External Magnetic Measurements Research Articles

Modified neural networks for rapid recovery of tokamak plasma parameters for real time control

Two modified neural network techniques are used for the identification of the equilibrium plasma parameters of the Superconducting Steady State Tokamak I from external magnetic measurements. This is expected to ultimately assist in a real time plasma control. As different from the conventional network structure where a single network with the optimum number of processing elements calculates the outputs, a multinetwork system connected in parallel does the calculations here in one of the methods. This network is called the double neural network. The accuracy of the recovered parameters is clearly more than the conventional network. The other type of neural network used here is based on the statistical function parametrization combined with a neural network. The principal component transformation removes linear dependences from the measurements and a dimensional reduction process reduces the dimensionality of the input space. This reduced and transformed input set, rather than the entire set, is fed into the neural network input. This is known as the principal component transformation-based neural network. The accuracy of the recovered parameters in the latter type of modified network is found to be a further improvement over the accuracy of the double neural network. This result differs from that obtained in an earlier work where the double neural network showed better performance. The conventional network and the function parametrization methods have also been used for comparison. The conventional network has been used for an optimization of the set of magnetic diagnostics. The effective set of sensors, as assessed by this network, are compared with the principal component based network. Fault tolerance of the neural networks has been tested. The double neural network showed the maximum resistance to faults in the diagnostics, while the principal component based network performed poorly. Finally the processing times of the methods have been compared. The double network and the principal component network involve the minimum computation time, although the conventional network also performs well enough to be used in real time.

Plasma boundary reconstruction from external magnetic measurements in the globus tokamak using the variable current loop method

Abstract An effective time-saving algorithm is proposed for protnpt real-time reconstruction of the plasma boundary based on variable current loop tnodels. An efficiency of the algorithm has been analysed in terms of the current loop number and measurement errors.

An adaptive method to identify the plasma magnetic contour from magnetic and polarimetric measurements

The identification of a plasma magnetic contour can be cast as an inverse problem in which a set of equivalent currents, representing (the effect of) the actual plasma current distribution, have to be determined in order to best fit a set of external measurements. The diagnostic systems are typically provided with arrays of magnetic measurements, including both flux and field probes, positioned outside the plasma chamber, and some non magnetic measurements, such as motion Stark effect or multichord FIR polarimetry. In the framework of the method discussed, the basic external (magnetic) measurements have been integrated with internal (polarimetric) measurements to improve the identification process and gain information about the internal plasma current profile. The inverse problem can be formulated as the pseudo-inversion of the transfer matrix linking the unknown equivalent currents to the magnetic and polarimetric measurements. In this paper, the equivalent currents method is improved by means of a procedure that adaptively tries to allocate the EC to obtain the best estimate of the plasma contour. The adaptive strategy is presented in detail and its performance evaluated against two ITER equilibrium plasma configurations.

Magnetic transitions inCeCu0.86Ge2andPrCu0.76Ge2as studied by magnetocaloric effect

The results of heat capacity in the presence of an external magnetic field and resistivity measurements on the compounds ${\mathrm{CeCu}}_{x}{\mathrm{Ge}}_{2}$ and ${\mathrm{PrCu}}_{y}{\mathrm{Ge}}_{2}$ with the starting $x=0.86$ and $y=0.76$ are reported. The magnetocaloric effect in the compounds was calculated from in-field heat-capacity data. The results clearly indicate the nature of magnetic transitions in both compounds and the metamagnetic transition with field in the cerium compounds. The observed magnetocaloric effect is modest in spite of much smaller magnetic moment of Ce and Pr compared to heavy rare earths.

Magnetic diagnostics: General principles and the problem of reconstruction of plasma current and pressure profiles in toroidal systems

Restrictions on magnetic diagnostics are discussed. Being related to the integral nature of the measurable quantities, these follow from the fundamental laws of electromagnetism. A series of examples demonstrating the strength of these restrictions is analysed. The general rule is emphasized that information obtained from external magnetic measurements is insufficient for reliable evaluation of plasma current and pressure profiles in tokamaks and in stellarators. The underlying reason is that outside the plasma the self-field of the equilibrium plasma currents is determined by the boundary conditions on the plasma surface alone.

Impact of positioning and number of polarimetric measurements on the plasma reconstruction in fusion devices

The identification of plasma parameters from different sets of measurements is a key topic in the thermonuclear fusion research. Most of the information relevant to the plasma shape and position control is usually gained via external magnetic measurements, but information related to internal distribution of current density is not accessible in this way. Other possible measurements are available. In this paper a performance analysis is done with respect to the adoption of polarimetric measurements.

Identification of the plasma magnetic contour from external magnetic measurements by means of equivalent currents

One of the main research issues in the thermonuclear fusion area is the identification of plasma contour starting from external magnetic measurements. Possible approaches to this inverse problem make use of equivalent currents to represent the plasma internal current density, regularizing in this way the magnetic field reconstruction. Of course, the choice of the representation basis for such equivalent currents is critical. The paper aims at analyzing the effect of the number and position of base currents on the performance of the identification algorithm.

Improvement of filamentary plasma identification via neural networks

The identification of plasma shape and position for control purposes in thermonuclear fusion devices is usually performed via external magnetic measurements. The result should be available in a few ms to guarantee an effective control action. Fast solution of such inverse problem can be achieved via Equivalent Currents (EC) method or Artificial Neural Networks (ANN). Anyway, in the case of EC, their location become critical during the dynamical evolution of the fusion event. ANN may be beneficial in optimally locating, in real time, the EC for various plasma configurations.

Effects of dynamical information in identification problems in electromagnetics

The identification of currents from external magnetic measurements is an inverse problem frequently encountered in a number of applications. This inverse problem can be regularized with SVD decomposition, but other information coming from the dynamical behavior of the system can be beneficial. In the paper such an approach is analyzed and compared to classical methods.

Integration of magnetic and nonmagnetic measurements for current profile reconstruction in RFX

A crucial issue in magnetically confined plasmas characterized by relevant internal current redistribution, such as high beta and low field toroidal devices, is the determination of their internal magnetic structure. The article presents a method for the integration of magnetic and nonmagnetic measurements in a model which considers a plasma described by stationary ideal magnetohydrodynamic equilibrium equations, with toroidal and poloidal plasma currents represented by distributed discrete filaments and current sheets. The model also includes the massive conductors representing the vessel, the shell, and the machine windings. The discrete current sets are determined by using as input data the total currents flowing in the plasma, in the windings and in the vessel, as deduced by external integral magnetic measurements. The obtained filamentary current sets are then adjusted by imposing further constraints. One of the constraints is given by the set of local magnetic field measurements provided by external pickup coils. A further and more significant constraint is imposed by far infrared polarimeter, which gives an integral condition for each implemented measurement chord. The method is validated by using experimental data from the reversed field pinch Reversed Field eXperiment, and the results suggest that the current density distribution is rather different from that usually predicted by conventional data inversion algorithms.

Analytical solutions to the Grad–Shafranov equation for tokamak equilibrium with dissimilar source functions

Exact solutions to the Grad–Shafranov equation for ideal magnetohydrodynamic (MHD) tokamak equilibria with dissimilar functional dependences of the pressure and poloidal current source profiles are presented. The current density profile has three free parameters, which is sufficiently flexible to describe equilibria consistent with external magnetic measurements. Experimental x-point and limiter plasma configurations can be represented by a superposition of solutions with the same eigenvalue. Both normal and reversed shear current profiles are allowed. An efficient algorithm for least squares fitting of numerically obtained experimental equilibria to the exact solution functions is described and applied to the ASDEX Upgrade (axially symmetric divertor experiment) tokamak [Plasma Physics and Controlled Nuclear Fusion Research 1992 (International Atomic Energy Agency, Vienna, 1993), Vol. I, p. 127].

Plasma boundary determination in ITER by the optimized current filament method

An accurate and simple technique for plasma boundary determination in a tokamak from external magnetic measurements is described. The method uses the filamentary current model of the plasma current profile, optimized to comply with the requirement of 1 cm accuracy in the determination of the plasma boundary in ITER. An error analysis is performed by numerical simulation of the ITER plasma configuration. The conclusion is that the method can provide this accuracy provided that the level of relative measurement errors can be kept below 1%.

Simplified magnetic diagnostic methods for tokamaks

Simplified methods of the magnetic diagnostics of tokamak equilibria are revisited. These methods allow interpretation of external magnetic measurements in the form of simple analytical formulas for physical parameters, as linear functions of measurements, similar to the ones used for high aspect ratio circular plasmas. At present, these methods can be considered as simplified versions of general ones, such as toroidal harmonics, local field expansion and function parametrization methods. A simplified function parametrization method is developed for simple non-circular plasma shapes. An error analysis of the various methods is performed by numerical simulations for the TCA/BR tokamak with moderate aspect ratio and plasma elongation up to 1.4.

Stabilization of kink instabilities by eddy currents in a segmented wall and comparison with ideal MHD theory

The characteristics of external kink instabilities observed during wall stabilization studies in the HBT-EP tokamak have been compared with the predictions of ideal MHD theory, in order to examine the stabilizing role of a resistive wall that is segmented both toroidally and poloidally. The reconstructed equilibria, for discharges with different plasma-wall configurations, are consistent with external and internal magnetic measurements, measured soft X ray profiles and measured equilibrium wall eddy currents. The stability analysis of these equilibria predicts patterns of instability induced eddy currents for a model wall that is continuous and perfectly conducting, and these patterns are in good agreement with the ones observed on the HBT-EP segmented wall. These eddy currents account for the observed stabilization of fast ideal modes when the wall is fully inserted, consistent with the prediction of marginal stability.

Exciton dynamics in ZnCdSe/ZnSe quantum-well structures

Exciton dynamics in ZnCdSe/ZnSe quantum-well structures have been studied from luminescence spectra obtained at T=2 K. The energy and phase relaxation times of localized exciton states have been determined from a study of the destruction of exciton optical alignment by an external magnetic field and direct measurements of the polarized-radiation decay kinetics in the picosecond range. The exciton polarization lifetimes measured by two independent techniques are found to be in a good agreement.

Fast and accurate methods of plasma boundary determination in ITER from external magnetic measurements

Three methods of plasma boundary determination from external magnetic measurements have been optimized and examined in numerical experiments for application to the ITER tokamak, namely the variable current filament, fixed current filament and local field expansion methods. In the absence of measurement errors the absolute error in the determination of the plasma boundary is less than 1 cm.

Identification of Alfvén mode location via multichannel interferometer measurements (abstract)

Quasicoherent magnetohydrodynamics modes with an Alfvén frequency scaling are seen routinely in TFTR neutral beam heated plasmas as well as some Ohmic plasmas. So far, they are only observed in external magnetic fluctuation measurement (Mirnov coils). A close correlation is observed between the changes in the mode frequency and electron density measured by the multichannel infrared interferometer. This correlation allows us to determine the location of the Alfvén modes. The result shows that they are near the plasma edge, r/a>0.85. This method is also used to identify the location of the toroidicity-induced Alfvén eigenmode driven by fast ions in a radiowave heating experiment. The result is consistent with the location determined by the reflectometer measurement.

Sensitivity of equilibrium profile reconstruction to motional Stark effect measurements

The magnetic-field pitch-angle profile, gamma p(R) identical to tan-1(Bpol/Btor), is measured on TFTR using a motional Stark effect (MSE) polarimeter. Measured pitch angle profiles, along with kinetic profiles and external magnetic measurements, are used to compute a self-consistent equilibrium using the free-boundary variational moments equilibrium code VMEC. Uncertainties in the q profile due to uncertainties in gamma P(R), magnetic measurements and kinetic measurements are found to be small. Subsequent uncertainties in the VMEC-calculated current density and shear profiles are also small

Comparison of the performance of distributed source estimation in the human brain using normal and vector magnetic field measurements

In neuromagnetism research, it is important to accurately estimate internal electrical sources in the human brain from the spatial and temporal distributions of magnetoencephalogram (MEG) activities over the head. In this study, we compared the performance of distributed internal source estimation in the human brain under two different MEG measurement conditions: (a) measurements of only the normal components of the external magnetic fields and (b) three-dimensional vector measurements of the external magnetic fields. We applied the sub-optimal least-squares subspace scanning source estimation technique to both measurement conditions. The results showed that with measurement of only the normal components, distributed sources tend to be estimated deeper in the brain than they should be, while three-dimensional vector measurements had the potential to provide a better estimation of the depth of the internal source distribution.

Detection of the free boundary plasma shift in a toroidal helical plasma on Heliotron-E

This paper describes the first successful realization of the magnetic detection of the free boundary plasma shift for helical plasmas. A procedure for determining the equilibrium plasma displacement in a stellarator by means of external magnetic field measurements (psi loops and modulated Rogowski coils) is discussed. Recent experimental results, the normalized displacement Δb/ap as a function of volume averaged beta ⟨β⟩, are discussed and compared with analytical and published numerical MHD computational results. The typical measured plasma boundary shift, Δb/ap, in the standard Heliotron-E configuration (Rp = 2.20 m, ap = 0.21 m, ι(0)/2π ~ 0.53, ι(ap)/2π ~ 2.8) is (8-10) × 10-3, when the volume averaged beta is 0.50%. The measured normalized plasma boundary shift is nearly proportional to the diamagnetic volume averaged beta, for values of beta up to 0.95%. The magnetically determined plasma boundary shift Δb is less than 3 mm. The experimental observations on shift (Δb/ap versus ⟨β⟩dia) are compared with the analytically expected plasma boundary shift. The measured shift lies in the range between the expected upper limit (Δb/ap = β(0)/2βeq) and the lower limit (Δb/ap= ⟨β⟩/2βeq), where βeq=[ι(ap)/2π]2(ap/Rp) ~ 0.77 for the standard configuration of Heliotron-E. It is found that the measured plasma boundary shift depends strongly on the initial vacuum magnetic configuration parameters such as the horizontal position of the magnetic axis and the rotational transform. When the vacuum magnetic axis is shifted inward towards the major axis, significant decreases of the normalized plasma shift (Δb/ap) and of the plasma induced vertical field are observed, which are interpreted as being due to a reduction of the Pfirsch-Schluter current