Since jagged-structure of the spectrum due to the interference between two undulator radiation is very sensitive to the electron energy, finite dispersion of the electron energy leads incomplete interference in the spectrum. It is obvious from the data for a lower beam current that the bunch lengthens for and shortens for , which is a clear evidence of that the inductive impedance dominates the bunch length. Then the wake field may be expressed as . Since the bunch shape contains wide-range frequency components, the average frequencies were derived as follows. We first obtain the frequency distribution of each measured point by applying Fourier transform to the bunch profile data taken by the streak camera and then averaged it.
Regions guided by dashed lines include influence of the microwave instability.
Excluding these regions, the inductive impedance seems to be constant in the frequency region up to 1.5 GHz. Absolute value of L is roughly estimate d to be . The negative operation showed us some attractive properties of the beam for the FEL operation. Although the threshold current for the microwave instability is rather low, the instability does not kill the beam and the peak current remains higher due to the bunch shortening than that in the positive operation. If the growth rate of the energy spread due to the FEL interaction exceeds that of the microwave instability, the FEL oscillation would be operated in a stable regime with keeping higher gain than the positive case.