Starting energy and current for a large diameter finite lengthbackward wave oscillator operated at the fundamental mode

We study the starting conditions for a large diameter (diameter/wavelength=4.8) finite length backward wave oscillator designed for 24-GHz operation at the fundamental TM₀₁ mode. This geometry is very promising for high power handling capability. We analyze two separate threshold conditions. First, finite length effects give rise to a threshold in electron beam energy below which oscillations cannot be sustained at any beam current. The second is the more familiar current threshold known as a start current. It is also found that the growth rate for the fundamental mode can be much larger than those of other higher order modes thus leading to coherent operation of large diameter sources free from mode competition