The Lie algebraic analyses for the pulsed beam transport in the electrostatic accelerating tubes were presented. The solutions through third order were obtained and could be extended to higher order if desired. In the analysis

the accelerating tube was divided into three elements: entrance aperture lens

uniform accelerating field and exit aperture lens. To obtain analytical forms of aberrations

the uniform accelerating region was also divided in several small segments

in which the Lie map was performed.