http://swrc.ontoware.org/ontology#Thesis
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
ja
中野 治久
ナカノ ハルヒサ
NAKANO Haruhisa
総研大甲第927号
<b>1. Research Purpose</b><br /> An anomalous transport in torus magnetic confinement plasma is expressed as<br /> a product of electron density and potential fluctuations. In order to elucidate the<br />anomalous transport experimentally, it is necessary to measure simultaneosly lo-<br />cal electron density and potential fluctuation. A heavy ion beam probe (HIBP)<br />is only a diagnostics device to be able to measure electron density and potential<br />simultaneously with high temporal (～ μs) and spatial resolution (～ mm) in high<br />temperature plasma (1 keV ～). In the HIBP diagnostics, electron density and<br />potential fluctuations are measured as the fluctuations of detected beam current<br />and change of beam energy, respectively. However, such simultaneous measure<br />ments in high temperature plasma have never been performed except ISX－B [l],<br />TEXT(－U) [2] tokamaks.<br /> In Compact Helical System (CHS), the HIBP has been used to measure mainly<br />the potential profile and its dynamics, which is much larger displacement than<br />fluctuation, and density fluctuations. The first purpose of this thesis is to extend<br />the potential ability of the HIBP and to achieve the simultaneous measurements<br /> of electron density and potential fluctuations in all radial positions in CHS plasma<br />by improving its ion source of a part of the ion gun of HIBP. The second pur-<br />pose of this thesis is to evaluate path integral effect, which is a well-known and<br /> long-standing problem for the HIBP diagnostics, and to reconstruct local density<br />fluctuation. The detected beam current fluctuation of HIBP contains information<br />of local electron density fluctuation at ionization point and fluctuations along pri-<br />mary and secondary beam trajectories. The latter effect of beam trajectory is<br />called a path integral effect. Several previous articles l3-6] exist on simulating<br />influences of its effect, assuming electron density and temperature and electron the<br />density fluctuation profiles. In this thesis, a method is proposed to eliminate the<br />path integral effect in real <i>" experimental data "</i> and to evaluate " actual" local elec-<br />tron density fluctuation profile.<br /><br /><b>2. Simultaneous measurements of electron density and po-tential fluctuation<br />2.1. Improvement oHon Source </b><br /> In CHS an ion source of alkali zeolite emitter type is used for the HIBP; the<br />cesium ions are released from the high temperature zeolite heated up to ～1000 ℃.<br />Previously, in an old socket, the cesium zeolite is indirectly heated through the<br />ceramic case heated by a filament (Fig. 3.1(a)). The indirect heating of the<br />socket of this type may prevent the zeolite, from attaining the sufficiently high<br />temperature. Then, the structure of the ion source is newly developed to increase<br />the higher beam current by direct heatly heating the zeolite.<br />The new socket structure is shown in Fig. 3.1(b). This socket allows heating<br />directly the zeolite, by setting the filament inside the zeolite. Using this socket of<br />direct heating, ten times higher beam current compared with the old is extracted<br />from the present ion source.<br /><br /><b>2.2. Simultaneous measurements</b><br /> Using the direct heating socket, simultaneous measurements of electron density<br />(detected beam current of HIBP) and potential fluctuations are successfully per-<br />formed in low density (<i>n<small>e</small></i> ～ 5 x 10<sup>18</sup> m<sup>-3</sup>) high temperature (<i>T<small>e</small></i> = 1.0 ～ 1.5 keV)<br />plasma in CHS. The major and minor radii of the CHS plasma <i>R</i>=1 m and minor <br />radius <i>α</i> = 0.2 m.<br /> The fluctuation distribution measurements were done with 2 mm resolution over<br />the whole radius form center to near the last closed field surface (LCFS) [7], as <br />is shown in Fig. 3.9. It is the first achievement as the simultaneous fluctuation<br />measurements for all radial positions in high temperature torus plasma, because<br />the previous works did not measure them simultaneously in center region because<br />of insufficient beam energy and/or detected beam current. The fluctuation spectra<br />measured in CHS shows broad bands characteristics to indicate turbulence nature.<br />It is found that fluctuation amplitudes become larger toward the plasma edge as<br />is similar to the observations of ISX-B and TEXT(-U).<br /><br /><b>3. Reconstruction local electron density fluctuation<br />3.1. Reconstruction local electron density fluctuation profiIe<br /></b> The average of the detected beam fluctuation amplitude is written by,<br /><br /> <i>η<sup>2</sup></i>(<i>p</i><sub>*</sub>)= <i>ξ</i> <sup>2</sup>(<i>p</i><sub>*</sub>)<br /> －2<font size="5">Σ </font><font size="5"><i>∫</i> </font> <sub><i>li</i></sub> ＜<i>ξ</i> (<i>p<sub>*</i></sub>)<i>ξ</i> (<i>p<sub>i</sub></i>)>＞<small>E</small><i>S<small>i</small></i>(<i>p<sub>i</i></sub>) w<small>i</small>(<i>p<sub>i</i></sub>)d<i>p<sub>i</sub></i> (1)<br /> <sup><i>i</i>=1,2</sup><br /> + <font size="5">Σ</font> <font size="5">Σ</font> <font size="5"> <i>∫</i> </font> <sub><i>li</i></sub> <font size="5"><i>∫</i> </font><sub><i>lj</i></sub> ＜<i>ξ</i> (<i>p<sub>i</i></sub>)ξ (<i>p<sub>j</i></sub>)＞<small>E</small>S<small>i</small>(<i>p<sub>i</i></sub>) S<small>j</small>(<i>p<sub>j</i></sub>) w<small>i</small>(<i>p<sub>i</i></sub>) w<small>j</small>(<i>p<sub>i</i></sub>)d<i>p<small>i</i></small>d<i>p<small>j</small></i><br /> <small><i>i</i>=1,2 <i> j</i>=1,2</small><br />where, <i>η</i>＝δ<i>I<small>d</small>/I<small>d</small></i>, <i>ξ</i> = <i>δn<small>e</small>/n<small>e</small>, S </i>and <i>w<small>i</small></i> are detected beam current fluctuation<br />rate and local electron density fluctuation rate point, ionization rate and integral<br />weight, respectively.Where <i>I<small>d</small>, n<small>e</small></i> represents detected beam current, local elec-<br />tron density, respectively, andδindicates fluctuation. The ionization rate can be<br />estimated as a function of electron density and temperature from Lotz's empirical<br />formula [8]. The electron density and temperature can be given with Thomson<br />scattering measurement. The bracket with subscript E, ＜ ＞<small>E</small>, represents the en-<br />semble average,and the terms including the bracket are the correlations between<br /> density fluctuations at two spatial points. If the correlation terms of fluctuations<br />are evaluated, local electron density fluctuation is estimated by solving the above<br />integral equation. <br /> On the right-hand-side of Eq. (1), the second and third terms are effects around<br />ionization point and along the beam trajectories, respectively. They are under-<br />stood if assuming a limiting case that the fluctuation should have the infinitesimal<br />short correlation length and the ensemble averaged terms should be expressed as<br />theδ-function. In addition to this, several simplification makes the Eq. (1) take<br />the followlng form, as<br /><br /> <i>η</i><sup>2</sup> = (1－〓<small>c</small>+〓<small>c</small>)<i>ξ</i><sup>2</sup> (2)<br /><br />where the first , second and third terms represent the local density fluctuation, the<br />screening effect and the accumulating effect. From this simplification, the path<br />integral effect is found to be composed of the screening and accumulating effects.<br />The degree of the path integral effect, whose coefficient ζ, is estimated from the<br />sum of the second and third terms in Eq. (2).<br /> Fig. 4.2(a) shows the dependence of the coefficient on electron density and<br />temperature, using cesium ion beam. The coefficient is calculated for our HIBP<br />geometry and CHS plasma assuming that the correlation length is 1 cm and the<br />used beam is cesium ion. Here, the primary and secondary beam trajectory lengths<br />are 0.2 m, corresponding to the CHS plasma radius. In this calculation, the<br />coefficient is 0.1 when <i>T<small>e</small></i> ～ 1 keV is 0.1 in <i>n<small>e</small></i> ～ 2.8 × 10<sup>18</sup> m<sup>-3</sup>. In this case, the<br />path integral effect can be almost negligible. On the other hand, the coefficient<br />is 1 when T<small>e</small> ～ 1 keV and <i>n<small>e</small></i> ～ 1.1 x 10<sup>19</sup> m<sup>-3</sup>, which represent detected beam<br />fluctuation amplitude is twice as local density fluctuation, and the path integral<br />effect is dominant.<br /> The ensemble averaged terms can be evaluated if the fluctuations correlation be-<br />tween two spatial points is assumed as the Gauss function, ƒ( Δ<i>x</i>) =exp(－0.5(Δ/lc)<sup>2</sup>),<br />where <i>lc</i> is a correlation length. The HIBP of CHS is equipped with three chan-<br />nels, so that the correlation length <i>lc</i> can be evaluated; the distance between two<br /> of the channels, Δ<i>x</i> ranges from 3 to 10 mm By substituting the estimated correla-<br />tion function into Eq. (2), the local electron density fluctuation amplitude profile<br />can be reconstructed. Fig. 5.6(b) shows an example of the reconstruction for the<br />case that the electron density and temperature are ～ 10<sup>19</sup> m<sup>-3</sup> and ～ 1 keV, re-<br />spectively. Here, the integral equation is solved after several times iteration. The<br />detected beam current and the local electron density fluctuation amplitudes are<br />within the range of error in the outer region (<i>p</i> > 0.6). However, in the inner<br />region (<i>p</i> < 0.6), the fluctuation amplitude of detected beam current is a half of<br />the local fluctuation amplitude.<br /><br /><b>3.2. Reconstruction of local electron density fluctuation spectrum</b><br /> The reconstruction method of local density fluctuation is extended to the esti-<br />mation of density fluctuation spectra. It is apparent that the power spectra can be<br />evaluated simply by appling the above method to the fluctuation power at each<br />frequency. However, the integral equation for low frequency (< 50 kHz) cannot be<br />often solved with iteration method. This is caused by the fact that the correlation<br />length appears to become longer than the actual value. <br /> This is considered to result from the path integral effect on the correlation length. <br />The fluctuations of local three channels are strongly affected by the fluctuation<br />in the outer plasma regions, and the fluctuations at local three channels become<br />to show quite similar behavior. A technique is derived to correct this longer<br />correlation length. Thanks to the technique, the corrected correlation length is<br />evaluated and the spectra of local density fluctuation are successfully obtained. <br /> Fig. 6.3(b) shows one example of the reconstructed spectrum of local electron<br />density fluctuation, whose position is <i>r/a</i> - 0.26 in the same plasma in Fig. 5.6. <br />The result shows that the path integral effect is larger in low frequency than that<br />in high frequency. <br /><br /><b>3.3. Consideration of the Bolt2;mann Relationship</b><br /> As a result of the estimation of local density, the detected beam fluctuation<br />can be roughly regarded as the local density fluctuation in low density regimes of<br />n<small>e</small> ～ 5 × 10<sup>18</sup> m<sup>-3</sup>. Consequently, the detected beam fluctuation shown in Fig. <br />3.9 reflects local density fluctuation. A rough comparison between the density<br />fluctuation and potential fluctuation (normalized by electron temperature) allows<br />examining the validity of the Boltzmann relationship. Fig. 7.1(a) shows the nor-<br />malized density fluctuation as a function of normalized potential fluctuations. In<br />Fig. 7.1(a), the different marks correspond to the different ranges of radial posi-<br />tion of the plasma; red and green and blue plots are data point in 0 < <i>r/a</i> < 0.3,<br /> 0.3 <<i> r/a</i> < 0.6 and<i> r/a ></i> 0.6, respectively. The lines are fit lines using the least<br />squared method. The results show that the Boltzma- relationship should be<br /> valid, although tendency is found that the normalized density fluctuation should<br />be larger than the normalized potential fluctuation. <br /><br /><b>4. Summary</b><br />The simultaneous measurements of electron density and potential fluctuations<br />are successfully made with heavy ion beam probe after the development of a new<br />ion source. The measurement is achieved in a wide range of radial region with<br />spatial resolution of 2 mm. A method is proposed to evaluate the path integral<br />effect that is a long-standing problem for density fluctuation measurement with<br /> the HIBPs. Applying this method on the CHS fluctuation measurements, the local<br />density fluctuation and its power spectrum are successfully evaluated.