Abstract
This chapter discusses phase shift induced by a free-electron laser (FEL) interaction. An FEL interaction with unbunched electrons at resonant energy induces a positive phase shift of the FEL field relative to the input phase. The positive phase shift corresponds to giving electrons positive energy detuning and results in the FEL amplification. The positive phase shift connects the zero small signal gain in low gain regime for resonant electrons to the exponential growth in high gain regime. The interaction between unbunched electrons and the FEL field with uniform amplitude and phase is considered in the time domain. The positive phase shift corresponds to giving positive detuning to the electron energy, and the FEL field is amplified regardless of the dimensionless current when the initial electron energy is resonant. The present amplification mechanism has been known as the collective instability. The diffraction effect or the frequency shift appears as a result of the phase shift but is much smaller than the phase shift effect.
Published Version
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