The Development of a Passive Electrostatic Electron Recycling System

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

D.R. Tessier1, Y. Niu1, D.P. Seccombe1,T.J. Reddish1, A.J. Alderman2, B. G. Birdsey2 , P. Hammond2, F.H. Read3

www.uwindsor.ca/reddish

RECYCLING ELECTRON PULSES

TRANSFER MATRICES AND STABILITY CONDITION

1

21212

21 1

1 ff

fm

10

01hm

2

21211

12 1

1 ff

fm

Lens 1 Transfer Matrix:Source to HDA Entrance

HDA Transfer Matrix:Mirror for ‘pass energy’.

Lens 2 Transfer Matrix:HDA Exit to Interaction Region

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.

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.

12

1ssMTr

STABILITY

• Our initial motivation was to develop an electron spectrometer capable of sub-meV energy resolution. While not loosing sight 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 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.

MOTIVATION

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!

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).

ELECTROSTATIC LENS DETAILS

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

In practice, the theoretical operational lens acceleration and focusing potentials can be related

to the above characteristic lengths via electron optical tables

and parameterisations.

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 whoseEnergy resolution increases linearly with N.

Time-dependent ENERGY FILTER!

ELECTRON RECYCLING SYSTEM

SPECIFICATIONS

Circumference ≈ 64.4 cmR inner hem= 37.5 mmR outer hem = 62.5 mm

Mean R = 50.0 mmrS (aperture) = 1.5 mm

E / Ep ≈ 3 %Average Orbit Period = 250 350 ns

The pulsed electron beam is directed onto the optic axis while the bottom hemispherical deflector analyzer (HDA) is switched to 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 it’s cyclical trajectory.

PF1

PF2

f2f1

F2F1K2K1

P Q

PP2 PP1

S

HE

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 s 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.

0 50 100 150 200 250 3001

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Top = Recycling Mode Bottom = Non-Recycling Mode

Slopes are proportional to e-t/9 and e-t/48.

s

0 2 10 6 4 10 6 6 10 6 8 10 6 1 10 50

25

50

75

100

DecayTime(s)

Pressure (Torr)

P

x 5103

Matrix methods are used to model the trajectories of charged particles within the ERS.

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KKffK

KKffKKKff

ffmmmM hst

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 above), reducing from 51 to 45 ns. After ~15s (~45 orbits) the width varies linearly with time with a gradient of ~2.15 ns/s.

ELECTRON PULSE WIDTHS

Since the Mean Free Path for the electron beam is:

)(

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EPn

The decay time () is related to and a characteristic (mean) speed, : Pv

1

Rediscovered circular

accelerator physics: Betatron

Oscillations!

ERS uses gold-plated oxygen free copper components.

The graph of the measured asymptotic He+ ion decay rates as a function of target gas pressure. They can be modeled with the indicated reciprocal equation; the number of electron orbits is presently limited by the ERS operating pressure, rather than other loss mechanisms. 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.

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.

0 4 8 12 16 20 24 28 32 36 40 44 4810

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s

0 10 20 30 40 500

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0 2.5 540

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PeakWidth (ns)

Time (s)

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48

5 105

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1.5 106

2 106

2.5 106

3 106

x20 x200 The upper (x200) data insert has the exponential decay (t = 13.6s) removed to highlight the recycling peaks.

46 48444240383634323028262420 2216 1812 148 104 60 2

5·105

1·106

2·106

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3·106

2.5·106

Time (s)

16124 810

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1·103

1·104

1·105

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1·106

20 2824 32 36 40 44 48s

0

x 20 x 200

Ceramics

HDA Entrance

Interaction Region

F1

P

Q

Apertures

V1 V2 V3 V4 = VPass

Mesh

D

HemisphericalDeflector Analyzer

Electron Lenses

ElectronSource

(Pulsed)

F.C.

“Recycling”Electron Beam

Interaction Region

Gas Beam (emerging out

of page)

C.E.M.(B)

C.E.M.(C)

C.E.M.(D)

C.E.M.(A)

HemisphericalDeflector Analyzer

(Pulsed)