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Practical analytic equations, for the ideal field, and numerical results from SIMION simulations, for the fringing field, are presented for the exit radius rπ and transit time tπ of electrons in a hemispherical deflector analyzer (HDA) over a wide range of analyzer parameters. Results are presented for a typically dimensioned HDA with mean radius R-=101.6 mm and interradial separation ΔR=R2-R1=58.4 mm able to accommodate a 40 mm diameter position sensitive detector (PSD). Results for three different entry positions R0 are compared: R0=R- (the conventional central entry) and two displaced (paracentric) entries: R0=82.55 mm and R0=116 mm. Exit spreads Δrπ, Δtπ and base energy resolution ΔEB are computed for HDA pass energies E0=10, 100, 500, and 1000 eV, entry aperture sizes Δr0≤1.5 mm, entry angular spreads |αmax|≤5°, and an electron beam with relative energy spread δE/E0≤0.4%. Overall, under realistic conditions, both paracentric entries demonstrate near ideal field behavior and clear superiority over the conventional entry at R0=R-. The R0=82.55 mm entry has better absolute energy and time spread resolutions, while the R0=116 mm has better relative energy resolutions, both offering attractive alternatives for time-of-flight and coincidence applications where both energy and timing resolutions are important.

Position, Energy, and Transit Time Distributions in a Hemispherical Deflector Analyzer with Position Sensitive Detector