  In the particle acceleration by stimulated emission of radiation (PASER), the
efficient interaction occurs when a train of micro-bunches whose periodicity
being identical to the resonance frequency of the medium. The previous
theoretical calculations based on the simplified model consider only the energy
exchange in the boundless condition, under the experimental condition, however,
the gas active medium must be guided by the metal waveguide. In this paper, we
have developed the model of energy exchange between a train of micro-bunches
and gas mixture active medium in waveguide boundary for the first time based on
the Theory of Electromagnetic Fields, and made detailed analysis and
calculations with MathCAD. The results show that the energy density could be
optimized to a certain value to get the maximum energy exchange.
