(A) A Convolution Method for Determining Temperature Rise in Targets Struck by Beams of Various Size

The temperature rise in targets struck by high-energy electrons can be calculated using the EGS4 code[1] simply by scoring the energy-deposition density in small cylindrical volumes centered upon, and divided along, the direction of the beam. The temperature rise per pulse, Tp (C/pulse), is then obtained for each volume using the specic heat of the material, and the time dependence of the heat flow can be calculated using conventional heat-transfer principles. Most typically the beam size is accounted for in a straight-forward way by sampling the incident coordinates, but this involves yet another statistical process that can result in a signicant increase in computation time in order to reduce the variance, particularly for thick targets at very high energies. In this paper an o-line convolution method is presented in which the symmetry of the geometry and the Gaussian shape of the beam is used, along with a set of EGS4 runs made with a δ-function (i.e., pencil) beam, to quickly obtain the temperature rise on the pulse for beams of any size. Examples are given for studies that have recently been performed at SLAC in the design of the Next Linear Collider.