Electrostatic surface waves in a magnetized plasma propagating in channels

Dispersion relations of electrostatic surface waves propagating in magnetized plasmas contained in an infinite duct and in an infinite cylindrical column surrounded by vacuum are derived by means of a Vlasov equation and fluid equations, respectively. The kinematic boundary condition imposed on the distribution function, the specular reflection conditions on the four sides of a duct, can be satisfied by placing infinite number of fictitious surface charge sheets spaced by the duct widths. The Vlasov equation that includes these surface charge sheets is solved by summing up the contribution due to the infinite charge sheets. The method of placing appropriate fictitious surface charge sheets enables one to treat the surface waves in bounded plasmas of Cartesian structure with mathematical efficiency, kinetically. The kinetic duct dispersion relation is compared with the dispersion relation for the magnetized cylindrical plasma column. When the square duct cross-sectional area as well as the cylinder radius become infinity, both dispersion relations become the dispersion relation of the upper-hybrid wave.