The gyrotron backward wave oscillator (gyro-BWO) is an efficient source of frequency-tunable high-power coherent radiation in the microwave to the terahertz range. It has attracted significant research interest recently due to its potential applications in many areas such as remote sensing, medical imaging, plasma heating and spectroscopy. A gyro-BWO using a helically corrugated interaction region (HCIR) has achieved an even wider frequency tuning range and higher efficiency compared with a conventional gyro-BWO with a smooth-bore cavity. This is due to the existence of an "ideal"eigenwave in the HCIR with a large and constant group velocity when the axial wave number is small. The eigenwave has a TE 21-like cross-sectional electric field distribution. For such a field structure it is favourable to use the second harmonic of the electron cyclotron frequency of an axis-encircling electron beam to interact with the wave. The advantage being that it lowers the required magnetic field strength by a factor of two whilst avoiding undesired parasitic oscillations. Therefore a cusp gun was used to produce an annular, axis-encircling electron beam with high velocity ratio, α (ratio of transverse velocity to axial velocity) for the gyro-BWO. This has inherent advantages over a solid beam for energy recovery due to the reduced beam power density in the collector surface making high power (∼ kWs) continuous wave (CW) operation of a gyro-BWO more feasible. The overall efficiency of the gyro-BWO is further improved by using a four-stage depressed collector which recovers the energy from the spent electrons of the gyro-BWO. The 3D particle-in-cell (PiC) code MAGIC was used to simulate the electron beam trajectories, beam-wave interaction and wave growth in the gyro-BWO. The trajectories of the electrons were simulated including their emission from the cathode, acceleration in the cusp gun region, transportation and interaction in the helical interaction region and deceleration in the depressed collector. Through the simulations a thermionic cusp electron gun was optimized to produce a 40 keV, 1.5 A, large-orbit, electron beam with an axial velocity spread Δv z /v z of ∼8% and a relative α spread Δα/α of ∼10% at an α value of 1.65. When driven by such a beam the gyro-BWO was simulated to have a 3 dB frequency bandwidth of 84-104 GHz, output power of 10 kW with an electronic efficiency of 17%. The optimization of the shape