Limiting current of axisymmetric relativistic charged-particle beam in coaxial drift tube

On the basis of numerical modeling, we discuss in the strong axial magnetic field approximation limiting current definitions of a charged-particle beam in finite and infinitely long coaxial drift tubes. A method of successive approximations in the bias voltage applied to the inner conductor of drift tube that allows one in the strong axial magnetic field approximation to obtain analytical estimates of the limiting current of axisymmetric charged-particle beam of finite thickness propagating in an infinitely long coaxial drift tube, which outer conductor is lined with a finite-width dielectric insert, is put forward. The proposed technique takes into account that the radial position of the extremal value of scalar potential inside the beam even in the strong magnetic field approximation depends on the geometry of infinitely long coaxial drift tube, transverse dimensions of the charged-particle beam and dielectric liner insert of the outer conductor of drift tube, as well as on the permittivity of the insert. Using this technique, it is not difficult to obtain analogous analytical estimates if the inner conductor of drift tube is in addition lined with a finite-width dielectric insert. In the strong magnetic field approximation, we also derive corresponding analytical generalizations to the infinitely long coaxial drift tubes of the limiting current of tenuous charged-particle beam. A comparison of proposed analytical expressions and limiting current definitions with results of numerical simulations is fulfilled.