UC Irvine

The physical phenomenon of amplification in traveling wave tubes can be understood mathematically as a result of system instability or exponentially growing eigenmodes. We study here instability in the uncoupled multi-stream electron beam model, focusing primarily on properties and solutions of the characteristic equation associated with the beam. In particular, we show that in general the zeroes of the characteristic function are distinct. Then, in the two-stream case, we construct a series representation of frequency-dependent solutions to the electron beam characteristic equation near the frequency at which these solutions transition from non-real (unstable eigenmodes) to real (oscillatory eigenmodes).