The magnetron injection gun is capable of generating relativistic electron beam with high velocity ratio and low velocity spread for a gyrotron backward-wave oscillator ͑gyro-BWO͒. However, the velocity ratio ͑␣͒ varies drastically against both the magnetic field and the beam voltage, which significantly limits the tuning bandwidth of a gyro-BWO. This study remedies this drawback by adding a variable trim field to adjust the magnetic compression ratio when changing the operating conditions.

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... retical results obtained by employing a two-dimensional electron gun code ͑EGUN͒ demonstrate a constant velocity ratio of 1.5 with a low axial velocity spread of 6% from 3.4-4.8 Tesla. These results are compared with a three-dimensional particle-tracing code ͑computer simulation technology, CST͒. The underlying physics for constant ␣ will be discussed in depth.