A dispersion-free radial transmission line (“DFRTL”) preferably for linear accelerators, having two plane conductors each with a central hole, and an electromagnetically permeable material (“EPM”) between the two conductors and surrounding a channel connecting the two holes. At least one of the material parameters of relative magnetic permeability, relative dielectric permittivity, and axial width of the EPM is varied as a function of radius, so that the characteristic impedance of the DFRTL is held substantially constant, and pulse transmission therethrough is substantially dispersion-free. Preferably, the EPM is divided into concentric radial sections, with the varied material parameters held constant in each respective section but stepwise varied between sections as a step function of the radius. The radial widths of the concentric sections are selected so that pulse traversal time across each section is the same, and the varied material parameters of the concentric sections are selected to minimize traversal error.