22P118-P
Phase imaging method for density measurement and simulation analysis
in the plug region of GAMMA10GAMMA10

Tomohiro Yamada, Masayuki Yoshikawa, Junko Kohagura, Yoriko Shima, Yuusuke Morikawa,
Daichi Akita, Mizuki Sakamoto and Tsuyoshi Imai,
Plasma Research Center, University of Tsukuba
1-1-1,Tennodai, Tsukuba, Ibaraki 305-8577, Japan305-8577

1-1-1

The phase imaging interferometer is set to measure electron density distribution at plug region inGAMMA10. We measure the phase difference between the microwave passing through the plasma and thereference wave by use of the phase imaging interferometer. We derive the electron density by Abeltransform technique. We try to decide plasma density distribution by using the finite difference time
domain simulations. Moreover, we construct the asymmetry Abel transform in case of the asymmetricplasma distribution, and check the validity of it.

1. Introduction
GAMMA10 is the largest tandem mirror device
utilizing a plasma confinement by not only
magnetic mirrors but also electrostatic potentials. It
consists of the central, anchor, and plug/barrier
mirror cells. We show the schematic diagram of thephase imaging device in Fig. 1. The phase imaging
interferometer system [1] is set horizontally tomeasure upper half of the plasma in the plug cell.
The phase imaging method is the method tomeasure the phase difference between the
microwave passing through the plasma and thereference microwave which depends on the line
integrated electron density. We can obtain
two-dimensional (2D) line integrated electron
density distributions by using the 2D detector. A 2D
plasma density distribution is useful to understandthe mechanisms of plasma confinement or
fluctuation measurements.
We use Abel transform technique to the line
integrated electron density distribution in order toderive the electron density radial distributions. In
previous measurements, we used Abel transform in
the assumption of axisymmetric distribution ofplasma density. However, the plasma profile is notalways axisymmetry. Then, using Abel transform
method for nonaxisymmetric plasma may havelarge error in the calculated electron density.
Therefore, we try to calculate the electron density
by the use of asymmetry Abel transform [2,3]which is assumed asymmetric distribution ofplasma density and to improve the accuracy ofobtained electron density. In order to calculate theasymmetric density distribution by the measured
radial electron line integrated density distribution,
we use finite difference time domain (FDTD)
method [4]. In this paper, we focus onestablishment of this method.

Fig.1. The schematic diagram of the phase imaging
device

2. Phase imaging method
The incident microwave (69.85 [GHz]) is divided
by a directional coupler. One wave is transmitted
wave which goes through the plasma and changesthe phase. The other wave is reference wave which
remains initial phase. This device detects the phasedifference ∆φ(x) between those two waves. Theincident wave is extended into a sheet beam by aplane mirror and a parabolic mirror, and it isirradiated to the upper half of the plasma crosssection. After that, the wave is concentrated into thedetector array by mirrors and lenses at receiver side.
On the other hand, the reference wave is transmitted
through waveguides and it is incorporated into thephase detector circuit with the transmitted wave.
We take heterodyne that is added oscillator of 70.00
GHz at receiver side in order to gain sufficient
power of the phase difference.

(1 − γ ) r − γ ( x − γ r ) dr , (3)2I ( x) = 2∫

rmax

r0

ε (r )

maxr − ( x − γ ( rmax − r ) )22

where r0=(x-γrmax)/(1-γ). We assume that thedensity is ε(r)=exp(-(r/30)2), equation (3) of
γ=0.3 is shown in Fig. 2. In this Fig. 2, the left sidefrom peak is derived from symmetricity.

3. FDTD simulations
3.1 Simulation method
We try to decide the plasma distribution by use of
FDTD method. The details are as follows; wedecide a plasma density distribution in the analysis
area, and compare the phase difference obtained by
the simulation and the phase difference obtained by
the experiment. If phase difference is in agreement,
the profile of plasma will be used for Abeltransform. If it is not in agreement, we set anotherplasma density distribution, and simulate again.
3.2 Simulation model
Analysis area is 2D space (x,y). The frequency of
incident wave is 69.85 GHz. In Fig. 1, the incident
wave reflects at plane mirror and parabolic mirror(radius of curvature is 796.7433 mm) and reaches
the plasma. Moreover, it reaches the detector withmirrors and lenses. We set parameters such as
distances and angles to match experimental device.
The asymmetric plasma contour distribution profile
is described from the following equation.

( x − γ (r− r )) + y 2 = r2
2max

(1)

Where γ is the deviation of density, rmax is maximum
radius of the plasma.
4. Asymmetric Abel transform
We derived the equation of the Abel transformwhich is described for asymmetric plasma
distribution such as equation (1), and checked thevalidity of it. In order to check the validity, weassume density, and compare it and the density
which is found from Abel transform of the discreteobserved value which is obtained from the assumeddensity. The discrete observed value of equation (1)is described as the following equation,I ( x) = 2∫

02
rmax
− x2

ε (r )dy .

(2)

Here ε(r) is the density of plasma. We replace theintegrant of equation (2) with r. When it is x>γrmax,Fig.2. The discrete observed value of γ=0.3

The assumed density, for example x=37.365, isε(x)=0.995. The Abel transformed density E(x)which is found from the discrete observed value of
x=37.365 is E(x)=0.995.
Therefore, we checked the validity of theasymmetry Abel transform which is described byasymmetric plasma distribution such as equation(1).
5. Summary
Improving the analytical accuracy by theinductive technique is the purpose of this study. We
construct the simulation model of phase imaging
device by using FDTD method, and derive thephase difference of asymmetric plasma distribution
such as equation (1). This simulation enables todecide γ which is the deviation of density. Moreover,
we derived the equation of the Abel transformwhich is described for asymmetric plasma
distribution such as equation (1), and checked thevalidity of it.
References[1] M. Yoshikawa, S. Negishi, Y. Shima, H. Hojo, A.
Mase, Y. Kogi, and T. Imai: Review of scientificinstruments vol. 81, No. 10, October 2010[2] M. Seki, S. Himeno: Hokkaido information univ.
bulletin volume13 issue1 : 17~32, 2001
[3] X. F. Ma, T. Takeda: Nuclear Instruments andMethods in Physics Research A 492 (2002) 178-189[4] Uno. Toru: Finite Difference Time Domain Method
for Electromagnetic Field and Antenna Analysis
CORONA PUBLISHING CO., LTD.