Electron Beam Machine for Continuous Metallurgical Processes

Abstract

Interest in harnessing the unique properties of electron beams to a wider range of applications has continued since its first industrial use, as a welding machine, in the 1950's. In recent years attention has been concentrated upon its application to continuous metallurgical processing. The design of a suitable machine is carried out , and original designs of electron gun and lens evolved. Studies are made of the interactions between an electron beam and the material to be processed; and a unique set of tables produced. Past theoretical investigations into the behaviour of electron beams in electromagnetic fields have produced solutions which are restrictive, due to the problem's complexities. Simplifications made to overcome this difficulty always produced inaccuracies. In an attempt to remove these constraints, while still maintaining accuracy, a generalised theory is derived. This derived theory includes a unique equation defined as the 'Kinetic Equation' which under certain circumstances reduces to Boltzmann's gas equation. Additionally a method for generating the stress-energy tensor of a given system is presented, and derived for the generalised theory. Its advantages are shown to be numerous, The prediction of electron beam behaviour in electromagnetic fields is reduced to that of simultaneously solving a set of differential equations. Due to their complexity it is shown that a solution can be best obtained by numerical methods employing the use of high speed digital computers. Several numerical method solutions are described for different situations of the electron beam, The solution given for predicting electron beam activity in electron guns is particularly original in that it is carried out in logarithmic cylindrical co-ordinates; and its many advantages are stressed. Finally, the accuracy of the solutional methods are tested. Measurements, from a model of the proposed machine, are made and compared to the theoretical predictions.