In this paper, electron bunching and power evolution along the axial length of the gyro-TWT amplifier are explained by making use of an electron flight diagram that shows individual electron trajectories during the entire amplification process. A typical gyro-TWT amplifier operating in TE 01 mode at 35 GHz with parameters beam voltage $\mathrm{V}_{0}=70\text{kV}$, beam current $\mathrm{I}_{0}=15$ Amp, waveguide radius = 5.42 mm, DC magnetic field $\mathrm{B}_{0}=1.32\ \mathrm{T}$, Hollow beam radius = 2.547 mm, Larmor radius = 0.58 mm resulted in 11.75 kW peak output power. Result obtained from the developed MATLAB code has been benchmarked against the published result and is found to be in good agreement.