Calculation of the heat-affected zone during pulsed electron-beam machining

The heating effect of a pulsed electron-beam incident onto a solid target is dependent on the beam parameters, on the electron penetration, and on heat conduction effects. The attainable beam current density is limited jointly by the electron-optical brightness condition and by the spherical aberration of the focussing lens. To calculate the temperature rise that exists at the end of the electron pulse, allowance must be made for the two-dimensional Gaussian spread of the beam over the surface as well as for the three-dimensional non-Gaussian spreads introduced by electron penetration and thermal conduction. In this paper expressions are derived for the rms diameters along the three coordinate axes of the temperature-rise distribution that exists at the end of the electron pulse. The optimum condition is determined by maximising the energy introduced into the target while the horizontal rms diameter is held constant. A comparison is made with a related study that has been made of the steady-state problem by Vine and Einstein [2].