The Hemispherical Deflection Analyzer (HDA) consists of two concentric hemispherical electrodes held at different potentials. Charged particles of only a certain kinetic energy, called the pass energy, can pass through the electrodes at constant radius, so the system acts as a narrow band KE filter.

Cut-away of idealized HDA showing 1000 eV electron (red) and 900 and 1100 eV electrons (blue) flying through.

The HDA is an approximation of an idealized HDA, also called a spherical capacitor, consisting of two concentric spherical electrodes held at different potentials. The spherical capacitor has a simple analytic formulas for potential and electric field at radius :

where

The pass energy at is , for particle charge .

Typical GEM files for ideal HDAs (spherical capacitors) are given below. Here, = -200000, = -2000, = 100, = 1000 eV, and = 0. The inner and outer radii are = 80 mm and = 120 mm.

Here is a typical 2D GEM file:

; sc2d.gem
pa_define(130,130,1,cylindrical,xy)
; outer electrode, R2
e(-333.3333) { fill { notin  { circle(0,0,119) } } }
; inner electrode, R1
e( 500.0000) { fill { within { circle(0,0,80) } } }

Here is a typical 3D GEM file:

; sc3d.gem
pa_define(130,130,130,planar,xyz)
; outer electrode, R2
e(-333.3333) { fill { notin  { sphere(0,0,0,119) } } }
; inner electrode, R1
e( 500.0000) { fill { within { sphere(0,0,0,80) } } }

Notice that the radius in the “notin” command is one grid unit less than R2 for improved accuracy.

Potential Energy (PE) surface of idealized HDA, showing 1000 eV electron (red) and 900 and 1100 eV electrons (blue) flying though.

See also

• Investigation of the accuracy of ion optics simulations using Kepler orbits in a spherical capacitor T.J.M. Zouros, Omer Sise, F.M. Spiegelhalder, and David J. Manura. International Journal of Mass Spectrometry. 2006.
• Surface Analysis Forum: HDA - Hemispherical Deflection Analyser
• Zouros, Benis, Schauer, Charged particle trajectories in an ideal paracentric hemispherical deflection analyser. AIP Conference Proceedings, Volume 576, Issue 1, pp. 76-79, 2001. doi:10.1063/1.1395253; online
• Zouros and Benis. The hemispherical deflector analyser revisited. I. Motion in the ideal 1/r potential, generalized entry conditions, Kepler orbits and spectrometer basic equation. Journal of Electron Spectroscopy and Related Phenomena 125 (2002) 221-248. doi:10.1016/S0368-2048(02)00137-8; online; erratum
• Zouros and Benis. Optimal energy resolution of a hemispherical analyzer with virtual entry. Applied Physics Letters 86, 094105, 2005. doi:10.1063/1.1871339; online
• Benis and Zouros. Improving the energy resolution of a hemispherical spectrograph using a paracentric entry at a non-zero potential. NIMPRA 440 (2000) 462-465 doi:10.1016/S0168-9002(99)00954-7; online
• Sise, Zouros, Ulu and Dogan, 2007, Novel and traditional fringing field correction schemes for the hemispherical analyser: Comparison of first-order focusing and energy resolution, Meas. Sci. Tech. 18 1853-1858. dx.doi.org/10.1088/0957-0233/18/7/009
• Dogan, Ulu, and Sise, 2007, Design of electron energy analysers for electron impact studies, Rad. Phys. Chem. 76 445-449. dx.doi.org/10.1016/j.radphyschem.2006.01.017
• T.J.M. Zouros. Theoretical investigation of the energy resolution of an ideal hemispherical deflector analyzer and its dependence on the distance from the focal place. Journal of Electron Spectroscopy and Related Phenomena 152 (2006) 67-77. doi:10.1016/j.elspec.2006.03.007 (http://dx.doi.org/10.1016/j.elspec.2006.06.004 erratum) corrects line shapes)
• J.H. Vilppola, J.T. Keisala, P.J. Tanskanen, and J. Huomo. Optimization of hemispherical electrostatic analyzer manufacturing with respect to resolution requirements. Rev. Sci Instrum. 64 (8), August 1993. doi:10.1063/1.1143958
• HyperPhysics: Spherical Capacitor
• Other local pages: Cylindrical Mirror Analyzer (CMA)