Present Status of the KSTAR Superconducting Magnet System Development

The mission of Korea Superconducting Tokamak Advanced Research (KSTAR)project is to develop an advanced steady-state superconducting tokamak for establishing a scientificand technological basis for an attractive fusion reactor. Because one of the KSTAR mission is toachieve a steady-state operation, the use of superconducting coils is an obvious choice for themagnet system. The KSTAR superconducting magnet system consists of 16 Toroidal Field (TF) coils and14 Poloidal Field (PF) coils. Internally-cooled Cable-In-Conduit Conductors (CICC) are put into usein both the TF and PF coil systems. The TF coil system provides a field of 3.5 T at the plasmacenter and the PF coil system is able to provide a flux swing of 17 V-sec. The major achievement inKSTAR magnet-system development includes the development of CICC, the development of a full-size TFmodel coil, the development of a coil system for background magnetic-field generation , theconstruction of a large-scale superconducting magnet and CICC test facility. TF and PF coils are inthe stage of fabrication to pave the way for the scheduled completion of KSTAR by the end of 2006.

The 5.8 T Cryogen-Free Gyrotron Superconducting Magnet System on HL-2A

A 5.8 T cryogen-free superconducting magnet （SCM） system with a warm bore hole of 160 mm in diameter, used for gyrotrons operating in the frequency range from 68 GHz to 140 GHz, is installed on the site of the HL-2A tokamak. The SCM consists of two separate solenoidal magnetic coils connected in series, a 4.2 K Gifford-McMahon （GM） refrigerator, a com- pressor, a coil power supply and two temperature monitors. The performance, test and preliminary experimental results of this SCM system are described in this paper. The magnetic field distribu- tion was measured along the axis, and a dummy tube was used for adjusting the magnet system. Finally, the magnet was used for the operation of a 68 GHz/500 kW gyrotron, which is part of an electron cyclotron resonance heating （ECRH） system. With an additional auxiliary coil and after adjusting tile magnet system, a maximum output power for the ECRH system of up to 400 kW was achieved.

MHD stagnation-point flow and heat transfer towards stretching sheet with induced magnetic field

The problem of the steady magnetohydrodynamic （MHD） stagnation-point flow of an incompressible viscous fluid over a stretching sheet is studied. The effect of an induced magnetic field is taken into account. The nonlinear partial differential equations are transformed into ordinary differential equations via the similarity transformation. The transformed boundary layer equations are solved numerically using the shooting method. Numerical results are obtained for various magnetic parameters and Prandtl numbers. The effects of the induced magnetic field on the skin friction coefficient, the local Nusselt number, the velocity, and the temperature profiles are presented graphically and discussed in detail.

A 3rd Order WENO GLM-MHD Scheme for Magnetic Reconnection

A new numerical scheme of 3rd order Weighted Essentially Non-Oscillatory (WENO) type for 2.5D mixed GLM-MHD in Cartesian coordinates is proposed. The MHD equations are modified by combining the arguments as by Dellar and Dedner et al to couple the divergence constraint with the evolution equations using a Generalized Lagrange Multiplier (GLM). Moreover, the magnetohydrodynamic part of the GLM-MHD system is still in conservation form. Meanwhile, this method is very easy to add to an existing code since the underlying MHD solver does not have to be modified. To show the validation and capacity of its application to MHD problem modelling, interaction between a magnetosonic shock and a denser cloud and magnetic reconnection problems are used to verify this new MHD code. The numerical tests for 2D Orszag and Tang's MHD vortex, interaction between a magnetosonic shock and a denser cloud and magnetic reconnection problems show that the third order WENO MHD solvers are robust and yield reliable results by the new mixed GLM or the mixed EGLM correction here even if it can not be shown that how the divergence errors are transported as well as damped as done for one dimensional ideal MHD by Dedner et al.

3D MHD Jet in a Non-Uniform Magnetic Field

The purpose of this paper is to present a two-phase 3D magnetohydrodynamics （MHD） flow model that combines the volume of fluid （VOF） method with the technique derived from induced-magnetic-field equations for liquid metal free surface MHD-jet-flow. Analogy between the induced-magnetic-filed equation and the conventional computational fluid dynamics （CFD） equation is made, so that the equation can be conveniently accounted for by CFD. A penalty factor numerical method is introduced in order to force the local divergence-free condition of the magnetic fields and an extension of the void insulating calculation domain is applied to ensure that the induced-magnetic field at its boundaries is null. These simulation results for lithium liquid metal jets under magnetic field configurations of Magnetic Torus （Mtor） and National Spherical Torus Experiment （NSTX） outboard divertor have shown that three dimensional jet can not be annihilated by magnetic braking and its cross-section will deform in such a way that the momentum flux of the jet is conserved. 3D MHD effects from a magnetic field gradient cause return currents to interact with applied magnetic fields and produce unfavorable Lorentz forces. Under 3D applied non-uniform magnetic fields of the divertor, unfavorable Lorentz forces lead to a substantial change in flow pattern and a reduction in flow velocity, with the jet cross-section moving to one side of the jet space. These critical phenomena can not be revealed by 2D models.

Momentum Transport in DIII-D Discharges with and Without Magnetohydrodynamics （MHD） Activity

Two phases of a DIII-D discharge with and without magnetohydrodynamics （MHD） activity are analysed using ONETWO code. The toroidal momentum flux is extracted from experimental data and compared with the predictions by neoclassical theory, Gyro-Landau fluid transport model （GLF23） and Multi-Mode model （MMM95）. It is found that without MHD activities GLF23 and MMM95 provide a reasonable description while with MHD activity no model alone can fully describe the experimental momentum flux. For the phase with MHD activity a simple model of resonant magnetic drag is tested and it cannot fully explain the plasma slowing down observed in experiment.

Dufour and Soret Effect on Steady MHD Flow in Presence of Heat Generation and Magnetic Field past an Inclined Stretching Sheet

An analysis of two-dimensional steady magneto-hydrodynamic free convection flow of an electrically conducting, viscous, incompressible fluid past an inclined stretching porous plate in the presence of a uniform magnetic field and thermal radiation with heat generation is made. Both the Dufour and Soret effects are considered for a hydrogen-air mixture as the non-chemically reacting fluid pair. The equations governing the flow, temperature and concentration fields are reduced to a system of joined non-linear ordinary differential equations by similarity transformation. Non-linear differential equations are integrated numerically by using Nachtsheim-Swigert shooting iteration technique along with sixth order Runge-Kutta integration scheme. Finally the significance of physical parameters which are of engineering interest are examined both in graphical and tabular form.

U型耦合管道内液态金属MHD效应研究

针对液态包层中常见的U型导电耦合管道内液态金属三维磁流体动力学(MHD)流动,利用自主开发的低磁雷诺数下液态金属磁流体流动的计算程序,获得了外加磁场和流体管道在不同倾斜角工况下管道内液态金属的流速、感应电流和压力分布。结果表明,U型耦合管道内液态金属的MHD流动中耦合段的耦合效应使MHD压降明显增大,是相同参数下单根管道内压降的2.4倍左右。在U型耦合管流动转向处,部分中心流体区产生与初始流向相反的逆流流速分布,而此处的磁流体压力梯度随外加磁场倾角的增大而增大,但在初始增加倾角时,压力梯度会略微减小。

近日太阳风中磁场回弯结构的MHD模拟

帕克太阳探针(Parker Solar Probe,PSP)在太阳附近发现大量磁力线回弯结构,通常还伴随有太阳风速度增加.这些磁力线回弯的产生机制到目前为止有多种解释,其中有代表性的一种是由慢太阳风中的喷流引起的.我们首先对PSP的就地观测数据进行了统计分析并给出了发生率和空间尺度随径向距离的演化情况,然后使用简化的1.5维磁流体动力学(magnetohydrodynamics,MHD)模型对喷流在太阳风中的演化进行了模拟,其中太阳风被简化为位于黄道面的球对称流.模拟结果表明喷流的确可以导致太阳附近磁力线发生偏转,验证了喷流可以对磁场方向改变有贡献的图景.不过喷流形成的原因还需要进一步研究.

不考虑磁层顶磁重联的全球三维MHD模型

本文介绍了一个新的磁层全球三维MHD模型 ,该模型可通过把IMF和地球磁场分开处理的方法“关闭”磁层顶的磁重联 ,从而可直观地显示不同IMF条件下磁层顶的IMF与地磁场的反平行区域 ,即磁重联最可能发生的地方 .结果表明 ,IMFBx 分量对磁层顶磁重联有重要影响 .由于可关闭磁重联 ,该模型还可有效地研究有无磁重联时 ,太阳风对磁层位形 (如晨 昏不对称性 )、粒子输运等重要问题的影响 ,有助于揭示磁层物理现象的基本特性 .

矩形管道中液态金属MHD流动数值模拟研究

基于感应电磁场方程发展了低磁雷诺数条件下充分发展液态金属管道流的数值模拟程序。为了校正程序,分别计算了两种工况:液态金属在全绝缘管道和部分绝缘管道中的流动,数值结果与Hunt和Shercliff的解析解吻合的很好,表明该程序具有很高的精度。最后利用发展的程序对液态金属钠钾合金在管壁材料为304不锈钢的全导电管道中的流动进行了数值模拟,并对流速分布和MHD压降结果与实验结果进行了比较,结果表明数值与实验结果吻合较好。

MHD控制激波诱导湍流边界层分离的机理分析

为了研究磁流体动力学(Magnetohydrodynamics:MHD)加速边界层对激波-湍流边界层相互作用的影响,用高阶有限差分法求解了小磁雷诺数近似的MHD湍流方程。其中,无粘通量采用WENN格式离散、粘性通量采用Roe平均中心差分离散,时间采用半隐式推进,并采取追赶法求解。计算给出了湍流、电场、磁场和电导率等参数对边界层分离的影响,数值结果显示:在同样的逆压梯度下,湍流边界层分离能更快地趋于稳态流场,且分离区比层流小;通过施加洛仑兹力加速,边界层速度型面变得更加饱满、位移厚度减小、分离点和再附点向激波与固壁的交点靠近,分离区尺寸减小甚至最终被消除。

MHD角速度传感器磁场设计研究

MHD角速度传感器是在轨进行高精度角颤振测量的关键器件。通过对2种MHD角速度传感器进行对比研究,确定径向磁场方式的传感器为更适宜我国当前空间发展需要的MHD角速度传感器。并设计了其径向磁场结构,获得在导电流体间隙处需要的磁感应强度,测试结果与模拟设计结果一致,为MHD角速度传感器研制奠定了一定的基础。

非均匀磁场中自由表面液态射流的MHD稳定性分析

基于在液态金属实验回路上的实验,对非均匀磁场中液态金属射流的MHD稳定性进行了研究,建立了一个描述射流性能的简化模型。由此简化模型所得的结果与从实验获得的结果相比较表明,它们相当吻合,并发现在此液态金属射流中存在一个固有稳定性区域。

LSFEM Implementation of MHD Numerical Solver

Many problems in physics are inherently of multi-scale nature. The issues of MHD turbulence or magnetic reconnection, namely in the hot and sparse, almost collision-less astrophysical plasmas, can stand as clear examples. The Finite Element Method (FEM) with adaptive gridding appears to be the appropriate numerical implementation for handling the broad range of scales contained in such high Lundquist-number MHD problems. In spite the FEM is now routinely used in engineering practice in solid-state and fluid dynamics, its usage for MHD simulations has recently only begun and only few implementations exist so far. In this paper we present our MHD solver based on the Least-Square FEM (LSFEM) formulation. We describe the transformation of the MHD equations into form required for finding the LSFEM functional and some practical issues in implementation of the method. The algorithm was tested on selected problems of ideal (non-resistive) and resistive MHD. The tests show the usability of LSFEM for solving MHD equations.

2.5维自适应磁场重联MHD模式

磁雷诺数（Rm）是影响磁场重联的重要因素．真实的物理环境中R。往往很高，例如，在行星际空间和太阳日冕中Rm通常大于104量级．高Rm条件下的磁重联表现出很多异常特性，然而高Rm条件下的磁场重联数值模拟需要很高的时空分辨率，否则很难分辨出重联过程中形成的薄电流片,本文基于自适应软件包PARAMESH将并行自适应网格技术引入磁场重联数值模拟，建立了一个2．5维自适应磁场重联MHD模式，研究高磁雷诺数条件下重联的动态演化过程，进而将不同磁雷诺数的参数进行对比研究．结果表明，该模式可以自动捕捉到磁场重联产生的奇性电流片，高磁雷诺数条件下产生的慢激波结构可提供一种快速磁能释放机制．

Dual solutions of MHD stagnation point flow and heat transfer over a stretching/shrinking sheet with generalized slip condition

An analysis was made to study the steady momentum and heat transfer characteristics of a viscous electrically conducting fluid near a stagnation point due to a stretching/shrinking sheet in the presence of a transverse magnetic field and generalized slip condition. Two flow problems corresponding to the planar and axisymmetric stretching/shrinking sheet were considered. By means of similarity transformations, the obtained resultant nonlinear ordinary differential equations were solved numerically using a shooting method for dual solutions of velocity and temperature profiles. Some important physical features of the flow and heat transfer in terms of the fluid velocity, the temperature distribution, the skin friction coefficient and the local Nusselt number for various values of the controlling governing parameters like velocity slip parameter, critical shear rate, magnetic field, ratio of stretching/shrinking rate to external flow rate and Prandtl number were analyzed and discussed. An increase of the critical shear rate decreases the fluid velocity whereas the local Nusselt number increases. The comparison of the present numerical results with the existing literature in a limiting case is given and found to be in an excellent agreement.

电磁驱动高能量密度动力学实验的一维磁流体力学多物理场数值模拟平台:SSS-MHD

超高压、超高密度物质状态生成和性质研究是当代极端物理学的重要前沿领域,电磁驱动的高能量密度物理实验对于该领域的意义尤为重要。这类实验虽然形式上多种多样,但在物理上有内在统一性,即均以力学守恒定律和宏观电磁理论为基本框架。为了建立统一数值模拟平台、依靠负载电流实验数据(或驱动电路真实数据)确定各种极端实验条件下负载构形的力学运动及其与各个物理场的耦合问题,将经受大量实际检验的冲击、爆轰动力学和激光效应计算的一维拉格朗日编码SSS,实质性扩展成为磁流体力学多物理场耦合编码SSS-MHD。对于具有典型意义的平面准等熵斜波压缩、高速平面固体飞片发射、固体套筒电磁内爆和炸药内爆磁通量压缩实验等各类高能量密度动力学实验案例的模拟计算结果表明,编码SSS-MHD计算与美国Z装置、中国CQ和CJ系列装置的实验及美国编码ALEGRA-1D和2D计算数据的相对偏差基本不超过5%。该数值模拟平台为极端材料动力学实验(包括气体、液体、化合物和金属)提供了有力的支撑,还将有助于多维磁流体力学多物理场编码的开发。

Combined heat and mass transfer by mixed convection MHD flow along a porous plate with chemical reaction in presence of heat source

An exact and a numerical solutions to the problem of a steady mixed convective MHD flow of an incompressible viscous electrically conducting fluid past an infinite vertical porous plate with combined heat and mass transfer are presented.A uniform magnetic field is assumed to be applied transversely to the direction of the flow with the consideration of the induced magnetic field with viscous and magnetic dissipations of energy.The porous plate is subjected to a constant suction velocity as well as a uniform mixed stream velocity.The governing equations are solved by the perturbation technique and a numerical method.The analytical expressions for the velocity field,the temperature field,the induced magnetic field,the skin-friction,and the rate of heat transfer at the plate are obtained.The numerical results are demonstrated graphically for various values of the parameters involved in the problem.The effects of the Hartmann number,the chemical reaction parameter,the magnetic Prandtl number,and the other parameters involved in the velocity field,the temperature field,the concentration field,and the induced magnetic field from the plate to the fluid are discussed.An increase in the heat source/sink or the Eckert number is found to strongly enhance the fluid velocity values.The induced magnetic field along the x-direction increases with the increase in the Hartmann number,the magnetic Prandtl number,the heat source/sink,and the viscous dissipation.It is found that the flow velocity,the fluid temperature,and the induced magnetic field decrease with the increase in the destructive chemical reaction.Applications of the study arise in the thermal plasma reactor modelling,the electromagnetic induction,the magnetohydrodynamic transport phenomena in chromatographic systems,and the magnetic field control of materials processing.

Formation of the bow shock indentation: MHD simulation results

Simulation results from a global magnetohydrodynamic(MHD)model are used to examine whether the bow shock has an indentation and characterize its formation conditions,as well as its physical mechanism.The bow shock is identified by an increase in plasma density of the solar wind,and the indentation of the bow shock is determined by the shock flaring angle.It is shown that when the interplanetary magnetic field(IMF)is southward and the Alfvén Mach number(Mα)of solar wind is high(>5),the bow shock indentation can be clearly determined.The reason is that the outflow region of magnetic reconnection(MR)that occurs in the low latitude area under southward IMF blocks the original flow in the magnetosheath around the magnetopause,forming a high-speed zone and a low-speed zone that are upstream and downstream of each other.This structure hinders the surrounding flow in the magnetosheath,and the bow shock behind the structure widens and forms an indentation.When Mαis low,the magnetosheath is thicker and the disturbing effect of the MR outflow region is less obvious.Under northward IMF,MR occurs at high latitudes,and the outflow region formed by reconnection does not block the flow inside the magnetosheath,thus the indentation is harder to form.The study of the conditions and formation process of the bow shock indentation will help to improve the accuracy of bow shock models.