Abstract
Abstract A method based on the paraxial ray equation is described for obtaining solutions to the equations of space-charge limited (low for electrostatic systems. According to usual practice any two parameters—voltage, curvature, and infinitesimal beam thickness—are prescribed along a central trajectory, and then the remaining parameters are found from the paraxial ray equation. The flow about the central trajectory is then found by solving for a curvilinear coordinate system satisfying the boundary conditions and with coordinate axes coinciding with the emitter and central trajectory. This is done by solving a set of ordinary differential equations derived from the paraxial ray equation. These are then combined according to a power series expansion to yield the complete flow solution anywhere along the central trajectory. The focusing electrodes are found by the method of analytic continuation. An ion propulsion gun designed by this method is described.
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