Emittance Effects on Gain in $W$ -Band TWTs

We consider the main effects of beam emittance on W-band traveling-wave tube (TWT) performance and gain. Specifically, we consider a representative dielectric TWT structure with ~5 dB/cm of gain driven by a 5-A, 20-keV, sheet electron beam that is focused by a wiggler magnetic field. The normalized beam transverse emittance must be about 1 μm or lower to ensure that both the transport is stable and the gain is not degraded by the effective energy spread arising from the emittance. This emittance limit scales roughly inversely with frequency.