First-order focusing and energy resolution optimization of a biased paracentric hemispherical spectrograph

The focusing properties and energy resolution of a hemispherical deflector analyzer (HDA) with a mean radius R = 101.6 mm and large electrode inter-radial distance Delta R = R-2 - R-1 = 58.4 mm are investigated as a function of entry position R-0 and bias (V) over tilde (0) equivalent to (V) over tilde (R-0). Electron optics simulations show that impressive improvements in energy resolution can be attained for particular empirically determined combinations of R-0 and (V) over tilde (0) values far from the conventional HDA entry values of R-0 = (R) over bar and (V) over tilde (0) = 0, without the use of any type of fringing field correctors. This behaviour is a direct result of the lensing properties of the strong fringing fields at the HDA entry, hitherto unexplored, which can be used to restore or even improve the first order focus conditions in a controlled way as shown here. (C) 2008 Elsevier B. V. All rights reserved.