Deep learning approaches to recover the plasma current density profile from the safety factor based on Grad–Shafranov solutions across multiple tokamaks

Many magnetohydrodynamic stability analyses require generation of a set of equilibria with a fixed safety factor q-profile while varying other plasma parameters.A neural network(NN)-based approach is investigated that facilitates such a process.Both multilayer perceptron(MLP)-based NN and convolutional neural network(CNN)models are trained to map the q-profile to the plasma current density J-profile,and vice versa,while satisfying the Grad–Shafranov radial force balance constraint.When the initial target models are trained,using a database of semianalytically constructed numerical equilibria,an initial CNN with one convolutional layer is found to perform better than an initial MLP model.In particular,a trained initial CNN model can also predict the q-or J-profile for experimental tokamak equilibria.The performance of both initial target models is further improved by fine-tuning the training database,i.e.by adding realistic experimental equilibria with Gaussian noise.The fine-tuned target models,referred to as fine-tuned MLP and fine-tuned CNN,well reproduce the target q-or J-profile across multiple tokamak devices.As an important application,these NN-based equilibrium profile convertors can be utilized to provide a good initial guess for iterative equilibrium solvers,where the desired input quantity is the safety factor instead of the plasma current density.

Realization of T_(e0)>10 keV long pulse operation over 100 s on EAST

In 2021,EAST realized a steady-state long pulse with a duration over 100 s and a core electron temperature over 10 keV.This is an integrated operation that resolves several key issues,including active control of wall conditioning,long-lasting fully noninductive current and divertor heat/particle flux.The fully noninductive current is driven by pure radio frequency(RF)waves with a lower hybrid current drive power of 2.5 MW and electron cyclotron resonance heating of 1.4 MW.This is an excellent experimental platform on the timescale of hundreds of seconds for studying multiscale instabilities,electron-dominant transport and particle recycling(plasma-wall interactions)under weak collisionality.

Effect of ideal internal MHD instabilities on NBI fast ion redistribution in ITER 15 MA scenario

Transport of fast ions is a crucial issue during the operation of ITER.Redistribution of neutral beam injection(NBI)fast ions by the ideal internal magnetohydrodynamic(MHD)instabilities in ITER is studied utilizing the guiding-center code ORBIT(White R B and Chance M S 1984Phys.Fluids 272455).Effects of the perturbation amplitude A of the internal kink,the perturbation frequency f of the fishbone instability,and the toroidal mode number n of the internal kink are investigated,respectively,in this work.The n=1 internal kink mode can cause NBI fast ions transporting in real space from regions of 0<s≤0.32 to 0.32<s≤0.53,where s labels the normalized plasma radial coordinate.The transport of fast ions is greater as the perturbation amplitude increases.The maximum relative change of the number of fast ions approaches 5%when the perturbation amplitude rises to 500 G.A strong transport is generated between the regions of 0<s≤0.05 and 0.05<s≤0.12 in the presence of the fishbone instability.Higher frequency results in greater transport,and the number of fast ions in 0<s≤0.05 is reduced by 30%at the fishbone frequency of 100 k Hz.Perturbations with higher n will lead to the excursion of fast ion transport regions outward along the radial direction.The loss of fast ions,however,is not affected by the internal MHD perturbation.Strong transport from 0<s≤0.05 to 0.05<s≤0.12 does not influence the plasma heating power of ITER,since the NBI fast ions are still located in the plasma core.On the other hand,the influence of fast ion transport from 0<s≤0.32 to 0.32<s≤0.53 needs further study.

极紫外波段Ar光谱分析在EAST偏滤器杂质屏蔽效应研究中的应用

在托卡马克偏滤器区域充入杂质气体是检验偏滤器杂质屏蔽效应的重要手段。利用快速极紫外EUV光谱仪对EAST托克马克装置上开展的偏滤器Ar杂质注入实验进行观测。结合NIST原子光谱数据库对2～50 nm范围内不同电离态Ar的线光谱进行了谱线识别,识别出ArⅣ,ArⅨ-Ⅺ,Ar XⅣ-XⅥ等若干个电离态的谱线。为了同时观测等离子体不同区域的Ar杂质行为,在杂质注入实验时重点监测Ar XⅥ35.39 nm（Ar XⅥ电离能918.4 eV,主要分布在等离子体芯部）和ArⅣ44.22 nm（ArⅣ电离能9.6 eV,主要分布在等离子体边界）这两条谱线。利用该两条谱线强度随时间演化的结果初步分析了偏滤器杂质屏蔽效应。在同一充气口不同等离子体位形下的实验结果表明偏滤器对于从偏滤器区域注入Ar杂质的屏蔽效果优于从主等离子体区域注入,并且下偏滤器及内冷泵的综合粒子排除能力优于上偏滤器。

Implementation of Gas Control Algorithm in EASTPCS

In this paper, gas control on EAST in open and closed loop is discussed and its implementation into EASTPCS （plasma control system for the experimental advanced supercon- ducting tokamak） is introduced. Using a model to describe the plasma density response to the gas puff command, a gas simulation server （simserver） using MATLAB simulink tools and real time workshop was built up. Proper operation of the gas control algorithm was verified using this simserver. The simulation results suggested that the gas control can be applied in the next EAST campaign.

Performance Enhancements in the EAST Digital Plasma Control System

The EAST plasma control system （PCS） is in continuous development to satisfy the EAST experimental requirements. In order to realize low latency and distortion-free signal transmission between PCS and servo systems such as the poloidal field power supply, in-vessel coil power supply and real-time scope, reflective memory boards （RFM） were applied. The new hardware layout and enhanced performance are reported. Newly implemented PCS control algorithms for gas control and real-time data display are also presented.

Equilibrium Reconstruction in EAST Tokamak

Reconstruction of experimental axisymmetric equilibria is an important part of tokamak data analysis. Fourier expansion is applied to reconstruct the vessel current distribution in EFIT code. Benchmarking and testing calculations are performed to evaluate and validate this algorithm. Two cases for circular and non-circular plasma discharges are presented. Fourier expansion used to fit the eddy current is a robust method and the real time EFIT can be introduced to the plasma control system in the coming campaign.

Development and Preliminary Commissioning Results of a Long Pulse 140 GHz ECRH System on EAST Tokamak(Invited)

A long pulse electron cyclotron resonance heating（ECRH）system has been developed to meet the requirements of steady-state operation for the EAST superconducting tokamak,and the first EC wave was successfully injected into plasma during the 2015 spring campaign.The system is mainly composed of four 140 GHz gyrotron systems,4 ITER-Like transmission lines,4 independent channel launchers and corresponding power supplies,a water cooling,control ＆inter-lock system etc.Each gyrotron is expected to deliver a maximum power of 1 MW and be operated at 100-1000 s pulse lengths.The No.1 and No.2 gyrotron systems have been installed.In the initial commissioning,a series of parameters of 1 MW 1 s,900 k W 10 s,800 k W 95 s and650 k W 753 s have been demonstrated successfully on the No.1 gyrotron system based on calorimetric dummy load measurements.Significant plasma heating and MHD instability suppression effects were observed in EAST experiments.In addition,high confinement（H-mode）discharges triggered by ECRH were obtained.

Eddy Calculation and Vacuum Field Reconstruction on EAST

A new method, by using eigenmodes to reduce the fitting parameters and precalculated eddy current based on a lump parameter circuit equation, is applied to reconstruct the vacuum field for EAST plasma startup.

Preliminary Study of Ideal Operational MHD Beta Limit in HL-2A Tokamak Plasmas

Magnetohydrodynamic （MHD） n=1 kink mode with n the toroidal mode number is studied and the operational beta limit, constrained by the mode, is calculated for the equilibrium of HL-2A by using the GATO code. Approximately the same beta limit is obtained for configurations with a value of the axial safety factor q0 both larger and less than 1. Without the stabilization of the conducting wall, the beta limit is found to be 0.821% corresponding to a normalized beta value of βN^c=2.56 for a typical HL-2A discharge with a plasma current Ip=0.245 MA, and the scaling of βN^c -constant is confirmed.

The stability margin on EAST tokamak

The experimental advanced superconducting tokamak （EAST） is the first full superconducting tokamak with a D-shaped cross-sectional plasma presently in operation. Its poloidal coils are relatively far from the plasma due to the necessary thermal isolation from the superconducting magnets, which leads to relatively weaker coupling between plasma and poloidal field. This may cause more difficulties in controlling the vertical instability by using the poloidal coils. The measured growth rates of vertical stability are compared with theoretical calculations, based on a rigid plasma model. Poloidal beta and internal inductance are varied to investigate their effects on the stability margin by changing the values of parameters αn and γn（Howl et al 1992 Phys. Fluids B 4 1724）, with plasma shape fixed to be a configuration with k = 1.9 and 5 = 0.5. A number of ways of studying the stability margin are investigated. Among them, changing the values of parameters κ and li is shown to be the most effective way to increase the stability margin. Finally, a guideline of stability margin Ms（ki, li, A） to a new discharge scenario showing whether plasmas can be stabilized is also presented in this paper.

Transport Modelling for EAST with LHRF and NBI

Lower hybrid simulation code （LSC） is integrated into transport code ONETWO to model discharges of EAST with heating and current drive using both lower hybrid wave and neutral beam injection. To test the integration, the current profiles driven by both lower hybrid wave and neutral beam injection are presented for a given equilibrium and sample density and temperature profiles before carrying out a time advancing simulation. For a steady state H-mode discharge, the temperature profiles are evolved using GLF23 transport model with a boundary value specified at the normalized minor radius pN = 0.9. A case of steady state with non-inductively driven current accounting for up to 80% is presented.

On the study of hydrodynamic instabilities in the presence of background magnetic fields in high-energy-density plasmas

Blast-wave-driven hydrodynamic instabilities are studied in the presence of a background B-field through experiments and simulations in the high-energy-density(HED)physics regime.In experiments conducted at the Laboratoire pour l’utilisation des lasers intenses(LULI),a laserdriven shock-tube platform was used to generate a hydrodynamically unstable interface with a prescribed sinusoidal surface perturbation,and short-pulse x-ray radiography was used to characterize the instability growth with and without a 10-T B-field.The LULI experiments were modeled in FLASH using resistive and ideal magnetohydrodynamics(MHD),and comparing the experiments and simulations suggests that the Spitzer model implemented in FLASH is necessary and sufficient for modeling these planar systems.These results suggest insufficient amplification of the seed B-field,due to resistive diffusion,to alter the hydrodynamic behavior.Although the ideal-MHD simulations did not represent the experiments accurately,they suggest that similar HED systems with dynamic plasma-β(=2μ_(0)ρv^(2)/B^(2))values of less than∼100 can reduce the growth of blast-wave-driven Rayleigh–Taylor instabilities.These findings validate the resistive-MHD FLASH modeling that is being used to design future experiments for studying B-field effects in HED plasmas.

Realization of minute-long steady-state H-mode discharges on EAST

In the 2016 EAST experimental campaign,a steady-state long-pulse H-mode discharge with an ITER-like tungsten divertor lasting longer than one minute has been obtained using only RF heating and current drive,through an integrated control of the wall conditioning,plasma configuration,divertor heat flux,particle exhaust,impurity management,and effective coupling of multiple RF heating and current drive sources at high injected power.The plasma current（Ip - 0.45 MA） was fully-noninductively driven（Vloop 〈 0.0 V） by a combination of-2.5 MW LHW,-0.4 MW ECH and -0.8 MW ICRF.This result demonstrates the progress of physics and technology studies on EAST,and will benefit the physics basis for steady state operation of ITER and CFETR.

Properties of vapor-deposited and solution-processed targets for laser-driven inertial confinement fusion experiments

Targets for low-adiabat direct-drive-implosion experiments on OMEGA must meet rigorous specifications and tight tolerances on the diameter,wall thickness,wall-thickness uniformity,and presence of surface features.Of these,restrictions on the size and number of defects(bumps and depressions)on the surface are the most challenging.The properties of targets that are made using vapor-deposition and solution-based microencapsulation techniques are reviewed.Targets were characterized using confocal microscopy,bright-and dark-field microscopy,atomic force microscopy,electron microscopy,and interferometry.Each technique has merits and limitations,and a combination of these techniques is necessary to adequately characterize a target.The main limitation with the glow-discharge polymerization(GDP)method for making targets is that it produces hundreds of domes with a lateral dimension of 0.7-2 μm.Polishing these targets reduces the size of some but not all domes,but it adds scratches and grooves to the surface.Solution-made polystyrene shells lack the dome features of GDP targets but have hundreds of submicrometer-size voids throughout the wall of the target;a few of these voids can be as large as~12 μm at the surface.

Strike Point Control on EAST Using an Isoflux Control Method

For the advanced tokamak,the particle deposition and thermal load on the divertor is a big challenge.By moving the strike points on divertor target plates,the position of particle deposition and thermal load can be shifted.We could adjust the Poloidal Field（PF） coil current to achieve the strike point position feedback control.Using isoflux control method,the strike point position can be controlled by controlling the X point position.On the basis of experimental data,we establish relational expressions between X point position and strike point position.Benchmark experiments are carried out to validate the correctness and robustness of the control methods.The strike point position is successfully controlled following our command in the EAST operation.

Energetic Particle Transport Prediction for CFETR Steady State Scenario Based on Critical Gradient Model

The critical gradient mode(CGM) is employed to predict the energetic particle(EP) transport induced by the Alfven eigenmode(AE).To improve the model,the normalized critical density gradient is set as an inverse proportional function of energetic particle density;consequently,the threshold evolves during EP transport.Moreover,in order to consider the EP orbit loss mechanism in CGM,ORBIT code is employed to calculate the EP loss cone in phase space.With these improvements,the AE enhances EPs radial transport,pushing the particles into the loss cone.The combination of the two mechanisms raises the lost fraction to 6.6%,which is higher than the linear superposition of the two mechanisms.However,the loss is still far lower than that observed in current experiments.Avoiding significant overlap between the AE unstable region and the loss cone is a key factor in minimizing EP loss.

Tests of the real-time vertical growth rate calculation on EAST

In order to measure controllability of vertical instability in EAST,the calculation of model-based vertical growth rate,called rt-gamma,has been successfully carried out in real time.The numerical computing method is adapted from rigid plasma response model in TokSys,which is a widely-used analysis tool for tokamak devices in Matlab environment,but the code is rewritten by taking advantage of GPU parallel computing capability to accelerate the computation.The calculation of rt-gamma is validated by comparing it with the corresponding result generated by TokSys for totally 3508 cases.It is shown that the average absolute value of relative errors is about 0.85%.In addition,the calculation program of rt-gamma has been successfully applied during 2019 EAST campaign.The comparison with experimental results is discussed in this paper.The real-time calculation tool is well able to calculate model-based vertical growth rate,which is convenient for fast and continuous evaluations of EAST control system stability performances.

Partition of Forecast Error into Positional and Structural Components

Weather manifests in spatiotemporally coherent structures.Weather forecasts hence are affected by both positional and structural or amplitude errors.This has been long recognized by practicing forecasters(cf.,e.g.,Tropical Cyclone track and intensity errors).Despite the emergence in recent decades of various objective methods for the diagnosis of positional forecast errors,most routine verification or statistical post-processing methods implicitly assume that forecasts have no positional error.The Forecast Error Decomposition(FED)method proposed in this study uses the Field Alignment technique which aligns a gridded forecast with its verifying analysis field.The total error is then partitioned into three orthogonal components:(a)large scale positional,(b)large scale structural,and(c)small scale error variance.The use of FED is demonstrated over a month-long MSLP data set.As expected,positional errors are often characterized by dipole patterns related to the displacement of features,while structural errors appear with single extrema,indicative of magnitude problems.The most important result of this study is that over the test period,more than 50%of the total mean sea level pressure forecast error variance is associated with large scale positional error.The importance of positional error in forecasts of other variables and over different time periods remain to be explored.