The coupled nonlinear equations governing the transmission of electromagnetic energy through a liquid particle cloud are formulated and solved both analytically and numerically. Vaporization of the droplets is included in both treatments. The cloud is assumed to be initially composed of an arbitrary distribution of particles in the direction of propagation. The incident electromagnetic radiation is assumed to be a plane harmonic wave with sufficient intensity to vaporize the particles in the path of the beam. The vaporization of the droplets decreases the extinction cross section allowing a greater percentage of the incident energy to be transmitted. The time required to transmit an arbitrary percentage of the incident beam across an arbitrary station in the column is determined. The results of the analytical solution are compared with finite difference calculations and excellent agreement is found to exist. Parametric curves are generated for power levels and times required to produce given results.