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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Numerical analysis for the free-boundary current reversal equilibrium in the AC plasma current operation in a tokamak

In recent decades,tokamak discharges with zero total toroidal current have been reported in tokamak experiments,and this is one of the key problems in alternating current(AC)operations.An efficient free-boundary equilibrium code is developed to investigate such advanced tokamak discharges with current reversal equilibrium configuration.The calculation results show that the reversal current equilibrium can maintain finite pressure and also has considerable effects on the position of the X-point and the magnetic separatrix shape,and hence also on the position of the strike point on the divertor plates,which is extremely useful for magnetic design,MHD stability analysis,and experimental data analysis etc.for the AC plasma current operation on tokamaks.     

Experimental Results of MHD Suppression with Modulated LHCD on the HT-7 Tokamak

Modulation of lower hybrid current drive was used successfully to suppress MHD activity. This was achieved in discharges with MHD m = 2 tearing modes during the discharge conditions Ip = 110 kA, Bt = 1.75 T, ne0 - 1.1 ×1013 cm-3. The delivering time of LHCD pulse is less then 30 μs. The amplitude, interval and the period of LHCD modulation pulse can be adjusted very conveniently. The modulation LHCD can be delivered very fast at any time during the discharge. The modulation LHCD period was always much shorter than the plasma resistive time (Tη≈100 ms). So the profile of plasma current is changed much faster than the plasma resistive time. The different forms of LHCD modulating can be proved.     

Influence of stationary driven helical current on the m=2/n=1 resistive tearing mode

The influence of stationary driven helical current on tearing mode instability in the m=2/n=1 rational surface is explored numerically using resistive magnetohydrodynamic simulation in cylindrical geometry. The results indicate that the flip instabilities result from the sustained injection of the sufficiently strong helical current driven in the island O-point. The driven helical current induces high order harmonics of instabilities due to the delay of suppressing timing and the increase of its current intensity. With the appropriate current density values, the development of the perturbed kinetic energy can be limited and the occurrence of the flip instabilities can be delayed for a long time. The radial deviation of the current deposition can lead to poor inhibition effect, and the effect of current bias on the boundary is greater than that on the axis.