Amplified FEL power vs for , , , , and : simulation (continuous line) and logistic approximation [Eq. (1)] (dotted line).
Behavior of the FEL amplified power after the saturation. (a) Same parameters of Fig. 1; (b) , , , , and : simulation (continuous line) and Eq. (12) (dotted line).
Amplified FEL power growth and total energy spread (same parameters as in Fig. 1). The induced energy spread oscillations are reproduced by an equation identical to Eq. (12) with and , .
Phase space plots vs (same parameters of Fig. 1). (a) First three oscillations ; (b) oscillations between .
Behavior of FEL amplified power and of the third harmonic after the saturation (same parameters as in Fig. 1). The oscillations of the first harmonic are reproduced by Eq. (12) with , , and .
Same as Fig. 2(a) for . The boxes show the induced energy distribution at the maximum of the emitted power and near the maximum damping of the power oscillations.
Energy distribution asymmetry coefficients vs for the case of Fig. 6 [(a) and (b) ]. , where , and . The moment of a Gaussian with rms is given by an expression analogous to with .
Evolution of the first and third harmonic with the inclusion of pulse propagation dynamics, same parameters of Fig. 1 and electron bunch length . In the boxes we have reported the corresponding pulses evolution [(a) first harmonic and (b) third harmonic]. The spiking occurs in correspondence of the minima of the oscillations and tend to be cleaned while the power grows towards the maximum.
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