The features of the steady state distribution function of the electron beam are discussed in this paper

and it is proposed that the steady state distribution function of a practical electron beam be represented in terms of momenta variables and position coordinates or in terms of three momenta variables. The complete form of Δρf0 and the first order perturbed distribution function for both H and E modes in thick beam masers are derived

and the decoupling property of waveguide modes in thick beam masers is proved. The general dispersion equations are derived for arbitraty H and E modes

arbitray cyclotrin harmonics and electron beams of arbitray thickness

with the term ef0/er0 included in calculation

and the features of both the waveguide maser and cavity maser are discussed. The analysis made in this paper provide a theoretical foundation for the calculation of thick beam maser and give more rigorous computed results for thin layer beam maser as well.