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Smith-Purcell radiation
and 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
1. Introduction
2. Early experiments at Oxford and recent
results from Frascati.
3. The future (higher energy, shorter bunch,
more theory at high g).
4. 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
q
l
nl
Dispersion relation:
l 1
n  (  cos )
n 
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 mW’s 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
2
3
 2 x0 
dI
e

Zl 2

 
R exp 


2 3


 d 1 4 c n
 e 
 2 x0 
n
 dI   2e 2 Z
2
R exp


2
3

l (1   cos )

 d 1

e 
2
3
• Term R2 depends on the details of the grating profile; le is the
‘evanescent wavelength’, le~gl
• For high g, good coupling is possible even at mm’s 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 results
Phys. 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. Frascati
Phys. 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 (g=4.52),
some at g=10.3
• 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 (~
50pmm.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 (g=10.3)
• E=4.75MeV, I=120mA,
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:
 dI 
 dI 
2

(
N
S

N
e inc
e S coh )




 d   Ne  d  1, x0 0
• there is possibility of coherent enhancement, if
the ‘coherence integral’ Scoh is not very small
Scoh



ei t f (t )dt
2
• 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
(E=4.75MeV)
• 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
(t=0).
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Features
1. Simple experimental set-up.
2. Non-intercepting, valid for any charged
particle beam, at almost all energies.
3. Ample radiated power.
4. Sensitivity to the bunch length and its
harmonics can be optimized by matching it
to the grating period.
5. 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 g 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 (13ps)
• 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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Predictions for tests at FELIX
• If bunch were 3ps
‘triangular’, then..
• Two different beam
positions above grating,
blue=1mm, red=5mm
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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
βc
z
x
b
... giving a radiated field like quadrupole radiation but compressed into
flat disk-shaped lobes with θx~1/γ 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 λ = 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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λ
200
μm
The dependence of the radiation
reduction factor on λ for an rms
bunch size of 30μm (0.1ps)
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l(m)
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Plot of radiated power
against bunch size (in
m) for
z
•red λ=100-250μm
•green λ=250-600μm
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....and the good news:
at high γ, the grating to beam separation can be up to ~γ  λ
without serious loss of radiation flux. No problem!
....and the bad news:
for maximum flux the width of the grating should be ~γ  λ.
... 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?
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