Characterization of spectral slit functions of magnetic particle spectrometers

Magnetic spectrometers are routinely used to measure high-energy (keV to MeV) charged particles produced by experiments using high power lasers. Understanding magnetic spectrometer spectral slit functions are critical to estimate the spectrometer's resolving power (E/dE), which is needed to forward model energy spectra prior to the experiment, optimize the spectrometer setup to a desired resolution, and fit experimental data afterward. Spectral slit functions vary with spectrometer magnetic field, slit size, slit shape, and image plate geometry. We have developed a model to determine the energy dispersion curve for particles entering at different points and angles on the entrance slit for an arbitrary spectrometer geometry and magnetic field profile. This information is then used to construct the multiple dispersion curves needed to compute spectral slit functions at any given particle energy. As an example, we show computations for the electron-positron-proton spectrometer on the National Ignition Facility with peak fields of 0.3, 0.6, and 0.9 T and their corresponding spectral slit functions. We also find that each particle energy has a focal point within the spectrometer where the energy resolution is near perfect. Finally, we compute an optimal image plate geometry such that resolving power is maximized across all energies.