Non-linear analysis of the gyro-BWO in three dimensions

The non-linear evolution of the gyrotron backward wave oscillator (gyro-BWO) is investigated numerically in the presence of a weakly non-uniform axial guide magnetic field. The set of coupled non-linear differential equations which govern the self-consistent evolution of the TE modes and the trajectories of an ensemble of electrons in a gyrotron are solved subject to boundary conditions for both the usual BWO (power extracted at the input end) and the reflection-type BWO (power extracted in the forward direction) configurations. Space charge effects are neglected in the analysis. Numerical simulations are carried out to model gyro-BWOs operating in the Ka -band with rectangular TE10 modes and near 104GHz with TE11 cylindrical modes. For a cold beam, calculations show that the efficiency of the device has a modest value of 10–15% in a uniform magnetic field but can be significantly enhanced to 25–30% by tapering the magnetic field. The frequency of the oscillator can be magnetically tuned over a 15% bandwidth. Beam thermal effects are also considered.