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

The recent 2-dimensional analytic theories of a free-electron laser (FEL) in the linear regime are reformulated in terms of three dimensionless ratios that describe the degree to which the characteristics of the electron beam deviate from the cold beam limit of a beam with no emittance or energy spread. In terms of these ratios, algebraic model equations of a fit that combines features of both of the 2-dimensional analyses 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.