SmithPurcell radiation and picosecond bunch diagnostics

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Smith-Purcell radiationand picosecond bunch
diagnostics

• George Doucas and Wade Allison
• Sub-Dept. of Particle Physics,
• University of Oxford

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Collaborators

• University of Oxford (J.H. Mulvey and M. Omori)
• Univ. of Essex (M.F. Kimmitt)
• Dartmouth College (J.E. Walsh, J.H. Brownell and
  H.L. Andrews)
• ENEA, Frascati (G. Gallerano, A. Doria, E.
  Giovenale and G. Messina)
• Support from Univ. of Oxford, British Council
  and Royal Society

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Outline

• Introduction
• Early experiments at Oxford and recent results
  from Frascati.
• The future (higher energy, shorter bunch, more
  theory at high g).
• Summary of where we are now.

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1. Introduction

• First observed in 1953(Phys. Rev. 92, 1069, 1953)
• The term is now used to describe radiation
  produced from the interaction of a charged
  particle beam with a periodic structure, such as
  a grating.
• Is one aspect of the effect of the
  electromagnetic field of moving charge, such as
  transition and diffraction radiation, but with
  some distinct advantages

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1. Basic relationship
q
u
xo
Dispersion relation
nl
q
l
Typically, in the far IR
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2. An elementary calculation

• A reasonably simple theory, capable of predicting
  behaviour under various experimental conditions
  is essential for any application.
• Not many papers with measured mWs on the
  graphs!!
• Treatment based on assumption that a passing
  electron induces image charges on the surface of
  the grating.
• These are then accelerated by the peaks and
  troughs of the periodic structure. (not the only
  approach!!)
• Accelerated charge produces radiation objective
  is to find the angular distribution of the
  emitted intensity I.

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2. An elementary calculation

• Final relationship, for the case of a single
  electron, at a height xo over a grating with
  period l and overall length Nl, is given by
• or
• Term R2 depends on the details of the grating
  profile ?e is the evanescent wavelength,
  ?e???
• For high ?, good coupling is possible even at
  mms distance
• For a continuous beam of current Ib, the emission
  is spontaneous and the radiated power is given
  by changing 2pe2 to 2peIb.

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3. Oxford resultsPhys. Rev. Lett., 69 (1992),
1761

• First to observe incoherent SP radiation from an
  essentially continuous, low-density relativistic
  beam.
• Limited by range of emission angles accessible
  and electron beam position jitter.
• Nevertheless, reasonable agreement with
  predictions of surface current model of radiation
  process.

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4. FrascatiPhys. Rev. Sp. Topics-Accel. Beams
5, 072802, (2002)

• Main motivation was to extend the range of
  emission angles accessible by light-collecting
  system.
• Confirm theoretical treatment by direct
  comparison of measured vs. calculated power.
• Improved experimental set-up and more reliable
  beam.
• Work supported by Royal Society.

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4. Frascati-experimental

• Microtron with discreet beam energies, starting
  at 1.8MeV, up to 5MeV, in steps of 0.8MeV.
• Most of the work at 1.8MeV (g4.52), some at
  g10.3
• Bunch length is approx. 15ps, bunch spacing
  333ps.
• Bunch train duration is approx. 5ms, with an
  average current of 200mA. Hence, each bunch has
  about 4.2x108 electrons.
• Normalized beam emittance is rather poor (
  50?mm.mrad)

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Experimental

• Signal taken to detector through polished copper
  pipe (?3m long)
• Detector is InSb electron bolometer, liquid
  helium cooled.
• Note reference point for power calculation.

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Data (g10.3)

• E4.75MeV, I120mA, 400 mesh/inch filter in front
  of detector.
• Observed power levels orders of magnitude higher
  (tens of mW) than those expected from
  incoherent theory.
• Spontaneous coherent enhancement of SP.

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Coherent enhancement

• For a bunch with Ne electrons
• there is possibility of coherent enhancement, if
  the coherence integral Scoh is not very small
• This is the bunch form factor, which depends on
  the distribution f (t) of the particles in the
  time domain.

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Coherent enhancement

• Begins to dominate as the wavelength of the
  radiation becomes comparable with the bunch
  length.
• Different assumed functions f (t) give very
  different angular distributions of coherent SP.
• Hence, coherent enhancement, not only increases
  the emitted power but it also provides a clear
  signature of the time profile of the bunch,
  through a measurement of the angular ( i.e.
  wavelength) distribution of the radiation.

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Coherence pulse shape

• Sample calculations, based on Frascati conditions
  (E4.75MeV)
• Beam size was 1x2mm and beam centroid about 2mm
  above grating.
• Assume pulse length of 16ps.
• Assume that 80 of particles are within this
  nominal length.

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Results-analysis

• Same data as before.
• Best fit for triangular shape, with 80 of
  particles inside 16ps.
• Shape is slightly asymmetric with respect to
  reference particle (t0).

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Features

• Simple experimental set-up.
• Non-intercepting, valid for any charged particle
  beam, at almost all energies.
• Ample radiated power.
• Sensitivity to the bunch length and its harmonics
  can be optimized by matching it to the grating
  period.
• Measurement of the spectrum of the radiation is
  facilitated by the natural dispersion of the
  grating.

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The future

• Interest in beam diagnostics for Linear Collider
  (LC-ABD bid to PPARC)
• Knowledge of the bunch longitudinal profile is
  important (beam-beam interaction) ?needed by
  FONT.
• Need input from groups that measure beam size,
  position and backgrounds.

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Issues

• Do we understand ? dependence?? new calculations
  in hand.
• Can we make precise predictions of coherent
  radiation for real bunches, gratings, beam pipe
  etc?? work in hand
• Can we measure the spectrum at high energies?
  Questions raised include
• Background radiation? help from simulation groups
• Test facilities with known short bunches?
• Other periodic structures?? work in hand
• Detector selection, filters etc.? need to build
  up expertise.
• Radiation damage??

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a. FELIX

• Higher energy (45-50MeV), shorter bunch (1-3ps)
• Simpler device, with no rotating mirrors but a
  series of collimated apertures, to detect
  simultaneously at a range of angles.
• IR detector array ?preferably pyroelectric
• Direct comparison with Electro-Optic technique.

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300 mm
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Predictions for tests at FELIX

• If bunch were 3ps triangular, then..
• Two different beam positions above grating,
  blue1mm, red5mm

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b. GeV region

• In parallel with these tests
• New EM field calculations for a high g bunch,
  passing over a single wire (WA)

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• A simple model
• Start with a fine wire along x-axis (radius
  20µm)
• A relativistic bunch travels parallel to z, a
  distance b from the wire (in y)

... then opposing currents I are induced in the
wire
ßc
b
... giving a radiated field like quadrupole
radiation but compressed into flat disk-shaped
lobes with ?x1/? from the plane perpendicular to
the wire
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....expanding the calculation to an array of 10
such wires, 300µm pitch ....then the two disks
segment into azimuthal lobes around the wire
axis eg at ? 100µm (with exaggerated polar
angle)
As before the red arrow is the wire direction and
the green arrow the beam.
Of course generally there is angular
dispersion of the radiation by the grating
according to wavelength....
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? 200µm
The dependence of the radiation reduction factor
on ? for an rms bunch size of 30µm (0.1ps)
?(m)
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• Plot of radiated power against bunch size (in m)
  for
• red ?100-250µm
• green ?250-600µm

?z
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• ....and the good news
• at high ?, the grating to beam separation can be
  up to ? ? ? without serious loss of radiation
  flux. No problem!
• ....and the bad news
• for maximum flux the width of the grating should
  be ? ? ?.
• ... but it has got to be in the beam pipe! So
  this effect will be responsible for a substantial
  reduction in the flux from a grating.
• Calculations on these problems and other ideas
  continue...
• We have already learned a lot of things which
  upon reflection were simply understood
• We aim to predict the results of tests
  quantitatively, depending of course on whether we
  know the actual bunch length!

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Summary

• Coherent SP radiation can be used, in principle,
  to determine the Fourier transform of the
  longitudinal profile of finite-length bunches.
• Demonstrated (first time ?), using 14ps bunches
  from Frascati Microtron, at low energies (1.8 and
  4.75MeV).
• Next runs are at FELIX, then
• Final Focus Test Beam (FFTB) at SLAC ( 1ps and
  30 GeV). is one possibility.
• TESLA?