\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts}
\begin{document}
Effects of the wiggler field on the propagation of two types of space-charge waves in a Raman free-electron laser are studied. The relativistic electron beam is affected by an axial magnetic field and only partially fills a cylindrical metallic waveguide. Using the electrostatic approximation in the beam frame and an appropriate boundary condition a set of two equations are found as the dispersion relation. These equations are solved numerically to study the characteristics of the plasma-like and the cyclotron-like waves.
\end{document}