried free parameter. The various equilibria arethen passed to the utility codes for calculation ofvalues. The equilibria with the lowest chi-squared
value is then taken to be the equilibria of interest. If
the chi-squared falls below a user defined value
then iteration ceases, otherwise the free parameters
are again varied. The choice of specificoptimization algorithm modifies this loop slightly
but essentially the algorithm remains intact. The
modified Levenberg-Marquardt algorithm to seethat the step produces a lower chi-squared value
than that found by the Jacobian evaluation. If not,the code searches near the lowest Jacobianevaluation for the best fit.

(A)

θ/π
ζ/π(B)

θ/πFig.3. The contour of magnetic field strength,(A) 3D figure, (B) 2D figure and heavy line indicatesline of Bmin

It was found from these results that there is alimit to optimizing of magnetic configuration byusing the value of second adiabatic invariants J. So
in this study, we are analyzing the particle orbit tooptimize the magnetic configuration.
3. Details of STELLOPT code
The STELLOPT code searches parameter space
for a given set of parameters looking for a'best-match' to desired values. This is accomplishedthrough iteration of the VMEC routine, calculationof various values from other utility codes (in thisstudy, we added ORBNEW which can analyze
particle orbit[2]) and characterization of a given
VMEC equilibria in terms of the desired parameters.
This characterization is done in terms ofChi-squared values where2 1

2f

 f equilbria .
2t arg et(1)The sigma here represents the tolerance of thetarget value. A given VMEC equilibria can becharacterized by a set of these chi-squared values

4. Optimize the value of loss rate
In this study, we added ORBNEW code, which
can analyze particle orbit, to STELLOPT code.
Then, we are optimizing magnetic configuration
with the helically trapped particle loss rate as one of
the evaluation functions.
The results of this study is under consideration
and will helpful to improve the confinement ofstellarator plasmas.
5. Reference[1] D.Spong,et al. : Nucl Fusion. 41(2001) 711[2] Allen H. Boozer : Phys. Fluids 23(1980) 904