Equilibrium reconstruction method for self-organized plasmas on reversed field pinches with polarimeter-interferometer

In the reversed field pinch(RFP),plasmas exhibit various self-organized states.Among these,the three-dimensional(3D)helical state known as the“quasi-single-helical”(QSH)state enhances RFP confinement.However,accurately describing the equilibrium is challenging due to the presence of 3D structures,magnetic islands,and chaotic regions.It is difficult to obtain a balance between the available diagnostic and the real equilibrium structure.To address this issue,we introduce KTX3DFit,a new 3D equilibrium reconstruction code specifically designed for the Keda Torus eXperiment(KTX)RFP.KTX3DFit utilizes the stepped-pressure equilibrium code(SPEC)to compute 3D equilibria and uses polarimetric interferometer signals from experiments.KTX3DFit is able to reconstruct equilibria in various states,including axisymmetric,doubleaxis helical(DAx),and single-helical-axis(SHAx)states.Notably,this study marks the first integration of the SPEC code with internal magnetic field data for equilibrium reconstruction and could be used for other 3D configurations.

Effects of vacuum magnetic field region on the compact torus trajectory in a tokamak plasma

The trajectory of the compact torus(CT)within a tokamak discharge is crucial to fueling.In this study,we developed a penetration model with a vacuum magnetic field region to accurately determine CT trajectories in tokamak discharges.This model was used to calculate the trajectory and penetration parameters of CT injections by applying both perpendicular and tangential injection schemes in both HL-2A and ITER tokamaks.For perpendicular injection along the tokamak's major radius direction from the outboard,CTs with the same injection parameters exhibited a 0.08 reduction in relative penetration depth when injected into HL-2A and a 0.13reduction when injected into ITER geometry when considering the vacuum magnetic field region compared with cases where this region was not considered.In addition,we proposed an optimization method for determining the CT's initial injection velocity to accurately calculate the initial injection velocity of CTs for central fueling in tokamaks.Furthermore,this paper discusses schemes for the tangential injection of CT into tokamak discharges.The optimal injection angle and CT magnetic moment direction for injection into both HL-2A and ITER were determined through numerical simulations.Finally,the kinetic energy loss occurring when the CT penetrated the vacuum magnetic field region in ITER was reduced byΔEk=975.08 J by optimizing the injection angle for the CT injected into ITER.These results provide valuable insights for optimizing injection angles in fusion experiments.Our model closely represents actual experimental scenarios and can assist the design of CT parameters.

Polarimeter–interferometer diagnostic using terahertz solid-state sources for fluctuation measurements on Keda Torus e Xperiment(KTX)

A multi-channel polarimeter-interferometer has been developed on the Keda Torus eXperiment(KTX)for the study of equilibrium dynamics and internal magnetic fluctuations.A three-wave technique based on terahertz solid-state sources(-650 GHz)is applied for simultaneous measurements of electron density and Faraday rotation angle.The output power of the microwave source is 2 mW.Faraday rotation effect using a rotating wave plate is tested with phase noise less than 0.8°,and the density phase noise is less than 0.9°.Measurement of Faraday rotation angle and density for discharges on KTX have demonstrated high sensitivity to internal MHD activities.

The impact of toroidal mode coupling on high-density discharges in J-TEXT

Density limit has long been a widely studied issue influencing the operating range of tokamaks.The rapid growth of the m/n=2/1(where m and n are poloidal and toroidal mode numbers,respectively)tearing mode is generally regarded as a primary precursor to the density limit disruption.In this experiment,the coupling of the m/n=1/1 mode and the m/n=2/1 mode in highdensity plasma was observed.During a sawtooth cycle,the frequencies of the two modes gradually converge until they become equal.After that,toroidal coupling occurs between the 1/1 and 2/1 modes,resulting in a mutually fixed phase relationship.With the occurrence of toroidal coupling,the 2/1 mode is stabilized.Prior to the disruption,the cessation of the 1/1 and 2/1 mode coupling,along with the rapid growth in the amplitude of the 2/1 mode,can be observed.Additionally,under the same parameters,comparing discharges with or without the 1/1 mode,it is found that the presence of the 1/1 mode leads to higher plasma density and temperature parameters.

Comparison of transport coefficients before and after density pump-out induced by resonant magnetic perturbation using a BOUT++ six-field model on the EAST tokamak

Many experiments have demonstrated that resonant magnetic perturbation(RMP) can affect the turbulent transport at the edge of the tokamak. Through the Experimental Advanced Superconducting Tokamak(EAST) density modulation experiment, the particle transport coefficients were calculated using the experimental data, and the result shows that the particle transport coefficients increase with RMP. In this study, the six-field two-fluid model in BOUT++ is used to simulate the transport before and after density pump-out induced by RMP,respectively referred as the case without RMP and the case with RMP. In the linear simulations,the instabilities generally decreases for cases with RMP. In the nonlinear simulation, ELM only appears in the case without RMP. Additionally, the particle transport coefficient was analyzed,and the result shows that the particle transport coefficient becomes larger for the case with RMP,which is consistent with the experimental conclusion. Moreover, its magnitude is comparable to the results calculated from experimental data.

高频振荡下缓慢前沿的电子束电流波形测量

推导了Rogowski线圈理论,给出了任意Rogowski线圈的表达式。通过使用高磁导率的磁芯材料,增加线圈匝数,设计出了能有效测量前沿变化0.1s、强度mA量级的电子束电流的Rogowski线圈,并测得了电子束等离子体装置中的电子束电流信号。利用推导的任意Rogowski线圈表达式,成功获得低频与高频共存的电流波形。测量结果表明,该电子束等离子体系统中存在束流振荡,振荡幅度达12%。

Development of a compact torus injection system for the Keda Torus eXperiment

A compact torus injection system,KTX-CTI,has been developed for the planned injection experiments on the Keda Torus e Xperiment(KTX)reversed field pinch(RFP)device to investigate the physics and engineering issues associated with interaction between a compact torus(CT)and RFP.The key interests include fueling directly into the reactor center,confinement improvement,and the injection of momentum and helicity into the RFP discharges.The CT velocity and mass have been measured using a multichannel optical fiber interferometer,and for the first time the time evolution of the CT density profile during CT propagation is obtained.The effects of discharge parameters on the number of injected particles,CT velocity and CT density have been characterized:the maximum hydrogen CT plasma mass,m,CTis 50μg,corresponding to 30%of the mass in a typical KTX plasma;the CT velocity exceeds 120 km s-1.It is observed for the first time that multiple CTs can be produced and emitted during a very short period(<100μs)in one discharge,which is significant for the future study of repetitive CT injection,even with an ultra-high frequency.

托卡马克无碰撞捕获电子模在时空表象中的群速度

按照章等[Zhang Y Z, Liu Z Y, Mahajan S M, Xie T, Liu J 2017 Phys. Plasmas 24 122304]发展的漂移波-带状流理论,将多重尺度导数展开法应用到电子漂移动理学方程,零级为描述微观尺度捕获电子模的线性本征模方程,一级为介观尺度受带状流调制的捕获电子模的包络方程.其中线性本征模方程已经在谢等[Xie T, Zhang Y Z, Mahajan S M, Wu F, He Hongda, Liu Z Y 2019 Phys. Plasmas 26 022503]的研究中被求解,利用该文得到的捕获电子模的本征值和二维模式结构计算包络方程中的群速度.径向群速度由托卡马克磁场的测地曲率贡献,极向群速度来自逆磁漂移速度和法向曲率,它们仅是极向角的函数,后者给出极向角到时间的映射.径向群速度作为时间的函数,其周期在毫秒量级,具有快速过零的特征.这为研究捕获电子模驱动带状流提供了充实的理论基础.

Design of the poloidal field system for KTX

The design of the poloidal field （PF） system includes the ohmic heating field system and the equilibrium （EQ） field system, and is the basis for the design of a magnetic confinement fusion device. A coupling between the poloidal and plasma currents, especially the eddy current in the stabilizing shell, yields design difficulties. The effects of the eddy current in the stabilizing shell on the poloidal magnetic field also cannot be ignored. A new PF system design is thus proposed. By using a low-μ material （μ = 0.001, ε = 1） instead of a conductive shell, an electromagnetic model is established that can provide a continuous eddy current distribution on the conductive shell. In this model, a 3D time-domain problem with shells translates into a 2D magnetostatic problem, and the accuracy of the calculation is improved. Based on these current distributions, we design the PF system and analyze how the EQ coils and conductive shell affect the plasma EQ when the plasma ramps up. To meet the mainframe design requirements and achieve an efficient power-supply design, the position and connection of the poloidal coils are optimized further.

The Design of the Plasma Control System in KTX

KTX（Keda Torus for eXperiment）is a new reversed field pinch device.The KTX plasma control system（PCS）can provide real-time,stable,flexible plasma control which is designed by ASIPP（Institute of Plasma Physics,Chinese Academy of Sciences）,based on the Linux cluster system and EPICS（Experimental Physics and Industrial Control System）framework,and developed from DIII-D（Doublet III-D）PCS.The control of the equilibrium field in KTX uses a PID（Proportional-Integral-Derivative）feedback controller.The control of the gas injection is an open loop control.The plasma control simulation system is one part of the plasma control system,which is used to test the plasma control algorithm if it is revised and updated.The KTX PCS has been successfully tested using HT-7（Hefei Torus 7）experiment data in simulation mode.In the next phase,an error field feedback control and KTX simulator will be added to the KTX PCS,and the KTX PCS will be applied in experiments in the future.

Construction of an Hα diagnostic system and its application to determine neutral hydrogen densities on the Keda Torus eXperiment

A 10-channel Hα diagnostic system has been designed with the rapid response rate of 300 kHz, spatial resolution of about 40 mm, and overlap between adjacent channels of about 3%, and it has been implemented successfully on Keda Torus eXperiment(KTX), a newly constructed, reversed field pinch(RFP) experimental device at the University of Science and Technology of China(USTC). This diagnostic system is a very important tool for the initial KTX operations. It is compact,with an aperture slit replacing the traditional optical lens system. A flexural interference filter is designed to prevent the center wavelength from shifting too much as the increase of angle from vertical incidence. To eliminate the stray light,the interior of the system is covered with the black aluminum foil having a very high absorptivity. Using the Hαemission data, together with the profiles of electron temperature and density obtained from the Langmuir probe, the neutral density profiles have been calculated for KTX plasmas. The rapid response rate and good spatial resolution of this Hαdiagnostic system will be beneficial for many studies in RFP plasma physics.

Fast radial scanning probe system on KTX

A fast radial scanning probe system was constructed for the Keda Torus eXperiment(KTX)to measure the profiles of boundary plasma parameters such as floating potential,electron density,temperature,transport fluxes,etc.The scanning probe system is driven by slow and fast motion mechanisms,corresponding to the stand-by movement of a stepping motor and the fast scanning movement of a high-torque servo-motor,respectively.In fast scanning,the scanner drives the probe radially up to 20 cm at a maximum velocity of 4.0 m s-1.A noncontact magnetic grating ruler with a high spatial resolution of 5μm is used for the displacement measurement.New scanning probe can reach the center of plasmas rapidly.The comparison of plasma floating potential profiles obtained by a fixed radial rake probe and the single scanning probe suggests that the high-speed scanning probe system is reliable for measuring edge plasma parameter profiles on the KTX device.

Blob properties in I-mode and ELM-free H-mode compared to L-mode on EAST

The blob properties in I-mode and ELM-free H-mode plasmas compared to L-mode have been investigated on the EAST tokamak,including the blob detection rate Nb,sizeδb,lifetimeτb and radial velocity vr,b.The blob properties in L-mode and I-mode are similar,and those in ELM-free H-mode are different to them.The blob Nbis smaller whileτbis larger in H-mode.The experimental blob sizeδband velocity scalings vr,b-δb show a good agreement with the theoretical models.The variation in blob properties during the L-I and H-L transitions,and their relations to the scrape-off layer(SOL)density,edge and SOL turbulence,and SOL collisionality are discussed.The suppression of the edge(inside the last closed flux surface)turbulence is not reflected in the blob behavior,while the blob detection rate shows a correlation with the SOL density and its low-frequency(3–50 kH z)fluctuations.In addition,the blob detection rate is found to increase with the divertor collisionalityΛdiv,indicating a dependence of blob behavior onΛdiv.The differences in blob detection rates among the three operating regimes might be due to their different SOL densities and collisionalities.The investigation contributes to understanding the influences of edge and SOL plasma parameters on the blob behavior.

The theoretical study on intermittency and propagation of geodesic acoustic mode in L-mode discharge near tokamak edge

Through a systematically developed theory,we demonstrate that the motion of Instanton identified in Zhang et al(2017 Phys.Plasmas 24122304)is highly correlated to the intermittent excitation and propagation of geodesic acoustic mode(GAM)that is observed in tokamaks.While many numerical simulations have observed the phenomena,it is the first theory that reveals the physical mechanism behind GAM intermittent excitation and propagation.The preceding work is based on the micro-turbulence associated with toroidal ion temperature gradient mode,and slab-based phenomenological model of zonal flow.When full toroidal effect is introduced into the system,two branches of zonal flow emerge:the torus-modified low frequency zonal flow(TLFZF),and GAM,necessitating a unified exploration of GAM and TLFZF.Indeed,we observe that the transition from the Caviton to Instanton is triggered by a rapid zero-crossing of radial group velocity of drift wave and is found to be strongly correlated with the GAM onset.Many features peculiar to intermittent GAMs,observed in real machines,are thus identified in the numerical experiment.The results will be displayed in figures and in a movie;first for single central rational surface,and then with coupled multiple central rational surfaces.The periodic bursting first shown disappears as being replaced by irregular one,more similar to the intermittent characteristics observed in GAM experiments.

Comparison of Three Methods in Extracting Coherent Modes from a Doppler Backscatter System

We compare three different methods to extract coherent modes from Doppler backscattering （DBS）, which are center of gravity （COG） of the complex amplitude spectrum, spectrum of DBS phase derivative （phase derivative method）, and phase spectrum, respectively. These three methods are all feasible to extract coherent modes, for example, geodesic acoustic mode oscillation. However, there are stilI differences between dealing with high frequency modes （several hundred kHz） and low frequency modes, （several kHz） hiding in DBS signal. There is a significant amount of power at low frequencies in the phase spectrum, which can be removed by using the phase derivative method and COG. High frequency modes are clearer by using the COO and the phase derivative method than the phase spectrum. The spectrum of DBS amplitude does not show the coherent modes detected by using COG, phase derivative method and phase spectrum. When two Doppler shifted peaks exist, coherent modes and their harmonics appear in the spectrum of DBS amplitude, which are introduced by the DBS phase.

The intermittent excitation of geodesic acoustic mode by resonant Instanton of electron drift wave envelope in L-mode discharge near tokamak edge

There are two distinct phases in the evolution of drift wave envelope in the presence of zonal flow.A long-lived standing wave phase,which we call the Caviton,and a short-lived traveling wave phase(in radial direction) we call the Instanton.Several abrupt phenomena observed in tokamaks,such as intermittent excitation of geodesic acoustic mode(GAM) shown in this paper,could be attributed to the sudden and fast radial motion of Instanton.The composite drift wave-zonal flow system evolves at the two well-separate scales:the micro-scale and the meso-scale.The eigenmode equation of the model defines the zero-order(micro-scale) variation;it is solved by making use of the two-dimensional(2 D) weakly asymmetric ballooning theory(WABT),a theory suitable for modes localized to rational surface like drift waves,and then refined by shifted inverse power method,an iterative finite difference method.The next order is the equation of electron drift wave(EDW) envelope(containing group velocity of EDW) which is modulated by the zonal flow generated by Reynolds stress of EDW.This equation is coupled to the zonal flow equation,and numerically solved in spatiotemporal representation;the results are displayed in self-explanatory graphs.One observes a strong correlation between the Caviton-Instanton transition and the zero-crossing of radial group velocity of EDW.The calculation brings out the defining characteristics of the Instanton:it begins as a linear traveling wave right after the transition.Then,it evolves to a nonlinear stage with increasing frequency all the way to 20 kHz.The modulation to Reynolds stress in zonal flow equation brought in by the nonlinear Instanton will cause resonant excitation to GAM.The intermittency is shown due to the random phase mixing between multiple central rational surfaces in the reaction region.

Ray Tracing for Doppler Backscattering System in the Experimental Advanced Superconducting Tokamak

The Doppler backscattering system has been widely used for turbulence measurements,and the microwave beam will be backscattered near the cut-off layer when the Brag condition is fulfilled.In tokamak,the ray-tracing code is used to obtain the radial position and perpendicular wave number of the scattering layer for turbulence velocity measurement and the WKB（Wentzel-Kramers-Brillouin） approximation should be satisfied for optical propagation.To calculate the backscattering location and wave number at the cut-off layer only,a single ray tracing in the cross section is enough,while for spatial and wave number resolution calculation,multiple rays reflecting the microwave beam size should be used.Considering the angle between the wave vector and the magnetic field,a three-dimension quasi-optical Gaussian ray tracing is sometimes needed.

The investigation of quasi coherent mode on EAST using Doppler reflectometry

An electrostatic Quasi coherent mode has been observed in density fluctuations and perpendicular velocity fluctuations with the frequency range of 3–80 k Hz on the Experimental Advanced Superconducting Tokamak using multi-channel Doppler reflectometry.It appears in the edge localized mode(ELM)-free period after L-H transition or in the inter-ELM period.The mode rotates almost together with the plasma with the poloidal wave number around 0.6cm-1 and its frequency chirps with plasma poloidal velocity.The mode can exist in a large radial coverage(ρ=0.75–0.98),and peaks near the top of pedestal,suggesting that it might be excited in the steep gradient pedestal region,and spread into the core area.

X-Mode Frequency Modulated Density Profile Reflectometer on EAST Tokamak

An extraordinary-mode （X-mode） frequency-modulated continuous-wave （FMCW） profile reflectometer has been built on EAST. In the reflectometer, continuous waves with fre- quency sweeping from 12.5 GHz to 18 GHz were generated through a Hyperabrupt Tuned-varactor Oscillator （HTO） source and a four times active multiplier was used to increase the frequency to V-band （50 GHz to 72 GHz）. The polarization of horn lens antenna is perpendicular to the mag- netic field line at the edge plasmas. According to the V-band frequency range and polarization, the system cover density range from 0.5 x 1019m-3 to 3.0 x 1019m-3 （when toroidal magnetic field is 1.8 T）, with time resolution of 12.5 ~ 50 #s. The density profile could be calculated by assuming the edge profile through an empirical equation. The maximum spatial error deduced by the method is about 4 cm. This reflectometer has been successfully applied in 2010 autumn EAST campaign, the temporal evolution of density profiles was acquired during the low confine- ment mode to high confinement mode transition. The density pedestal of EAST Tokamak was observed and the top value and gradient of the density pedestal were estimated.

Identification of Low-Frequency Zonal Flow in a Linear Magnetic Plasma Device

A low-frequency(f<2 kHz)potential structure(LFPS)is observed in a linear magnetic plasma device using Langmuir probe arrays.The center frequency of this structure is near zero.This structure has azimuthal and axial symmetries while with a finite radial wavenumber.The complete 3D spectra features of this structure have been identified to have the characteristics expected for zonal flows.