In a gyrofrequency multiplier, the entire electron beam enters the out
put cavity optimally phased to lose energy in a first-order interactio
n (in contrast to the second-order standard gyrotron process) resultin
g in a high conversion efficiency. Because the electrons radiate at a
high harmonic of the cyclotron frequency, a gyrofrequency multiplier i
s capable of efficiently generating power in the millimeter to submill
imeter wave region. The operational principles of the gyrofrequency mu
ltiplier are described in this paper. Results from nonlinear simulatio
n show that radial guiding-center spread of the beam can dramatically
affect the device's efficiency while velocity spread effects are negli
gible. The design is presented for a 150 kW, 17.4 GHz, sixth-harmonic
gyrofrequency multiplier-which is under construction and is predicted
to yield 3l% conversion efficiency of the electon beam into the output
wave. The 300 keV, 1.67 A axis-encircling beam is produced by a 1 MW,
2.9 GHz gyroresonant RF accelerator.