The increase in temperature of a rectangular film when subjected to electron irradiation and/or high-temperature thermal irradiation

Theoretical expressions are derived to enable the temperature increase to be calculated at any point in a rectangular film that is bombarded by an electron beam of constant current density across its circular cross section. The beam may be incident at any point in the film provided that it does not strike the supporting grid bars which are held at constant temperature. The theory applies when the effects of thermal radiation from the film may be neglected and includes the case of low-temperature studies where the radiation input from the surroundings of the film is much greater than the radiation emitted by the film. Sample calculations are given for a copper film 20 nm thick supported on a 200 mesh copper grid. It is important to note that the calculated results give lower limits to the temperature increases because in a practical case a film is not ideally thermally anchored to the grid bars as is assumed in the theory.