A bunch compression scheme designed to obtain high efficiency in relat
ivistic traveling-wave tube (TWT) amplifiers is reported. Bunch compre
ssion is achieved by making the bunches stay in more positive slopes o
f the axial electric field in the amplifier. The resulting momentum gr
adient across the bunch tends to oppose space-charge spreading and hel
ps to sustain short bunch lengths for long distances. A faster than li
ght structure is employed to produce the required bunching. At the opt
imal bunching point, a transition is made to a lower phase velocity st
ructure where the narrow bunches are decelerated. An RF conversion eff
iciency of >50% in an X-band amplifier is achieved in particle-in-cell
(PIC) simulations. This contrasts strongly with the 20%-30% efficienc
ies achievable from typical relativistic TWT's, where the bunching is
not optimized.