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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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.     

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在建的HL-2M装置的环向场线圈采用了比特板式结构,介绍了采用封闭多边形电流丝模型计算分析HL-2M装置环向场线圈电磁场和纹波情况;环向场线圈电流与环向场引起的电磁力以及与极向场产生的倾覆力也做了计算.计算结果对环向场线圈的设计具有一定的参考意义.     

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利用有限元分析软件ANSYS对不同截面的真空室做静力分析,结果表明圆弧形结构比多边形结构强度好。分别对8、16个重力支撑的真空室做静力分析,得到真空室与重力支撑连接位置的应力变化,优选了真空室重力支撑数量。优化设计了真空室与重力支撑连接位置,使其在烘烤时热应力减小。     

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用SURFMN和SURFMN_TFCOIL代码计算了由HL-2M装置磁场线圈安装误差产生的误差场。根据国外托克马克装置TF和PF线圈安装误差的取值范围,以及HL-2A装置安装的经验,计算选取的TF线圈和PF线圈最大位移范围为3~8mm,最大倾斜角度为0.05~0.1°。选取9组数据计算了误差场的概率密度分布和累计概率分布。结果发现：在TF和PF线圈安装误差取值范围内,随磁场线圈最大移位增大概率密度显著变平,误差场B3-mode/BT的分布范围显著增大;磁场线圈的位移比倾斜对误差场的影响更大;当磁场线圈最大位移达到5mm时误差场大于2×10-4的概率都比较大,特别是线圈最大位移等于8mm时,误差场大于2×10-4的概率在60%以上。     

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A hybrid structure was adopted for the PF coil of the building HL-2M device. In the process of discharge, there is a strong coupling between the coils, each coil will be subjected to a large electromagnetic force. In this paper, PF coil electromagnetic force is computed by the analytic method under the discharge conditions of the largest I_p =3MA plasma current and various configurations. These calculation results are of reference value for the design of PF coil and its support structure.     

超弦与M理论

 1.弦与相互作用统一理论20世纪物理学的两个最伟大成就是量子论与相对论。量子场论描述微观世界的基本粒子及其相互作用。广义相对论作为引力理论描述像星体、星系、黑洞及宇宙一类大尺度、巨质量体系。理解一般物理系统要么利用量子场论,要么求助于广义相对论,不会交叉动用这两个不同的理论体系。但是的确存在一些极端物理情景既涉及巨质量(需要广义相对论)又牵连极小距离尺度(需要量子场论),这类体系的正确理解必须建立在一个广义相对论与量子场论相互协调的框架内,换句话说就是需要量子引力理论。     

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By measuring the spatial coordinates of several points on the figure joints and slice joints of the toroidal field coils on HL-2M device, the outer contour planes of the coils are fitted with the spatial data of the points by the least squared method and the tilt angle of central axis is calculated by the spatial relation between the planes and the central axis. With the simplified model and numerical simulation, the tilt angles of different spatial points with several standard deviations of measurement are calculated. The average relative error of tilt angle is 0.10‰ and the relative standard deviation is 1.21‰ with a low standard deviation of metrology (σ=0.05mm).