Steady-state electron trajectories and growth rate in electromagnetically pumped free-electron laser with specific nonuniform magnetic field

Abstract

A theory of the dispersion relation for electromagnetically pumped free-electron laser in the presence of a special tapered axial guide magnetic field is presented. An analysis of the steady-state electron trajectories is obtained by solving the equations of motion. Next an eleventh-degree polynomial equation for electromagnetic and space-charge wave is derived. Numerical solution of the polynomial equation of the dispersion relation yield the complex wave number as a function of the frequency of the waves. These results are used to illustrate the dependence of growth rate curves on the axial guide field frequency. It is found that the tapered guide field shifts electron trajectories and enhances the growth rate in the comparison of employing uniform axial magnetic field, without needing a strong guide magnetic field.