Relativistic Charged-Particle Beam Space-Charge Limited Current in Finite Length Coaxial Drift Tube

In the strong axial (guide) magnetic field and uniform beam density approximations, we calculate scalar potential distribution induced by axisymmetric annular relativistic charged-particle beam in a finite-length coaxial drift tube. This scalar potential distribution allows us to find an approximate radial position at which the extremum of the scalar potential is attained in the coaxial drift tube inside the annular relativistic charged-particle beam. By knowing the approximate extremal radial position, we obtain the analytical estimate for the space-charge limited (SCL) current of axisymmetric annular (finite thickness) relativistic charged-particle beam propagating in strong axial magnetic field in a finite length coaxial drift tube and establish a simple correspondence of this result to that in a long coaxial drift tube. A comparison of numerical nonlinear calculations and the analytical estimate for the SCL current in the finite-length coaxial drift tube is also given.