Plasma Response to Resonant Perturbations at Tokamak Edge

In certain circumstances, plasma response suppresses magnetic islands expected at perturbed resonant magnetic surfaces. We investigate the plasma response to the resonant magnetic perturbations in a large aspect ratio tokamak perturbed by external resonant helical windings, considering polar toroidal coordinates for which analytical toroidal equilibrium solutions and perturbing fields are available. We apply an empirical approach to mimic the plasma screening effects by introducing presumed plasma current sheets on the resonance surfaces to cancel the RMP effects. Numerical examples show the effect of plasma response reducing magnetic islands at the plasma edge and also regularizing field lines around the resonant surface. The distribution of connection lengths along the plasma cross section indicates that the plasma response increases the connection lengths since more toroidal turns are performed until a field line reaches the tokamak wall.     

The structure of chaotic magnetic field lines in a tokamak withexternal nonsymmetric magnetic perturbations

We consider the effects of external nonsymmetric magnetostatic perturbations caused by resonant helical windings and a chaotic magnetic limiter on the plasma confined in a tokamak. The main purpose of both types of perturbation is to create a region in which field lines are chaotic in the Lagrangian sense: two initially nearby field lines diverge exponentially through many turns around the tokamak. The equilibrium field is obtained from the equations of magneto-hydrodynamic equilibrium written down in a polar toroidal coordinate system. The magnetic fields generated by the resonant helical windings and the chaotic magnetic limiter are obtained through an analytical solution of Laplace equation. The magnetic field line equations are integrated to give a Hamiltonian mapping of field lines that we use to characterize the structure of chaotic field lines. In the case of resonant windings, we obtained the map by both numerical integration and a Hamiltonian formulation. For a chaotic limiter, we analytically derived a symplectic map by using a Hamiltonian formulation     

Internal magnetic field measurement in tokamak plasmas using a Zeeman polarimeter

In a tokamak plasma, the poloidal magnetic field profile closely depends on the current density profile. We can deduce the internal magnetic field from the analysis of circular polarization of the spectral lines emitted by the plasma. The theory of the measurement and a detailed design of the Zeeman polarimeter constructed to measure the poloidal field profile in the ADITYA tokamak are presented. The Fabry-Perot which we have employed in our design, with photodiode arrays followed by lock-in detection of the polarization signal, allows the measurement of the fractional circular polarization. In this system He-II line with wavelength 4686 Å is adopted as the monitoring spectral line. The line emission used in the present measurement is not well localized in the plasma, necessiating the use of a spatial inversion procedure to obtain the local values of the field.     

Observation of floating potential asymmetry in the edge plasma of the SINP tokamak

Edge plasma properties in a tokamak is an interesting subject of study from the view point of confinement and stability of tokamak plasma. The edge plasma of SINP-tokamak has been investigated using specially designed Langmuir probes. We have observed a poloidal asymmetry of floating potentials, particularly the top-bottom floating potential differences are quite noticeable, which in turn produces a vertical electric field (E_v). This E_v remains throughout the discharge but changes its direction at certain point of time which seems to depend on applied vertical magnetic field (B_v).     

HL-1装置主机的工程调试

本文叙述了HL-1装置主机在工程调试和等离子体放电中所涉及的主要技术问题。文中详述了场形和变压器芯柱伏秒数的一些测量结果,并阐述了主机的工作状况和一些技术性能。目前该装置已运行于B_t=2.3T,I_p=135kA参数下,运行情况表明:HL-1装置主机有着较好的技术性能,基本上满足物理实验的要求。     

Stochasticity from external magnetic field measurements

To determine whether or not magnetic field lines inside a tokamak plasma are stochastic we need the Fourier coefficients of any perturbing radial field inside the plasma. Usually what is measured with magnetic pick-up coils is the root mean square poloidal field outside the plasma. Although no unique transformation is available, we present a model which allows an interpretation of the measured (external) root mean square field in terms of the internal Fourier harmonics. The results are applied to particular TEXT discharges, and suggest a link between magnetic stochasticity and an increasing (more positive) radial electric field, as measured with a heavy ion beam probe     

Measurement of natural plasma flow along the field lines in the scrape-Off layer on the JT-60U divertor tokamak

The plasma profile and parallel plasma flow in the scrape-off layer (SOL) were systematically measured using reciprocating Mach probes installed at the outer midplane and near the divertor magnetic null (x point) in the JT-60U tokamak with a single null divertor. For the ion vertical drift due to the toroidal magnetic field gradient (ion nablaB drift) directed towards the divertor, SOL plasma flow along the magnetic field lines away from the divertor ("flow reversal") was discovered at the midplane far from the divertor. A quantitative evaluation of the ion "Pfirsch-Schluter flow," wherein the parallel flow is naturally produced in a toroidal plasma, was consistent with the measurement.     

Physical mechanisms in divertors and their impact on the core

The magnetic separatrix in a diverted tokamak determines the boundary between closed and open magnetic field lines. Even though the main influences on the physics of SOL and core regions may be different and shift from the plasma-neutral coupling and impurity radiation in the scrape-off layer (SOL) to anomalous plasma transport in the core, the influence of this boundary persists over some width, both into the core region and into the SOL. We give a short review of the progress in the divertor-SOL physics and discuss the links between edge core and SOL plasmas which are likely to have an important role in different edge-plasma phenomena.     

Topology of toroidal helical fields in non-circular cross-sectional tokamaks

The ordinary differential magnetic field line equations are solved numerically; the tokamak magnetic structure is studied on Hefei Tokamak-7 Upgrade （HT-TU） when the equilibrium field with a monotonic q-profile is perturbed by a helical magnetic field. We find that a single mode （m, n） helical perturbation can cause the formation of islands on rational surfaces with q=m/n and q=（m±1,±2,±3,...）/n due to the toroidicity and plasma shape （i.e. elongation and triangularity）, while there are many undestroyed magnetic surfaces called Kolmogorov-Arnold-Moser （KAM） barriers on irrational surfaces. The islands on the same rational surface do not have the same size. When the ratio between the perturbing magnetic field Br（r） and the toroidal magnetic field amplitude Bφ0 is large enough, the magnetic island chains on different rational surfaces will overlap and chaotic orbits appear in the overlapping area, and the magnetic field becomes stochastic. It is remarkable that the stochastic layer appears first in the plasma edge region.     

用偏压限制器控制KT－5C托卡马克等离子体边缘电场的实验研究

在托卡马克ＫＴ－５Ｃ上，我们首次采用可灵活组合的多块限制器进行了施加偏压以控制等离子体边缘电场的实验，结果表明，在本装置上限制器加正偏压优于加负偏压，正偏压改变等离子体边缘电场效果更明显。偏压限制器收集面积、纵场和偏置电压的大小对偏压效果的影响都是敏感的。改变限制器收集面积和偏压导致的边缘电场的变化最终将趋于饱和，另外发现，偏压限制器与等离子体柱的相对位置对等离子体边缘电场的影响也是重要的。     

Theory for explosive ideal magnetohydrodynamic instabilities in plasmas

Flux tubes confined in tokamaks are observed to erupt explosively in some plasma disruptions and edge localized modes. Similar eruptions occur in astrophysical plasmas, for example, in solar flares and magnetospheric substorms. A single unifying nonlinear evolution equation describing such behavior in both astrophysical and tokamak plasmas is derived. This theory predicts that flux tubes rise explosively, narrow, and twist to pass through overlying magnetic field lines without reconnection.     

环径比为2的托卡马克反应堆中氘氚燃烧等离子体特性

本文对环径比为2（A=2）的托卡马克反应堆中氘氚燃烧等离子体的特性，利用一类简单的平衡位形，即Solov’ev位形，进行了研究。作为基准，采用了Troyon比压极限和Greenwald密度极限，以及 ITER的H-模约束定标关系。我们发现，除了增大拉长比外，大的三角变形也有利于提高比压值及获得高的聚变功率输出。与 ITER设计相比，对相同的总等离子体电流而言，A=2的反应堆因边缘安全因子很大，具有可以避免破裂不稳定性的优点。由于减小环径比时环内侧的可利用空间相应减小，这类反应堆的一个主要缺点是环向磁场强度也会减小，从而降低聚变堆品质。实际研究工作中要对这些方面做出某种折衷。另外，虽然由于我们采用了简单的位形，我们不能对自举电流的准直性进行优化，但是通过本研究仍然可以对中等环径比反应堆系统（目前是研究工作的空白）的特点获得了解。     

A review on the solution of Grad–Shafranov equation in the cylindrical coordinates based on the Chebyshev collocation technique

Equilibrium reconstruction consists of identifying, from experimental measurements, a distribution of the plasma current density that satisfies the pressure balance constraint. Numerous methods exist to solve the Grad–Shafranov equation, describing the equilibrium of plasma confined by an axisymmetric magnetic field. In this paper, we have proposed a new numerical solution to the Grad–Shafranov equation (an axisymmetric, magnetic field transformed in cylindrical coordinates solved with the Chebyshev collocation method) when the source term (current density function) on the right-hand side is linear. The Chebyshev collocation method is a method for computing highly accurate numerical solutions of differential equations. We describe a circular cross-section of the tokamak and present numerical result of magnetic surfaces on the IR-T1 tokamak and then compare the results with an analytical solution.     

HL-2A 装置的边缘参数测量

HL-2A 装置中平面边缘的等离子体特性通过磁力传动的马赫/ 雷诺协强/ 朗缪尔10 探针组进行了研究。10 探针组安装在可径向向里和向外移动, 并可绕轴旋转360^o 的传动杆上, 用于测量主等离子体边缘的温度、密度、悬浮电位、空间电位、径向和极向电场、湍流的雷诺协强、径向和极向等离子体流速及其径向分布。HL- 2A 装置的实验结果表明, 边缘等离子体扰动诱发的雷诺协强产生了边缘极向流; 雷诺协强的径向梯度驱动带状流抑制了湍流输运。     

Forced magnetic reconnection and field penetration of an externally applied rotating helical magnetic field in the TEXTOR tokamak

The magnetic field penetration process into a magnetized plasma is of basic interest both for plasma physics and astrophysics. In this context special measurements on the field penetration and field amplification are performed by a Hall probe on the dynamic ergodic divertor (DED) on the TEXTOR tokamak and the data are interpreted by a two-fluid plasma model. It is observed that the growth of the forced magnetic reconnection by the rotating DED field is accompanied by a change of the plasma fluid rotation. The differential rotation frequency between the DED field and the plasma plays an important role in the process of the excitation of tearing modes. The momentum input from the rotating DED field to the plasma is interpreted by both a ponderomotive force at the rational surface and a radial electric field modified by an edge ergodization.     

Effect of a magnetic field on the radiation emitted by a nonequilibrium hydrogen and deuterium plasma

Radiative transfer in a nonequilibrium plasma in an external electric field is considered. The system of kinetic equations determining the populations of atomic levels is written taking into account the combination of collision and radiative processes and is solved together with the kinetic equation for photon of various frequencies, which are emitted and absorbed in the radiative transitions from the states of the continuous and discrete spectra. The shape of spectral lines is determined from the solution of the quantum-mechanical problem on the emission of an atom in the electric field of the plasma and an external magnetic field, taking the Doppler effect into consideration. The developed approach is used in the model calculation of radiative transfer under the conditions corresponding to the edge plasma in a tokamak, which is simulated by a homogeneous plane layer of a deuterium plasma. It is shown that the joint action of the external magnetic field and the electric plasma fields considerably affects the spectral and integrated characteristics of the radiation.     

Nuclear fusion: bringing a star down to Earth

Nuclear fusion offers the potential for being a near limitless energy source by fusing together deuterium and tritium nuclei to form helium inside a plasma burning at 100 million K. However, scientific and engineering challenges remain. This paper describes how such a plasma can be confined on Earth, and discusses the similarities and differences with fusion in stars. It focuses on the magnetic confinement technique and, in particular, the method used in a tokamak. The confinement achieved in the equilibrium state is reviewed and it is shown how the confinement can be too good, leading to explosive instabilities at the plasma edge called edge localised modes (ELMs). It is shown how the impact of ELMs can be minimised by the application of magnetic perturbations and discusses the physics behind the penetration of these perturbations into what is ideally a perfect conducting plasma.     

Effect of parallel flows and toroidicity on cross-field transport of pellet ablation matter in tokamak plasmas

The first complete set of time-dependent equations describing the cross-field drift of ionized pellet ablation matter in tokamak plasma caused by polarization in the nonuniform magnetic field has been developed and solved numerically. Important new features impacting the drift dynamics have been identified, including the effect of pressure profile variations in the tokamak plasma, curvature drive by near-sonic field-aligned (parallel) flows, and the rotational transform of the magnetic field lines, and are considered from the viewpoint of the parallel vorticity equation. These new features are necessary to obtain favorable quantitative agreement between theory and experimental fuel deposition profiles for both inner and outer wall launched pellet injection cases on the DIII-D tokamak.     

托卡马克的快速Mapping方法

本文介绍一种托卡马克等离子体实验装置的快速Mapping方法。它用于揭示由外加线圈产生的径向场与托卡马克磁场共振产生的磁岛和随机场结构。说明了它在TEXT上的应用及其结果。 关键词：