Limiting current enhancements for a relativistic electron beam propagating through coaxial cylinders

An investigation of the space-charge-limited (SCL) currents for un-neutralized relativistic electron beams drifting through an infinitely long dielectrically lined coaxial cylindrical structure with a biased inner conductor is presented. To begin, an approximate limiting current expression is developed for an un-neutralized finite-width relativistic electron beam drifting through a biased coaxial cylindrical structure, which contains no dielectric liner. The SCL currents are then numerically calculated and compared to the approximation and it is shown that there is good agreement between the two. Building on this, the SCL currents are then numerically calculated when a dielectric liner, which encloses the finite-width electron beam, is present. It is shown that when a dielectric liner is present, there is a point at which increases in the SCL currents saturate and increasing the relative dielectric constant provides no additional increase in the expected SCL currents. In addition, it is demonstrated that the dielectric liner, in conjunction with the biased inner conductor, provides significant SCL current enhancements when compared to a system with no dielectric liner and no biased inner conductor. Finally, the possibility of dielectric breakdown is addressed as well as the amount of accumulated charge at the vacuum-dielectric interface.