Analysis of emissions from prebunched electron beams

The emissions of the prebunched electron beam, including the coherent spontaneous emission and the self-amplified stimulated emission, are analyzed by using one-dimensional FEL theory. Neglecting the interaction of the electrons and the radiation field, the formula of the coherent spontaneous emission is given, the power of which is proportional to the square of the initial bunching factor and of the undulator length. For the general emission case of the prebunched electron beam, the evolution equation of the optical field is deducted. Then the analytical expression of the emission power is obtained for the resonant case; it is applicable to the regions from the low gain to the high gain. It is found that when the undulator length is shorter than four gain lengths, the emission is just the coherent spontaneous emission, and conversely, it is the self-amplified stimulated emission growing exponentially. For the nonresonant prebunched electron beam, the variations of the emission intensity with the detuning parameter for different interaction length are presented. The radiation field characters of the prebunched electron beam are discussed and compared with that of the seeded FEL amplifier.

Figure 1

The optical power growing vs undulator length (${\varphi }_0^{\prime }=0$). The red line (b): the prebunched mode [Eq. (12)]. The pink dashed line (c): the coherent spontaneous emission [Eq. (8)]. The blue dot line (e): the exponential gain formula [Eq. (14)]. The black line(s): the seeded amplifier mode [Eq. (13)].

Figure 2

The variation of the emission intensity with the detuning parameter for different interaction length. The solid line: prebunching mode; the dashed line: seeding mode.

Figure 3

Shortened saturation length with initial bunching [Eq. (22)] and seed power [Eq. (23)].