Recent Advances in Beam Diagnostic
Techniques
R. B. Fiorito
TR Research Inc., 3 Lauer Terrace, Silver Spring, MD 20901 and
Institute for Research in Electronics and Applied Physics
University of Maryland, College Park, MD 20742
Abstract. We describe recent advances in diagnostics of the transverse phase space of charged
particle beams. The emphasis of this paper is on the utilization of beam-based optical radiation
for the precise measurement of the spatial distribution, divergence and emittance of relativistic
charged particle beams. The properties and uses of incoherent as well as coherent optical
transition, diffraction and synchrotron radiation for beam diagnosis are discussed.
INTRODUCTION
Over the several decades there has been a gradual trend to exploit the properties of
various types of radiation produced by charged particles, such as Cherenkov,
undulator, synchrotron and transition radiation, for beam diagnostics. Both the spatial
and spectral-angular distributions of the radiation have been utilized. In addition,
techniques that are well developed in optics, such as interferometry, auto-correlation
and electro-optic effects, have been applied to process beam radiation for diagnostic
purposes. These developments have significantly improved the precision and accuracy
of diagnostics and, consequently, improved the understanding of the physics of beams
in accelerators and in high brightness radiation devices, such as free electron lasers
and undulators.
In this paper we shall discuss recent advances in optical diagnostic methods, which
probe the transverse phase space of the beam. The review is not intended to be
exhaustive. Rather, we will primarily discuss general techniques, which can be applied
to a variety of accelerators. Furthermore, because of space limitations, only a few of
many new diagnostic concepts that are being developed can be included.
CP647, Advanced Accelerator Concepts: Tenth Workshop, edited by C. E. Clayton and P. Muggli
© 2002 American Institute of Physics 0-7354-0102-0/02/$19.00
96
RMS DIAGNOSTIC TECHNIQUES
Optical Transition Radiation
Incoherent OTR Interferometry
Optical transition radiation (OTR) is widely used to image the transverse profile of
charged particle beams. The radiation is prompt, linear to beam charge and has the
highest spatial resolution of any known method [1]. Furthermore, the spatial resolution
of OTR is independent of the energy of the beam - a fact that has been well
established both theoretically and experimentally [2-5]. Thus, OTR has been utilized
over a very wide range of particle energies - 1 MeV to 30 GeV - for beam imaging
applications.
Less well known, but nonetheless important, is the application of the spectral and
angular distributions of OTR for beam diagnostics. A number of methods to measure
beam divergence, trajectory angle and emittance have been developed which utilize
these distributions [6].
Experimentally, OTR is observed from thin metallic or dielectric foils inserted into
the beam either in the forward direction, i.e. the direction of the velocity vector of the
beam, or in the backward direction. A unique property of backward OTR is that the
radiation follows the angle of specular reflection of ordinary light. Thus by inclining
the foil or mirror at 45 degrees, OTR is directed at right angles with respect to the
beam direction - a property which is highly advantageous for diagnostic purposes.
Two parallel, inclined foils can be used to produce an OTR interferometer [7].
Interference is produced by the coherent addition of forward OTR from the front foil
and backward OTR from the second foil, which is typically a mirrored surface. Then
the total spectral-angular intensity per electron of interference OTR is given by:
d2!
4a
02
. 2rnL. _2 2
sm [—(y +0 )],
7i co(y +0 )
(1)
and the total observed radiation from N electrons is:
where a is the fine structure constant, 0 is the angle of observation measured with
respect to the direction of specular reflection, L is the inter-foil spacing, y is the
Lorentz factor of the beam, A, is the observed wavelength, co is the angular frequency,
Q is the solid angle, B(k) is the bunch form factor, which is defined as the square of
the Fourier transform of the spatial distribution of the beam, k = (k0x, k0y, co/c) is the
wave vector and c is the velocity of light in vacuum. When K « 4, the bunch length,
I QC N ; this is the temporally incoherent regime, which we will discuss in this Section.
When A, > h and the bunch form factor is unity, I ~ N2, and the radiation is totally
97
coherent. When 1 > B(k) > 0, the radiation is partially coherent. This case will be
discussed below in the following Section.
For a given L and A,, OTR interferences are highly sensitive to beam divergence,
energy and trajectory angle and can be used to diagnose these parameters. Adjusting
L, A, and the bandwidth A A, / c&n tune the interferometer to produce fringes whose
visibility is sensitive to any desired range of divergence. OTR interferometry (OTRI)
has been used to measure normalized divergences (a = y0 ) as low as 0.05 [6].
Furthermore, the position of the interferences peaks is a sensitive (-1%) energy
diagnostic [7], and the angular offset of the interference pattern from a fixed direction
is a sensitive trajectory angle diagnostic [8].
If simultaneous images of the x and y spatial distributions of the beam at an x and y
waist are obtained, the rms emittances can be determined from the product of the rms
divergence and rms beam size [6].
As an example of the use of OTRI as a divergence diagnostic, we present the results
of some recent experiments performed at the Naval Postgraduate School's 95 MeV
electron beam linac [9]. Figure 1. (left) shows an OTR interferogram taken at a
horizontal (x) beam waist; (right) an interferogram taken at a y waist. A visual
comparison of the two pictures illustrates that the visibility in the x directions is
smaller than in the y direction i.e. the x divergence is higher than the y divergence.
Horizontal and vertical line scans of these two interferograms, when fitted to
theoretical generated line scans obtained by convolving Eq. (1) with a Gaussian
distribution of x and y beam angles, give Qxrms =1.0 ±0.1 mrad and 0^ =0.7 ±0.1
mrad confirming the visual observations.
FIGURE 1. Left: incoherent OTRI from a 95 MeV beam, taken at an x waist; right: at a y waist. [From
Ref. 9]
Coherent OTR Interferometry
A new diagnostic method to measure beam size and divergence of micro-bunched
beams has recently been reported employing coherent OTR interferences (COTRI)
[10]. The measurements were done at the Low Energy Undulator Test Line (LEUTL)
of the APS at Argonne National Laboratory, which bunches a 217 MeV electron beam
at optical wavelengths. Temporally coherent OTR is generated at wavelengths A, > 538
nm from the electrons in the bunch. This radiation forms COTRI when used in a twofoil interferometer.
The intensity of COTRI is primarily determined by the second term in Eq. (2),
which contains the bunch form factor, B(k). The bunch form factor is actually the
product of two terms: the transverse and longitudinal form factors. The former is a
function of the transverse beam size, the latter a function of the combined effects of
longitudinal beam size and the amount of micro bunching by the undulator.
The effect of the transverse bunch form factor on COTRI is shown in Figure 2.
[10]. The Figure shows theoretical COTRI line scans for various beam sizes and for a
fixed percent (0.2%) micro bunching. Note the substantial increase in peak signal of
COTRI in comparison to incoherent OTRI. However, the increase is substantially less
than N2 (i.e. the total form factor is less than unity) because of the small amount of
micro bunching. Nevertheless, Figure 2. shows that COTRI is a highly sensitive beam
size diagnostic even when the radiation is partially coherent. For larger microbunching percentages, the intensity of COTRI becomes orders of magnitude greater
than incoherent OTRI [10].
-0.005
0.000
0.005
Angle (radians)
FIGURE 2. The effect of beam size on coherent OTRI observed at the LEUTL undulator at a beam
energy of 217 MeV for a fixed small (0.2%) micro bunching. [From Ref. 10]
Diffraction Radiation
Diffraction radiation (DR) is produced when a charged particle passes near a region
in space where the dielectric constant changes from that in which the particle is
initially traveling. DR is under intense investigation by a number of research groups,
because of its promise as a non-interceptive diagnostic for high-energy beams. [1115]. DR has a long history of theoretical investigation [16]. However only a handful of
experimental studies of DR have been performed to date. We report some results of
recent experiments, which have been performed to develop non-invasive DR
transverse phase space diagnostics.
Optical DR Experiments at KEK
Experiments to investigate several types of diffraction radiation produced at optical
wavelengths (ODR) are underway at the KEK ATF 1.28 GeV electron beam
extraction line [17].
99
Angular distribution
FIGURE 3. Left: schematic of edge diffraction radiation experiment; right: theoretical angular
distribution for various impact parameters h. [From Ref. 17]
These experiments include the study of DR from a single edge, a slit and TR from a
foil whose radial dimension d < y A,/2. n
Figure 3. (left) shows a schematic of an edge DR experiment. Figure 3. (right)
shows the intensity of DR as a function of impact parameter h. DR is produced in the
optical region of the spectrum for beam impact parameters satisfying the condition
h < jK/2n, where A, = 500 nm is the observed wavelength and y S500 is the Lorenz
factor of the beam. The intention of this experiment is to measure beam offset in the
accelerator non-interceptively by observing the angular distribution of optical DR.
Optical Diffraction-Transition Radiation Interferometry
We are pursuing theoretical and experimental investigations to extend the range of
conventional OTRI beam divergence measurements to lower energy and higher
quality beams. Conventional OTRI has an important limitation, i.e. foil scattering
produced in the first foil of the interferometer sets a lower limit on the divergence,
which can be measured with this technique. This problem becomes important e.g.
when the normalized divergence is a few percent and energy of the beam is less than
10 MeV.
We have found a way to overcome this limitation by replacing the front solid foil of
the interferometer with a highly transparent (50%) micromesh. The mesh hole size is
chosen to be much smaller than the diameter of the beam. The beam produces forward
directed OTR from the solid material of the mesh and optical diffraction radiation
from the holes. Beam particle traveling through the holes suffer no scattering. The
forward directed OTR and ODR from the holes interfere with backward OTR
produced by the mirror to form ODR-OTR interferences and OTR from the solid
portion of the mesh and the mirror combine to produce OTR-OTR interferences. By
controlling the size, period and thickness of the mesh, we have been able to design an
interferometer in which the ODR-OTR interferences (ODTRI) are visible above the
OTR-OTR interferences [18]. The ODTRI are used to measure the beam divergence.
100
1.2
1.0 •
————
THEORY CT =0.6 mrad
0.8 •
! 0.6
0.4
0.2
0.0
ANGLE, 1/y UNITS
FIGURE 4. Left: ODTRI from a micromesh-mirror interferometer; right: vertical line scan of ODTRI
fitted to theoretical curve.
In addition to conventional OTRI, we have also used ODTRI to measure the
divergence of the 95 MeV electron beam at the Naval Postgraduate School using a
copper micromesh. The mesh is 5 micron thick and has 25ju rectangular holes with a
33ju hole period. The beam radius was about 2 mm for this experiment.
An ODTR interferogram. which is shown in Figure 4. (left), was taken at a vertical
(y) beam waist condition. The theoretical fit to the data shown on the right is obtained
by a simulation code that we developed to design and analyze ODTRI [18]. This is the
first reported experimental data to show ODR-OTR interferences, and the first
comparison of such data to theory. The divergences measured with ODTRI and OTRI,
as shown in Figure 1., are in good agreement.
We are developing ODTRI to measure the divergence of the 10 MeV Maryland
Infrared Free Electron Laser (MIRFEL) and investigating its application to other low
energy beams such as the 5 MeV injector at SLAC.
Optical Synchrotron Interferometry
Optical synchrotron radiation (OSR) has been successfully used to image the beam
and measure its divergence. Recently, the spatial coherence function of OSR has been
employed to measure beam size with very high accuracy [19,20]. This method is based
on the application of the Cittert-Zernike Theorem [21], which states that degree of
spatial coherence of radiation from a finite sized source is the Fourier transform of the
intensity. The spatial coherence function can be measured by observing the
interferences from a double slit. Michelson first used such a technique to measure the
angular size of a star.
Figure 5. shows an OSR interferogram taken at the High Energy Ring at the SLAC
PEP II collider [20]. The degree of modulation, i.e. the fringe visibility, is a direct
measurement of the degree of spatial coherence, which is a sensitive function of the
beam size. For a point source the coherence function is unity and the fringes are 100%
modulated. For a highly divergent source it is zero and the fringe modulation or
visibility is zero. When fitted to theory, the interference pattern shown in Figure 5.
produces a beam size of 232 microns.
101
FIGURE
Scanofofoptical
opticalsynchrotron
synchrotronradiation
radiation interferences
interferences for
FIGURE
5. 5.
Scan
for the
theHERA
HERAon
onPEP
PEPIIII(SLAC).
(SLAC).[From
[From
Ref.
20,
©
2001
IEEE.]
Ref. 20, © 2001 IEEE.]
OPTICALPHASE
PHASE SPACE
SPACE MAPPING
MAPPING METHODS
OPTICAL
METHODS
Determination of the transverse phase space distribution of charged particle beams
Determination of the transverse phase space distribution of charged particle beams
is important for understanding the effects of electric and magnetic fields produced by
is external
important
for understanding
the and
effects
of electric
magnetic
fields produced
devices
such as chicanes
cavities
as well and
as internal
discontinuities
withinby
external
devices
such
as
chicanes
and
cavities
as
well
as
internal
discontinuities
within
the accelerator transport system.
the accelerator
transport
system.
The common
technique
to measure transverse phase space is the so-called "pepper
The
common
technique
to measure
transverse
space
is the so-called
“pepper
pot" technique, which employs
perforated
platesphase
or slits
to collimate
the beam.
In
pot”
technique,
employs
plates
or slitscollimated,
to collimate
beam. In
cases
where: 1)which
the beam
is largeperforated
enough to be
effectively
2) thethe
collimator
cases
1) the
beam to
is large
enough
to bewith
effectively
collimated,
2) theand
collimator
holeswhere:
are small
enough
produce
beamlets
negligible
space charge
3) the
holes
enough energy
to produce
with of
negligible
space ischarge
and 3)the
the
beamare
hassmall
low enough
so thatbeamlets
permeability
the collimator
not serious,
beam
has low enough
energy
so that
permeability
of the
collimator
is not serious,
the
conventional
pepper pot
is quite
effective.
However,
when
these conditions
are not
conventional
pot is quite
However,
conditions
not
met - whichpepper
is the frequently
theeffective.
case for high
energy,when
high these
brightness
beamsare
- the
met
- which
is the frequently
the case
foralternative
high energy,
high
brightness
pepper
pot technique
is ineffective
and an
method
must
be used. beams - the
pepper
technique
ineffective
and an to
alternative
must
Wepot
will
describe is
two
new approaches
solve thismethod
problem
bothbeofused.
which employ
optical
tomography
andtoan
optical
analogue both
to the
conventional
We willradiation:
describe beam
two new
approaches
solve
this problem
of which
employ
pepperradiation:
pot technique.
optical
beam tomography and an optical analogue to the conventional
pepper pot technique.
Beam Tomography
Beam Tomography
The central idea of beam tomography is to reconstruct the transverse phase space of
the
fromidea
a series
of real
space projections.
The method
on thephase
fundamental
Thebeam
central
of beam
tomography
is to reconstruct
therelies
transverse
space of
theorem
of
tomography
known
as
the
Radon
Theorem,
which
states
that an N
the beam from a series of real space projections. The method relies on the fundamental
dimensional
image can beknown
reconstructed
a series
of N-l which
projections.
theorem
of tomography
as the from
Radon
Theorem,
statesThe
thatRadon
an N
Theorem
is
applied
to
beams
by
using
a
magnetic
quadrupole
scan
and
OTR
to
dimensional image can be reconstructed from a series of N-1 projections. The
Radon
produce the necessary "projections". The idea is that each setting of the quadrupole
Theorem is applied to beams by using a magnetic quadrupole scan and OTR to
focusing rotates the two-dimensional phase space (x,x' or y,y') of the beam. The
produce the necessary “projections”. The idea is that each setting of the quadrupole
corresponding OTR image for each setting is equivalent to a one dimensional (x or y)
focusing
rotates the
(x,x’space
or y,y’)
of the The
beam.
The
spatial projection
of two-dimensional
the corresponding phase
x,x' or space
y,y' phase
distribution.
value
corresponding
OTR
image
for
each
setting
is
equivalent
to
a
one
dimensional
(x
or
of the technique is that no prior assumptions about the phase space distribution isy)
spatial
projection
of thethe
corresponding
x,x’
or at
y,y’
phasefoil
space
distribution.
The
value
necessary
and further,
method can be
used
a single
station
at the beam
line.
of the
technique
is
that
no
prior
assumptions
about
the
phase
space
distribution
This technique was originally implemented by McKee, O'Shea and Madey [22] andis
necessary
and further,
the method
be used at[23,24].
a single foil station at the beam line.
further developed
by Ben-zvi
and can
collaborators
This technique was originally implemented by McKee, O’Shea and Madey [22] and
further developed by Ben-zvi and collaborators [23,24].
102
FIGURE 6. Left: diagram of x,y spatial distribution of the beam and its projections at various angles;
Right: reconstructed x, x' phase space of a 35 MeV electron beam. [Reprinted from Ref. 22, © 1995,
with permission from Elsevier Science.]
Figure 6. (left) shows an x,y spatial distribution of a beam along with projections at
various angles. The algorithms developed by McKee, et. al. associate the distribution
obtained at each quad setting with a rotation of the beam phase space. The projections
of the distribution for each quad setting can be used to reconstruct the x,x' and y,y'
phase spaces of the beam. Figure 6. (right) shows the completely reconstructed x,x'
phase space distribution of a 35 MeV electron beam obtained by applying the Radon
transform on the quadrupole scan data.
Optical Pepper Pot Technique
We are developing a new method to map the transverse phase space, which is an
optical analogue to the standard pepper pot collimation method [9]. This method uses
OTRI and an optical mask to achieve the same results as the conventional pepper pot
but dispenses with the need to collimate the beam particles. The approach uses thin,
highly permeable foils to create an OTR interference pattern and an OTR image of the
beam. The radiation from the interferometer is first transported and focused to produce
a magnified image of the beam at the site of an optical mask, which is composed of a
single pinhole or multiple pinholes. The OTRI emerging from each pinhole is then
analyzed to produce a localized divergence and trajectory angle. From this data and
knowledge of the position within the beam spatial distribution, i.e. the position of the
pinhole registered with respect to the beam image, the transverse phase space can be
reconstructed.
Figure 7. (left) shows an image of an arbitrarily focused beam imaged on the
backside of a single pinhole mask. The pinhole is 1 mm in diameter and the beam
image is magnified by a factor of two. Figure 7. (right) shows a fit to the OTRI
observed from the pinhole, which produces a localized divergence for the part of the
beam intercepted by the pinhole.
103
ANGLE, 1/y UNITS
FIGURE 7. Left: images of beam and pinhole superimposed; right: vertical line scan of OTRI pattern
obtained by focusing light passing through the pinhole at infinity.
Figure 8. shows a map of the vertical phase space of the 95 MeV beam obtained
from three pinhole positions, arbitrarily labeled 4, 2 and 5. Position 2 is shown above
in Figure 6.; position 4 is directly above position 2 and position 5 is directly below.
The rectangles shown in Figure 8. delineate the area in phase space occupied by the
portion of the beam sampled for each position of the pinhole. The width of the
rectangle is the local beam divergence and the centroid of the rectangle, the local
trajectory angle. Even for the sparse number of measured points, Figure 8. clearly
shows that the phase space in the vertical (y) direction is not an ellipse. Such detailed
information about the phase space distribution is not available in rms measurements.
Furthermore, the map can be obtained for any beam envelope, i.e. it does not require
any particular beam focusing condition. We are continuing to develop this method.
The goal is to produce more accurate time integrated and time resolved optical
transverse phase space maps.
Y COORDINATE, mm
FIGURE 8. Optical vertical phase space map. [From Ref. 9]
ACKNOWLEDGMENT
The work of the author and his colleagues presented herein was supported by U.S.
Department of Energy STTR Grants DEFG02-01ER86 (130) and (132).
104
REFERENCES
1.
2.
3.
4.
Murokh, A. Rosenzweig, J. Ben-Zvi, I. Wang, X. Yakimenko, V., Limitations on measuring a
transverse profile of ultra dense electron beams with scintillators. In: Proc. of the 2001 Particle
Accel. Conf., Piscataway, NJ, USA: IEEE, 2001. p. 1333-5 vol.2.
Rule, D.W. and Fiorito, R.B., "Imaging Micron Sized Beams with OTR", AIP Conf. Proc. 229
(1991).
Denard, J. C., et. al., "High power beam profile monitor with optical transition radiation", in:
Proc. of the 1997 Part. Accel. Conf., Piscataway, NJ, USA: IEEE, 1998. p. 2198-200 vol.2.
Lebedev, V., Nuc. Instrum and Methods A, 372, 344 (1996); see also Castellano, M. and
Verzilov, V., Phys. Rev. ST Accel. Beams 1, 062801 (1998).
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
Catravas, et. al., "Beam Profile Measurement at 30 GeV Using OTR", Proc. of the 1999
Particle Accel. Conference ,Piscataway, NJ, USA: IEEE, 1999. p.2111-2113.
Fiorito, R.B. and Rule, D.W. "Optical Transition Radiation Beam Emittance Diagnostics", in
AIP Conf. Proc. 319(1994).
Wartski, L. et. al., J. Appl. Phys., 46, 3644 (1975).
Le Sage, G., et. al., Phys. Rev. ST, Accel. and Beams, 2, 12802 (1999).
Fiorito, R.B., Shkvarunets, A.G. and O'Shea, P.G., "Optical Method to Measure the
Transverse Phase Space of a Charged Particle Beam", Proc. of the Beam Instrum. Workshop
2002, Brookhaven Natl. Lab., May 6-9, 2002 (to be published).
Lumpkin, A. H., et. al., "Advanced Intra-undulator Electron Beam Diagnostics Using COTR
Techniques", ibid; see also Phys. Rev. Lett., 88, 234801-1, (2002).
Castellano, M., et. al. Phys. Rev. E 63, 056501 (2001).
Castellano, M., Nuc. Instrum. and Meth. A, 394, 275 (1994).
Fiorito, R.B. and Rule, D.W., Nuc. Instrum. and Methods B., 173, 67-82 (2001).
Potylitsin, A., Nuc. Instrum. And Meth. B, 145, 169 (1998).
Potylitsina, N. and Artu, X., "Diffraction radiation from ultrarelativistic particles passing
through a slit." Nuc. Instrum. and Methods B, Special Topical Isssue: Proc. of the 5th Internatl.
Sympos. on Relativistic Electrons in Periodic Structures, Lake Aya, Altai, Russia , Sept. 2001
(to be published).
Bolotovskii, B.M. and Galstyan, E.A. Physics-Uspekhi, vol.43, no.8, Aug. 2000. p. 755-76.
Muto, T., et. al. "Measurements of Optical Diffraction Radiation", in Proc. of LC02: Ninth
International Workshop on Linear Colliders Workshop, Stanford Linear Accelerator Center,
Stanford, CA. Feb. 2002 (to be published).
Shkvarunets, A.G., Fiorito, R.B. and P.G., O'Shea, "Optical Diffraction-Transition Radiation
Interferometry and its Application to the Measurement of Beam Divergence", Nuc. Instrum.
and Methods B, Special Topical Isssue: Proc. of the Fifth Internatl. Sympos. on Relativistic
Electrons in Periodic Structures, Lake Aya, Altai, Russia , Sept. 2001 (accepted for
publication).
Katoh, M. and Mitsuhashi, T., "Measurement of beam size at the Photon Factory with the SR
interferometer". In: Proc. of the 1999 Particle Accelerator Conference , Piscataway, NJ, USA:
IEEE, 1999. p. 2307-9 vol.4.
Fisher, A. et. al., "Beam-Size Measurements on PEP-II Using Synchrotron-Light Interferometry" Proc.
of the 2001 Particle Accel. Conf., Piscataway, NJ, USA: IEEE, 2001. p.547-549.
21. Takayama, Y. and Kamada, S., Phys. Rev. E, 59, 7128 (1999).
22. McKee, O'Shea, P.G. and Madey, J.M.J., Nuc. Instrum. and Methods A, 358,264 (1995).
23. Ben-Zvi, I. Qiu, J.X and Wang, X.J., "Picosecond-Resolution 'Slice'
Emittance Measurement of Electron-Bunches" , Proc.of the 1997 Particle
Accelerator Conference, Vancouver BC Canada, May 12-16, 1997 page 1971.
24. Yakimenko, V. et. al.,"Emittance Control of a Beam by Shaping the Transverse Charge
Distribution, Using a Tomography Diagnostic, 6th Europ. Part. Accel. Conf. (EPAC), June 2226, 1998, Stockholm, Sweden., p.1641.
105