PHYSICALLY TRANSPARENT FORMULATION OF A FREE-ELECTRON LASER IN THE LINEAR GAIN REGIME

The recent 2-dimensional analytic theories of a free-electron laser (F EL) in the linear regime are reformulated in terms of three dimensionl ess ratios that describe the degree to which the characteristics of th e electron beam deviate from the cold beam limit of a beam with no emi ttance or energy spread. In terms of these ratios, algebraic model equ ations of a fit that combines features of both of the 2-dimensional an alyses are given as a convenient computational tool. Graphs of the FEL gain eigenvalue computed with the combined 2-D formulation illustrate that the gain and the output power at saturation are reduced from the 1-D value, when any of the ratios is larger than unity.