称号及び氏名

博士（工学） Bui Xuan Nhat Son

学位授与の日付

令和 5 年 9 月 23 日

論「Time-dependent calorimetric analysis for estimation and文

名

control of heat load to plasma facing components infuture fusion reactors（将来の核融合炉におけるプラズマ対向機器への熱負荷の評価と制御のための時間依存熱量解析）」

論文審査委員

主査

松浦 寛人

副査

川又 修一

副査

梅澤 憲司

論文要旨

Nuclear fusion energy, which is expected to be a new sustainable source ofenergy, has gained public attention recently. In contrast to the nuclear fission
reaction in which the heavy elements are split turning mass into energy, the energyof a nuclear fusion reaction is from the combination of light elements. Generally,
the fusion reactions produce more energy, less risk of nuclear waste, and even noCO2 emission. Successful development of fusion energy, however, requires further
studies including plasma operation, materials, fuel breeding, heat exhaust, andsafety. Such studies have been conducted on many fusion devices in the world.
Divertor is an important component in the fusion reactor. Its main function is toremove the impurity particle during the operation. The divertor is the component
which receives the most severe heat load concentration in the fusion reactor. To
ensure a safe operation in the fusion reactors, ti is necessary to control the divertor
heat flux. Accordingly, monitoring divertor heat flux becomes an urgent task toverify the ability of control processes. In this thesis, studies of sensor design andestimation methods to precisely monitor divertor heat fluxes are proposed.
In Chapter 1, general information about nuclear fusion energy and magneticallyconfinement plasmas are presented. Besides, the goals and outline of this thesis areincluded in this chapter.
In Chapter ,2 the calorimetric methods for divertor heat flux estimation areintroduced. In general, the divertor heat flux can be inversely evaluated frommonitored temperature data with the heat conduction model. Such a model
assumes a control volume (CV) containing the temperature measurement point andmust satisfy the heat conservation law. In other words, heat flux crossing theboundary, heat generation in the CV, and internal energy evolution must balance.
Temperature response function has been developed to describe CV temperature
response toward the step-like heat flux applied at the irradiated surface. By fitting
such a response function to the monitored temperature data, the time-dependent
heat flux can be obtained.
Chapter 3 describes the improvement of a temperature response function in 1dimensional (1D). The 1D temperature response function is applicable for thesmall sensor target where the heat flux is assumed to be homogeneous at its
irradiated surface. In the previous work, the temperature response functions in 1dimension (1D) for different back-side boundary conditions have been proposedand successfully described the delay of the thermocouple (TC) signal owing to thediffusion time in the target material. However, as an empirical phenomenon,
another time delay in the order of several hundred ms has been observed repeatedly
in our sensor data. Due to this unknown delay, observing the changes in heat flux
for fast events during plasma discharge is impossible. In this chapter, the primary
delay mathematical model, which is used to describe TC signals subjected to timedelay is proposed. Using the primary delay model, the unknown time delay
involved in TC systems can be measured experimentally. According to the findings,
the main causes of delayed signals in TC systems are the intrinsic delay of TC
wires with finite heat capacity and contact heat resistance between TC and thetarget surface. In addition, a method to artificially reconstruct the delayed signal
from the measured value of time delay is suggested.
Chapter 4 involves the expansion of the temperature response function into 2dimensional (2D). In the fusion devices, the heat flux profile is in cm order. If thesensor target is bigger than such an order, the temperature distribution will beinhomogeneous and the heat flux estimation using the ID temperature response
function will be insufficient. In this chapter, 2D temperature response functions
are proposed including parallel and perpendicular directions to the tile surface. The
surface temperature data from the LHD divertor tile is analyzed with the 2D
temperature response function. The results obtain temperature and heat flux spatial
profiles, as well as their time evolution. Using the 2D response function,

temperature profiles can be successfully reconstructed from sparse temperature
data with low spatial resolutions. The findings suggest that 10 thermometerchannels would be sufficient to reproduce the temperature profiles from the target
size in the order of 10 cm. This number can even be optimized if magnetic fielddata is known in advance so that the thermometers can be concentrated only in thearea of consideration.
In Chapter 5, the construction of a novel sensor to monitor the heat flux in longpulse scenario is proposed. Currently, in most of the existing fusion devices, theplasma discharge duration is in the order of hundred milliseconds. However, thepulse duration in the future DEMOs is expected to be much longer and requires
active cooling to sustain plasmas and ensure a safe operation. In such a scenario,
the effects of heat loss will dominate the observed heat fluxes. The new sensor
consists of a glass target with a relatively low conductivity. TCs are embedded in
the top and bottom surfaces so that the effect of heat loss can be distinguished.
Findings show that the heat loss time constant of the target is in the order ofhundred seconds. Using this sensor, the heat flux estimation is performed withirradiation time ranging from minutes to more than an hour. For the fast events, theheat flux estimation methods proposed in the previous chapters can be applied. On
the other hand, when the irradiation time becomes long, the heat flux can beestimated with a simplified heat balance model which takes into account the effectof heat loss. This provides some hints to construct the heat flux sensor and develop
the heat flux estimation method for future commercial fusion reactors.
Chapter 6 is the summary of the previous chapters and the conclusion of this thesis.
Cooperation of the temperature response functions with the pulse decomposition

method can be a useful tool for the estimation of divertor heat fluxes. In this thesis,
the temperature response functions have been modified to describe the time delay
effect and expanded to deduce multi-dimensional heat fluxes. Moreover, a novel
sensor has been developed and successfully estimate the long-pulse heat flux withconsideration of heat loss effect. The reconstruction of divertor heat flux can beimproved by carefully determining the sensor target boundary condition orconsideration of heat transfer in different direction. This will be left for future
research.

審査結果の要旨
本論文は、近年ゼロカーボン政策の切り札として期待されている核融合炉建設に際して克服すべき炉工学的問題の解決につながる研究をすすめたものである。強力な磁場で閉じ込められた、水素の同位体から生成される超高温プラズマを安定に保持するため、核融合反応で生まれるヘリウムやプラズマ対抗材料から困窮する不純物イオンを中性化して排出する必要がある。このための機器、あるいは概念をダイバータと呼ぶ。そのため、ダイバータの主要部であるターゲット板には太陽表面に匹敵する熱流束が手中する。この熱流束の正確な値を決定し、プラズマ対抗材料の温度変化を予測する方法を確立するのが本研究の目的で、特に注目すべき成果は以下のとおりである。
(1)プラズマ照射された固体表面への熱流束は、固体内部の熱伝導の逆問題を解き、固体内の温度モニタの測定を再現するような、照射面側の境界条件として決定される。既存研究で、温度モニタ点がプラズマ照射面から任意の距離にあっても対応できるような温度応答関数を導出したが、京都大学や筑波大学で設計、製作した熱流束センサーの応答が、予想よりはるかにゆっくりしていることが示されていた。これは温度変化と熱電対信号の間の時間遅れに起因するものであり、一次遅れの数学モデルをつかって、補正できることと、実際のセンサーごとに特徴的な遅れ時間をあらかじめ実測できることが示された。本研究のこの成果は、筑波大学での加熱用ビームを使った実験や、京都大学での最新の熱流束センサーでの測定で、その有効性が示されている。
(2)ダイバータは特別な磁場構造を構成してシート状のプラズマをターゲット板に導かれる。その際、シートの厚みはターゲット板の大きさより小さいため、プラズマ照射面に沿った、温度や熱流束の分布が重要になる。他方、実用核融合炉では計測ポートの設置が制限されるため、IR カメライメージによる温度の分布計測はできなくなる。本研究では、温度応答関数をフーリエ級数の利用により多次元化し、展開係数を有限数のセンサーのデータから決定する方法を提案した。核融合研究所の実験装置のダイバータタイルの表面温度測定データに、この方法を適用し、必要な測定チャンネル数などについての検討を進めた。
(3)実用的な核融合炉では、放電時間が 1 時間を超えると予想されている。そのためプラズマ対抗機器は、熱流束センサーを含めて、何らかの冷却系で除熱されることになる。
しかしながら、既存の実験装置での研究では、この冷却効果を正しく取り入れていない

にも拘わらず、放電時間が短いためこの問題は見過ごされていた。本研究では、長時間放電である応用プラズマの分野での熱バランスモデルと、これまで開発した高速応答の熱流束計測を組み合わせる可能性を初めて検討した。
以上の諸成果は、次世代の核融合炉での熱流束センサーの設計についての重要な知見を与える。本研究はこのように特定のプラズマ装置のセンサーや解析法の改良のみならず、将来にわたっての応用の上からも有益な情報を提供したものであり、核融合工学の学術的・産業的な発展に貢献するところ大である。また、申請者が自立して研究活動を行うのに必要な能力と学識を有することを証したものである。
学位論文審査委員会は、本論文の審査および最終試験の結果から、博士（工学）の学位を授与することを適当と認める。