A plasma-filled slow wave device, e.g., a backward wave oscillator (BW
O), offers high efficiency for the generation of TM waves around 10 GH
z, by a relativistic electron beam. A large-amplitude TM mode can para
metrically drive a millimeter wave unstable by coupling it to a negati
ve energy beam space charge mode. The frequency of radiation is maximu
m when it propagates in the TM01 mode. In the Raman regime of operatio
n the growth rate of instability scales directly as one-fourth power o
f beam density and inversely as 21/4 power of relativistic gamma facto
r. The nonlocal effects reduce the growth rate. (C) 1997 American Inst
itute of Physics.