In this paper,we consider a metallic waveguide with Piet Hein cross section filled by cold unmagnetized plasma. First by introducing a Piet Hein waveguide and considering a suitable approximation,wave equation as two differential equations are presented. Then electromagnetic fields for TM and TE modes in the Piet Hein waveguide filled plasma are analytically obtained and plotted. Using the boundary conditions in the Piet Hein plasma waveguide the dispersion relations for TM and TE modes are analytically derived and plotted. Electron dynamics in the fields associated with a transverse magnetic and electric wave propagating inside the considered Piet Hein plasma waveguide is investigated. The equations of electron motion in the considered Piet Hein plasma waveguide by fourth-order Runge Kutta method for TM and TE modes are solved. The motion path and kinetic energy of electron injected into the purposed configuration for two modes are graphically investigated. In principle, it is shown that the electron can be accelerated in this condition. Therefore, by optimizing the microwave parameters together with the injected energy and waveguide dimensions, a huge amount of energy gain can be obtained if the proposed mechanism can be used in multiple stages.

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