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).     

Free-boundary plasma equilibria with toroidal plasma flows

Magnetohydrodynamic equilibrium schemes with toroidal plasma flows and scrape-off layer are developed for the 'divertor-type' and 'limiter-type' free boundaries in the tokamak cylindrical coordinate. With a toroidal plasma flow, the flux functions are considerably different under the isentropic and isothermal assumptions. The effects of the toroidal flow on the magnetic axis shift are investigated. In a high beta plasma, the magnetic shifts due to the toroidal flow are almost the same for both the isentropic and isothermal cases and are about 0.04a0 (a0 is the minor radius) for M₀ = 0.2 (the toroidal Alfvén Mach number on the magnetic axis). In addition, the X-point is slightly shifted upward by 0.0125a0. But the magnetic axis and the X-point shift due to the toroidal flow may be neglected because M0 is usually less than 0.05 in a real tokamak. The effects of the toroidal flow on the plasma parameters are also investigated. The high toroidal flow shifts the plasma outward due to the centrifugal effect. Temperature profiles are noticeable different because the plasma temperature is a flux function in the isothermal case.     

High Field Tokamaks for Burning Plasma Experiments

A direct consequence of the ELMy H-mode regime of tokamaks is that, for a constant value of the energy gain Q, both the plasma linear dimension and the normalized plasma density and beta are decreasing functions of the toroidal magnetic field. In this paper, starting from the conditions foreseen for the latest versions of ITER, we derive the plasma parameters of three tokamak plasmas with a toroidal magnetic field of 8, 10, and 13 T.     

Observation and characterization of the effect of electron cyclotron waves on toroidal rotation in EAST L-mode discharges

The change in the toroidal rotation of plasma caused by electron cyclotron wave (ECW) injection has been observed in EAST.It is found that the response of the rotation is similar for all possible ECW toroidal injection angles.The core toroidal rotation velocity increases in the co-current direction along with a rise in the plasma temperature and stored energy.The profile of the electron temperature,ion temperature and toroidal rotation velocity gradually become peaked.The change in toroidal rotation in the core increases with the ECW injection power.Different behavior is observed when the ECWs are injected into low hybrid current drive (LHCD) target plasmas,where the electron temperature and rotation profile become peaked,while the ion temperature profile flattens after ECW injection,suggesting different transport characteristics in energy and momentum.     

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 noninvasive 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.     

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.     

Observation of Central Toroidal Rotation Induced by ICRF on EAST

Core plasma rotation of both L-mode and H-mode discharges with ion cyclotron range of frequency(ICRF) minority heating(MH) scheme was measured with a tangential X-ray imaging crystal spectrometer on EAST(Experimental Advanced Superconducting Tokamak).Cocurrent central impurity toroidal rotation change was observed in ICRF-heated L-and H-mode plasmas.Rotation increment as high as 30 km/s was generated at ~1.7 MW ICRF power.Scaling results showed similar trend as the Rice scaling but with significant scattering,especially in L-mode plasmas.We varied the plasma current,toroidal field and magnetic configuration individually to study their effect on L-mode plasma rotation,while keeping the other major plasma parameters and heating unchanged during the scanning.It was found that larger plasma current could induce plasma rotation more efficiently.A scan of the toroidal magnetic field indicated that the largest rotation was obtained for on-axis ICRF heating.A comparison between lower-single-null(LSN)and double-null(DN) configurations showed that LSN discharges rendered a larger rotation change for the same power input and plasma parameters.     

Status of design and procurement activities in JT-60SA

The JT-60SA experiment is one of the three projects to be undertaken in Japan as part of the Broader Approach Agreement, conducted jointly by Europe and Japan, and complementing the construction of ITER in Europe. It is a fully superconducting tokamak capable of confining break-even equivalent deuterium plasmas with equilibria covering high plasma shaping with a low aspect ratio at a maximum plasma current of I_p = 5.5 MA. In late 2007 the BA Parties, prompted by cost concerns, asked the JT-60SA Team to carry out a re-baselining effort with the purpose to fit in the original budget while aiming to retain the machine mission, performance, and experimental flexibility. Subsequently the Integrated Project Team has undertaken a machine re-optimization followed by engineering design activities aimed to reduce costs while maintaining the machine radius and plasma current. This effort led the Parties to the approval of the new design in late 2008 and hence final design and procurement activities have commenced. The paper will describe the process leading to the re-baselining, the resulting final design and technical solutions and the present status of procurement activities.     

Simplifying the ST and AT Concepts

As stated in a IEA Burning Plasma Workshop Review (Donné et al. in Fusion Sci Technol 49:79, 2006) “…there is not much flexibility in the fueling of ITER”. High-performance tokamak and ST plasmas greatly benefit from plasma rotation and rotation shear to increase energy confinement time and sustain high beta, made possible due to toroidal momentum injection from neutral beams. Advanced ST and AT scenarios rely on optimized density and pressure profiles that must be maintained for efficient device performance. In addition these discharges require the capability for off-axis current drive. Controlled variable-depth deep fueling that also injects toroidal momentum, in combination with the capability for off-axis current drive, would allow the AT/ST concepts to operate at close to projected performance levels. Advanced fuelling based on compact toroid injection and Electron Bernstein Wave off-axis current drive in conjunction with solenoid-free plasma start-up are proposed as methods to improve FNSF device performance and simplify the ST/AT Demo.     

Plasma Flows within the Context of Biasing Experiments

The understanding and reduction of turbulent transport in magnetic confinement devices is not only an academic task, but also the matter of practical interest, since high confinement is chosen as the regime for ITER and possible future reactors it reduces both the size and the cost. Since the pioneering work on CCT a lot of work has been devoted to the effect of electric field biasing carried out on many tokamaks, which in general leads to a strongly varying radial electric fields as a function of radius and a resulting sheared E×B flow, giving rise to improved confinement properties.The issue of plasma flows is utterly fundamental for understanding of tokamaks aimed at the achievement of fusion energy. This appears in the well known neoclassical theory as the most accomplished and self-consistent basis for understanding of fusion plasmas. It pertains to the novel concept of "zonal flows" emerging from the recent development of gyro-kinetic transport codes. The poloidal and toroidal flows are also cruc     

Lower hybrid heating and current drive system for a tokamak reactor

A lower hybrid heating system has been designed for heating a tokamak reactor to ignition and for sustaining steady-state operation by driving the toroidal plasma current. The power spectrum from an active/passive waveguide grill is computed, and the resulting equilibrium current density profile is computed from a full electromagnetic WKB analysis of wave propagation in a cylinder. The corresponding toroidal current profile is a low-current equilibrium which is stable to various ideal modes at an economically acceptable beta. The electronic circuitry is designed to minimize the electric power required for current drive, and the resulting design appears to provide reliable operation in a reactor environment. The same system can drive current during reactor startup if some of the waveguides are modified slightly. A typical sequence of startup equilibria is calculated.     

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.     

ICRH ITER-like antenna tested on TS commissioning,electrical modeling and load resilience studies

A prototype of ICRF antenna based on the load-resilient electrical layout anticipated for ITER has been built at CEA-Cadarache. It consists of two toroidally adjacent resonant double loops (RDLs) based on the conjugate-T concept proposed for the ITER ICRF array. This prototype has been recently validated in Tore Supra plasmas exhibiting fast density perturbations in front of the antenna. This paper reports on the load resilience properties of the antenna prototype, as well as the RF modeling and the commissioning. Significant effort on modeling, coupled to an extensive low power campaign, has allowed characterization of the antenna in both vacuum and plasma loading conditions. Plasma load modelings computed with the code TOPICA – very helpful to set up the matching points on plasmas – are found to be in good agreement with the experimental results. The main studies focus on load resilience properties have been carried out in L-mode plasmas. Supersonic molecular beam injection (SMBI), able to launch a series of very short/dense gas jets at Mach number up to 5, was used to mimic the sudden increases of the antenna coupling provoked by ELMs. The results are found to be in good agreement with RF circuit calculations that include 3D modeling.     

Numerical Simulation Approaches to Evaluating the Electromagnetic Loads on the EAST Vacuum Vessel

Numerical simulation approaches are developed to compute the electromagnetic forces on the EAST vacuum vessel during major disruptions and vertical displacement events, with the halo current also considered. The finite element model built with ANSYS includes the vacuum vessel, the plasma facing components and their support structure, and the toroidal and poloidal field coils. The numerical methods are explained to convince of its validity. The eddy current induced by the magnetic flux variation and the conducting current caused by the halo current are also presented for discussion. The electromagnetic forces resulting from the numerical simulation are proven to be useful for structure design optimization. Similar methods can be applied in the upgrades of the EAST device.     

MHD Instabilities and Their Effects on Plasma Confinement in Large Helical Device Plasmas with Intense Neutral Beam Injection

MHD stability of the Large Helical Device (LHD) plasmas produced with intense neutral beam injection is experimentally studied. When the steep pressure gradient near the edge is produced through L-H transition or linear density ramp experiment, interchange-like MHD modes whose rational surface is located very close to the last closed flux surface are strongly excited in a certain discharge condition and affect the plasma transport appreciably. In NBI-heated plasmas produced at low toroidal field, various Alfven eigenmodes are often excited. Bursting toroidal Alfven egenmodes excited by the presence of energetic ions induce appreciable amount of energetic ion loss, but also trigger the formation of internal and edge transport barriers.     

Nonlinear Generation of Zonal Fields by the Beta-Induced Alfven Eigenmode in Tokamak

The zonal fields effect on the beta-induced Alfven eigenmode(BAE)destabilized by the energetic particles in toroidal plasmas is studied through the gyrokinetic particle simulations.It is found that the localized zonal fields with a negative value around the mode rational surface are generated by the nonlinear BAE.In the weakly driven case,the zonal fields with a strong geodesic acoustic mode(GAM)component have weak effects on the nonlinear BAE evolution.In the strongly driven case,the zonal fields are dominated by a more significant zero frequency component and have stronger effects on the nonlinear BAE evolution.     

Solenoid-free Plasma Start-up in NSTX using Transient CHI

Experiments in NSTX have now unambiguously demonstrated the coupling of toroidal plasmas produced by the technique of CHI to inductive sustainment and ramp-up of the toroidal plasma current. This is an important step because an alternate method for plasma startup is essential for developing a fusion reactor based on the spherical torus concept. Elimination of the central solenoid would also allow greater flexibility in the choice of the aspect ratio in tokamak designs now being considered. The transient CHI method for spherical torus startup was originally developed on the HIT-II experiment at the University of Washington.     

Nonlinear Generation of Zonal Fields by the Beta-Induced Alfvén Eigenmode in Tokamak

The zonal fields effect on the beta-induced Alfvén eigenmode (BAE) destabilized by the energetic particles in toroidal plasmas is studied through the gyrokinetic particle simulations. It is found that the localized zonal fields with a negative value around the mode rational surface are generated by the nonlinear BAE. In the weakly driven case, the zonal fields with a strong geodesic acoustic mode (GAM) component have weak effects on the nonlinear BAE evolution. In the strongly driven case, the zonal fields are dominated by a more significant zero frequency component and have stronger effects on the nonlinear BAE evolution.     

Progress Toward Steady-State Operation on Tore Supra

Important technological and physics issues related to steady-state operation required for next step are being examined on Tore Supra,after a major upgrade of internal components in order to increase the heat extraction capability to 25 MW for 1000 s.Here,we show first experimental results,where all the plasma facing components were actively cooled during pulses exceeding four minutes,with reactor-relevant heat load.New physics was observed in non-inductively driven plasmas,including a stationary peaked radial profile of the plasma density generated by an anomalous inward pinch;and a regime characterized by sinusoidal oscillations of central electron temperature,governed by non-linear coupling between heat transport and plasma current analogous to a predator-prey mechanism.     

Adaptive Grids in Simulations of Toroidal Plasma Starting from Magneto-Hydrodynamic Equilibrium

This paper introduces the notion of Tokamak Magneto-Hydrodynamics(TMHD),which explicitly reflects the anisotropy of a high temperature tokamak plasma.The set of TMHD equations is formulated for simulation of macroscopic plasma dynamics and disruptions in tokamaks.Free from the Courant restriction on the time step,this set of equations is adequate to plasma dynamics with realistic parameters of high performance plasmas and does not require any extension of the MHD plasma model.At the same time,TMHD requires the use of magnetic field aligned numerical grids.Examples of their use in 2-dimensional cases of tokamak equilibria and dynamics of the wall touching kink mode are presented.For the 3-dimensional case of an ergodic magnetic field,this paper introduces the reference magnetic coordinates as a practical algorithm for generating adaptive grids for TMHD.