A neural network technique has been used to predict disruptions in the ADITYA tokamak. A time series prediction method is employed whereby a series of past values of some time dependent quantity is used to predict its value in the future. The time varying observables used in the present work are the different diagnostic signals from four Mirnov probes, one soft X ray monitor and one Hα monitor. The predicted quantities are the same observables at some future time. The neural network is trained with the past values of the different diagnostic signals as inputs and the future values of the same quantities as targets. The trained neural network is used to forecast in a multistep sequence. This amounts to a prediction several time steps earlier. Very good prediction results have been obtained up to 8 ms earlier with little distortion of the signals and no appreciable time lag, a capability which is believed to be well suited to the task of on-line predictions of disruptions in ADITYA. As actual experimental signals are used, confidence regarding the performance of the neural network on hardware implementation is automatically ensured.
An attempt is made to make a prediction of the disruption boundaries for the density limit disruption case using a neural network. Using experimental signals as input, the network should, in the long run, be able to provide information to the real time control systems about the density limit at which a discharge is likely to disrupt, so that the density can be kept below that limit. Several diagnostic signals are used from the ADITYA tokamak and are presented at selected time instants to the neural network inputs, in order to predict, at each of these instants, the density boundary. A disruption threshold has been established in order to examine the possibility of using the network as a real time disruption alarm. For most of the discharges this threshold is reached much before the actual disruption. The neural network is also used to make an optimization of the particular set of diagnostics in order to obtain the ones most crucial for predicting the density limit. The results of optimization have some of the features of the scaling laws of Murakami and Hugill. The optimized network compares well with the original one.
Equilibrium magnetic configurations of W7-X stellarator plasma were analysed in this study. The statistical method of Function Parametrization was used to recover the physical properties of the magnetic configurations, such as the flux surface geometry, the magnetic field, the iota profile , etc, from simulated experimental data. The study was carried out with a net toroidal current. Idealized "measurements" were first used to recover the configuration. These "measurements" were then perturbed with noise and the effect of this perturbation on the recovered configuration parameters was estimated. The noise was scanned over a range large enough to encompass that expected in the actual experiment. In the process, it was possible to ascertain the limit of tolerable noise that can be allowed in the inputs so as not to significantly perturb the outputs recovered with noiseless "measurements". Generally, a cubic polynomial model was found to be necessary for noise levels below 10%. For higher noise levels, a quadratic polynomial performed as well as the cubic. The noise level of 10% was also the approximate limit up to which the recovery with ideal measurements was generally reproduced. For the flux geometry recovery, however, the quadratic model performed similar to the cubic for any value of noise, with the latter model proving to be significantly better only for the noiseless case. Also, with noisy predictors the recovery error for the flux surfaces increases linearly with effective radius from the plasma core up to the edge.1
W7-X, a five-period, fully optimized stellarator, currently under construction at IPP-Greifswald, Germany, is built with superconducting coils to show the steady state capability of stellarators. However, the steady state needs continuous equilibrium information for monitoring and controlling the discharge. Although the timescales are long compared with tokamaks, the computational effort for calculating three-dimensional magnetohydrodynamic equilibria is also orders of magnitude higher. This has led us to start the development of a fast equilibrium recovery for W7-X. As a starting point and also for investigating the richness of magnetic configurations, of which only nine physically interesting examples have been examined till now, a fast recovery of vacuum magnetic configurations, described by the flux surface geometry and profile parameters, is carried out using the function parametrization (FP) and artificial neural networks (ANN) methods. Additionally, we parametrize the detectable major magnetic island chains (5/6, 5/5, 5/4) in the form of their locations, r (is) eff , and their width, w (is) . The quality of FP recovery is compared with ANN, where the vacuum parameters are non-linearly regressed in terms of linear combinations of the coil currents. The results show that a quadratic FP model is generally sufficient for a good recovery of the parameters which are related to the magnetic axis. However, a cubic model is necessary for modelling accurately the magnetic island-related parameters. ANN models offer no improvement over the cubic FP model.
A geieralized inverse of a multifunction is denned using the Axiom of Choice, This inverse reduce to the usual one for a function and is derived from the lower inverse of a multifunction. Tie important notions of Section 2 are: (i) the basic subset induced by a multifunction that eplaces each saturated set by a representative of that set, and (ii) the sum projection which is ;he (left) inverse of an inclusion into υ,·Χ» and its relation to a projection on YliXi trough t.e evaluation. Section 3 introduces the topological generalized inverse of a function using the bols of initial and final topologies, and solves an ill-posed problem Ax = y in terms of the gen
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