One-Dimensional Semianalytical Model for Optimizing the Standing-Wave Direct Energy Converter

A method to optimize the spacing of decelerator electrodes in the standing-wave direct energy converter has been developed. The standing-wave direct energy converter is introduced as a simplified version of, and possible milestone toward, the traveling-wave direct energy converter to facilitate a general understanding of the physics of the traveling-wave direct energy converter, as well as to simplify the modeling and results. The standing-wave direct energy converter may also stand alone as an alternative to the traveling-wave direct energy converter. The method developed takes advantage of analytical simplifications in capacitance calculations to avoid the use of a computational mesh, thereby modeling the standing-wave direct energy converter system with low simulation runtimes while using explicit numerical methods to advance groups of ions, referred to as ion bunches. The optimization scheme returns the optimal electrode spacing and circuit resistance value given the inputs of the initial ion energy, ion bunch density, operating frequency, decelerator electrode radius, and number of decelerator electrodes. The method approximates the ion bunches as point charges on the axis of the device, and the limitations of this approximation are considered. The expansion of the ion bunch is treated analytically and imposes a limiting tradeoff between the density of the ion bunches and the duration of ion deceleration. Performance trends and other tradeoffs are also presented.