A Passive Electrostatic Electron Recycling Spectrometer

1
A Passive Electrostatic Electron Recycling
Spectrometer
D.R. Tessier1, Y. Niu1, D.P. Seccombe1,T.J.
Reddish1, A.J. Alderman2, B. G. Birdsey2 , P.
Hammond2, F.H. Read3
1. Department of Physics, University of Windsor,
Windsor, Ontario, N9B 3P4, Canada 2. School of
Physics, University of Western Australia, Crawley
WA 6009, Australia 3. The School of Physics and
Astronomy, University of Manchester, Manchester,
UK, M13 9PL
TRANSFER MATRICES AND STABILITY CONDITION
MOTIVATION

• Our initial motivation was to develop an electron
  spectrometer capable of sub-meV energy
  resolution. While not loosing slight of that aim,
  we have created a desk-top sized
  charged-particle storage ring using only passive
  electrostatic components.
• The physical geometry is that of a race-track,
  but the energy variation around the ring means it
  is more like a rollercoaster. Moreover, the
  collision energy - and the energy resolution -
  can be varied while still maintaining storage.
• Electrons that do not interact with the target
  gas are recycled and given multiple
  opportunities for scattering.
• The Electron Recycling Spectrometer (ERS) is
  capable storing more exotic charged particles,
  such as positrons, polarised electrons, ions, and
  other low energy particles with tenuous beams.

Electrostatic thick lens with focal lengths f1
and f2 and the mid-focal lengths F1 and F2 is
shown in the diagram (right), P and Q refer to
the positions of the target and the entrance to
the HDA, respectively. K1 P F1 K2 Q F2
Matrix methods are used to model the trajectories
of charged particles within the ERS.
Collision cross sections with gases are small!
After all the effort to create a mono-energetic
electron beam...most miss the target! Can we use
the system more efficiently? Then why not
recycle the remainders!
In practice, the theoretical operational lens
acceleration and focusing potentials can be
related to the above characteristic lengths via
electron optical tables and parameterisations.
Lens 1 Transfer Matrix Source to HDA Entrance
HDA Transfer Matrix Mirror for pass energy.
ELECTRON RECYCLING SYSTEM
The pulsed electron beam is directed onto the
optic axis while the bottom hemispherical
deflector analyzer (HDA) is switched to its non
deflecting mode. The electron beam travels to
the top HDA, traverses it and then passes through
the interaction region where each electron has a
chance to collide with the target gas. Those that
do not scatter continue on to the bottom HDA (now
switched to its deflecting mode) to restart its
cyclical trajectory.
Lens 2 Transfer Matrix HDA Exit to Interaction
Region
STABILITY
Physically, this signifies both the overall
linear and angular magnifications are ?1, and so
do not blow up with multiple (N) orbits.
Furthermore, conservation of phase space
requires the determinant of the transfer matrix
to be unity when there is no overall acceleration.
Transfer matrix for half an orbit (2 lenses 1
HDA)
Transfer matrix for 1 complete orbit is Mss
Mst Mst Make Mss the unit matrix for the
trajectories to retrace their paths.
TYPE N OPERATION MODE Remarkably stable
even when Aberrations and Energy Dispersion are
considered. Energy resolution simply the
resolving capability of one orbit. Ignoring
higher order aberration terms, the energy
resolution is stable with N. STORAGE RING!
TYPE 1 OPERATION MODE Inherently unstable
sensitive to aberrations. If the effects of
aberrations in the lenses are significantly less
than the hemispherical energy dispersion, one
could envisage a system whose Energy resolution
increases linearly with N. Time-dependent ENERGY
FILTER!
Rediscovered circular accelerator physics
Betatron Oscillations!
SPECIFICATIONS Circumference 64.4 cm R inner
hem 37.5 mm R outer hem 62.5 mm Mean R 50.0
mm rS (aperture) 1.5 mm DE / Ep 3 Average
Orbit Period 250 ? 350 ns
ELECTROSTATIC LENS DETAILS
One of the four identical electrostatic lenses in
the ERS is displayed, (left). These cylindrical
lenses are based on the P/D Q/D 3.0 lens
geometry, where D 15mm is the lens diameter.
The grey ceramic spacers provide rigorous
mechanical alignment and electrical insulation.
The cylindrical interaction region element
contains 4 symmetrically positioned conical holes
(2 are shown in this cross section view) that are
electrically shielded via fine meshes. Gas enters
this region via a copper hypodermic needle and
preferentially escapes through the large conical
holes, rather than the 2 electron optical
apertures (radius 1.25 mm).
HELIUM ION RESULTS
Helium time of flight ion distributions (right)
for (i) non-recycling (lower trace) and (ii)
recycling (upper trace) modes. The data have been
accumulated for equal amounts of time with a gas
pressure of 5 x10-7 Torr. A small, prompt UV
photon signal (not shown) defines t 0 and the
ions begin to appear 6 ms later. The asymptotic
linear decay rates are indicated and the ratios
of the net counts is 16. If one considers all the
data below 10 counts as noise, then there are
essentially no ions after t 60 ?s in the
non-recycling mode. Consequently, ions detected
at t 320 ?s in the recycling mode originate
from stored electrons in the ERS between 260 and
314 ?s. For these spectra the electron orbit time
was 240 ns hence the long ion decay tail
implies that the electron beam (mean energy 20
eV) has achieved over 1000 orbits, a distance of
650 m. The characteristic decay time is 48 ?s
(for this pressure) although ions are still
observable at over 6 times this time value.
ELECTRON PULSE WIDTHS
Since the Mean Free Path for the electron beam is
The decay time (?) is related to ? and a
characteristic (mean) speed, ?
ERS uses gold-plated oxygen free copper
components.
The peak width (full width at half maximum, FWHM)
variation with time for the electron signal shown
below. The peak width becomes measurably narrower
within the first 5 orbits (which have the
highest statistical quality see insert),
reducing from 51 to 45 ns. After 5 orbits the
width varies according to the equation given with
W0 45.31 (? 0.01) ns and ?T 0.74 ns (?
0.01). This diffusion equation assumes a
decoupling between the source and ERS temporal
properties, and an absence of perturbations
influencing the recycling beam. (See
Pedersen et al, Phys Rev A 65 042704 (2002))
The graph of the measured asymptotic He ion
decay rates as a function of target gas pressures
spanning from 3.6x10-7 to 8.0x10-6 Torr . They
can be modeled with the indicated reciprocal
equation. Evidently the number of electron orbits
is presently limited by the ERS operating
pressure, rather than any other loss mechanism.
Further improvements could be made by using a
localized gas source (e.g. a supersonic beam)
and differential pumping.
CPO Electron Optical Simulationof the ERS.
1107
RECYCLING ELECTRON PULSES
1106
1105
The spectrum (right) shows a log plot of the raw
data consisting of sharp peaks due to electrons
and a broad underlying continuum of metastable
helium atoms. This background is removed in the
spectrum below, which highlights the decaying
amplitude of the electron signal. The (x200)
insert shows the uniformly decaying long-tail
seen in the other plot, characterized by a 13.6
?s decay time. The sharp peaks corresponds
primarily to fast electrons that have elastically
scattered off the helium target gas. It has the
time structure of the stored beam, such that each
peak corresponds to a further orbit of the
initial injection pulse.
1104
1103
100
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48
0
ms
3106
2.5106
x 20
x 200
The upper (x200) data insert has the exponential
decay (t 13.6ms) removed to highlight the
recycling peaks.
2106
1.5106
1106
5105
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Time (ms)
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