This work is an attempt to elucidate effects that may limit efficiency in m
agnetrons operated at relativistic voltages (V similar to 500 kV), Three-di
mensional (3-D) particle-in-cell (PIC) simulation is used to investigate th
e behavior of 14- and 22-cavity, cylindrical, rising-sun magnetrons, Power
is extracted radially through a single iris located at the end of every oth
er cavity, Numerical results show that in general output power and efficien
cy increase approximately linearly with increasing iris width (decreasing v
acuum Q) until the total Q becomes too low for stable oscillation in the pi
-made to be maintained. Beyond this point, mode competition or switching o
ccur and efficiency decreases. Results reveal that the minimum value of Q (
maximum efficiency) that can be achieved prior to the onset of mode competi
tion is significantly affected by the magnitude of the 0-space-harmonic of
the ir-mode, a unique characteristic of rising-suns, and by the magnitude o
f the electron current density (space-charge effects). When these effects a
re minimized, numerical simulation predicts that gigawatt-level power produ
ction at 55% efficiency may be possible at relativistic voltage.