Towards a scalable fully-implicit fully-coupled resistive MHD formulation with stabilized FE methods

This paper explores the development of a scalable, nonlinear, fully-implicit stabilized unstructured finite element (FE) capability for 2D incompressible (reduced) resistive MHD. The discussion considers the implementation of a stabilized FE formulation in context of a fully-implicit time integration and direct-to-steady-state solution capability. The nonlinear solver strategy employs Newton–Krylov methods, which are preconditioned using fully-coupled algebraic multilevel preconditioners. These preconditioners are shown to enable a robust, scalable and efficient solution approach for the large-scale sparse linear systems generated by the Newton linearization. Verification results demonstrate the expected order-of-accuracy for the stabilized FE discretization. The approach is tested on a variety of prototype problems, including both low-Lundquist number (e.g., an MHD Faraday conduction pump and a hydromagnetic Rayleigh–Bernard linear stability calculation) and moderately-high Lundquist number (magnetic island coalescence problem) examples. Initial results that explore the scaling of the solution methods are presented on up to 4096 processors for problems with up to 64M unknowns on a CrayXT3/4. Additionally, a large-scale proof-of-capability calculation for 1 billion unknowns for the MHD Faraday pump problem on 24,000 cores is presented.     

Maxwell's equations in divergence form for general media with applications to MHD

Maxwell's equations in media with general constitutive relations are reformulated in covariant form as a system of divergence equations without constraints. Our reformulation enables us to express general electro-magneto-fluid problems as hyperbolic systems in divergence form. We illustrate this method on the MHD problem. In the absence of constraints, a general representation is derived for the characteristics form for first-order systems of quasi-linear partial differential equations in vector fields and scalars. Using this covariant formulation of characteristics, we find that the principle of covariance imposes a very rigid structure on the infinitesimally small amplitude waves in MHD. To demonstrate the power of the reformulation, we study numerically ultra-relativistic wave breaking using the divergence formulation of MHD.This material is based upon work supported by NSF grant AST 84-51725. Some of the work has been performed at the Department of Applied Mathematics, Caltech     

Self-organized criticality in MHD driven plasma edge turbulence

We analyze long-range time correlations and self-similar characteristics of the electrostatic turbulence at the plasma edge and scrape-off layer in the Tokamak Chauffage Alfvén Brésillien (TCABR), with low and high Magnetohydrodynamics (MHD) activity. We find evidence of self-organized criticality (SOC), mainly in the region near the tokamak limiter. Comparative analyses of data before and during the MHD activity reveals that during the high MHD activity the Hurst parameter decreases. Finally, we present a cellular automaton whose parameters are adjusted to simulate the analyzed turbulence SOC change with the MHD activity variation.     

Numerical modelling of magnetogasdynamic processes in the pulsed setup duct

A computational model for processes in the duct of an experimental setup consisting of a shock tube and an MHD duct is presented. The one-dimensional model is used for determining the flow characteristics in the entire setup duct, and the three-dimensional model is used for studying the current layer dynamics in the MHD channel. Computations have enabled the elucidation of flow structure and of the peculiarities of current layer formation.     

Experimental investigation of magnetohydrodynamic action on a heat flux toward the surface of a model

Experimental data for magnetohydrodynamic (MHD) action on a supersonic nitrogen flow about an axisymmetric model are presented. The experiments were carried out in the Big Shock Tube (Ioffe Physical-Technical Institute), at the end of which a test section equipped with a supersonic nozzle was mounted. A test conic model coupled with a cylinder is attached to the output cross section of the nozzle. A magnetic field is produced by a solenoid placed on the cylindrical part of the model through which a pulsed current due to an external voltage source discharging passes. Electrodes on the conic part of the model initiate a gas discharge, which rotates about the axis of the model in the solenoidal magnetic field. The influence of the magnetic field on the gasdynamic pattern of the flow near the model and on the heat flux toward its surface is investigated. Schlieren patterns of the flow about the model, photographic scans of the discharge glow, and heat flux measurements are taken. It is found that the magnetic field has an effect on the gasdynamic pattern of the flow near the model and on the heat flux toward its surface. The dependence of MHD effects on the external voltage polarity is also revealed.     

Fast ion induced shearing of 2D Alfvén eigenmodes measured by electron cyclotron emission imaging

Two-dimensional images of electron temperature perturbations are obtained with electron cyclotron emission imaging (ECEI) on the DIII-D tokamak and compared to Alfvén eigenmode structures obtained by numerical modeling using both ideal MHD and hybrid MHD-gyrofluid codes. While many features of the observations are found to be in excellent agreement with simulations using an ideal MHD code (NOVA), other characteristics distinctly reveal the influence of fast ions on the mode structures. These features are found to be well described by the nonperturbative hybrid MHD-gyrofluid model TAEFL.     

HL-1装置电流上升段MHD不稳定性

在托卡马克放电的初始阶段,由于存在变化的等离子体电流,一般会出现等离子体电流的趋肤分布,这种分布会导致MHD不稳定性的发展和产生破裂。早期的托卡马克实验,对放电初始阶段的MHD扰动现象做过许多讨论和研究。A1cator-A在电流上升段观测到的大多数破裂发生在q_L=1.6模处,同时观察到MHD扰动模式随时间从高模向低模的发展。电流初始阶段的上升率对平顶段的放电特性也有重大影响,在FT上,只有在等离子体电流上升率为1.2—2.6MA.s~(-1)时,才能实现低q_L的等离子体参数运行。     

新经典MHD效应与内扭曲模本征方程

本文从一简化的新经典ＭＨＤ方程组出发，利用气球模表示及多尺度近似等方法，在ｑ＝１磁面附近的过渡层内导出了包含新经典ＭＨＤ效应的内扭曲模本征方程。与从前相关工作的比较表明，新经典ＭＨＤ效应对通常采用的磁流体或电阻磁流体内扭曲模本征方程，均产生十分重要的修正。     

HL—1装置电流上升段辐射与杂质特性

托卡马克等离子体中的杂质会影响托卡马克的放电品质及等离子体特性。许多理论和实验对杂质的产生和输运做了深入详细的研究。等离子体电流起始阶段,由于约束性能不好,会引起大量的杂质产生,辐射损失增大是杂质增加引起的直接后果。杂质辐射是等离子体辐射的主要组成部分之一,等离子体线辐射功率～Z_(eff)~6,复合辐射功率～Z_(eff)~4,轫致辐     

On the propagation and interaction of ultralow-frequency waves in a waveguide with gyrotropic plasma

The propagation of ultralow-frequency (ULF) electromagnetic waves in a waveguide filled with magnetoactive plasma is consieered on the basis of the monoaxial crystal approximation which is more general than the MHD approximation. The formulas for the phase and group velocities of the ordinary (magnetoacoustic) and extraordinary waves (similar to Alfvén waves in the MHD approximation) are derived. It is shown that analysis outside the scope of the MHD approximation results in a finite (nonzero) velocity of energy propagation of the extraordinary wave (Alfvén wave at the limit) along the waveguide. The possible waveguide mode triplets satisfying the conditions of synchronism are found. Three-wave resonant parametric and nonlinear interaction between waves with such characteristics leads to effective spectral transformation of the ULF radiation. Radiophysical Research Institute, Nizhny Novgorod; State Technical University of Nizhny Novgorod. Translated from lzvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, Nos. 1–2, pp. 111–122, January–February, 1997.     

FCI结构及其电导率对MHD效应影响实验研究

实验研究了通道插件(FCI)压力平衡孔(PEH)和压力平衡狭缝(PES)结构、绝缘和非绝缘材质对磁流体动力学(MHD)效应的影响,结果表明：带PEH或PES、绝缘或非绝缘材质的FCI产生的流速分布有很大的差异;对MHD压降而言,FCI结构PEHs或PES差异的影响大于FCI绝缘或非绝缘材质差异引起的影响;对流速分布而则刚好相反。二次流引起的局部流速骤增的MHD效应(简称为S-MHD效应)对控制管道内流速分布和降低MHD压降有作用,这些实验结果为弄清FCI的MHD效应机制和液态金属包层设计提供了实验认知与有价值的参考。     

FCI�ṹ����絼�ʶ�MHDЧӦӰ��ʵ���о�

实验研究了通道插件(FCI)压力平衡孔(PEH)和压力平衡狭缝(PES)结构、绝缘和非绝缘材质对磁流体动力学(MHD)效应的影响,结果表明：带PEH或PES、绝缘或非绝缘材质的FCI产生的流速分布有很大的差异;对MHD压降而言,FCI结构PEHs或PES差异的影响大于FCI绝缘或非绝缘材质差异引起的影响;对流速分布而则刚好相反。二次流引起的局部流速骤增的MHD效应(简称为S-MHD效应)对控制管道内流速分布和降低MHD压降有作用,这些实验结果为弄清FCI的MHD效应机制和液态金属包层设计提供了实验认知与有价值的参考。     

Formation of compression shocks in a nonequilibrium plasma flow in a magnetic field

Plasma flow in a linearly widening, ideally sectioned, short-circuited magnetohydrodynamic (MHD) channel is studied. MHD flows are classified into two types: continuous flows and flows with a compressional MHD shock in plasmas that are stable and unstable against the onset of ionization instability. Specific features in the evolution of a stationary compression MHD shock are investigated, and its position as a function of the Stewart number is determined. It is found that, in a plasma flow in which ionization instability develops, a compression MHD shock arises at lower values of the MHD interaction parameter than in a stable plasma flow. An unidentified type of instability of MHD discontinuities is revealed.     

On the material response in stimulated Brillouin scattering

We re-examine behavior of the material response in stimulated Brillouin scattering and from this revise its theoretical formalism. We show that the response out of exact Brillouin resonance splits into two processes: one is the induction of a moving density grating, propagation characteristics of which follow these of the beat pattern of pump and Stokes fields, and the other is the induction of an acoustic wave, frequency of which coincides with that of the beat pattern but which propagates at the acoustic velocity in the medium. The resulting equations for the response amplitudes are solved analytically in several representative cases.     

Analytical solution of a system of magnetohydrodynamic equations in a quasi-one-dimensional approximation for the monotonic variation of the flow velocity along a channel

An analytical solution is obtained for the system of magnetohydrodynamic (MHD) equations in a quasi-one-dimensional approximation for flow regimes with a monotonic variation of the velocity along a MHD channel. The problem of optimal choice of the parameters of an MHD generator for the given ratio of the areas of the outlet and inlet MHD channel cross sections is considered using the resultant analytic solution.     

高超声速飞行器磁控热防护系统建模分析

针对高超声速飞行器防热, 搭建了螺线管磁控热防护系统的物理模型. 采用低磁雷诺数磁流体数学模型, 分析了外加磁场强度及磁场形态对磁控热防护效果的影响. 对比了三种磁场类型(磁偶极子、螺线管、均布磁场)下磁控热防护效果的差异, 分析了螺线管几何参数对磁控热防护效果的影响. 研究表明, 磁场降低表面热流作用存在“饱和现象”; 三种磁场形态的磁控热防护能力从小到大依次为磁偶极子、螺线管、均布磁场; 相同驻点磁感应强度条件下, 增大螺线管半径有利于提高磁控热防护效果, 缩短螺线管与驻点距离不利于驻点和肩部防热, 螺线管长度对磁控热防护效果影响相对较小.     

Calculations of the parameters of the air plasma produced by an electron beam in the channel of an MHD generator with a nonequilibrium conductivity

Approximate analytic expressions for calculating the electron density in both steady and unsteady plasmas produced by pulsed electron beams are derived and proved to agree well with numerical calculations. It is shown that the algorithm for calculating the parameters of a nonequilibrium plasma in the channel of an MHD plasma generator depends on the type of generator. The effect of the magnetic field strength on the electron density and electric conductivity of the air plasma produced by an electron beam in the channel of a Faraday MHD generator is investigated. The influence of the parameters of the flow and ionizer on the efficiency of an MHD generator with a nonequilibrium conductivity is analyzed.     

一种基于新型斜率限制器的理想磁流体方程的高分辨率熵相容格式

针对磁流体动力学方程, 通过分析数据重建所需的条件, 构造一种基于MUSCL(Monotone Upstream-Centred Scheme for Conservation Laws)型重建方法的斜率限制器, 获得了一种求解理想磁流体动力学方程的高分辨率熵相容格式。该格式在解的光滑区域具有高精度; 在解的间断区域可以合理地控制耗散, 可有效避免非物理现象的产生。采用熵稳定格式、熵相容格式和新的高分辨率熵相容格式对一维、二维理想磁流体动力学方程进行数值模拟。结果表明: 新格式能准确地捕捉解的结构, 且具有无振荡、高分辨、鲁棒等特性。     

Use of MHD systems in hypersonic aircraft

The possibilities of using magnetohydrodynamic (MHD) systems on hypersonic aircraft are discussed. The distinctive features of using MHD systems in the flow path of ramjet engines are examined. A quasi-one-dimensional mathematical model for the engine is presented which includes the MHD interaction with the flow. It is shown that the specific impulse of an engine system can be raised by using MHD systems. Zh. Tekh. Fiz. 68, 43–47 (November 1998)     

Strong "quantum" chaos in the global ballooning mode spectrum of three-dimensional plasmas

The spectrum of ideal magnetohydrodynamic (MHD) pressure-driven (ballooning) modes in strongly nonaxisymmetric toroidal systems is difficult to analyze numerically owing to the singular nature of ideal MHD caused by lack of an inherent scale length. In this paper, ideal MHD is regularized by using a k-space cutoff, making the ray tracing for the WKB ballooning formalism a chaotic Hamiltonian billiard problem. The minimum width of the toroidal Fourier spectrum needed for resolving toroidally localized ballooning modes with a global eigenvalue code is estimated from the Weyl formula. This phase-space-volume estimation method is applied to two stellarator cases.