Dispersion and attenuation in a Smith-Purcell free electron laser

• Published in: Physical review special topics. PRST-AB. Accelerators and beams Vol. 8; no. 5; p. 050703
• Main Authors: Andrews, H. L., Boulware, C. H., Brau, C. A., Jarvis, J. D.
• Format: Journal Article
• Language: English
• Published: College Park American Physical Society 01.05.2005
• Subjects: Electron beams; Electron energy; Electrons; Evanescent waves; Feedback; Free electron lasers; Group velocity; Lasers; Traveling wave tubes; Wave attenuation
• ISSN: 1098-4402; 1098-4402; 2469-9888
• DOI: 10.1103/PhysRevSTAB.8.050703

It has previously been shown that the electron beam in a Smith-Purcell free-electron laser interacts with a synchronous evanescent wave. At high electron energy, the group velocity of this wave is positive and the device operates on a convective instability, in the manner of a traveling-wave tube. For operation as an oscillator, the gain must exceed the losses in the external feedback system. At low electron energy, the group velocity of the synchronous evanescent wave is negative and the device operates on an absolute instability, like a backward-wave oscillator, and no external feedback is required. For oscillation to occur, the current must exceed the so-called start current. At an intermediate energy, called the Bragg condition, the group velocity vg of the evanescent wave vanishes and both the gain and the attenuation due to resistive losses in the grating diverge. It is shown that near the Bragg condition the gain depends on vg−1/3 , while the attenuation depends on vg−1 . Since the attenuation increases faster than the gain near the Bragg condition, the Smith-Purcell free-electron laser cannot operate at the point of maximum gain. The effects of resistive losses become increasingly important as Smith-Purcell free-electron lasers move to shorter wavelengths.