This paper deals with the study of propagation of electromagnetic wave in a rectangular waveguide filled with an inhomogeneous plasma in which electron density varies linearly in a transverse direction to the mode propagation. A transcendental equation in ω (microwave frequency) is obtained that governs the mode propagation. In addition, an attempt is made to examine the effect of density inhomogeneity on the energy gain acquired by the electron (electron bunch) when it is injected in the waveguide along the direction of the mode propagation. On the basis of angle of deflection of the electron motion we optimize the microwave parameters so that the electron does not strike with the waveguide walls. Conditions have been discussed for achieving larger energy gain. The plasma density inhomogeneity is found to play a crucial role on the cutoff frequency, fields and dispersion relation of the TE₁₀ mode as well as on the acceleration gradient in the waveguide.

In this article, $E{H}_{01}$ field components are evaluated in a cylindrical waveguide filled with plasma in the presence of external static magnetic field applied along the direction of the mode propagation. The electron acceleration inside the plasma-filled cylindrical waveguide is investigated numerically for a single-electron model. It is found that the electron acceleration is very sensitive to the initial phase of mode-field components, external static magnetic field, plasma density, point of injection of the electron, and microwave power density. The maximum amplitude of the $E{H}_{01}$ mode’s field components is approximately 100 times greater than the vacuum-waveguide case for operating microwave frequency $f=7.64\mathrm{GHz}$ , plasma density $n_0=1.08\times {10}^{17}{\mathrm{m}}^{-3}$ , initial phase angle ${\varphi }_0=60°$ , and microwave power $\sim 14\mathrm{MW}$ in a cylindrical waveguide with a radius of $2.1\mathrm{cm}$ . An electron with $100\mathrm{keV}$ gets $27\mathrm{MeV}$ energy gain in $2.5\mathrm{cm}$ along the waveguide length in the presence of external power $\sim 14\mathrm{MW}$ with a microwave frequency of $7.64\mathrm{GHz}$ . The electron trajectory is also analyzed under the effects of magnetic field when the electron is injected in the waveguide at $r=R∕2$ .

Isolated terawatt (TW) attosecond (as) hard X-ray pulse is greatly desired for four-dimensional investigations of natural phenomena with picometer spatial and attosecond temporal resolutions. Since the demand for such sources is continuously increasing, the possibility of generating such pulse by a single current spike without the use of optical or electron delay units in an undulator line is addressed. The conditions of a current spike (width and height) and a modulation laser pulse (wavelength and power) is also discussed. We demonstrate that an isolated TW-level as a hard X-ray can be produced by a properly chosen single current spike in an electron bunch with simulation results. By using realistic specifications of an electron bunch of the Pohang Accelerator Laboratory X-ray Free-Electron Laser (PAL-XFEL), we show that an isolated, >1.0 TW and ~36 as X-ray pulse at 12.4 keV can be generated in an optimized-tapered undulator line. This result opens a new vista for current XFEL operation: the attosecond XFEL.