Numerical study of equilibrium solutions for axisymmetric plasmas with toroidal flow obtained using Solovev approach

Solovev approach of finding equilibrium solutions, which was extended to include the vacuum solutions provided by Zheng, Wooton, and Solano, was found extremely useful for the purpose of shaping studies. Its extension to toroidal equilibria with a general plasma flow was examined theoretically in a companion paper by Chu, Hu and Guo. The only meaningful extension was found for plasmas with a pure toroidal rotation and with a constant Mach number. A set of functions {SOLOVEV_ZWSm} was obtained which fixed location of the magnetic axis for equilibria with quasi-constant current density profile, with toroidal flow at constant Mach number and with specific heat capacity 1. The set {Solovev_ZWSm} should have complete shaping capability for plasma shapes with positive curvature at the boundary; but not for plasmas with negative curvature boundary points, i.e. the doublets or bean shaped tokamaks. We report here extensive numerical studies showing the shaping capability of {Solovev_ZWSm} for plasmas with pure toroidal rotations, including the change in topology of the solution when the rotation mach number changes. Included plasma topology are the sphere (spheromaks); and the tokamaks (including the doublets).     

Geodesic acoustic modes in tokamak plasmas with anisotropic distribution and a radial equilibrium electric field

The dispersion relation of standard geodesic acoustic modes in tokamak plasmas with anisotropic distribution and a radial equilibrium electric field is derived and analyzed. Both frequencies and damping rates increase with respect to the poloidal Mach number which indicates the strength of the radial electric field. The strength of anisotropy is denoted by the ratio of the parallel temperature(T_‖) to the perpendicular temperature(T_⊥). It is shown that, when the parallel temperature is lower than the perpendicular temperature, the enhanced anisotropy tends to enlarge the real frequency but reduces the damping rate, and when the parallel temperature is higher than the perpendicular temperature, the effect is opposite. The radial equilibrium electric field has stronger effect on the frequency and damping rate for the case with higher parallel temperature than the case with higher perpendicular temperature.     

Unexpanded nonlinear electromagnetic gyrokinetic equations for magnetized plasmas

Nonlinear electromagnetic gyrokinetic equations have been constructed without expanding the field variables into background and finite but small-amplitude fluctuating components. At the long-wavelength limit, these unexpanded nonlinear gyrokinetic equations recover the well-known drift-kinetic equations. At the expanded limit, they recover the usual nonlinear gyrokinetic equations. These equations can therefore be applied to long-term simulations covering from microscopic to macroscopic spatial scales.     

A plasma equilibrium model for rapid estimation of SF-MPDT performance

In this work,a zero-dimensional plasma model for self-field magnetoplasmadynamic thrusters(SF-MPDTs) is proposed,which is based on the ion-number balance equation and energy balance equation,and can calculate the average electron temperature and the average ion temperature inside the discharge chamber conveniently.At the same time,the model can also predict the thruster performance,and the thruster performance predicted by the model is compared with experimental results,which proved the reliability of the model.     

Acceleration optimization of real-time equilibrium reconstruction for HL-2A tokamak discharge control

Real-time equilibrium reconstruction is crucially important for plasma shape control in the process of tokamak plasma discharge.However,as the reconstruction algorithm is computationally intensive,it is very difficult to improve its accuracy and reduce the computation time,and some optimizations need to be done.This article describes the three most important aspects of this optimization:(1) compiler optimization;(2) some optimization for middle-scale matrix multiplication on the graphic processing unit and an algorithm which can solve the block tri-diagonal linear system efficiently in parallel;(3) a new algorithm to locate the XO point on the central processing unit.A static test proves the correctness and a dynamic test proves the feasibility of using the new code for real-time reconstruction with 129?×?129 grids;it can complete one iteration around 575 μs for each equilibrium reconstruction.The plasma displacements from real-time equilibrium reconstruction are compared with the experimental measurements,and the calculated results are consistent with the measured ones,which can be used as a reference for the real-time control of HL-2 A discharge.     

The residual zonal flow in tokamak plasmas with a poloidal electric field

In a tokamak plasma with auxiliary heating by cyclotron waves, a poloidal electric field will be produced, and as a consequence influence the residual zonal flow(RZF) level. The poloidal electric field can also be induced through biasing electrodes at the edge region of tokamaks.Numerical evaluation for a large aspect ratio circular cross section tokamak for the electron cyclotron wave heating indicates that the RZF level decreases significantly when the poloidal electric field increases. Qualitatively, the ion cyclotron wave heating is able to increase the RZF level. It is difficult to apply the calculation to the real cyclotron wave heating experiments since we need to know factors such as the plasma profiles, the exact power deposition and the cross section geometry, etc. It is possible to use the cyclotron wave heating to control the zonal flow and then to control the turbulence level in tokamak experiments.     

Machine learning of turbulent transport in fusion plasmas with neural network

Turbulent transport resulting from drift waves,typically,the ion temperature gradient(ITG)mode and trapped electron mode(TEM),is of great significance in magnetic confinement fusion.It is also well known that turbulence simulation is a challenging issue in both the complex physical model and huge CPU cost as well as long computation time.In this work,a credible turbulence transport prediction model,extended fluid code(ExFC-NN),based on a neural network(NN)approach is established using simulation data by performing an ExFC,in which multi-scale multi-mode fluctuations,such as ITG and TEM turbulence are involved.Results show that the characteristics of turbulent transport can be successfully predicted including the type of dominant turbulence and the radial averaged fluxes under any set of local gradient parameters.Furthermore,a global NN model can well reproduce the radial profiles of turbulence perturbation intensities and fluxes much faster than existing codes.A large number of comparative predictions show that the newly constructed NN model can realize rapid experimental analysis and provide reference data for experimental parameter design in the future.     

Control of flow separation over a wing model with plasma synthetic jets

An array of 30 plasma synthetic jet actuators (PSJAs) is deployed using a modified multichannel discharge circuit to suppress the flow separation over a straight-wing model. The lift and drag of the wing model are measured by a force balance, and the velocity fields over the suction surface are captured by a particle imaging velocimetry system. Results show that the flow separation of the straight wing originates from the middle of the model and expands towards the wingtips as the angle of attack increases. The flow separation can be suppressed effectively by the PSJAs array. The best flow control effect is achieved at a dimensionless discharge frequency of F⁺ = 1, with the peak lift coefficient increased by 10.5% and the stall angle postponed by 2°. To further optimize the power consumption of the PSJAs, the influence of the density of PSJAs on the flow control effect is investigated. A threshold of the density exits (with the spanwise spacing of PSJAs being 0.2 times of the chord length in the current research), below which the flow control effect starts to deteriorate remarkably. In addition, for comparison purposes, a dielectric barrier discharge (DBD) plasma actuator is installed at the same location of the PSJAs. At the same power consumption, 4.9% increase of the peak lift coefficient is achieved by DBD, while that achieved by PSJAs reaches 5.6%.     

Numerical Study of Tokamak Equilibrium with Toroidal Flow on EAST

The effect of the toroidal flow on the equilibrium of tokamak plasmas is a sensitive point for high performance plasma and its precise control. In this paper the effect is studied numerically using the EFIT （Equilibrium Fitting） code on EAST （Experimental Advanced Superconducting Tokamak）. Firstly, the numerical calculation exhibits a clear outward shift of pressure contour from the magnetic surfaces in the plasma core and the shift grows with the increase of the toroidal velocity. The peak shift of 8% is observed when the ratio between the plasma velocity and the Alfvdn speed equals to 0.15. Secondly, it is shown that the magnetic surfaces shift outwards from those without flow. With a certain plasma current the safety factor on the magnetic axis decreases as the plasma flow velocity increases. The magnetic shear increases about 10% on the plasma boundary compared with the case without flow.     

Automated electron temperature fitting of Langmuir probe I-V trace in plasmas with multiple Maxwellian EEDFs

An algorithm for automated fitting of the effective electron temperature from a planar Langmuir probe I–V trace taken in a plasma with multiple Maxwellian electron populations is developed through MATLAB coding. The code automatically finds a fitting range suitable for analyzing the temperatures of each of the electron populations. The algorithm is used to analyze I–V traces from both the Institute of Plasma Physics Chinese Academy of Sciences’s Diagnostic Test Source device and a similar multi-dipole chamber at the University of Wisconsin–Madison. I–V traces reconstructed from the parameters fitted by the algorithm not only agree with the measured I–V trace but also reveal physical properties consistent with those found in previous studies. Cylindrical probe traces are also analyzed with the algorithm and it is shown that the major source of error in such attempts is the disruption of the inflection point due to both decreased signal-to-noise ratio and greater sheath expansion. It is thus recommended to use planar probes with radii much greater than the plasma Debye length when signal-to-noise ratio is poor.     

Application of 3D MHD equilibrium calculation to RMP experiments in the J-TEXT tokamak

The application of resonant magnetic perturbation(RMP) coils could break the initial axisymmetry and change the magnetic topology in tokamak systems. To understand the plasma equilibrium response to the RMP fields, three-dimensional(3 D) non-linear magnetohydrodynamics equilibrium calculations have been carried out using the HINT code for an RMP field-penetration experiment on J-TEXT. The HINT code does not assume perfectly nested flux surfaces, and is able to consider directly the change of magnetic topology due to the RMP field penetrations. Correlations between 3 D equilibrium calculations and experimental observations are presented. The magnetic topologies calculated by HINT were compared with the field topologies obtained from a vacuum approximation method. It turns out that the effects of redistribution of plasma pressure and current due to the formation of magnetic islands at various resonant rational surfaces should be considered self-consistently for understanding the change of magnetic structure. Such changes include changes in the shape and size of magnetic islands, and the distribution of stochastic fields around the magnetic islands and at the plasma boundary, which plays an important role for plasma-wall interactions.     

Thermophysical properties of pure gases and mixtures at temperatures of 300-30 000 K and atmospheric pressure:thermodynamic properties and solution of equilibrium compositions

The equilibrium compositions and thermodynamic properties(density,enthalpy,etc at constant pressure)of plasma of pure gases and mixtures under local thermodynamic nonequilibrium have been calculated in this paper.The homotopy Levenberg-Marquardt algorithm was proposed to accurately solve nonlinear equations with singular Jacobian matrices,and is constructed by the Saha equation and Guldberg-Waage equation combined with mass conservation,the electric neutrality principle and Dalton's partial pressure law,to solve the problem of dependence on the initial value in the process of iteration calculation.In this research,the equations at a higher temperature were solved and used as the auxiliary equations,and the homotopy control parameters'sequence of the homotopy equations was selected by equal ratios.For auxiliary equations,the iterative initial value was obtained by assuming that there were only the highest-valence atomic cations and electrons at this temperature,and the plasma equilibrium composition distribution with the required accuracy was ultimately solved under the current conditions employing the Levenberg-Marquardt algorithm.The control parameter sequence was arranged according to the geometric sequence and the homotopy step was gradually shortened to ensure continuity of the homotopy process.Finally,the equilibrium composition and thermodynamic properties of pure N2,Mg(30％)-C02(70％)and Mg(40％)-CO(50％)-N2(10％)mixture plasma at atmospheric pressure were calculated and the calculation process of some specified temperatures was shown and analyzed.The calculation accuracy of equilibrium composition is higher than other findings in the literature.The results for the thermodynamic properties are in good agreement with data reported by the literature.     

Behavior of tungsten with exposure to deuterium plasmas

Four kinds of tungsten (W) materials, i.e. (1) foil of 50 μm thick (f-W), (2) polycrystalline (Pc-W) with grain size of ∼3 μm, (3) recrystallized (Re-W) with grain size of ∼50 μm and (4) vacuum plasma spraying (VPS-W) coatings, were irradiated employing linear plasma generators, with fluxes ?1 × 10²² D/m²/s and energies ?100 eV/D. Scanning electron microscopy (SEM) was used to observe blister formation at the surfaces. The SEM surface morphology and cross section observation indicates that blister formation is related to the microstructure and surface state of different material grades. Results of trapping and deuterium retention measured by thermal desorption spectroscopy (TDS) and nuclear reaction analysis (NRA) show also a close correlation between the retention and the microstructure and surface state.     

Correlation of III/V semiconductor etch results with physical parameters of high-density reactive plasmas excited by electron cyclotron resonance

Reactive ion etching is the interaction of reactive plasmas with surfaces. To obtain a detailed understanding of this process, significant properties of reactive composite low-pressure plasmas driven by electron cyclotron resonance (ECR) were investigated and compared with the radial uniformity of the etch rate. The determination of the electronic properties of chlorine-and hydrogen-containing plasmas enabled the understanding of the pressure-dependent behavior of the plasma density and provided better insights into the electronic parameters of reactive etch gases. From the electrical evaluation of I(V ) characteristics obtained using a Langmuir probe, plasmas of different compositions were investigated. The standard method of Druyvesteyn to derive the electron energy distribution functions by the second derivative of the I(V ) characteristics was replaced by a mathematical model which has been evolved to be more robust against noise, mainly, because the first derivative of the I(V ) characteristics is used. Special attention was given to the power of the energy dependence in the exponent. In particular, for plasmas that are generated by ECR with EM modes, the existence of Maxwellian distribution functions is not to be taken as a self-evident fact, but the bi-Maxwellian distribution was proven for Ar-and Kr-stabilized plasmas. In addition to the electron temperature, the global uniform discharge model has been shown to be useful for calculating the neutral gas temperature. To what extent the invasive method of using a Langmuir probe could be replaced with the non-invasive optical method of emission spectroscopy, particularly actinometry, was investigated, and the resulting data exhibited the same relative behavior as the Langmuir data. The correlation with etchrate data reveals the large chemical part of the removal process—most striking when the data is compared with etching in pure argon. Although the relative amount of the radial variation of plasma density and etch rate is approximately ±5%, the etch rate shows a slightly concave shape in contrast to the plasma density.     

Toroidal component of velocity for geodesic acoustic modes in the edge plasmas of the J-TEXT tokamak

The toroidal component of the velocity for geodesic acoustic modes (GAMs) is first demonstrated.Multiple Langmuir probe arrays set up near the top tokamak of the J-TEXT were utilized for this study.A significant peak at the GAM frequency is observed in Mach number fluctuations.The toroidal velocity for the GAMs is estimated as ～10-100 m s-1 and increases with the poloidal velocity.The ratio of toroidal component to the poloidal one of the velocity is mainly located in the interval between 0.3 and 1.0.With higher safety factors q,the ratio almost does not change with decreasing the safety factor,whereas it goes up sharply at low q.The coherencies between poloidal electric fields and Mach number fluctuations in turbulence frequency bands are also evaluated,and are higher than those between radial electric fields and Mach number fluctuations.     

核电站建造用EJ标准的中外接轨关系问题探讨

在核电站设计自主化过程中,必然会遇到中外设计与建造标准如何协调和处理的问题。本文就现行核工业标准如何寻找出中外标准的接轨关系作了探讨。     

Classification of two-phase flow regimes via image analysis and a neuro-wavelet approach

A non-intrusive method of two-phase flow identification is investigated in this paper. It is based on image processing of data obtained partly from dynamic neutron radiography recordings of real two-phase flow in a heated metal channel, and partly by visible light from a two-component mixture of water and air. Classification of the flow regime types is performed by an artificial neural network (ANN) algorithm. The input data to the ANN are some statistical moments of the wavelet pre-processed pixel intensity data of the images. The pre-processing used in this paper consists of a one-step multiresolution analysis of the 2-D image data. The investigations of the neutron radiography images, where all four flow regimes are represented, show that bubbly and annular flows can be identified with a high confidence, but slug and churn-turbulent flows are more often mixed up in between themselves. The reason for the faulty identifications, at least partially, lies in the insufficient quality of these images. In the measurements with air-water two-component mixture, only bubbly and slug flow regimes were available, and these were identified with nearly 100% success ratio. The maximum success ratio attainable was approximately the same whether the raw data was used without wavelet preprocessing or with a wavelet preprocessing of the input data. However, the use of wavelet preprocessing decreased the training time (number of epochs) with about a factor 100.     

Investigation of self-generated magnetic field and dynamics of a pulsed plasma flow

Due to the growing interest in studying the compression and disruption of the plasma filament in magnetic fusion devices and Z-pinches, this work may be important for new developments in the field of controlled thermonuclear fusion. Recently, on a coaxial plasma accelerator, we managed to obtain the relatively long-lived (∼300 μs) plasma filaments with its self-magnetic field. This was achieved after modification of the experimental setup by using high-capacitive and low-inductive energy storage capacitor banks, as well as electrical cables with low reactive impedance. Furthermore, we were able to avoid the reverse reflection of the plasma flux from the end of the plasma accelerator by installing a special plasma-absorbing target. Thus, these constructive changes of the experimental setup allowed us to investigate the physical properties of the plasma filament by using the comprehensive diagnostics including Rogowski coil, magnetic probes, and Faraday cup. As a result, such important plasma parameters as density of ions and temperature of electrons in plasma flux, time dependent plasma filament's azimuthal magnetic field were measured in discharge gap and at a distance of 23.5 cm from the tip of the cathode. In addition, the current oscillograms and I–V characteristics of the plasma accelerator were obtained. In the experiments, we also observed the charge separation during the acceleration of plasma flow via oscillograms of electron and ion beam currents.     

Physics design of initial and approach to equilibrium cores of a reactor concept for thorium utilization

A thermal reactor concept ‘a thorium breeder reactor’ (ATBR) was conceived and reported by the authors during 1998. The distinctive physical characteristics of ATBR core with different types of seed fuels have been discussed in subsequent publications. The equilibrium core of ATBR with Pu seed was shown to exhibit a flat and low excess reactivity for a fuel cycle duration of two years. Notably this is achieved by no conventional burnable poison but by intrinsic balancing of reactivity between fissile and fertile zones. In this paper we present the design of the initial core and the refueling strategy for subsequent fuel cycles to enable a smooth transition to the equilibrium core. Three fuel types with characteristics similar to the three batch fuels of equilibrium core were designed for the initial core. Fuel requirement for the initial core is 4673 kg of reactor grade (RG) Pu for a cycle length of two years at 1875 MWt as against the 2200 kg needed for each fuel cycle of equilibrium core for same quantum of energy. The core reactivity variation during the first fuel cycle is monotonic fall and is relatively high (∼40 mk) but gradually diminishes to ±5 mk for fuel cycles 5–8.     

Enhanced removal of benzene in nonthermal plasma with ozonation,flow recycling,and flow recirculation

A double stage AC/DC sequential high voltage reactor has been developed to study the decomposition of benzene in the air stream at atmospheric pressure. The removal efficiency was measured as a function of ozonation, flow recycling, and flow recirculation. Ozonation in the inlet, and recycling of the exhaust stream increased the removal of benzene, also with increasing of specific input energy (J l⁻¹) the effect of inlet flow ozonation on benzene decomposition was enhanced. The highest removal efficiency was obtained up to >99% in recirculation six times, while CO₂ selectivity reached 99.9% and energy efficiency was 0.59 g kWh⁻¹. O₃ production/ decomposition > production of OH radicals > electronic and ionic collisions were indicated as the main mechanisms influencing benzene abatement in this research.