Effect of strong uniform axial magnetic field on the TE and TM modes fields and injected electron dynamic in the plasma waveguide with Piet Hein cross section

In this paper,considering the effect of a strong uniformly axial magnetic field on the plasma dielectric tensor, electromagnetic fields and other results in a waveguide with a metal wall with a cross-section in the shape of a Piet Hein curve containing cold and strongly magnetized plasma is investigated using an appropriate approximation. First, by introducing the Pitt Hein waveguide, the electromagnetic wave equation in this type of waveguide is presented , using a suitable approximation and by separating the variables, as two separate differential equations. The electric and magnetic fields as well as the dispersion relations for the TM and TE modes are then calculated in a Piet Hein waveguide with a metal wall containing strongly magnetized cold plasma, and the dispersion relations and resulting fields are plotted., Next, the motion of an injected electron into this waveguide and the effect of a strong uniformly axial magnetic field on the electron energy is investigated. The electron motion and energy equations are written in the Pitt Hein plasma waveguide in the presence of a strong uniform axial magnetic field and are solved using fourth-order Runge Kutta method for TM and TE modes. The motion path and kinetic energy of the electrons injected into the waveguide have been graphically investigated for both modes.