互感系数M12=M21的证明

从定义、磁能、磁矢势、磁偶极子、自由能5个方面出发分别证明了互感系数M12=M21,并对几种证明方法进行了分析对比,提出了自己的看法.     

互感系数M21=M12的直接证明

从互感系数的定义式出发,证明了线圈１对线圈２的互感系数Ｍ２１等于线圈２对线圈１的互感系数Ｍ１２。     

矢量分析证明互感系数M12=M21

本文应用矢量分析的方法对互感系数M12＝M21给出了一般性证明。     

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The manufacturing process of integral special-shaped forgings of the HL-2M vacuum vessel support trunnion was introduced, and the material testing was conducted by cutting the samples from the forging body. The test results show that the yield strength of the surface and core position of the trunnion forgings are 1100MPa and 1057MPa respectively, the grain size grade of those two positions can be up to grade 4, and all mechanical performance parameters can meet the design requirements.     

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HL-2M vacuum vessel is designed with a D-shaped, double thin-wall structure, which consists of inner shell, outer shell, ribs and ports. Torus inside and outside diameters are 2m and 5.22m, respectively. Torus height is 3.02m. The whole torus will be welded with 20 sectors. Inconel 625 ??Inconel 718 and 316L are selected for the vessel material. Finite element analyses of vacuum vessel are conducted. The results show that vacuum vessel structure can meet the design requirements of the machine.     

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A 16-channel J-type thermocouple instrument with digital calibration for the lower hybrid current drive (LHCD) system on HL-2M tokamak was developed to achieve 16 channel temperature measurements. The temperature measurement range is 0~250°C with the absolute error value less than 1°C. The temperature can be displayed on the liquid crystal display (LCD) and read on the computer remotely. The J-type thermocouple instrument has been successfully used in the debugging experiment of the LHCD heating system of HL-2M tokamak. The temperature of output cavity of the high power klystron has been measured under different output power conditions to ensure the safety of the klystron in operation.     

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The water-cooled model of the toroidal field coils was established calculated according to the heat conduction and the convective heat transfer equation. The results show that the thermal contact resistance and the electrical contact resistance of the interface between the finger joint and the copper plate had a larger effect on the temperature rise of the finger joint. At maximum current of 140kA and the current flattop 7s, the maximum temperature rise of the toroidal coils with the finger joint was below 40??, so the maximum temperature of the coils wouldn’t exceed 80??, and the temperature of the toroidal field was below 30?? after an interval of 15min. However, at maximum current of 190kA, the current flattop time was determined by the thermal contact resistance, the electrical contact resistance and initial temperature.     

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利用TSC程序对HL-2M装置的纯欧姆放电参数进行了首次数值放电模拟,证实了极向场线圈系统具有实现预设的宏观等离子体参数的能力。数值放电模拟还利用基本的位移控制和等离子体电流控制系统实现了从孔栏位形到下单零偏滤器位形的稳定演变。模拟提供的一些主要结果为工程和物理目标设计提供重要的参考。     

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HL-2M装置低杂波天线被设计为多栅阵列天线,天线由4行波导组成,每行32个子波导。子波导宽度为0.99cm,壁厚0.3cm,相邻子波导相差取90°。计算得到的反射系数R=0.0261,N||峰值中心为2.375。边缘等离子体电子密度梯度对波谱峰值中心位置没有影响,波峰相对宽度则随之增大而减小。在边缘等离子体电子密度梯度 的情况下,相邻子波导相差为81°时,天线方向性系数最好,为0.2010;反射最小,为0.0223,此时波谱峰值中心为2.125。     

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利用ANSYS CFX有限元程序建立了HL-2M欧姆测试线圈和冷却水模型,应用热传导和对流换热方程建立了流固边界层,对线圈的温升和冷却进行了流固耦合计算。计算结果表明,线圈由焦耳热引起的最高温升与电流密度、等效放电运行时间有关,而冷却水流量对最高温升影响较小,冷却水流量主要决定线圈的冷却时间间隔的长度,欧姆测试线圈的最长冷却时间间隔为5min。     

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The simulation results of the plasma reconstruction were obtained and compared with the accurate balance results. With the introduction of random errors in the simulation process, robustness of the inversion procedure had been verified. The reconstruction results using the experimental data from EAST device had been compared with the inversion results from EAST’s RTEFIT to verify the correctness of the results that a single time and the continuous-time inversion. The results show that, choosing the current distribution model and magnetic diagnostic data through the equilibrium reconstruction algorithm can correctly identify the plasma shape.     

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Based on one dimension simulations implemented by software and analytical method, the design and calculation of water cooling system for HL-2M TF, PF and CS coils are introduced. The hydraulic parameters for the cooling design is provided. By optimizing available pressure and flow distribution in the cooling system, maximum flow of the subsystems power output is 400m³•h⁻¹ and maximum pressure is 1.8MPa. The optimization results of hydraulic parameters meet the requirement of coils thermal exchange under the maximum velocity 4.5m•s⁻¹.     

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为环向场线圈防倾覆结构及其它支撑部件的设计提供依据,采用有限元实体模型分析方法,通过电磁-结构耦合计算对HL-2M装置的环向场线圈进行电磁力分析。计算结果表明,在目前的防倾覆结构和一般的运行情况下,环向场线圈所受最大剪切应力约为7.2MPa,在材料许用应力范围之内。     

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介绍了HL-2M装置控制系统的静态架构、动态行为、控制理论以及模拟仿真。设计采用通讯网络将各控制子系统有机地连接起来,以实现各子系统的实时通讯和控制。等离子体放电控制系统将保证实验的各种参数达到预定要求,监控系统的故障处理机制可以减少各种实验异常对装置造成破坏,磁场控制系统的各种控制器则用来控制等离子体电流和位形,模拟仿真系统可以实现方便地验证控制器的目的。     

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为利于HL-2M真空室(VV)及极向场线圈(PFC)的整体安装,环向场线圈(TFC)采用比特板式结构,这种结构需要用到高强度高导电性能的大尺寸异形铜合金厚板以便满足线圈复杂受力的要求.通过应力分析,确定了在TFC上使用的3种铜合金.介绍了大尺寸异形铜合金板材的制造工艺和铜板多项性能的测试结果,结果表明异形铜合金板材的尺寸及各项性能均满足了HL-2M装置环向场线圈的工程设计及加工要求.     

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针对HL-2M环向场线圈的紧固件的作用和力学性能要求,设计了各不相同的紧固件结构形式,并对各部件的材料、尺寸、螺纹形式、螺母型式、垫片型式、螺套型式等细节进行了相应的研究和选择.对膨胀螺栓的阴阳膨胀套结构进行了相应的模拟分析计算,并进行了相应的实验来验证膨胀螺栓结构的合理性.     

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介绍了HL-2M环向场线圈的基本结构设计及其承受的电磁载荷,分析了水平预加载、中心柱预应力筒以及环向抗扭支撑对线圈匝间剪切应力的影响.结果表明,水平预加载及预应力筒在中心柱内产生的压应力有利于提高中心柱的抗扭刚度;环向支撑刚度增加可减小线圈的面内剪切应力.在正常运行工况下,环向场线圈的最大匝间剪切应力小于8MPa,其结构设计满足线圈强度要求.对于大破裂瞬态事件,匝间最大剪切应力约12MPa,接近绝缘材料的剪切疲劳极限,建议采取破裂抑制措施避免该情况发生.