Limiting current of axisymmetric relativistic charged-particle beam propagating in strong axial magnetic field in coaxial drift tube

Abstract

In the strong axial magnetic field approximation, we calculate the space-charge limited (SCL) current of axisymmetric relativistic charged-particle beam in a coaxial drift tube of finite length. Results are compared to analytical estimates and numerical modeling of SCL current in the infinitely long drift tube. For the infinitely long drift tube, which inner conductor is biased and the outer conductor is lined with a finite-width dielectric insert, analytic approximations for the SCL current in the bias voltage are developed.

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

“…Considering the simplest case of the grounded conducting drift tube walls (cf., [11]), we apply the following homogeneous boundary conditions for solutions to (1):…”

“…Following an approach of estimating SCL currents advocated in [5] (see also [11]), we initially consider (1), where on its right-hand side β is rendered constant, i.e., as a linear PDE (˜ 0 (r ) = 0 (r ; 0)). Then, it can be easily solved by the method of Green's function.…”

“…These provide a useful limit to the finite length circular cylindrical geometry. Therefore, in the linear approximation, one can write an analytical expression for the (dimensionless) scalar potential distribution ( f = qϕ/(m q c 2 )) induced by an annular, finite thickness, axisymmetric relativistic electron beam in a finite length coaxial drift tube analogously to that in an unbounded one [8], [11]…”

“…E STIMATES of space-charge limited (SCL) current in planar diode [1], [2], circular cylindrical [3]- [5], and coaxial [6]- [8] geometries for (relativistic) charged-particle beams propagating in the strong guide magnetic field provide reasonable evaluation for SCL current values of pulsed (relativistic) charged-particle beams used in various modern applications (see [9], [10] and references in [11]). It turned out that the question of the scalar potential transverse distribution is of a paramount importance to such estimates.…”

“…Earlier, several authors studied the SCL current of relativistic charged-particle beams propagating in unbounded (i.e., long) in the direction of the beam transport cylindrical [13] and coaxial drift tubes [14], [15] in the strong guide magnetic field. We proposed simple but reliable analytical and numerical estimates of SCL current of annular relativistic finite thickness charged-particle beams propagating in long (unbounded) coaxial drift tubes, which may also have dielectric inserts lining the tube coaxial conductors and a bias voltage applied between the inner and outer conductors of the drift tube, in the strong magnetic field approximation [8], [11]. Some researchers have found analytical and developed numerical estimates of the charged-particle beam SCL current in finite in the (longitudinal) direction of the beam propagation (i.e., bounded) cylindrical drift tubes [12], [16]- [20].…”