c c A Toroidal Spectrometer for Photoionization Studies J Wightman 1, S Collins 1, G Bagley 1, G Richmond 1, C Dawson 1, S Cvejanovic 1, D Seccombe 2, and T Reddish 2 1 Physics Department, University of Newcastle, Newcastle upon Tyne, U.K., NE1 7RU 2 Physics Department, University of Windsor, 401 Sunset Ave, Windsor, Ontario, Canada, N9B 3P4. † Web-Site: Introduction Toroidal Photoelectron Spectrometer We have developed a photoelectron-photoelectron multi-coincidence spectrometer in which the two electrons, of specified energies, are detected over a wide range of emission angles. The spectrometer based on a toroidal geometry, which has properties ideally suited for measuring electron angle distributions. Toroidal analysers have the capability to energy select the photoelectrons while preserving the initial angle of emission. As a direct consequence of their focusing properties, the angular distribution of the electrons is mapped directly on to the detector. A schematic diagram of the apparatus is shown, indicating the relative orientation of the two partial toroidal analysers and their respective detectors. The electrostatic analysers are independent, i.e. they are able to detect dissimilar electron energies, with different resolutions. Electrons emerge from central interaction region defined by the intersection of the photon and gas beams. Photoelectrons emitted in the plane orthogonal to the photon beam that enter the analysers are focused at the toroidal entrance slit. Electrons of a specific energy traverse the gap between two toroidal surfaces to the exit slits of each analyser. The exit lenses accelerate and re- focus the energy-resolved electrons to their respective two-dimensional position-sensitive detectors. The final images are circular arcs in shape (with circle centres on the photon axis), in which the position around the perimeter is directly related to the initial azimuthal photoelectron emission angle. This emission angle is of course relative to the light polarisation direction. The multi-coincidence capability can be realised as electrons arriving anywhere on one detector can be correlated with electrons detected simultaneously anywhere on the other detector. This enables independent angular distributions to be measured concurrently. This capability is one of the novel features of the apparatus and is a great asset in compensating for the small photodouble ionization, ( ,2e), cross sections. Electron Lenses (Left) A scale diagram showing the entrance lenses and target region in the spectrometer in the radial - or energy-dispersive - plane. In the diagram, the photon beam enters the interaction region from above and the flux is monitored with an aluminium photodiode. The entrance lenses are the slits formed by a series of coaxial cylindrical surfaces of increasing radii. The acceptance angle in the radial plane is  8  and the slit width variation among the lens elements is also shown. (Right) A scale diagram of the exit lens which transports the angle-dispersed, energy-resolved electrons from the exit of the toroidal analyser to the two- dimensional position-sensitive detector. The elements are formed from slits in the curved surfaces on a series of co- axial cones and the electron beam impinges on the first of two microchannel plates at an angle of 52  to the normal. T h e o r y 3D Geometry Characterised by: Cylindrical radius a, Spherical radius b, and Deflection Angle . In principle, toroidal analysers can be made to focus simultaneously in both in energy and angle. Toroids are the ‘topological link’ between hemispherical (c = 0) and 127  cylindrical (c =  ) analysers Toffoletto et al, Nuc Inst & Meth B12 (1985) Cylindrical Radius a (Electron Lenses not shown) Energy-Dispersive Preserves Angular Information Design Notes:  Entrance / Exit Lenses – Cylindrical / Conical Symmetry  Require ‘small’ interaction region –relative to ‘cylindrical radius’  Electric field termination – lenses and toroids  Needs rigorous 3-D mechanical alignment!  Rejection of metal-scattered electrons  Requires calibration (angular scale and efficiency) Interaction Region Spherical Radius b Figure 1 A schematic diagram showing the configuration of the two (partial) toroidal analysers along with lines indicating central trajectories of electrons with a selection of emission angles. (The electron lenses are not shown for reasons of clarity). Figure 2: The mechanical acceptance angles within the perpendicular plane are 100  and 180 , but these are reduced to 60  and 140  respectively, due to electric field termination effects within the electron optics. The acceptance angle out of the perpendicular plane is ~  8 . Reddish et al Rev. Sci. Instrum. 68 (1997) 2685 Multilayered Conical Gas Jet Problem: Hypodermic needle not perpendicular to the detection plane. Solution: Gas jet coaxial with photon beam. However, larger surface area of metal- hence the potential for more background noise. Central hole  =4mm 3 Layers - 90 grooves Each 0.25mm wide and ~25 mm long, with tilt angles of: 55 , 45  and 35  for layers 1-3. Gas focuses at 2-3mm away from exit face. Seccombe et al (2001) Rev Sci Instrum Photoelectron Angular Distributions The differential cross section in perpendicular plane with S 2 = 0 is: a)determine the degree of polarisation of the light source, b)determine the angular extent of the image c)derive a normalisation curve, for each photoelectron energy, to correct the beer Red Analyser Angle Blue Analyser Angle Energies of detected electrons set by spectrometer (calibrated by other methods). Angles given by position around the perimeter of circular arc-shaped images. Grid size determined after the experiment – subject to available statistics. Angular scale and efficiencies are determined and applied to the data. Angular map of Raw Coincidence Data E 1, x 1, y 1, E 2, x 2, y 2, and  t recorded at each photon energy. True coincidence count rate: He ~ 1s -1, D 2 ~ 1min -1 (integrated over all angles)  = +2  = 0  = -1   S 1 = +1 where  (E) = Asymmetry parameter (-1  +2), and S 1 is a Stoke’s parameter giving the degree of linear polarization. He + n = 1 state has a  of 2 for all photoelectron Energies (i.e: cos 2  distribution). He + n = 2 state has variable , and acts as important consistency check. Measurements are made regularly throughout the data collection process and are used to: Data from: Wehlitz et al J. Phys. B., 26 (1993) L783 measured spectra for the differences in detection efficiency as a function of emission angle. Electron-Electron Coincidences Detector Images and Coincidence Peak Image from the small (60  - red) analyser Image from the large (180  - blue) analyser Photoelectron angular distributions from single ionisation processes can be imaged directly on a position-sensitive detector.  Toroidal analyser gives ‘simultaneous’ view of physically useful angular range.  Record angular image while scanning photoelectron energy. Angular distribution surface plots. The strong variations in the distributions are due to resonance interference, which are also shown in the more usual  parameter form. Wightman et al J. Elec. Spec. 95 (1998) 203 Angle-Dispersed Photoelectron Spectroscopy Kr + 2 P 3/2 Kr + 2 P 1/2 He D2D2 Photodouble Ionization of Helium and D 2 with E 1 = E 2 = 10eV, S 1 = 0.67 Characteristic two lobes with node at  12 = .  1 = 132°  1 = 98° The results obtained have extended our theoretical understanding of fundamental processes in atomic and molecular physics and are providing stringent tests for emerging theories Reddish et al Phys Rev Letts (1997) , Wightman et al J Phys B (1998) Seccombe et al J Phys B 35 (2002) 3767 Funding Agencies: Graduate Students Working on Project