1. Toroidal Photoelectron Spectrometer for Coincidence Studies A. Padmanabhan 1, P. A. Thorn 1, L. Zuin 2, M. A. MacDonald 2, T. J. Reddish 1 1 Physics Department, University of Windsor, 401 Sunset Ave, Windsor, Ontario, Canada, N9B 3P4. 2 Canadian Light Source, 101 Perimeter Road, University of Saskatchewan, Saskatoon, SK, Canada, S7N 0X4 † Email: reddish@uwindsor.ca Web-Site: http://www.uwindsor.ca/reddish Toroidal Analysers 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) 282-297. Cylindrical Radius a (Electron Lenses not shown) Design Notes:  Requires ‘small’ interaction region – relative to ‘cylindrical radius’  Needs electric field termination in both the lenses and toroids  Needs rigorous 3-D mechanical alignment!  Requires calibration (angular scale and efficiency) Interaction Region Spherical Radius b Energies of detected electrons set by spectrometer (calibrated by other methods). Angular grid size determined after the experiment – subject to available statistics. Angular scale and efficiencies are determined independently and applied to the data. Red Analyser Angle Blue Analyser Angle Angular map of raw electron – electron coincidence data from double ionisation of helium. E 1, x 1, y 1, E 2, x 2, y 2, and  t recorded at each photon energy. Detector Images and Coincidence Yield Image from the small (60  - red) analyser Image from the large (180  - blue) analyser Photoelectron Angular Distributions The differential cross section in perpendicular plane is: a)determine the angular extent of the image b)derive a normalisation curve, for each photoelectron energy to correct the  = +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 and is usually 1.0 for light from an undulator. He + n = 1 state has a  of 2 for all photoelectron energies (i.e: cos 2  distribution), whereas 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. Funding Agencies: Multilayered Conical Gas Jet Problem: Hypodermic needle not perpendicular to the detection plane – increased potential for systematic errors in the angular distributions. Solution: Cylindrically symmetric gas beam coaxial with photon beam; this also provides space for an extra analyser. 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 72 2550 Photon beam ● Electron Lenses (Left) A scale diagram showing the entrance lenses and target region in the spectrometer in the radial - or energy-dispersive - plane. The entrance lenses are the slits formed by a series of coaxial cylindrical surfaces of increasing radii (see right). 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 (see photo far right). Photon Beam Photodiode c c 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 the theoretical understanding of fundamental electron- correlation processes in atomic and molecular physics and provide stringent tests for emerging theories Reddish et al Phys Rev Letts (1997) 79 2438, Wightman et al J Phys B (1998) 31 1753 Seccombe et al J Phys B 35 (2002) 3767 Introduction Toroidal Photoelectron Spectrometer A photoelectron-photoelectron coincidence spectrometer has been developed 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, since toroidal analysers can be made to energy select the photoelectrons while preserving the initial angle of emission. A schematic diagram of the apparatus is shown below 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, which is defined relative to the light polarisation direction. 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. 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). Reddish et al Rev. Sci. Instrum. 68 (1997) 2685 Perpendicular Plane Geometry k   , k 1 and k 2 Future Prospects This apparatus was primarily developed to investigate electron-electron correlation in double ionization of atomic and molecular targets – a subject that continues to be of intense theoretical interest. The main challenge now is multiple particle detection - e.g. ( ,e+ion), ( ,2e+ion), ( ,3e) - using Auger and/or photoelectrons in coincidence with fragment ions on simple systems that are theoretically tractable. Such studies will be most sensitive to electron-ion correlation / dichroism / interference effects in the ionization/dissociation of light molecules. Experimentally, this requires helical / linear undulators at the Canadian Light Source, together with the continued development of detector technology.