Plasma Equilibrium Reconstruction Research Articles

EFIT Equilibrium Reconstruction Including Polarimetry Measurements on Tore Supra

To improve the accuracy of the after-shot plasma equilibrium reconstruction on Tore Supra, the previous EFIT code, which utilizes only magnetic measurements as a constraint (we shall call it EFIT-mag in the text), has been modified into EFIT-pol by taking the far infrared polarimeter measurements into account. With a correct choice of the input parameters (mainly for the P’ and FF’ polynomial orders and for the weights on Faraday angles), the results reconstructed by EFIT-pol are in good agreement with the experimental values deduced from the magnetic measurements as well as with the CRONOS code simulations. In this paper, after a brief description of the EFIT code, the approach used to parameterize EFIT-pol is presented, and the accuracy improvement is shown for a typical shot of Tore Supra, as well as through statistics on a database of 95 shots of different plasma currents and additional powers.

Measurements of the internal magnetic field using the B-Stark motional Stark effect diagnostic on DIII-D (invited)

Results are presented from the B-Stark diagnostic installed on the DIII-D tokamak. This diagnostic provides measurements of the magnitude and direction of the internal magnetic field. The B-Stark system is a version of a motional Stark effect (MSE) diagnostic based on the relative line intensities and spacing of the Stark split D(α) emission from injected neutral beams. This technique may have advantages over MSE polarimetry based diagnostics in future devices, such as the ITER. The B-Stark diagnostic technique and calibration procedures are discussed. The system is shown to provide accurate measurements of B(θ)/B(T) and ∣B∣ over a range of plasma conditions. Measurements have been made with toroidal fields in the range of 1.2-2.1 T, plasma currents in the range 0.5-2.0 MA, densities between 1.7 and 9.0×10(19) m(-3), and neutral beam voltages between 50 and 81 keV. The viewing direction and polarization dependent transmission properties of the collection optics are found using an in situ beam into gas calibration. These results are compared to values found from plasma equilibrium reconstructions and the MSE polarimetry system on DIII-D.

Drift-free magnetic equilibrium reconstruction using the response to plasma position modulation

Inductive magnetic sensors are widely used for plasma equilibrium reconstruction and control. However, their measurements involve electronic integration and can therefore experience drift leading to inaccurate plasma positioning. For this reason, we have studied an original drift-free approach to estimate the plasma equilibrium. The principle of this correction is based on modulation of the plasma position and current at three independent frequencies and analysing the modulated magnetic signals to provide additional estimation on the equilibrium. Using a plasma model based on current wires, the accuracy of such a method is assessed for Tore Supra in terms of the signal to noise ratio. The plasma position is recovered within a precision of 5 mm for a signal to noise ratio better than 80 dB. Applying our approach to dedicated experiments performed on the Tore Supra tokamak, we confirm the quality of the result and find that we can estimate the radial and vertical positions of the plasma to 1 mm with a one standard deviation confidence interval.

Real-time plasma equilibrium reconstruction in a Tokamak

The problem of equilibrium of a plasma in a Tokamak is a free boundary problem described by the Grad-Shafranov equation in axisymmetric configurations. The right hand side of this equation is a non linear source, which represents the toroidal component of the plasma current density. This paper deals with the real time identification of this non linear source from experimental measurements. The proposed method is based on a fixed point algorithm, a finite element resolution, a reduced basis method and a least-square optimization formulation.

Design of Magnetic Measurement System on SUNIST Spherical Tokamak

A magnetic measurement system consisting of magnetic probes and flux loops for spherical tokamak SUNIST, is uniquely designed due to the strongly shaped plasma cross section and the narrow space near the central solenoid. Plasma equilibrium reconstruction with the current filament method is performed to determine the number and positions of the magnetic probes and flux loops, as well as their design precision required.

Edge Te and ne profiles during type-I ELM mitigation experiments with perturbation fields on JET

Edge localized mode (ELM) mitigation experiments have been carried out at JET in type-I ELMy H-mode plasmas. ELM mitigation was achieved through a stochastic edge induced by the ex-vessel error field correction coils system and was found to be independent of the distance of the plasma edge to the JET wall. In all cases the detrimental effect of the ELM on pedestal confinement was considerably reduced during the stochastization phase. The new high resolution Thomson scattering (HRTS) diagnostic, which has recently become operational at JET, is used to study the behaviour of electron temperature, density and pressure pedestal profiles during the mitigation phase. The pedestal properties are monitored in a consistent way by applying a hyperbolic tangent fit to the HRTS measurements. Stability modelling with the ELITE code using the fits to the spatially resolved pedestal profile measurements suggests that the observed ELM mitigation can be understood in terms of the peeling–ballooning model. The mitigation correlates with a reduction of the edge pressure gradient (due to both a reduced height and an increased width of the edge pressure transport barrier) which is consistent with the linear ELM stability theory. It is observed that in the case of an n = 1 external field, the barrier position and height are correlated with the toroidal direction of the applied perturbation. Agreement is found between the barrier position measured by HRTS and obtained from plasma equilibrium reconstruction. The external perturbation induces a deformation of the plasma column that is primarily toroidally symmetric with a secondary component that is toroidally asymmetric

Efficient Generation of Closed Magnetic Flux Surfaces in a Large Spherical Tokamak Using Coaxial Helicity Injection

A method of coaxial helicity injection has successfully produced a closed flux current without the use of the central solenoid in the NSTX device, on a size scale closer to a spherical torus reactor, for a proof-of-principle demonstration of this concept. For the first time, a remarkable 60 times current multiplication factor was achieved. Grad-Shafranov plasma equilibrium reconstructions are used to verify the existence of closed flux current. In some discharges the generated current persists for a surprisingly long time approximately 400 ms.

Assessment of new ex-vessel magnetic measurements in JET

A new ex-vessel magnetic diagnostics was installed in JET during the 2005 shutdown with the objectives of (i) providing experimental data for better modeling of the iron in the axisymmetric codes for plasma equilibrium reconstruction and (ii) testing the reliability of direct field measurements from Hall probes. The latter is of great interest for future ITER-like devices, where long lasting flat top phases are expected, in a high neutron yield and a high temperature environment. The experimental data achieved during the restart phase were analyzed with the aid of simulation codes. Each individual signal was assessed for inclusion in the general JET diagnostics system. The system is ready for use in the 2006 experimental campaigns.

Magnetic probe response function calibrations for plasma equilibrium reconstructions of CDX-U

A novel response function calibration technique has been developed to account for time-dependent nonaxisymmetric eddy currents near magnetic sensors in toroidal magnetic confinement devices. The response function technique provides a means to cross calibrate against all available external field coil systems to calculate the absolute sensitivity of each magnetic field sensor, even when induced eddy currents are present in the vacuum vessel wall. The response function information derived in the calibration process can be used in equilibrium reconstructions to separate plasma signals from signals due to externally produced eddy currents at magnetic field sensor locations, without invoking localized wall current distribution details. The response function technique was used for the first ever equilibrium reconstructions of spherical torus plasmas, when applied to the Current Drive Experiment-Upgrade (CDX-U) device. In conjunction with the equilibrium and stability code (ESC), equilibria were obtained for recent CDX-U experiments with lithium plasma-facing components. A description of the CDX-U magnetic sensor configuration and the response function calibration technique will be presented along with examples of resulting plasma equilibrium for CDX-U lithium wall operations.

Design of ex-vessel magnetic probes for JET-EP

A new magnetic diagnostics system has been designed for the 2005 JET experimental campaigns onward. The system, which is integrated into the existing magnetic diagnostics, consists of in-vessel and ex-vessel sensors, and is intended to provide an improvement in the accuracy and reliability of the present equilibrium reconstruction and iron modelling capabilities [V. Coccorese, et al., Design of new magnetic sensors for JET, in: Proceedings of the 15th Topical Conference High-Temperature Plasma Diagnostics, April 19–22, 2004, San Diego, CA, USA, in press]. In this paper, the ex-vessel system is described, which consists of an array of pick-up coils, Hall probes and flux loops probes to be installed in the proximity of the upper horizontal iron limbs and inside the iron collar. The sensors are designed to produce an absolute measurement of the magnetic field configuration in the vicinity of the magnetic structure of the machine, which is considered valuable information for the tuning of the axisymmetric models used for plasma equilibrium reconstruction. On the basis of recent results obtained with Hall probe prototypes on JET, the choice of type and location of probes, together with other design and manufacturing issues of the ex-vessel magnetic diagnostics are presented and discussed.

Real-time control of DIII–D plasma discharges using a Linux alpha computing cluster

This paper describes an upgrade for the real-time computing system responsible for monitoring and controlling plasma, discharges in the DIII–D tokamak (J.L. Luxon, L.G. Davis, Fusion Technol. 8 (1985) 441) at General Atomics (GA). The current system employs six CSPI i860 VME format processors working in parallel to acquire data in real-time and perform feed back control of plasma shape and position parameters. Work has commenced on integration of a new computing system based on commonly available PCI bus based processors that communicate over the 2 Gbit/s Myrinet (Myricom, Inc., CA, USA) network. The new system will greatly improve the processing power available to the algorithms required for computing plasma equilibrium reconstructions in real-time. A factor of 20 anticipated performance increase will allow for improved accuracy and frequency response for plasma shape estimation and control. The migration from VME to PCI Myrinet computer clustering will improve the data acquisition capabilities by opening up access to additional DIII–D temperature and density diagnostics. The upgrade will increase the inter-processor communication speed and provide the flexibility to integrate additional processors to match the cost and computing needs of the tokamak research program.

Equilibrium reconstruction in the START tokamak

The computation of magnetic equilibria in the START spherical tokamak is more difficult than those in more conventional large aspect ratio tokamaks. This difficulty arises partly as a result of the use of induction compression to generate high current plasma, as this precludes the positioning of magnetic diagnostics close to the outboard side of the plasma. In addition, the effect of a conducting wall with a high, but finite, conductivity must be included. A method is presented for obtaining plasma equilibrium reconstructions based on the EFIT code. New constraints are used to relate isoflux surface locations deduced from radial profile measurements of electron temperature. A model of flux diffusion through the vessel wall is developed. It is shown that neglecting flux diffusion in the vessel wall can lead to a significant underestimate in the calculation of the plasma βt. Using a relatively sparse set of magnetic signals, βt can be obtained to within a fractional error of ±10%. Using constraints to relate isoflux surface locations, the principle involved in determining the internal q profile is demonstrated.

Experimental plasma equilibrium reconstruction from kinetic and magnetic measurements in the FTU tokamak

The behaviour of the FTU tokamak plasma has been analysed by using two reconstructive MHD equilibrium codes: the first code works by using the magnetic data alone and the second one by including as well the shape of the kinetic pressure profile, as obtained from the measured profiles of electron temperature Te and density ne. The code that analyses the magnetic data alone provides a good evaluation of the macroscopic quantities such as the poloidal beta βp and the internal inductance li, if the plasma elongation is greater than 1.04. No detailed information about the toroidal current density profile Jϕ and the safety factor profile q can be obtained from the magnetic data alone. On the other hand, the coupling of magnetic and kinetic data is able to provide a reasonable estimate of the toroidal current density profile and of its behaviour during the plasma discharge. The reliability of the Jϕ and q profile reconstruction has been explored and validated by a detailed comparison with the observed MHD behaviour of the FTU plasma discharges. A good agreement between the appearance of the sawtooth activity and the drop of the safety factor on the magnetic axis go to unity is observed. Also, at least for edge safety factors qψ less than 4, the sawtooth inversion radius is found to be very close to the q=1 surface. A remarkable correspondence between Jϕ and Te3/2 is found in sawtoothing discharges. The structure of the snake oscillation in pellet injected discharges is found to be strictly correlated to the position of the q=1 surface. A cylindrical linear tearing mode stability calculation applied to the reconstructed Jϕ profile has shown qualitative agreement with the appearance of the Mirnov oscillations. Finally, the magnetic reconnections between double resonant surfaces during the rise of the plasma current or after the pellet injection have provided an interesting validation of the Jϕ profile reconstruction