DIVIMP Modeling of Impurity Transport in EAST

Simulations of carbon impurity transport in SOL/divertor plasmas with Ohmic heating on EAST tokamak were performed using the two-dimensional（2D）Monte Carlo impurity transport code DIVIMP.The background plasmas for DIVIMP simulations were externally taken from B2.5/Eirene calculation.Besides the basic output of DIVIMP,the 2D density distributions of the carbon impurity with different ionization states and neutral carbon atoms were obtained,the2D distributions of CII and CIII emissivities from C＋1and C＋2radiation respectively were also calculated.Comparison between the measured and calculated CIII emissivities showed favorable agreement,indicating that the impurity physics transport models,as implemented in the DIVIMP code,are suitable for the EAST tokamak plasma condition.     

托卡马克等离子体杂质密度的光谱法测量研究

本文介绍了基于托卡马克等离子体被动光谱诊断获得杂质密度的方法。通过被动光谱诊断测量获得杂质线辐射的空间多道弦积分强度分布,利用强度标定系数转换为绝对光亮度分布;通过测量弦与等离子体位形,将弦积分的强度分布反演变换为径向体发射率。根据线辐射强度激发截面求出对应电离态的离子密度,最后采用杂质输运程序模拟计算得出总密度分布。以东方超环(Experimental Advanced Superconducting Tokamak,EAST)托卡马克装置上软X射线-极紫外光谱(Soft X-ray and Extreme Ultraviolet Spectrometers,XEUV)诊断测量到的Mo XXIX-Mo XXXII为例,描叙了获得Mo杂质密度分布的过程,获得的总误差小于10%。     

Simulation studies of tungsten impurity behaviors during neon impurity seeding with tungsten bundled charge state model using SOLPS-ITER on EAST

An investigation into tungsten (W) impurity behaviors with the update of the EAST lower W divertor for H-mode has been carried out using SOLPS-ITER. This work aims to study the effect of external neon (Ne) impurity seeding on W impurity sputtering with the bundled charge state model. As the Ne seeding rate increases, plasma parameters, W concentration (), and eroded W flux () at both targets are compared and analyzed between the highly resolved bundled model 'jett' and the full W charge state model. The results indicate that 'jett' can produce divertor behaviors essentially in agreement with the full W charge state model. The bundled scheme with high resolution in low W charge states (20+) has no obvious effect on the Ne impurity distribution and thus little effect on W sputtering by Ne. Meanwhile, parametric scans of radial particle and thermal transport diffusivities (and) in the SOL are simulated using the 'jett' bundled model. The results indicate that the transport diffusivity variations have significant influences on the divertor parameters, especially for W impurity sputtering.     

Critical conditions in an infinitely reflected,multiplying slab using two-group,integral transport theory

A two-group formulation of the integral transport equation has been carried out for the infinitely reflected critical slab. The coupled integral equations that arise are re-formulated using a special transformation so that the problem is reduced to an integration over the slab only. The effect of the infinite reflector is incorporated into a modified kernel of the integral equation. The new integral equations are solved numerically and some comparisons are made with published experimental and theoretical critical sizes. Some conjectures are made about the agreement obtained. The calculations are illustrated by graphs showing the fast and thermal fluxes. Finally, we calculate some values of Galanin's constant for the slab and study its convergence as the accuracy of the numerical method is improved.     

Study on Radial Position of Impurity Ions in Core and Edge Plasma of LHD Using Space-Resolved EUV Spectrometer

Radial profiles of impurity ions of carbon, neon and iron were measured for high-temperature plasmas in large helical device (LHD) using a space-resolved extreme ultraviolet (EUV) spectrometer in the wavelength range of 60 to 400?. The radial positions of the impurity ions obtained are compared with the local ionization energies, Ei of these impurity ions and the electron temperatures TeZ there. The impurity ions with 0.3?Ei?1.0 keV are always located in outer region of plasma, i.e., 0.7?ρ?1.0, and those with Ei?0.3keV are located in the ergodic layer, i.e., 1.0?ρ?1.1, with a sharp peak edge., where ρ is the normalized radial position. It is newly found that TeZ is approximately equal to Ei for the impurity ions with Ei?0.3keV, whereas roughly half the value of Ei for the impurity ions with 0.3?Ei?1.0keV. It is known that TeZ is considerably lower than Ei in the plasma edge and approaches to Ei in the plasma core. Therefore, this result seems to originate from the difference in the transverse transport between the plasma edge at ρ?1.0 and the ergodic layer at ρ?1.0. The transverse transport is studied with an impurity transport simulation code. The result revealed that the difference appearing in the impurity radial positions can be qualitatively explained by the different values of diffusion coefficient, e.g., D=0.2 and 1.0m2/s, which can be taken as a typical index of the transverse transport.     

Observation of Impurity Accumulation After Hydrogen Multi-Pellet Injection in Large Helical Device

Impurity accumulation is studied for neutral beam-heated discharges after hydrogen multi-pellet injection in Large Helical Device (LHD). Iron density profiles are derived from radial profiles of EUV line emissions of FeXV-XXIV with the help of the collisional-radiative model. A peaked density profile of Fe²³⁺ is simulated by using one-dimensional impurity transport code. The result indicates a large inward velocity of -6 m/s at the impurity accumulation phase. However, the discharge is not entirely affected by the impurity accumulation, since the concentration of iron impurity, estimated to be 3.3x10^-5 to the electron density, is considerably small. On the other hand, a flat profile is observed for the carbon density of C⁶⁺, which is derived from the Z_eff profile, indicating a small inward velocity of -1 m/s. These results suggest atomic number dependence in the impurity accumulation of LHD, which is similar to the tokamak result.     

The Behavior of Radial Electric Field and Toroidal Rotation in the Edge Plasma of Divertor Tokamak

A new method for describing the nature of radial electric field and its relation with toroidal rotation in edge plasma of small size divertor tokamak is proposed in this work. The expression of radial electric field in the edge plasma of small size divertor tokamak can be divided into two parts. The first part E _r ⁽⁰⁾ is related to electrostatic potential of plasma in edge plasma of this tokamak. The second part E _r ⁽¹⁾ is related to contribution of toroidal rotation of radial current in edge plasma of this tokamak. The results of this work provide the following: (1) A new one-dimensional ordinary differential equation for toroidal velocity is obtained. The one-dimensional ordinary differential equation suggest new tool to explaining tokamak experiments involving measurements of plasma rotation and radial electric field. (2) Also the results of this work shows that, the main contribution to the radial electric field inside separatrix (plasma core) gives the term E _r ⁽¹⁾.     

Perpendicular Conductivity and Self-Consistent Electric Fields in Small Size Divertor Tokamak Plasma Edge

The radial electric field of small size divertor tokamak in the vicinity of separtrix is simulated by using B2-SOLPS5.0 2D code, in which the most complete system of transport equations (Rozhansky et al., Nucl Fusion, 41:4, 2001) is solved including all the important perpendicular current and E × B drifts. Simulations demonstrated the following results: (a) It is shown that in the vicinity of the separatrix, the radial potential profile is determined by perpendicular currents (b) since, due to the pressure asymmetry, radial diamagnetic current integrated over the closed flux surface is not automatically zero, additional radial currents balance the diamagnetic current and make the average net current zero. (c) On the closed flux surfaces far from separetrix, where the pressure is almost constant, the calculated parallel currents (toroidal current) agree with Pfirsch–Schlueter currents.     

Aspects of plasma-wall interaction in the ASDEX divertor experiment

ASDEX (Axially SymmetriC Divertor Experiment) is a large tokamak now under construction at IPP Garching. The main parameters are: major radius 1.65 m, plasma radius 0.4 m, toroidal field on axis 2.8 T and plasma current 500 kA. The experiment is scheduled to go into operation in about two years. The first aim of the experiment is to test the divertor action, i.e. plasma stability without material limiter and reduction of impurity influx. Since the divertor will essentially be of the unload-type, the latter problem should be solved by reducing wall bombardment. On the premises of sufficient stability the plasma-wall interaction will occur on the divertor slits, in the main divertor chamber and (with refuelling) on the wall owing to charge exchange neutrals. Plans for surface studies are being discussed.     

Effect of edge magnetic island on carbon screening in the J-TEXT tokamak

The effect of externally applied resonant magnetic perturbation(RMP)on carbon impurity behavior is investigated in the J-TEXT tokamak.It is found that the m/n=3/1 islands have an impurity screening effect,which becomes obvious while the edge magnetic island is generated via RMP field penetration.The impurity screening effect shows a dependence on the RMP phase with the field penetration,which is strongest if the O point of the magnetic island is near the low-field-side(LFS)limiter plate.By combining a methane injection experimental study and STRAHL impurity transport analysis,we found that the variation of the impurity transport dominates the impurity screening effect.The impurity diffusion at the inner plasma region(r/a＜0.8)is enhanced with a significant increase in outward convection velocity at the edge region in the case of the magnetic island's O point near the LFS limiter plate.The impurity transport coefficient varies by a much lower level for the case with the magnetic island's X point near the LFS limiter plate.The interaction of the magnetic island and the LFS limiter plate is thought to contribute to the impurity transport variation with the dependence on the RMP phase.A possible reason is the interaction between the magnetic island and the LFS limiter.     

Experiment Results about the Relationship of Edge Turbulence and Atomic Processes in the HT-7 Tokamak

Using a reciprocating Langmuir probe system, the boundary plasma behaviors were investigated before and after lithium/silicon coating. Accompanying the effective reduction of impurity radiation, strong shears of radial electric field and poloidal velocity came into being and the turbulence suppression and de-correlation were observed in the edge region of coated wall plasma. All these led to the reduction of the edge transport and improvement of plasma confinement. In the central line averaged density scanning experiments, an enhanced shear of the radial electric field was observed in the edge plasma with the increase of the density, which may account for the enhancement of the transport barrier and the improvement of particle confinement.The results suggest a close link between wall conditions and boundary plasma. In addition to the relationship, (～Te)/Te ～(～n)n/ne and θ_(～T)e(～n)e ～π, had been observed in the plasma edge region, which indicates the important role of the ionization and radiation in turbulence driving.     

Interpretation of High-Q Scattering Experiments

A theoretical model has been developed for the calculation of the states of ionization of target atoms after impact by an energetic high charge state ion. The calculational method is based upon using the three-body classical-trajectory Monte Carlo approach combined with the independent electron model to determine the target ionization cross sections. Calculated cross sections for rare gas targets are in qualitative agreement with experimental values for incident ion charge states of q = +4 to +54 and energies in the 1 to 5 MeV/amu range. The calculations indicate that the "gross" ionization cross sections measured using the "condenser-plate" approach can be scaled to one reduced curve for each target species by plotting cross section divided by incident ion charge state versus energy per nucleon divided by incident ion charge state.     

Development of Z_(eff) diagnostic system on the Globus-M(M2) tokamak and the first experimental results

Studying the behavior of effective ion charge Zeff,which indicates the degree of pollution of plasma and can provide valuable information about many processes taking place in plasma,mechanisms of the releasing impurities,transport,etc is of great interest.This paper describes the development of the Zeffdiagnostic system for the Globus-M2 tokamak.The effective ion charge is determined on the basis of measurements of the bremsstrahlung intensity and Thomson scattering data—Teand neprofiles.The results of the first Zeffmeasurements obtained for several discharges on the Globus-M tokamak are presented in this paper.The results have been validated by simulation using the ASTRA transport code for the same discharges,and it has demonstrated a good agreement with the experimental results.     

Kinetic micro-instabilities in the presence of impurities in toroidal magnetized plasmas

The theoretical and numerical studies on kinetic micro-instabilities,including ion temperature gradient(ITG) driven modes,trapped electron modes(TEMs) in the presence of impurity ions as well as impurity modes(IMs),induced by impurity density gradient alone,in toroidal magnetized plasmas,such as tokamak and reversed-field pinch(RFP) are reviewed briefly.The basic theory for IMs,the electrostatic instabilities in tokamak and RFP plasmas are discussed.The observations of hybrid and coexistence of the instabilities are categorized systematically.The effects of impurity ions on electromagnetic instabilities such as ITG modes,the kinetic ballooning modes(KBMs) and kinetic shear Alfvén modes induced by impurity ions in tokamak plasmas of finite β(=plasma pressure/magnetic pressure) are analyzed.The interesting topics for future investigation are suggested.     

Neutron transport in a reactor system with temperature feedback

When the effect of temperature feedback in a reactor system is considered the neutron transport equation for the neutron density is supplemented by a temperature equation which is a partial differential equation of parabolic type if heat conduction is taken into consideration. This consideration leads to a coupled system of nonlinear partial integro-differential equations. The aim of this paper is to present an iterative scheme for the determination of the solution of the nonlinear coupled system and to establish some qualitative property of the solution. The iterative scheme consists of two monotone sequences which converge monotonically from above and below, respectively, to a unique solution. The qualitative aspect includes the existence and uniqueness of a positive solution, upper and lower bounds of the solution and stability of a steady-state solution.     

FEQ: a new flux coordinates based equilibrium solver including both magnetic axis and separatrix

Accurate tokamak plasma equilibrium solution in flux coordinates is crucial for many stability and transport studies. Different approaches for dealing with singularities in solving the nonlinear Grad–Shafranov (GS) equation in flux coordinates or also known as straight field line coordinates are proposed in this paper. The GS equation is solved by iterating the position of grids directly in flux coordinates, and hence, no additional errors are introduced due to mapping process for a convergent solution. The singularity at magnetic axis in flux coordinates is removed by using a novel coordinate transform technique. Different from other techniques previously developed, no assumption in boundary condition at magnetic axis is used. This is consistent with the fact that there is no physical boundary at the magnetic axis. A flux coordinate system with poloidal coordinate chosen as the geometric poloidal angle is proposed. It conquers the difficulty in no definition of poloidal coordinate in flux coordinates at separatrix because of the singularity at x-point(s) in a divertor configuration. It also simplifies the process for computing poloidal flux coordinate during the iteration for solving the nonlinear GS equation. Non-uniform grids can be applied in both radial and poloidal coordinates, which allows it to increase the spacial resolution near x-point(s) in a divertor configuration. Based on the model proposed in this paper, a new Flux coordinates based EQuilibrium solver (FEQ) in tokamaks is developed. The numerical solutions from this code agree well with both the analytic Solov'ev solution and the numerical one from the EFIT code for a divertor configuration in the EAST tokamak. This code can be applied for simulating different equilibria with prescribed shape, pressure and current profiles, i.e. including both limiter and divertor configurations, positive triangularity and negative triangularity, different β, arbitrary magnetic shear profile etc. It provides a powerful and convenient fixed-boundary inverse equilibrium solver including both magnetic axis and separatrix in the solution for tokamak researches.     

Radiative Cooling Rates for Low-Z Impurities in Non-coronal Equilibrium State

The local or transient radiation losses in tokamak plasmas can greatly exceed those in the coronal equilibrium. This excess is especially pronounced at the plasma edge. The reason for the increase of radiation in a peripheral plasma is as follows. The impurities are lost fast from the plasma edge and the new impurity source is supplied to this region. The charged states of impurities, therefore, do not reach their coronal equilibrium ones. These impurity ions have more electrons than those in the coronal equilibrium, and as a result emit the higher radiation power. In the simplest case, the non-coronal radiative rate can be determined only by two parameters: the electron temperature \(T_{\text {e}}\) and the so-called “residence parameter” \(n_{\text {e}}\tau _{\text {i}}\), where \(\tau _{\text {i}}\) is the impurity residence time in the plasma. Despite the strong simplification, such an approach allows to do simple estimates of non-coronal radiation. In this paper, two dimensional polynomial fits describing radiative cooling rates and mean charge are obtained for eight impurity species: helium, lithium, beryllium, carbon, nitrogen, oxygen, neon, and argon. The results are presented in figures and tables. The figures show curves calculated from the original atomic database and least-squares polynomial fits to these curves. The tables contains coefficients for this fits. The obtained fits can be useful for qualitative estimates and simple numerical calculations.     

Observation of coherent mode induced by a molybdenum dust on EAST

The influence of a molybdenum dust buildup on plasma edge turbulence has been studied in the EAST tokamak.The motion of the dust from the upper divertor region is detected by a fast visible CCD camera,the XUV spectrometer arrays,and the EUV spectrometer.The MoXV emission intensity sharply increases compared with the spectral lines of various ionization states of other elements,which implies that the dust particles are the molybdenum impurities.The radial distribution of Mo14+ion simulated by a simplified 1D transport model indicates that the molybdenum dust mainly deposits in the pedestal bottom region.Moreover,it is observed that the coherent mode(CM)appears at ρ=0.94 after the molybdenum impurities enter the main plasma region.The influx of molybdenum impurities results in increasing pedestal electron density and decreasing pedestal electron temperature in contrast to that before the event of impurities dropping.It is also found that the electron density gradient in the pedestal increases when the ablation of the molybdenum impurities is observed in the pedestal region.The qualitative experimental results indicate that the onset of CM is likely related to the increase of the density gradient and edge collisionality in the pedestal.In comparison to the density gradient,the enhancement of CM amplitude largely depends on the increase of the edge collisionality.     

Plasma Shape and Current Control Simulation of HT-7U Tokamak

This paper describoes the discharge simulation of HT-7U tokamak plasma equilibrium and plasma current by solving MHD equations and surface average transport equations using an equilibrium evolution code. The simulated result shows the evolution of plasma parameter versus time .The simulated result can play an important role in the design of the plasma equilibrium and control system of a tokamak.