Three-Dimensional Theory and Simulation of Non-Relativistic Elliptic Electron and Ion Beam Generation

Summary form only given. A theory of non-relativistic, laminar, space-charge-limited, ellipse-shaped charged-particle beam formation is presented. In the elliptic diode, electrons or ions are accelerated by a static voltage differential and transversely focused by external electrodes. The electrode surfaces are derived as equipotentials external to the beam using a Laplace transform - Mathieu function formulation of the electrostatic potential. Three-dimensional simulations utilizing the trajectory code OMNITRAK are performed, confirming the analytic predictions of a high-quality, laminar beam. The elliptic diode can aid in the design of high-efficiency sheet-beam microwave sources as well as in heavy ion beam devices. In particular, the theory is applied to the design of a 6:1 elliptic electron beam for a 200 W, 2 GHz amplifier. It is also applied to the design of a 3:2 elliptic heavy ion beam for high-energy density physics research. For these applications, the theoretical treatment of the diode is extended to consider the perturbative effects of anode hole lensing and finiteness and nonuniformities of beam-forming electrodes. Considerations with regard to beam matching into a periodic magnetic focusing lattice are also discussed