Three Dimensional Theory and Simulation of an Ellipse Shaped Charged-Particle Beam Gun

A three-dimensional (3D) theory of non-relativistic, laminar, space-charge-limited, ellipse-shaped, charged-particle beam formation has been developed recently [1] whereby charged particles (electrons or ions) are accelerated across a diode by a static voltage differential and focused transversely by Pierce-type external electrodes placed along analytically specified surfaces. The treatment is extended to consider whether the diode geometry solutions thus obtained are robust to perturbations and limitations of the sort likely to be encountered in a realistic device: finite extent, part misalignment, tolerances for mechanical and thermal stresses, etc. Analytic and semi-analytic estimates are presented along with simulations utilizing the 3D trajectory code, OMNITRAK [2]. It is found that the elliptic-beam solution is quite stable and robust, and its desirable properties can be maintained in a realistic diode.