Multipactor in a coaxial transmission line. I. Analytical study

Theoretical considerations of the electron multipactor have mostly been restricted to the simplified case of plane-parallel geometry with a uniform field. However, a nonuniform field may not only affect the results quantitatively, but may also lead to qualitatively new effects. In the present work, the effects of a nonuniform radiofrequency field on the properties of multipactor initiation are analyzed in the case of a cylindrical coaxial transmission line. A useful approximate solution of the nonlinear differential equation of motion for the electrons is derived and simple analytical estimates are developed to show that in this system the multipactor mechanism becomes qualitatively different for sufficiently small inner coaxial radii. When the inner radius is of the order of the outer one, the multipactor properties are very similar to those of its counterpart in plane-parallel geometry. However, when the inner radius is less than a certain threshold value, single-surface multipactor becomes possible.