Analysis of slippage in THz-FEL with a parallel plate waveguide

•We find that dϕ′dkz is proportional to the slippage.•The expressions of slippage are derived according to dϕ′dkz and the resonant condition.•The conditions for getting the zero-slippage and maximal slippage are derived.•For the HUST THz-FEL, the maximal slippage occurs when Δ approximately equals to 0.5.•The parallel plate waveguide with the gap of 4–6 mm is considered for HUST THz-FEL.

An approach is proposed to analyze the slippage of waveguide FEL. Based on what we find that the derivative of the detuning parameter with respect to the axial wavenumber is proportional to the slippage, several expressions of slippage are derived for analyzing slippage. The analysis results show that both zero-slippage and maximal slippage can be obtained at specific conditions. Especially for the given parameters of THz-FEL oscillator which is under development at Huazhong University of Science and Technology (HUST), the maximal slippage occurs when the parameter ΔΔ approximately equals to 0.5. Then by analyzing the slippage in HUST THz-FEL oscillator, the parallel plate waveguide with the dimension of 4–6 mm is considered for optimum design.