Time response improvement for divertor heat flux monitoring in nuclear fusion devices

Tiểu ban B Vật lý hạt nhân, Số liệu hạt nhân, Phân tích hạt nhân và Máy gia tốc Section B Nuclear physics, Nuclear data, Nuclear analysis and Accelerator 173 TIME RESPONSE IMPROVEMENT FOR DIVERTOR HEA[.]

Tiểu ban B: Vật lý hạt nhân, Số liệu hạt nhân, Phân tích hạt nhân Máy gia tốc Section B: Nuclear physics, Nuclear data, Nuclear analysis and Accelerator TIME RESPONSE IMPROVEMENT FOR DIVERTOR HEAT FLUX MONITORING IN NUCLEAR FUSION DEVICES BUI XUAN NHAT SONA,*, HIROTO MATSUURAA, YOUSUKE NAKASHIMAB a Osaka Prefecture University, Osaka 599-8570, Japan b University of Tsukuba, Tsukuba 305-8577, Japan *E-mail: mc106010@riast.osakafu-u.ac.jp Abstract: ITER is expected to be the first fusion device that produces net energy with fusion energy gain factor of more than 10 During unsteady stages in the operation, short time plasma heat load would be higher than that of the sun surface and finally exposes to the divertor plate Thus, monitoring and controlling the heat load to plasma facing material are essential issues in plasma physics, material science, and heat transfer technology The scope of this study is to deduce the time dependent heat flux from temperature evolution of plasma facing material target To that, constructed sensor must reproduce the real temperature evolution, and the corresponding estimation model must satisfy the heat conservation law Recently, sensor designs have been upgraded to have a smaller effective size to reduce thermal diffusion time However, a common delay coming from TC system with order of approximately hundreds ms is reported to involve in the thermocouple signal in several fusion devices in Japan such as Heliotron J (Kyoto University), GAMMA 10/PDX (University of Tsukuba), and LHD (National Institute for Fusion Science) To verify the estimation model and investigate the reason of time delay, we have conducted sensor test in neutral beam (short pulse) facility Besides, commercial thermocouple delay tests were also carried out for the same purpose Details would be presented on the conference site Keywords: fusion plasma, heat flux estimation, heat conduction INTRODUCTION ITER is expected to be the first fusion device that produces net energy with fusion energy gain factor of more than 10 In steady-state, the plasma heat flux onto reactor vessel wall can reach 10 MW/m and induce temperature increment in plasma-facing components (PFCs) [1,2] If the system's cooling ability is insufficient, the PFC target temperature will keep increasing and cause severe damage to the system Therefore, such a heat flux needs to be under control for a safe operation in fusion devices Before the heat load reaches to PFCs, neutral gas is injected to the core plasma for reducing its energy This procedure, so called plasma detachment [3], is a well-known method for controlling heat load in fusion devices To check the control ability of this process, developing divertor heat flux measurement is an urgent task This demands not only a value of PFC temperature but also its time evolution Accordingly, the heat flux monitoring system must have a fast response for a precise and detailed estimation In our study, divertor heat flux is estimated from temperature evolution data of the TC system and a suitable heat conduction model Such a model assumes a control volume to contain the temperature measurement point and satisfies the energy conversation laws [4] In other words, heat flux to the boundary, heat generation in the control volume, and internal energy must balance In the experiment using Hybrid Directional Probe (HDP) in Heliotron J (Kyoto University– Japan) [5] and that using Hybrid Directional Langmuir Probe (HDLP) in LHD (National Institute of Fusion Science– Japan) [6], our heat conduction model had been confirmed to be able to reproduce the temperature evolution during the plasma shot Plasma detachment happened less than 10ms and can be seen clearly in the ion current time trace [6] In contrast, the heat flux evolution estimated from HDLP data reproduced this event with much slower response This delay could be explained by the thermal diffusion time of the target material In case of using HDLP, temperature signal needed more than s to reach to the measuring point after plasma irradiation To estimate heat flux from fast event like plasma detachment, sensors should be upgraded to have a fast response (for example, 10 to 100 ms) To overcome the limit of diffusion time, we constructed a target with thickness in the order of 1mm for calorimeters in GAMMA 10/PDX (University of Tsukuba- Japan) [8] Even so, a common time delay of several hundreds ms was found experimentally in the TC signal Consequently, the TC system may have other kinds of delay rather than the target diffusion time In this work, we modify the heat conduction model with consideration of TC system time delay Besides, causes of time delay and ideas to minimize them will be discussed 173 Tuyển tập báo cáo Hội nghị Khoa học Cơng nghệ hạt nhân tồn quốc lần thứ 14 Proceedings of Vietnam conference on nuclear science and technology VINANST-14 THE MAIN PART OF REPORT Primary delay model Time delay involves in most of control systems In a TC system, time delay might be induced by target diffusion time, TC response and other unknown reasons Schematic design of a typical calorimeter for heat flux estimation is shown in Figure with L is calorimeter target thickness, x is location of embedded TC from target irradiated surface With 𝛼 refer to the diffusivity of target material, target 4𝐿2 thermal diffusion time 𝜏 = 𝜋2𝛼 is proportional to the target thickness L Even so, effect of target diffusion 𝑥 time can be reduced by setting TC closer to the irradiated surface since TC response 𝜏 𝑇𝐶 = 𝜏 𝐿 is proportional to distance x of embedded TC As mentioned above, another delay rather than target diffusion time was found in our previous experiments It might be from metal sheath heat transport, electric circuit elements, or the contact between TC and the target surface For a convenient model calculation, we consider such a delay as unknown time delay 𝜏0 Figure 10 A schematic diagram of a calorimeter target with thickness of L A thermocouple is attached at position x from the irradiated surface (𝜏~ 𝑥 ) If a signal convertor can be modeled asa primary delay system with time delay 𝜏0 and conversion factor K, its input u(t) and output y(t) obey the following relation 𝑑𝑦(𝑡) (1) 𝜏0 + 𝑦(𝑡) = 𝑢(𝑡) 𝑑𝑡 𝐾 The mathematical solution of this system is 𝑡 𝑡 −𝑡 𝑦(𝑡) = 𝑦(0)𝑒 𝜏0 + 𝑒 𝜏0 ∫ ′ 𝑡 𝑢(𝑡 ′ )𝑒 𝜏0 𝑑𝑡 ′ 𝐾𝜏0 (2) In [4], temperature response to step-like heat flux 𝑞0 to an insulation target was introduced In this work, we modified the response function s as the effects of diffusion time 𝜏 and finite delay 𝜏0 can be both described: 𝑆(𝑥, 𝑡) 4𝑡 𝜏0 −𝑡 𝑥 𝑥 −𝑡 = ( − (1 − exp ( ))) + (− + ( ) ) (1 − exp ( )) 𝛥𝑇 𝜋 𝜏 𝜏 𝜏0 𝜋 𝐿 𝐿 𝜏0 ∞ 𝑥 𝑡 𝑡 − 𝐴 ∑ 𝐶𝑛 sin (𝐵𝑛 ) (exp (−𝜏 ) − exp (− )) 𝑛 𝐿 − 𝜏𝑛 𝜏0 𝜏 𝜏0 𝑛=0 𝜏 where 𝜅 is heat conductivity of target material, 𝐴 = 174 −8 𝜋2 , ∆𝑇 = 𝑞0 𝐿 𝜅 , (3) Tiểu ban B: Vật lý hạt nhân, Số liệu hạt nhân, Phân tích hạt nhân Máy gia tốc Section B: Nuclear physics, Nuclear data, Nuclear analysis and Accelerator 𝐴𝑛 = (2𝑛+1)2 , 𝐵𝑛 = 𝜋(2𝑛+1) , 𝐶𝑛 = 𝐴𝑛 𝐵𝑛 and 𝜏𝑛 = (2𝑛 + 1)2 Basing on the primary delay model in equation (3), if heat flux and target properties are set, the corresponding temperature evolution can be reproduced Figure indicates TC signals when a 200 ms heat pulse applied to an insulation target The purple curve refers to the ideal temperature evolution without time delay Green, blue, and orange curves correspond to the signals deformed by delays 10-, 30-, 50 ms, respectively With the longer time delay, TC signal takes a longer time to reach the saturated temperature In that way, the step-like heat pulse cannot be estimated precisely Figure 11 Time delay can deform the TC signal so that the heat flux estimation can be imprecise 2.2 Testing with short pulse neutral beam In [4], Osakabe et al first proposed to deduce heat flux experimentally by the sensor with two TCs The calorimeter for monitoring the heat flux evolution in GAMMA 10/PDX (University of Tsukuba) [7] is described in Figure The calorimeter target was made from cooper with a thickness of 10 mm TCs were set at 1.5-, and 3.5 mm from the irradiated surface corresponding to 8- and 42- ms diffusion time, respectively Neutral beam (NB) injection was chosen to verify the primary delay model because it induces clear and simple temperature response Figure 12 Schematic diagram of a calorimeter in neutral beam short pulse test After irradiation by10 ms NB pulse, the raw signals from calorimeter system involve 50Hz noise from the power supply As shown in Figure 4, the TC signals became clear after low pass filtering with Hz cut off In comparison with NB pulse timing, TC response in this test is slow It started even after NB pulse termination 175 Tuyển tập báo cáo Hội nghị Khoa học Cơng nghệ hạt nhân tồn quốc lần thứ 14 Proceedings of Vietnam conference on nuclear science and technology VINANST-14 Figure 13 TC data from neutral beam test before (left) and after (right) applying the low pass filtering Green, blue and orange waveform correspond to signal from channel 1, channel 2, and channel 3, respectively The model calculation in equation (3) can reproduce the temperature evolution in each TC position basing on the timing of the applied NB pulse Figure reveals the comparisons between real TC signal and its model calculation in channels of the calorimeter By carefully choosing calculation parameter and comparing the result to experimental data, values of time delay 𝜏0 and received heat flux 𝑞0 in each channel can be supposed As a result, time delay of 80-, 120-, and more than 300 ms are assumed to involve in TC signal of channel 2, channel 3, and channel 1, respectively Detailed information is described in Table Figure 14 Comparisons between model calculation and experimental TC signal from channels in shot number 210304-165921 Table Parameters for primary delay model calculation in NB test Diffusion time 𝝉 Time delay 𝝉𝟎 Heat flux 𝒒𝟎 (ms) (ms) (W/m2) Channel (x = 3.5 mm) 42 300 or more 1.55E+05 Channel (x = 1.5 mm) 80 2.10E+05 Channel (x = 3.5 mm) 42 120 2.1E+05 2.3 Time delay direct estimation Although the TCs were set closer to irradiated surface for a faster response, the TC system was assumed to have other delay in the order of 100 ms in the experiment with NB pulse In this section, we introduce the time delay estimation of TCs in different experimental condition The experiment set-up is described in the left-hand side Figure In this experiment, a soldering iron was used as a heat source A Molybdenum plate with 0.2 mm of thickness was used as the target to minimize diffusion time of target Behind it, TC was embedded to record the temperature evolution when the soldering iron touch to target surface TC signal then amplified to improve the S/N ratio before transmitting to an oscilloscope (OSC) In another OSC channel, we measure the voltage difference between target and the soldering iron to check their contacting time After the experiment, there are two kinds of data recorded: TC signal and contacting signal 176 Tiểu ban B: Vật lý hạt nhân, Số liệu hạt nhân, Phân tích hạt nhân Máy gia tốc Section B: Nuclear physics, Nuclear data, Nuclear analysis and Accelerator Figure 15 Experiment set up for time delay estimation (left) and the result for bare TC with the radius of 1.5 mm (right) In Figure right-hand side graphs, comparison between the signal of TC with the radius of 1.5 mm and the corresponding model calculation is revealed Blue waveform with random noise is the real TC signal The duration [t0, t1] is determined from contacting data Modeling calculation during [t0, t1] is basing on equation (3) The orange waveform is the result of the ideal temperature signal (without time delay) while the red one is that with consideration of time delay In each experiment condition, several values of time delay are assumed Then the one which can reproduce the best fit between model calculation and experimental data can be chosen as the result delay time Insulation amplifiers in our TC systems were tested using this method A common delay of approximately ms was estimated in all the observed amplifiers This value also meets agreement with the information from the manufacturer Thus, we move to the next stage to measure the time delay of commercial TCs Four TCs with radius of 1.5-, 1-, 0.5-, and 0.25 mm were used in this investigation Firstly, we estimated the time delay of the bare TCs Secondly, the observed TC was embedded to the backside of the Molybdenum target using Kapton tape Then, additional measurements for TC contacting without using any backside cover were conducted After all, the corresponding time delay can be summarized as shown in Table Table Values of TC time delay in different conditions Experiment condition Bare TC (Ø = 1.5mm) Bare TC (Ø = 1mm) Bare TC (Ø = 0.5mm) Bare TC (Ø = 0.25mm) TC (Ø = 1mm) + Mo plate TC (Ø = 1mm) + Mo plate + Kapton tape TC (Ø = 0.5mm) + Mo plate + Kapton tape TC (Ø = 0.25mm) + Mo plate + Kapton tape Delay (ms) 290 70 20 10 330 150 35 20 2.4 Discussion The primary delay model can describe temperature evolution under the effects of time delay and target diffusion time In the test with NB pulse, the model calculation agrees well to the signal from channel and channel However, the overshoot signal in channel cannot be explained by this model The supposition for time delay value via this experiment is not contradict to the previous study Time delay appears in all measurements using TCs Time delay of bare TCs is proportional to its radius When TC is embedded on a target, the contact between them is an important issue Temperature response of the same TC can be slower if the TC is not tightly contacted From Table 2, time delay of a TC with radius of mm (in case of bad contact to target) is 330 ms This delay can be a half smaller if the same TC is embedded to target using Kapton tape Furthermore, if a TC with smaller radius is embedded with the same contacting method, time delay can be reduced to the expected range as mentioned in the introduction 177 Tuyển tập báo cáo Hội nghị Khoa học Cơng nghệ hạt nhân tồn quốc lần thứ 14 Proceedings of Vietnam conference on nuclear science and technology VINANST-14 2.5 Conclusion Among the TC problems, delay owing to TC radius and contact with target is dominant to the slow response of TC system The primary time delay model and time delay estimation experiment could be a promising tool for further TC system calibration before installing them to fusion devices In case the time delay cannot be reduced more, compensation method to reconstruct the real temperature evolution from the appearance TC signals can be obtained if the time delay of TC system is experimentally measured in advance REFERENCES [1] Hirai T 2005 Material Transactions 46 412 [2] Hirai T 2010 Advances in Science and Technology 73 [3] Ohno N 2001 Nuclear Fusion 41 1055 [4] Osakabe M 2001 Review of Scientific Instruments 72 586 [5] Matsuura H 2010 Plasma and Fusion Research S1045 [6] Matsuura H 2014 Contributions to Plasma Physics 54 285 [7] Matsuura H 2019 IEEE Transactions on Plasma Science 47 3026 [8] Ohuchi M 2016 AIP Conference Proceeding 1771 050011 178 ... (2) In [4], temperature response to step-like heat flux