An Electrostatic Storage Ring for Low Energy Electron CollisionsT 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, UKIntroductionA 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 ms have been observed, corresponding to ~200 orbits.RecyclingThe 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 RecyclingStandard matrix methods are used to predict the trajectories of charged particles within storage rings.www.uwindsor.ca/reddishElectrostatic thick lens. Focal lengths: f1 and f2; mid-focal lengths: F1 and F2; position of target and image: P and Q, respectively. K1 = P F1 ; K2 = Q F2.where and L are real. Employing the two expressions for Mss, as described in [2], results in:In any real system the lens geometry is fixed and the lens parameters f1, f2, K1, K2, 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. Mss can be determined as the product of the transfer matrices for smaller sections of the storage ring. Hence Mss= MstMts, where Mst is the transfer matrix for the source to target section of the storage ring and Mts, that for the target to source section.Under symmetric operating conditions the potentials, V3, of the source and interaction regions are equal. Additionally the potentials of the top and bottom hemispheres, V1, are the same and the potentials, V2, are the same for all four lenses. Therefore the ERS is symmetric in both reflection planes A and B (see schematic diagram) and Mst is equal to Mts. Mst = m2mhm1, where m1, mh, and m2 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.Below is a mosaic plot showing the logarithm of ERS yield as a function of storage time and V2 for V3/V1 = 2. There are several regions of stability, the strongest at V2 = 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 (V2t) and bottom (V2b) 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 V1t = 9V, V1b = 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 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.

Box sizes with text.Hit to start anew line of text.

Adjust the width of the box to change the paragraph width. Box's height adjusts according to text.

HDA 2

x Displacement (mm)

Target

Lens 1

HDA 2

HDA 1

HDA 1

Source

Lens 4

Lens 2

Lens 3

y Displacement (mm)

Box sizes with text.Hit to start anew line of text.

30

120

140

130

90

100

110

V2

0

20

150

Time (ms)

(2,1)

(5,2)

(3,1)

Mode

(3,2)

160

V3/V1 = 2

(7,2)

(4,1)

10

0