Cherenkov FEL Reaction With Plasma-Filled Cylindrical Waveguide in Fractional D-Dimensional Space

The possibility of generating an electromagnetic (EM) wave by a free-electron laser (FEL) beam from the Cherenkov device to control the cylindrical waveguide's field attenuation filled with plasma has been investigated by analytical formalism. This new study sheds light on Cherenkov FEL (C-FEL) beam interaction with electrons of inhomogeneous warm plasma to generate an EM wave in fractional dimensional space. The new analysis of traveling and standing waves in terms of Hankel and Bessel functions paves a way for introducing controlled EM wave propagation based on fractional D-dimensional space. It has been found that the C-FEL beam excites the EM wave and enhances the propagation of the electrical field through fractional dimensional space with propagation constant depending on the Langmuir frequency. Within the plasma in the cylindrical waveguide, a TM mode emerges, which contains spatial frequencies with a faster growth rate for traveling waves than standing waves.