A re-examination of the traveling wave interaction

A re-examination of the traveling wave interaction (in the helix traveling wave tube and the free-electron laser) is performed using three-dimensional linear stability analyses for an idealized annular electron beam model in order to investigate the validity of the well-known scaling laws in which the gain varies as the cube (fourth) root of the current when space-charge effects are negligible (dominant). The results indicate that these scaling laws are simplistic generalizations which break down for broad bandwidth interactions, and that the actual variation of the pain, with the current can be more complex. A three-dimensional nonlinear analysis of a free-electron laser using a more realistic electron beam model is also discussed in which these scaling laws are also shown to break down,