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It is common practice in the engineering analysis process to use an approximate image method for the computation of the current in buried horizontal conductors (in the literature, this is often referred to as the “modified image” or “reflection coefficient” method). According to this approach, the earth/air interface is replaced by a positive mirror image of the charge and current in the conductor, and its field is multiplied by a suitable reflection coefficient. Different opinions on the validity of this approximation have been expressed in published debates, but more systematic analysis of the error introduced by this approach is not available in the literature. To establish the amount of error, we compare the computation results of the image model with the rigorous Sommerfeld integral method for a wide range of parameters. Contrary to widespread opinion, our results suggest that the modified image (or reflection coefficient) method in EFIE-based solutions (e.g., the Pocklington equation) leads to a large error (larger than 20%) in the low-frequency range for the computation of the current distribution in conductors longer than 10 m. In such a case, MPIE-based methods are preferred for use to achieve a smaller error (approximately 5%). Guidelines for the application of image models related to the conductor, earth and excitation parameters, upper frequency limit, and modeling method are presented. [ABSTRACT FROM AUTHOR]

This paper deals with an analytical solution of the time domain Pocklington integro-differential equation for the transient current flowing along the horizontal grounding electrode of finite length. The electrode is excited with an equivalent current source representing the lightning strike current. Presence of the earth–air interface is taken into account through the formulation, via simplified reflection coefficient arising from the modified image theory. The analytical solution is carried out using the Laplace transform and the Cauchy residue theorem, respectively. Results obtained by the analytical solution are compared to those calculated using numerical solution of the corresponding frequency domain Pocklington equation in conjunction with the Inverse Fast Fourier Transform. The results obtained via different methods agree satisfactorily. [ABSTRACT FROM PUBLISHER]

A neural network (NN) implementation of an adaptive optimal stochastic output feedback control is developed to stabilize the resistive wall mode (RWM), a critically important instability in fusion machines like tokamaks. The design of an adaptive optimal stochastic output feedback control was discussed and reported earlier by Sun, Sen, and Longman. The system dynamics is experimentally determined via the extended least square method with an exponential forgetting factor and covariance resetting. The optimal output feedback controller is redesigned periodically online based on the system identification. The output measurements and past control inputs are used to construct new control inputs. These are achieved by an architecture of NNs consisting of a pool of sequentially linked Hopfield networks and implemented in hardware with digital NN processors made by the Accurate Automation Corporation. The simulations have shown that the NN adaptive output controller can stabilize the time-dependent RWM in a slowly evolving tokamak discharge. This is accomplished within a time delay of the inverse of the nonlinear growth rate, which is the time scale of the development of the possibly dangerous levels of fluctuations. This stabilization is similar to that of the simulation with a C++ implementation. It is expected that significant gains can be achieved for the systems of a higher order, which are to be found in future fusion devices. [ABSTRACT FROM PUBLISHER]