A dispersion-free radial transmission line preferably for linear accelerators, having two plane conductors each with a central hole, and an electromagnetically permeable material between the two conductors and surrounding a central channel connecting the two central holes. At least one of the material parameters of relative magnetic permeability, relative dielectric permittivity, and axial width of the permeable material is varied as a function of radius, so that the characteristic impedance of the radial transmission line is held substantially constant, and pulse transmission through the radial transmission line is substantially dispersion-free. Preferably, the electromagnetically permeable material is divided into concentric radial sections, with the varied material parameters held constant in each respective section but stepwise varied from section to section 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 so that the traversal error is minimized.
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