Fields and injected electron dynamic in the coaxial waveguide with Piet Hein cross section filled plasma considering TE and TM modes

In this paper, we consider a metallic coaxial waveguide with Piet Hein cross section filled by cold unmagnetized homogenous plasma. First by introducing a Piet Hein waveguide and considering a suitable approximation, wave equation as two differential equations is presented. Then, electromagnetic fields associated with a transverse magnetic wave (TM) and a transverse electric wave (TE) propagating inside the Piet Hein coaxial waveguide-filled plasma are obtained and plotted. Using the boundary conditions in the Piet Hein coaxial waveguide containing cold plasma, the dispersion relations for TM and TE modes are derived and plotted. The energy and dynamic of an injected external electron with initial energy using radiation of an electromagnetic source in the Piet Hein, plasma coaxial waveguides for TM and TE modes are investigated. The obtained differential equations related to electron motion and energy are numerically solved by the fourth-order Runge-Kutta method. Numerical computations are made and the motion path and kinetic energy of electron injected into the purposed Piet Hein plasma coaxial waveguides for two considered modes are graphically presented.