Effect of Equilibrium Current Profiles on External Kink Modes in Tokamaks

Based on a linearized MHD model, the effect of equilibrium current profiles on external kink modes in tokamaks is studied by MARS code. Three types of equilibrium current profiles are adopted in this work. Firstly, a set of parabolic equilibrium current profiles are chosen. In these profiles the maximum current values in the center of the plasma are fixed, and the currents have different gradient and jump at the plasma boundary. The effects of the current gradient and jump on the growth rate of external kink mode are investigated. It is found that the current jump which causes the q profiles to change plays an important role in the externM kink modes in tokamaks. Secondly, a set of step equilibrium current profiles with different jump positions are chosen. The effect of jump position on external kink modes is discussed. Thirdly, a set of parabolic equilibrium current profiles with current bumps are chosen for the case of off-axis heating. The effects of height~ width and position of the current bumps on external kink modes are analyzed. The fiat equilibrium current profiles are disadvantageous for the MHD stabilities of tokamaks, because of the large current jump at the plasma edge. The peaked equilibrium current profiles and a large and localized current bump near the plasma edge benefit the MHD stabilities of tokamaks.     

Equilibrium field coil systems in lowq Elongated Tokamaks

A parametric numerical study of ideal equilibrium field (EF) coil systems was performed for lowq (q=2) tokamaks as a function of aspect ratios, values, elongation, and distance of the equivalent copper shell from the plasma surface. The total power consumption of the EF coil system was studied as a function of these variables. It was found that for each aspect ratio there is an optimal elongation for which the total EF coil current (NI) and hence resistive power has a pronounced minimum. The value of this optimal elongation is very large for an aspect ratio close to 2. For large aspect ratio the optimal elongation asymptotically approaches 1. Other computer-phenomenological scaling laws describing basic properties of the system (inductance, decay index, location of magnetic axis, vertical field, mean major radius of the plasma current, total flux on plasma due to the EF system) are also presented and compared to published seminanalytic scaling laws.     

MHD Equilibrium Configuration Reconstructions for HL-2A Tokamak

The EFIT （Equilibrium Fitting） code is modified for the equilibrium configuration reconstruction in HL-2A. Signals from Langmuir probe （LP） at the divertor targ...     

Bootstrap Current in Spherical Tokamaks

Variational principle for the neoclassical theory has been developed by including a momentum restoring term in the electron-electron collisional operator,which gives an additional free parameter maximizing the heat production rate.All transport coefficients are obtained including the bootstrap current.The essential feature of the study is that the aspect ratio affects the function of the electron -electron collison vanishes.The resulting diffusion coefficient is in rough agreement with Hazeltine,When the aspect ratio approaches to infinity,the results are in agreement with Rosenbluth.The formalism gives the two extreme cases a connection.The theory is particularly important for the calculation of bootstrap current in spherical tokamaks and the present tokamaks,in which the square root of the inverse aspect ratio.in general,is not small.     

General Description of Ideal Tokamak MHD Instability Ⅱ

In this subsequent study on general descripiton of ideal tokamak MHD instability,the part II,by using a coordinate with rectified magnetic field lines,the eigenmode equations describing the low-mode-number toroidal ALfven modes(TAE,and EAE) are derived through a further expansion of the shear Alfven equation of motion.     

Study of Plasma MHD Equilibrium in HL-2A Tokamak

EFIT（Equilibrium Fitting） code is successfully transplanted for HL-2A tokamak parameters. The evolution of the equilibrium configurations for shot 2898 is simulated. It is shown that the discharge starts with a limiter configuration and develops into a divertor configuration gradually after t = 200 ms. The latter lasts until the end of the discharge at t = 900 ms. The evolution of the major plasma shape parameters such as the boundary magnetic fluxes, the positions of the x-point and magnetic axis, and the minor radii obtained are calculated and compared with the experimental results. The agreement between the simulation and experiments are shown to be reasonable. The possibility for discharge quality improvement is discussed.     

Observation of MHD Instabilities Driven by Energetic Electrons in the Large Helical Device

Coherent magnetic fluctuations in an acoustic range of frequency have been regularly observed in low-density(n_e0.2×10~(19)m~(-3))plasmas with strong second harmonic electron cyclotron resonance heating(ECRH)on the Large Helical Device.Hard X-ray measurements indicated that energetic electrons are generated in these ECRH discharges.The magnetic fluctuations are suppressed in higher density discharges where energetic electrons are not present.The ECRH power modulation experiment indicated that the observed magnetohydrodynamic(MHD)mode has an acoustic nature rather than an Alfvenic nature.     

MHD stability analysis for advanced tokamak modes in the KSTAR device

The Korea Superconducting Tokamak Advanced Research (KSTAR) device aims to demonstrating the steady-state operation of high-performance advanced tokamak (AT) modes. In order to meet this research goal it is critical to have a good magnetohydrodynamic (MHD) stability, so that KSTAR adopted a strong plasma shape and a conducting wall close to plasma for such stability. An early calculation during the KSTAR design phase had shown that a target AT mode stable up to β_N above 5 can be then obtained. A recent work by Katsuro-Hopkins et al. [O. Katsuro-Hopkins, S.A. Sabbagh, J.M. Bialek, H.K. Park, J.G. Bak, J. Chung, et al., Equilibrium and global MHD stability study of KSTAR high beta plasmas under passive and active mode control, Nucl. Fusion 50(2010) 025019] showed, however, that the maximum β_N value can be substantially lower than 5, unlike the earlier result. In this work, we present a more detailed study on the MHD stability limit of the KSTAR target AT mode and try to clarify the discrepancy observed in the previous two works. It is shown that in the reverse-shear plasma the target mode with β_N above 5 can be obtained if the pressure profile is relatively peaked, but the maximum β_N value is substantially reduced below 5 if the pressure profile becomes broader. This result suggests the importance of a proper control of the pressure profile to get the high-beta AT mode in KSTAR.     

等离子体参数对中性束注入下快离子自举电流影响

本文数值研究了等离子体参数对大纵横比托卡马克装置中性束注入时产生的快离子净电流密度分布的影响。研究表明净电流密度的大小随背景等离子体温度的增大而增大,随等离子体密度的增大而减小,等离子体有效电荷对净电流密度的大小影响较小,但随有效电荷的增大净电流密度的峰值向等离子体边缘偏移。     

Impact of Toroidal Effect on Lower Hybrid Current Drive in Tokamak

The main topics concerning lower hybrid wave heating （LHH） and lower hybrid current drive （LHCD） in tokamak systems are presented. The inherent properties of tokamak systems give the ‘gap＇ filling on Brambilla＇s spectrum, which are conducive to LHCD, but, on the other hand, induce a consumption of wave energy by the trapped electrons, which reduce the current drive efficiency. The methods for the enhancement of the current drive efficiency may be derived from detailed analyses by drawing upon the ray tracing technology on toroidal geometry and the Fokker-Planck theory on velocity space.     

Measurement of Current Profile in a Tokamak Through AC Modulation

The plasma current is modulated with an alternating current （ac） component in a frequency range of 90 Hz - 900 Hz in the plateau discharge phase in the CT-6B tokamak. A plasma electric conductivity profile in a form of （1 - r^2/a^2）^α with a parameter α which is fitted with the experimental data, can be determined. The effects of magnetic shear in a tokamak field configuration on the current penetration are taken into account in the numerical simulation. The measurement method and obtained results are discussed.     

The Experiment of Modulated Toroidal Current on HT-7 and HT-6M Tokamak

The Experiments of Modulated Toroidal Current were done on the HT-6M tokamak and HT-7 superconducting tokamak. The toroidal current was modulated by programming the Ohmic heating field. Modulation of the plasma current has been used successfully to suppress MHD activity in discharges near the density limit where large MHD m = 2 tearing modes were suppressed by sufficiently large plasma current oscillations. The improved Ohmic confinement phase was observed during modulating toroidal current (MTC) on the Hefei Tokamak-6M (HT-6M) and Hefei superconducting Tokamak-7 (HT-7). A toroidal frequency-modulated current, induced by a modulated loop voltage, was added on the plasma equilibrium current. The ratio of A.C. amplitude of plasma current to the main plasma current △Ip/Ip is about 12% ～ 30%. The different formats of the frequency-modulated toroidal current were compared.     

Effects of Lead Wire Position along Resistive Electrode on Current Distribution in Faraday-Type MHD Duct

Effects of the lead wire position along the resistive electrodes on the current distribution in a segmented Faraday-type MHD duct when the resistivity of electrodes is larger than the optimal one are investigated. Detailed two-dimensional calculations for current distributions for flat-shaped resistive electrodes indicate that the highly resistive flat electrode with a lead wire placed away from one end can give a substantially uniform current distribution and reduce the Hall electric field at the electrode-insulator interfaces. Also it is shown that the internal resistance due to resistive electrodes for relatively large Hall parameters may be still comparable with the internal resistance for conductive electrodes when the lead wire is shifted to the appropriate position on the resistive electrode.     

Real Time Equilibrium Reconstruction Algorithm in EAST Tokamak

The EAST (HT-7U) superconducting tokamak is a national project of China on fusion research, with a capability of long-pulse (∽1000 s) operation. In order to realize a longduration steady-state operation of EAST,some significant capability of real-time control is required. It would be very crucial to obtain the current profile parameters and the plasma shapes in real time by a flexible control system. As those discharge parameters cannot be directly measured,so a current profile consistent with the magnetohydrodynamic equilibrium should be evaluatedfrom external magnetic measurements, based on a linearized iterative least square method, which can meet the requirements of the measurements. The arithmetic that the EFIT (equilibrium fitting code) is used for reference will be given in this paper and the computational efforts are reduced by parametrizing the current profile linearly in terms of a number of physical parameters.In order to introduce this reconstruction algorithm clearly,the main hardware design will be listed also.     

Ion-Banana-Orbit-Width Effect on Bootstrap Current for Small Magnetic Islands

A simple and direct theoretical method has been proposed to investigate the so- called ion-banana-orbit-width (IBW) effect on the bootstrap current in the region of magnetic islands generated by the neoclassical tearing mode (NTM). The result shows that, when the IBW approaches the island width, the (ion) bootstrap current can be partly restored inside the island while the pressure profile is flattened. This can lead to the reduction of the bootstrap current drive on the NTM. The strength of the IBW effect on the NTM is related to the safety factor and the inverse aspect ratio on the rational surface.     

Coupling Effect between Equilibrium Field and Heating Field and Modification of the Power Supply System on SUNIST Spherical Tokamak

Strong inductive coupling between the heating field and equilibrium field is confirmed to be responsible for the poor plasma equilibrium in initial discharges on the SUNIST spherical tokamak. A modification project for the power supply system of equilibrium field coils is successfully performed to increase the duration time of plasma current flattop from nmch less than 1ms to about 2 ms.     

Equilibrium evolution on the resistive time scale in a tokamak reactor

In the Engineering Test Facility (ETF), the plasma pulse duration is expected to be hundreds of seconds, which is comparable to the resistive time scale that governs the resistive diffusion of the equilibrium. The resistive evolution of the safety factorq profile may, for MHD stability reasons, limit the duration of the plasma burn in a tokamak reactor. It may be possible to control this evolution and extend the plasma burn time through proper profile tailoring. We study the evolution of theq profile on the resistive time scale numerically using a one- and-one-half-dimensional (1 1/2-D) single fluid transport code. Two high beta (T 7–16%) cases are considered: (a) a beam-driven hydrogen plasma with no nuclear alpha heating for which the beam energy is used as a device to control the temperature profile, and (b) an ignited D-T plasma in which the neutral injection has been turned off. For the beam-driven plasma, it is shown that low beam energy heating profiles lead to resistive steady states having broad temperature profiles and flatq profiles, while high beam energy heating profiles lead to resistive steady states having peaked temperature profiles and deepq profiles. The centralized nuclear heating in an ignited D-T plasma causes the evolution of theq profile for this case to behave much like that in the high energy, beam-driven case: namely, theq values near the plasma center decrease on the resistive time scale until a deep, resistive, steady-stateq profile is reached.Research sponsored by the Office of Fusion Energy, U.S. Department of Energy, under contract W-7405-eng-26 with the Union Carbide Corporation.     

The Singular Value Decomposition as a Tool of Investigating Central MHD Instabilities in the HL-1M Tokamak

A variety of strong MHD instabilities are always resulted from MHD activity of Tokamak plasmas. Central MHD instabilities can be observed with pinhole cameras to record soft x-ray (SXR) emission from the plasma along many chords with a high temporal resolution. The investigation of MHD instabilities often necessitates an analysis on spatial-temporal signals. The method of Singular Value Decomposition (SVD) can split such signals into orthogonal spatial and temporal vectors, By this means, the repetition time and the characteristic radius of various MHD phenomena such as sawteeth and snake-like perturbation can be obtained. Moreover, the (1,1) MHD mode is analyzed in great detail by SVD and used to determine the radius of the q = 1 surface.     

Current drive operation in a tokamak

Three modes of current drive operation in a tokamak — continuous, cyclic, and rfinitiated-are studied for air core and iron core transformer. It is found that the air core transformer is in general more flexible than the iron core transformer for current drive operation. For continuous operation, the shutoff time of the Ohmic heating circuit of the air core transformer can be reduced to zero by using a bias current. On the other hand, the shutoff time of the iron core transformer remains finite even if the bias current is used, because of hysteresis. For cyclic operation, methods of shortening the recharging time are investigated for both types of transformer. The effects of the transformer on rf-initiated operation are investigated. A model design of a saturable iron core tokamak for current drive experiments is also presented.     

identification and Analysis of Magnetic Structures on HL-2A

A method for the identification and analysis of magnetic islands is presented based on the calculation of the perturbative current and magnetic field in plasmas. A cylindrical approximation is adopted and the toroidal effect on plasma equilibrium is also included. This method has been used on the HL-2A tokamak for analysing the magnetic island structures.