ANALYSIS OF THE EIGENVALUE EQUATION OF THE FEL AMPLIFIER WITH AXISYMMETRICAL ELECTRON-BEAM AND DIAPHRAGM FOCUSING LINE

The paper presents analysis of the eigenvalue problem of the FEL ampli fier with axisymmetric electron beam and diaphragm focusing line. This novel type of an FEL amplifier has perspective to be used for applica tions where high average and peak radiation power is required [E.L. Sa ldin et al., Nucl. Instr. and Meth. A 361 (1995) 317; these Proceeding s, Nucl. Instr. and Meth. 375 (1996) 389; Nucl. Instr. and Meth. A 361 (1995) 101]. An FEL model is discussed wherein diffraction effects, s pace charge fields and energy spread of electrons in the beam are take n into account. To take into account diffraction effects at the diaphr agms we apply the rigorous impedance boundary conditions proposed by V einstein. The rigorous solutions of the eigenvalue problem have been f ound for the stepped electron beam profile. Analytical expressions for eigenfunctions of active open waveguide and formulae of their expansi on in the eigenfunctions of passive open waveguide, are derived, too. Asymptotic behaviour of the obtained solutions is studied in details.