Abstract
This paper discusses the extension to different electron beam aspect ratio of the Child-Langmuir law for the maximum achievable current density in electron guns. Using a simple model, we derive quantitative formulas in good agreement with simulation codes. The new scaling laws for the peak current density of temporally long and transversely narrow initial beam distributions can be used to estimate the maximum beam brightness and suggest new paths for injector optimization.
Highlights
This paper discusses the extension to different electron beam aspect ratio of the Child-Langmuir law for the maximum achievable current density in electron guns
Modern photoguns have made a tremendous impact on the range of applications of electron accelerators with the improvement of the source beam brightness by orders of magnitude with respect to previous generations of electron sources
The maximum current density in an electron source is typically given by the Child-Langmuir law (C-L, [5]) which is found by self-consistently solving the Poisson equation, the equations of motion for the electrons and the continuity equation in an accelerating gap of voltage V
Summary
In order to get a physical picture for the electric field and particle dynamics, we model the beam as formed by infinitely thin disks of surface charge density σ which are continuously emitted at the cathode plane. Equation (2) shows a dependence of the emitted current on the externally applied electric field instead of the total voltage, which is expected in the approximations of vanishingly small transverse dimensions where the anode can be considered infinitely far away from the cathode.
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