Finite difference computer simulation of two diverging electrostatic analyzers: The soft particle spectrometer and the spectrographic particle imager

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Abstract
We have completed a finite difference computer simulation of two diverging electrostatic analyzers. In both analyzers, the deflecting plates are cylindrical surfaces which flare out from each other like two arms of a hyperbola. The analyzers are the soft particle spectrometer (SPS) and the spectrographic particle imager (SPI), which correspond, respectively, to an energy spectrometer and an energy spectrograph. The simulation consists of two steps: (1) a finite difference computation of the electrostatic potential field inside the instrument; and (2) a ray-tracing computation in which many particles are ray traced through the instrument and statistics are gathered on the particles that make it to the collecting region. In both cases, the simulation is two-dimensional, restricted to the central plane of the instrument. This limitation turns out to be unimportant because the statistics acquired during simulation agree well with experimentally acquired statistics for each instrument. In the case of SPI, the computer simulation has been used to provide information on how variation of geometric parameters affects the quantities that describe a good spectrograph.