BEAM HEATING IN AN ASYMMETRICALLY ILLUMINATED THIN CIRCULAR FILM

The method of images is used to calculate the temperature increase produced in a circular film when the film is illuminated at any point by an electron beam of circular cross-section and constant current density over its cross-section. Formulae are given in dimensionless form for (i) the temperature increase anywhere along the line joining the centres of the beam and of the film, (ii) the temperature increase at the centre of the beam (nu(c)), and (iii) the position and value of the maximum temperature increase in the film (nu(M)). The relative sizes of nu(c) and nu(M) are discussed and it is shown that (nu(M)-nu(c))/nu(M) less-than-or-equal-to 0.079. The theory applies best to metallic films where power loss by means of thermal conductivity is dominant. A brief discussion is given of the cases where thermal radiation is important, sample calculations are given for carbon and copper films, and the effect of focusing the electron beam at constant current is considered.