ANALYSIS OF ENERGY BROADENING IN ELECTRON AND ION BEAMS.

The ″Boersch effect″ is treated as a process in which multiple, small-angle Coulomb scatterings convert transverse beam energy into axial energy spread. The primary source of the transverse energy is thermal agitation; however, where beams pass through focal points, an additional source is the transverse components of ray-crossing motions. The analysis leads to expressions for energy broadening in several basic beam geometries, including cylindrical beams, diverging beams adjacent to point sources, and beam crossovers. An unexpected result for the latter geometry is that, with combined thermal and crossover motions, less energy broadening is generated than would result from thermal agitation alone. Broadening levels predicted by this paper agree well with earlier published energy spread measurements.