Considering the effects of outfield and image charge, the Fowler-Nordeim formula was improved. The physical mechanism of the terahertz source with cathode arrays field emission was analyzed by using of the improved barrier penetration formula. By using the transit-time effect, the energy exchange caused by the beam-wave interaction was derived, and based on which, it is discussed the energy increment of the electron beam, the electron beam power, load conductance and beam-wave conversion efficiency.