@misc{oai:ir.soken.ac.jp:00000523,
author = {中野, 治久 and ナカノ, ハルヒサ and NAKANO, Haruhisa},
month = {2016-02-17, 2016-02-17},
note = {1. Research Purpose
An anomalous transport in torus magnetic confinement plasma is expressed as
a product of electron density and potential fluctuations. In order to elucidate the
anomalous transport experimentally, it is necessary to measure simultaneosly lo-
cal electron density and potential fluctuation. A heavy ion beam probe (HIBP)
is only a diagnostics device to be able to measure electron density and potential
simultaneously with high temporal (～ μs) and spatial resolution (～ mm) in high
temperature plasma (1 keV ～). In the HIBP diagnostics, electron density and
potential fluctuations are measured as the fluctuations of detected beam current
and change of beam energy, respectively. However, such simultaneous measure
ments in high temperature plasma have never been performed except ISX－B [l],
TEXT(－U) [2] tokamaks.
In Compact Helical System (CHS), the HIBP has been used to measure mainly
the potential profile and its dynamics, which is much larger displacement than
fluctuation, and density fluctuations. The first purpose of this thesis is to extend
the potential ability of the HIBP and to achieve the simultaneous measurements
of electron density and potential fluctuations in all radial positions in CHS plasma
by improving its ion source of a part of the ion gun of HIBP. The second pur-
pose of this thesis is to evaluate path integral effect, which is a well-known and
long-standing problem for the HIBP diagnostics, and to reconstruct local density
fluctuation. The detected beam current fluctuation of HIBP contains information
of local electron density fluctuation at ionization point and fluctuations along pri-
mary and secondary beam trajectories. The latter effect of beam trajectory is
called a path integral effect. Several previous articles l3-6] exist on simulating
influences of its effect, assuming electron density and temperature and electron the
density fluctuation profiles. In this thesis, a method is proposed to eliminate the
path integral effect in real " experimental data " and to evaluate " actual" local elec-
tron density fluctuation profile.
2. Simultaneous measurements of electron density and po-tential fluctuation
2.1. Improvement oHon Source
In CHS an ion source of alkali zeolite emitter type is used for the HIBP; the
cesium ions are released from the high temperature zeolite heated up to ～1000 ℃.
Previously, in an old socket, the cesium zeolite is indirectly heated through the
ceramic case heated by a filament (Fig. 3.1(a)). The indirect heating of the
socket of this type may prevent the zeolite, from attaining the sufficiently high
temperature. Then, the structure of the ion source is newly developed to increase
the higher beam current by direct heatly heating the zeolite.
The new socket structure is shown in Fig. 3.1(b). This socket allows heating
directly the zeolite, by setting the filament inside the zeolite. Using this socket of
direct heating, ten times higher beam current compared with the old is extracted
from the present ion source.
2.2. Simultaneous measurements
Using the direct heating socket, simultaneous measurements of electron density
(detected beam current of HIBP) and potential fluctuations are successfully per-
formed in low density (ne ～ 5 x 1018 m-3) high temperature (Te = 1.0 ～ 1.5 keV)
plasma in CHS. The major and minor radii of the CHS plasma R=1 m and minor
radius α = 0.2 m.
The fluctuation distribution measurements were done with 2 mm resolution over
the whole radius form center to near the last closed field surface (LCFS) [7], as
is shown in Fig. 3.9. It is the first achievement as the simultaneous fluctuation
measurements for all radial positions in high temperature torus plasma, because
the previous works did not measure them simultaneously in center region because
of insufficient beam energy and/or detected beam current. The fluctuation spectra
measured in CHS shows broad bands characteristics to indicate turbulence nature.
It is found that fluctuation amplitudes become larger toward the plasma edge as
is similar to the observations of ISX-B and TEXT(-U).
3. Reconstruction local electron density fluctuation
3.1. Reconstruction local electron density fluctuation profiIe
The average of the detected beam fluctuation amplitude is written by,
η2(p*)= ξ 2(p*)
－2Σ ∫ li ＜ξ (p*)ξ (pi)>＞ESi(pi) wi(pi)dpi (1)
i=1,2
+ Σ Σ ∫ li ∫ lj ＜ξ (pi)ξ (pj)＞ESi(pi) Sj(pj) wi(pi) wj(pi)dpidpj
i=1,2 j=1,2
where, η＝δId/Id, ξ = δne/ne, S and wi are detected beam current fluctuation
rate and local electron density fluctuation rate point, ionization rate and integral
weight, respectively.Where Id, ne represents detected beam current, local elec-
tron density, respectively, andδindicates fluctuation. The ionization rate can be
estimated as a function of electron density and temperature from Lotz's empirical
formula [8]. The electron density and temperature can be given with Thomson
scattering measurement. The bracket with subscript E, ＜ ＞E, represents the en-
semble average,and the terms including the bracket are the correlations between
density fluctuations at two spatial points. If the correlation terms of fluctuations
are evaluated, local electron density fluctuation is estimated by solving the above
integral equation.
On the right-hand-side of Eq. (1), the second and third terms are effects around
ionization point and along the beam trajectories, respectively. They are under-
stood if assuming a limiting case that the fluctuation should have the infinitesimal
short correlation length and the ensemble averaged terms should be expressed as
theδ-function. In addition to this, several simplification makes the Eq. (1) take
the followlng form, as
η2 = (1－〓c+〓c)ξ2 (2)
where the first , second and third terms represent the local density fluctuation, the
screening effect and the accumulating effect. From this simplification, the path
integral effect is found to be composed of the screening and accumulating effects.
The degree of the path integral effect, whose coefficient ζ, is estimated from the
sum of the second and third terms in Eq. (2).
Fig. 4.2(a) shows the dependence of the coefficient on electron density and
temperature, using cesium ion beam. The coefficient is calculated for our HIBP
geometry and CHS plasma assuming that the correlation length is 1 cm and the
used beam is cesium ion. Here, the primary and secondary beam trajectory lengths
are 0.2 m, corresponding to the CHS plasma radius. In this calculation, the
coefficient is 0.1 when Te ～ 1 keV is 0.1 in ne ～ 2.8 × 1018 m-3. In this case, the
path integral effect can be almost negligible. On the other hand, the coefficient
is 1 when Te ～ 1 keV and ne ～ 1.1 x 1019 m-3, which represent detected beam
fluctuation amplitude is twice as local density fluctuation, and the path integral
effect is dominant.
The ensemble averaged terms can be evaluated if the fluctuations correlation be-
tween two spatial points is assumed as the Gauss function, ƒ( Δx) =exp(－0.5(Δ/lc)2),
where lc is a correlation length. The HIBP of CHS is equipped with three chan-
nels, so that the correlation length lc can be evaluated; the distance between two
of the channels, Δx ranges from 3 to 10 mm By substituting the estimated correla-
tion function into Eq. (2), the local electron density fluctuation amplitude profile
can be reconstructed. Fig. 5.6(b) shows an example of the reconstruction for the
case that the electron density and temperature are ～ 1019 m-3 and ～ 1 keV, re-
spectively. Here, the integral equation is solved after several times iteration. The
detected beam current and the local electron density fluctuation amplitudes are
within the range of error in the outer region (p > 0.6). However, in the inner
region (p < 0.6), the fluctuation amplitude of detected beam current is a half of
the local fluctuation amplitude.
3.2. Reconstruction of local electron density fluctuation spectrum
The reconstruction method of local density fluctuation is extended to the esti-
mation of density fluctuation spectra. It is apparent that the power spectra can be
evaluated simply by appling the above method to the fluctuation power at each
frequency. However, the integral equation for low frequency (< 50 kHz) cannot be
often solved with iteration method. This is caused by the fact that the correlation
length appears to become longer than the actual value.
This is considered to result from the path integral effect on the correlation length.
The fluctuations of local three channels are strongly affected by the fluctuation
in the outer plasma regions, and the fluctuations at local three channels become
to show quite similar behavior. A technique is derived to correct this longer
correlation length. Thanks to the technique, the corrected correlation length is
evaluated and the spectra of local density fluctuation are successfully obtained.
Fig. 6.3(b) shows one example of the reconstructed spectrum of local electron
density fluctuation, whose position is r/a - 0.26 in the same plasma in Fig. 5.6.
The result shows that the path integral effect is larger in low frequency than that
in high frequency.
3.3. Consideration of the Bolt2;mann Relationship
As a result of the estimation of local density, the detected beam fluctuation
can be roughly regarded as the local density fluctuation in low density regimes of
ne ～ 5 × 1018 m-3. Consequently, the detected beam fluctuation shown in Fig.
3.9 reflects local density fluctuation. A rough comparison between the density
fluctuation and potential fluctuation (normalized by electron temperature) allows
examining the validity of the Boltzmann relationship. Fig. 7.1(a) shows the nor-
malized density fluctuation as a function of normalized potential fluctuations. In
Fig. 7.1(a), the different marks correspond to the different ranges of radial posi-
tion of the plasma; red and green and blue plots are data point in 0 < r/a < 0.3,
0.3 < r/a < 0.6 and r/a > 0.6, respectively. The lines are fit lines using the least
squared method. The results show that the Boltzma- relationship should be
valid, although tendency is found that the normalized density fluctuation should
be larger than the normalized potential fluctuation.
4. Summary
The simultaneous measurements of electron density and potential fluctuations
are successfully made with heavy ion beam probe after the development of a new
ion source. The measurement is achieved in a wide range of radial region with
spatial resolution of 2 mm. A method is proposed to evaluate the path integral
effect that is a long-standing problem for density fluctuation measurement with
the HIBPs. Applying this method on the CHS fluctuation measurements, the local
density fluctuation and its power spectrum are successfully evaluated., 総研大甲第927号},
title = {重イオンビームプローブを用いた揺動分布計測と経路積分効果の評価法の確立},
year = {}
}