1. An Electrostatic Storage Ring for Low Energy Electron Collisions T J Reddish †, D R Tessier †, P Hammond *, A J Alderman *, M R Sullivan †, P A Thorn † and F H Read ‡ † Department of Physics, University of Windsor, Windsor, Canada N9B 3P4 * School of Physics, CAMSP, University of Western Australia, Perth WA 6009, Australia ‡ School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK Introduction A racetrack shaped, desk-top sized electrostatic storage ring has been developed [1]. The apparatus is capable of storing any low energy charged particle (i.e. electrons, positrons, ions) and in the longer term, will be used for ultra-high resolution electron spectroscopy. We are currently investigating the performance of the spectrometer using electrons and hence refer to the system as an Electron Recycling Spectrometer (ERS). We will shortly be extending this design concept to ions. Specifications Orbital circumference of the storage ring is 0.65m. Typical orbit time is 250ns – 350ns for electrons, depending on energy. Electrons energies at the interaction region ≤ 150 eV. Storage lifetimes of ~50  s have been observed, corresponding to ~200 orbits. Photo of the apparatus. Recycling The sharp peaks in the spectrum below correspond primarily to fast electrons that have elastically scattered from helium target gas. (A background signal from metastable helium ions has been removed form the spectrum.) Each peak corresponds to a further orbit of the initial injection pulse and clearly shows recycling continuing for 48  s. Also highlighted in this spectrum is the decaying amplitude of the electron signal. The (x 200) insert shows the recycling peaks uniformly decaying in amplitude and characterized by a 13.6  s decay life-time. [1] Tessier et al., Phys. Rev. Lett., 99 253201, 2007. Criteria For Stable Recycling Lens 1 Transfer Matrix:HDA Transfer Matrix: Lens 2 Transfer Matrix: Standard matrix methods are used to predict the trajectories of charged particles within storage rings. www.uwindsor.ca/reddish Electrostatic thick lens. Focal lengths: f 1 and f 2 ; mid-focal lengths: F 1 and F 2 ; position of target and image: P and Q, respectively. K 1 = P – F 1 ; K 2 = Q – F 2. where θ and L are real. Employing the two expressions for M ss, as described in [2], results in: From circular accelerator theory, M ss can also be expressed as: In any real system the lens geometry is fixed and the lens parameters f 1, f 2, K 1, K 2, defined in the Figure above, are controlled by the applied voltages. Physically, this signifies both the overall linear and angular magnifications are  1, and therefore do not diverge with multiple orbits. M ss can be determined as the product of the transfer matrices for smaller sections of the storage ring. Hence M ss = M st M ts, where M st is the transfer matrix for the source to target section of the storage ring and M ts, that for the target to source section. Under symmetric operating conditions the potentials, V 3, of the source and interaction regions are equal. Additionally the potentials of the top and bottom hemispheres, V 1, are the same and the potentials, V 2, are the same for all four lenses. Therefore the ERS is symmetric in both reflection planes A and B (see schematic diagram) and M st is equal to M ts. M st = m 2 m h m 1, where m 1, m h, and m 2 are defined below. ( H,m ) modes describe a trajectory that, if paraxial, retraces itself every H/m orbits. In [2] we show that odd H, even m modes are unstable due to angular aberrations in the hemispherical analysers. Peak width (FWHM) variation with orbit number for the TOF spectrum to the left. After ~ 5 orbits the width varies according to the equation given with W 0 = 45.31 (  0.01) ns and  T = 0.74 ns (  0.01), See [1] and Pedersen et al, Phys Rev A 65 042704 (2002). Half orbit transfer matrix: f2f2 f1f1 K1K1 K2K2 Above is a plot of characteristic lens parameters as a function of V 2 for V 3 /V 1 = 2 (where V 3 is the potential at the source and interaction regions, and V 1 is the potential of the hemispheres) derived from the parameterizations given by Harting and Read (Electrostatic Lenses, 1976, Elsevier). The bold blue line indicates the values of K 1 K 2 /f 1 f 2 for which the stability condition is satisfied. Two regions of stability are predicted in V 2 for symmetric operating conditions: a narrow region between ~3.1 and 6.8V and a broad region between ~86 and 159.4V. See [2] for further details. Below is a mosaic plot showing the logarithm of ERS yield as a function of storage time and V 2 for V 3 /V 1 = 2. There are several regions of stability, the strongest at V 2 = 130 V corresponding to the ( H, m ) = (2,1) mode. The other regions are also in good agreement with the predictions, as shown. See [2] for more details. We now consider asymmetric operating conditions. This is achieved by breaking the symmetry in reflection plane A. To do this we set different potentials on the lenses in the top (V 2 t) and bottom (V 2 b) halves of the ERS and/or set different pass energies to the top and bottom hemispherical analysers. The left figure below shows the predicted regions of stability for a range of lens potentials, with V 1 t = 9V, V 1 b = 18V. The blue shaded areas in the figure are regions of expected stability. The right figure below is experimental data taken with the same potentials as the theory on the left. [2] Hammond et al. N. J. Phys. 11 043033, 2009. Lens 2 is physically the same as lens 1, but traversed by the electrons in the opposite direction. The upper (x200) data insert has the exponential decay ( τ = 13.6  s) removed to highlight the recycling peaks. 464844424038363432302826242022161812148104602 5·10 5 1·10 6 2·10 6 1.5·10 6 3·10 6 2.5·10 6 Time (  s) x 20x 200 General condition for stable orbits is:, where M ss is the transfer matrix for the whole storage ring., ERS stability condition: where m and H are integers, such that 0 < m < H. Schematic diagram of the apparatus. The above figure shows the numerically computed non- paraxial trajectory of an electron undertaking multiple orbits of the ERS close to the H = 2 and m = 1 condition. Although the trajectory does not retrace itself after 2 orbits, which occurs when (2,1) is exactly satisfied, it does still produce an overall time averaged stable beam.