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Novel nonintercepting diagnostic techniques for low-emittance relativistic electron beams
970
Nuclear Instruments and Methods in Physics Research B40/41 (1989) 970-972 North-Holland, Amsterdam
NOVEL NONINTERCEPTING DIAGNOSTIC TECHNIQUES FOR LOW-EMITTANCE RELATIVISTIC ELECTRON BEAMS M.J. MORAN and B. CHANG LawrenceLivermore National Laboratory, Livermore, CA 94550, USA
Relativistic electron beams are being generated with emittances low enough that diffraction radiation can be used for beam diagnostics. Techniques based on diffraction radiation can be used to measure the beam transverse momentum distribution and to measure the transverse spatial distribution. The radiation is intense and can be in the visible spectral region where optical diagnostic techniques can be used to maximum advantage.
Modem accelerators now generate relativistic electron beams with emittances that are so low that they are difficult to measure with traditional techniques. Optimization of the accelerator and efficient coupling to experiments of interest require diagnostic techniques capable of studying details of the electron-beam phase space. If diagnostic capabilities are going to keep pace with improvements in accelerator technology, then new techniques are needed with improved spatial and angular resolutions and the ability to characterize multiple parameters simultaneously for single beam pulses. For example, a recent paper has described the use of X-rays from an undulator to characterize both the transverse spatial and momentum distributions of an 8 GeV beam (at PEP) in a low-emittance mode [l]. Other similar work has described the use of optical transition radiation (TR) to simultaneously characterize the transverse spatial and momentum distributions of lower-energy electron beams [2]. The purpose of this paper is to describe the use of the diffraction radiation (DR) generated when an electron passes through an aperture to characterize the temporal and transverse spatial and momentum distributions of low-emittance electron beams [3]. A full theoretical description of diffraction radiation is too cumbersome to present here. However, approximate solutions based on “pseudo” or “virtual” photon descriptions of the time-dependent field of a relativistic electron are adequate for the present application [3]. In the pseudo photon description the Coulomb field is written as a flux of photons copropagating with the electron. The DR generated when an electron passes through an aperture is calculated by applying optical diffraction theory to the virtual photon flux. This approach does not represent a full solution of Maxwell’s equations for a given situation, but does give useful descriptions of the spatial and spectral distributions of the radiated photon flux. 0168-583X/89/$03.50 0 Elsevier Science Publishers B.V (North-Holland Physics Publishing Division)
The source of the DR can be understood qualitatively by considering the pseudo photons to be confined within a diameter D centered about the about the electron trajectory. D is a function of the photon radial frequency w and is given by:
where c is the speed of light in vacuum, y is the particle total energy divided by its rest mass, and X = 27rc/w. If the electron passes through the center of an aperture with a dimension a >> D(w) for the photon frequency of interest (fig. l), then there will be very little scattered radiation because the pseudo photons don’t “see” the aperture. However, if the electron passes through an aperture where a I D, then the pseudo photons will be scattered efficiently. The radiation will have an intensity comparable to the intensities available from other radia-
Fig. 1. Schematic diagram of the diffraction radiation geometry for a linear slit. The coordinate origin is at the particle position in the slit. Photon angles of emission, B_,, are measured in the y = 0 and x = 0 planes, respectively.
M.J. Moran, B. Chang / Novel nonintercepting
diagnostic techniques
971
tion mechanisms such as synchrotron radiation or TR. One feature of the DR is that there will be an effective cutoff frequency w._, where w, = 2yc/u, above which the radiated flux wiil be extremely small. This behavior will help to minimize the power radiated into higher photon energies and allows DR diagnostics to be designed for specific spectral ranges. As an example of this type of behavior, consider the DR generated when an electron passes through a linear slit of width a [3]:
where
expf -y-(f-
( )i
k &=_‘_41_. _E 4dc f .
+
exp[ -y+(f
Fig. 2. Diffraction radiation angular distributions vs electron position in the slit. The radiated intensity d2N/dQ vs 0, of
+iky)l
f+ik,
ik,,)]
f-ik,
I
’
(lb)
2-eV photons (10% bandwidth) for an 8 GeV electron in a 5 mm wide slit vs distance from the slit edge.
and E,
=
-_f.-
477% -
ew[ -r-(f
- iky)]
f-ik,
@cl
where dN is the number of photons with frequency w that are radiated into bandwidth do and solid angle dJ2, and E, and E,, are the polarized electric field amplitudes in the x- and y-directions, respectively. Further, k=o,/c, k,=ksinBcos+, k,=ksinBsincp, v is the electron speed and V = Q(yv), y+ and y_ are the distances of the electron from the top and bottom of the slit, respectively (y + + y_ = a, see fig. 1). Generally speaking, eq. (1) describes an emitted beam with a half-angle of l/y centered on the direction of electron motion. The intensity and polarization of the beam depend on the particle and slit parameters. Eq. (1) describes the DR generated by a single particle passing through the slit. The DR generated by a beam pulse will represent an integral over the spatial and momentum distributions of the electrons in the pulse. The simplest application is to use the DR as a diagnostic for measuring the transverse momentum distributions of a relativistic electron beam. The DR intensity can also be used to establish that the beam is confined to the central portion of a slit (or aperture) and thereby characterize the beam dimension(s) and position. The DR can be used to measure the transverse spatial beam distribution along the slit axis, but the resolution will be no better than D. The example below will illustrate these applications with beam parameters
f = {&-7,
that are associated with operation of PEP in a low-emittance mode. Fig. 2 shows the angular distribution of y-polarized (the DR here is about 80% y-polarized) photons generated when an 8 GeV electron passes through a 5 mm slit. The calculation uses 2 eV photon energy (- 600 nm) with 10% bandwidth. The angular distribution in the y-z plane (+ = n/2) is shown as a function of the height at which the electron passes through the slit. When the electron passes through the center of the slit (y+ = a/2) the distribution has an on-axis zero, peaks at angles of about f l/y, and the integrated intensity is minimum. When passing at the slit edge (y, = 0) the distribution has an on-axis peak, a FWHM of about 2/y, and the peak intensity is about ten times higher. Thus, a transverse spatial distribution of electrons (characterized by a vertical width uY) can be confined to the central portion of the slit by ~~~~ng the radiated intensity. If this does not give adequate resolution, then the slit width can be reduced. The photon flux distributions will remain roughly constant if the radiation is monitored with constant fractional bandwidth and at a frequency that keeps the ratio a/D(w) constant. If the slit is narrowed to the point that a s D(o), then the DR will be intense, regardless of the particle positions in the slit. In order to achieve large differences in intensity between the edge and middle portions of the slit, it is necessary to maintain a 2 40( 60). These considerations apply to confining the beam in the y-direction At the same time, an optical near-field image of emission from the slit would allow determination of the beam position in the x-direction, and would measure ox, the horizontal beam size, if a, 2 D(w). VII. ACCELERATOR
TECHNOLOGY
M.J. Moran, B. Chang / Novel nonintercepting diagnostic techniques
912
ZOO.“”
I””
,‘I”
I’,“.
W ,c--.
‘I :( r-, ._/ / ‘N-e’
150 -
100 -
-100
-
,/-‘_\‘\
-150
:(
-
\L-/
II ___M
-200 -50
-100
0
Angle
50
(y = 0 plane,
-100
100
’ 0
-50 Angle
&wad)
” 50
(y ii 0 plane.
100
prad)
Fig. 3. Angular distribution of radiation for an 8 GeV electron passing through the center of the slit. (a) x-polarization: solid contours = 20 photons/electron, dotted contours = 5 photons/electron sr; (b) y-polarization: solid contours = 100 photons/electron ST, dotted contours = 25 photons/electron ST.
Fig. 3 shows contour angular
distributions
the center and
lobes
The zeros
diffraction slit.
angular from:
tegrated
minima
FWHM
photons
separation
= 110
in the main
respectively.
For
electrons,
tions can be measured
of about
are associated
50 with
urad.
peaks
can
be esti-
The
angle-in-
are about
4 X lo-*
for the x- and y-polariza-
beam
pulses
containing
the near- and far-field with standard
more
distribu-
solid state imaging
arrays. The distributions basis
shown in fig. 3 can be used as the
of a measurement
distribution beam
pulse.
about
l/y
of the transverse
(characterized The
main
This work was performed under the auspices of the US Department of Energy by the Lawrence Livermore National Laboratory under Contract no. W-7405-ENG48.
from the edges of the
of the zeros
photons/elect
than, say, 10”
through
show on-axis
angular
Ati = h/a
fluxes
and 2 x lo-’ tions,
with
of the electron
plots
in the y-direction
of the pseudo
The
mated
plots of the x- and y-polarized
for passage
of the slit. The
intense
prad.
minimum of the total intensity (both polarizations) becomes extremely sensitive to smaller u: and ui. For well-defined beams it might be possible to use this behavior to characterize u: and ui when the beam divergence is less than l/y. The paragraphs above point out some new ways in which DR might serve as a diagnostic for low-emittance relativistic electron beams. Application of such techniques will depend on the particular situation of interest, and eq. (1) gives a simple relation for identifying appropriate experimental regimes. DR does not represent a new phenomenon, but its use has become feasible because e--beams now are available for which u,, au I D(o) in the optical spectral region. In some cases (such as the SLC beam at SLAC [4]) this equality also holds true for photon energies in the soft X-ray spectral region. Radiation in these spectral regions lends itselve to detection and imaging with standard equipment and techniques. Thus, the practical convenience and the inherent angular and spatial definition of DR might prove to be useful in some beam-diagnostic applications.
momentum
by IJ: and ui) of an electron lobes
and the far-field
have optical
angular image
widths
of
can be used
directly to measure 17: and 0, when the angular divergence of the beam is greater than l/y. When the beam is collimated to angles smaller than l/v, then the on-axis
[l] G. Brown, J. Cerino, A. Hofmann, R. Liu, T. Troxel, P. Wang, H. Wiedemann, H. Winick, M. Bemdt, R. Brown, J. Christensen, M. Donald, B. Graham, R. Gray, E. Guerra, C. Harris, C. Hollosi, T. Jones, J. Jowett, P. Morton, J.M. Paterson, R. Pennacchi, L. Rivkin, T. Taylor, F. Turner and J. Turner, Proc. of the 1987 IEEE Particle Accelerator Conf., Washington, DC, March 16-19, 1987, p. 461. [2] D.W. Rule, Proc. 9th Int. Conf. on Applications of Accelerators in Research and Industry, Denton, TX, 1986, Nucl. Instr. and Meth. B24/25 (1987) 901. [3] M.L. Ter-Mikaelian, High-Energy Electromagnetic Processes in Condensed Media (Wiley, 1972) p. 383. [4] W. Kozanccki (SLAC), private communication.
Nuclear Instruments and Methods in Physics Research B40/41 (1989) 970-972 North-Holland, Amsterdam
NOVEL NONINTERCEPTING DIAGNOSTIC TECHNIQUES FOR LOW-EMITTANCE RELATIVISTIC ELECTRON BEAMS M.J. MORAN and B. CHANG LawrenceLivermore National Laboratory, Livermore, CA 94550, USA
Relativistic electron beams are being generated with emittances low enough that diffraction radiation can be used for beam diagnostics. Techniques based on diffraction radiation can be used to measure the beam transverse momentum distribution and to measure the transverse spatial distribution. The radiation is intense and can be in the visible spectral region where optical diagnostic techniques can be used to maximum advantage.
Modem accelerators now generate relativistic electron beams with emittances that are so low that they are difficult to measure with traditional techniques. Optimization of the accelerator and efficient coupling to experiments of interest require diagnostic techniques capable of studying details of the electron-beam phase space. If diagnostic capabilities are going to keep pace with improvements in accelerator technology, then new techniques are needed with improved spatial and angular resolutions and the ability to characterize multiple parameters simultaneously for single beam pulses. For example, a recent paper has described the use of X-rays from an undulator to characterize both the transverse spatial and momentum distributions of an 8 GeV beam (at PEP) in a low-emittance mode [l]. Other similar work has described the use of optical transition radiation (TR) to simultaneously characterize the transverse spatial and momentum distributions of lower-energy electron beams [2]. The purpose of this paper is to describe the use of the diffraction radiation (DR) generated when an electron passes through an aperture to characterize the temporal and transverse spatial and momentum distributions of low-emittance electron beams [3]. A full theoretical description of diffraction radiation is too cumbersome to present here. However, approximate solutions based on “pseudo” or “virtual” photon descriptions of the time-dependent field of a relativistic electron are adequate for the present application [3]. In the pseudo photon description the Coulomb field is written as a flux of photons copropagating with the electron. The DR generated when an electron passes through an aperture is calculated by applying optical diffraction theory to the virtual photon flux. This approach does not represent a full solution of Maxwell’s equations for a given situation, but does give useful descriptions of the spatial and spectral distributions of the radiated photon flux. 0168-583X/89/$03.50 0 Elsevier Science Publishers B.V (North-Holland Physics Publishing Division)
The source of the DR can be understood qualitatively by considering the pseudo photons to be confined within a diameter D centered about the about the electron trajectory. D is a function of the photon radial frequency w and is given by:
where c is the speed of light in vacuum, y is the particle total energy divided by its rest mass, and X = 27rc/w. If the electron passes through the center of an aperture with a dimension a >> D(w) for the photon frequency of interest (fig. l), then there will be very little scattered radiation because the pseudo photons don’t “see” the aperture. However, if the electron passes through an aperture where a I D, then the pseudo photons will be scattered efficiently. The radiation will have an intensity comparable to the intensities available from other radia-
Fig. 1. Schematic diagram of the diffraction radiation geometry for a linear slit. The coordinate origin is at the particle position in the slit. Photon angles of emission, B_,, are measured in the y = 0 and x = 0 planes, respectively.
M.J. Moran, B. Chang / Novel nonintercepting
diagnostic techniques
971
tion mechanisms such as synchrotron radiation or TR. One feature of the DR is that there will be an effective cutoff frequency w._, where w, = 2yc/u, above which the radiated flux wiil be extremely small. This behavior will help to minimize the power radiated into higher photon energies and allows DR diagnostics to be designed for specific spectral ranges. As an example of this type of behavior, consider the DR generated when an electron passes through a linear slit of width a [3]:
where
expf -y-(f-
( )i
k &=_‘_41_. _E 4dc f .
+
exp[ -y+(f
Fig. 2. Diffraction radiation angular distributions vs electron position in the slit. The radiated intensity d2N/dQ vs 0, of
+iky)l
f+ik,
ik,,)]
f-ik,
I
’
(lb)
2-eV photons (10% bandwidth) for an 8 GeV electron in a 5 mm wide slit vs distance from the slit edge.
and E,
=
-_f.-
477% -
ew[ -r-(f
- iky)]
f-ik,
@cl
where dN is the number of photons with frequency w that are radiated into bandwidth do and solid angle dJ2, and E, and E,, are the polarized electric field amplitudes in the x- and y-directions, respectively. Further, k=o,/c, k,=ksinBcos+, k,=ksinBsincp, v is the electron speed and V = Q(yv), y+ and y_ are the distances of the electron from the top and bottom of the slit, respectively (y + + y_ = a, see fig. 1). Generally speaking, eq. (1) describes an emitted beam with a half-angle of l/y centered on the direction of electron motion. The intensity and polarization of the beam depend on the particle and slit parameters. Eq. (1) describes the DR generated by a single particle passing through the slit. The DR generated by a beam pulse will represent an integral over the spatial and momentum distributions of the electrons in the pulse. The simplest application is to use the DR as a diagnostic for measuring the transverse momentum distributions of a relativistic electron beam. The DR intensity can also be used to establish that the beam is confined to the central portion of a slit (or aperture) and thereby characterize the beam dimension(s) and position. The DR can be used to measure the transverse spatial beam distribution along the slit axis, but the resolution will be no better than D. The example below will illustrate these applications with beam parameters
f = {&-7,
that are associated with operation of PEP in a low-emittance mode. Fig. 2 shows the angular distribution of y-polarized (the DR here is about 80% y-polarized) photons generated when an 8 GeV electron passes through a 5 mm slit. The calculation uses 2 eV photon energy (- 600 nm) with 10% bandwidth. The angular distribution in the y-z plane (+ = n/2) is shown as a function of the height at which the electron passes through the slit. When the electron passes through the center of the slit (y+ = a/2) the distribution has an on-axis zero, peaks at angles of about f l/y, and the integrated intensity is minimum. When passing at the slit edge (y, = 0) the distribution has an on-axis peak, a FWHM of about 2/y, and the peak intensity is about ten times higher. Thus, a transverse spatial distribution of electrons (characterized by a vertical width uY) can be confined to the central portion of the slit by ~~~~ng the radiated intensity. If this does not give adequate resolution, then the slit width can be reduced. The photon flux distributions will remain roughly constant if the radiation is monitored with constant fractional bandwidth and at a frequency that keeps the ratio a/D(w) constant. If the slit is narrowed to the point that a s D(o), then the DR will be intense, regardless of the particle positions in the slit. In order to achieve large differences in intensity between the edge and middle portions of the slit, it is necessary to maintain a 2 40( 60). These considerations apply to confining the beam in the y-direction At the same time, an optical near-field image of emission from the slit would allow determination of the beam position in the x-direction, and would measure ox, the horizontal beam size, if a, 2 D(w). VII. ACCELERATOR
TECHNOLOGY
M.J. Moran, B. Chang / Novel nonintercepting diagnostic techniques
912
ZOO.“”
I””
,‘I”
I’,“.
W ,c--.
‘I :( r-, ._/ / ‘N-e’
150 -
100 -
-100
-
,/-‘_\‘\
-150
:(
-
\L-/
II ___M
-200 -50
-100
0
Angle
50
(y = 0 plane,
-100
100
’ 0
-50 Angle
&wad)
” 50
(y ii 0 plane.
100
prad)
Fig. 3. Angular distribution of radiation for an 8 GeV electron passing through the center of the slit. (a) x-polarization: solid contours = 20 photons/electron, dotted contours = 5 photons/electron sr; (b) y-polarization: solid contours = 100 photons/electron ST, dotted contours = 25 photons/electron ST.
Fig. 3 shows contour angular
distributions
the center and
lobes
The zeros
diffraction slit.
angular from:
tegrated
minima
FWHM
photons
separation
= 110
in the main
respectively.
For
electrons,
tions can be measured
of about
are associated
50 with
urad.
peaks
can
be esti-
The
angle-in-
are about
4 X lo-*
for the x- and y-polariza-
beam
pulses
containing
the near- and far-field with standard
more
distribu-
solid state imaging
arrays. The distributions basis
shown in fig. 3 can be used as the
of a measurement
distribution beam
pulse.
about
l/y
of the transverse
(characterized The
main
This work was performed under the auspices of the US Department of Energy by the Lawrence Livermore National Laboratory under Contract no. W-7405-ENG48.
from the edges of the
of the zeros
photons/elect
than, say, 10”
through
show on-axis
angular
Ati = h/a
fluxes
and 2 x lo-’ tions,
with
of the electron
plots
in the y-direction
of the pseudo
The
mated
plots of the x- and y-polarized
for passage
of the slit. The
intense
prad.
minimum of the total intensity (both polarizations) becomes extremely sensitive to smaller u: and ui. For well-defined beams it might be possible to use this behavior to characterize u: and ui when the beam divergence is less than l/y. The paragraphs above point out some new ways in which DR might serve as a diagnostic for low-emittance relativistic electron beams. Application of such techniques will depend on the particular situation of interest, and eq. (1) gives a simple relation for identifying appropriate experimental regimes. DR does not represent a new phenomenon, but its use has become feasible because e--beams now are available for which u,, au I D(o) in the optical spectral region. In some cases (such as the SLC beam at SLAC [4]) this equality also holds true for photon energies in the soft X-ray spectral region. Radiation in these spectral regions lends itselve to detection and imaging with standard equipment and techniques. Thus, the practical convenience and the inherent angular and spatial definition of DR might prove to be useful in some beam-diagnostic applications.
momentum
by IJ: and ui) of an electron lobes
and the far-field
have optical
angular image
widths
of
can be used
directly to measure 17: and 0, when the angular divergence of the beam is greater than l/y. When the beam is collimated to angles smaller than l/v, then the on-axis
[l] G. Brown, J. Cerino, A. Hofmann, R. Liu, T. Troxel, P. Wang, H. Wiedemann, H. Winick, M. Bemdt, R. Brown, J. Christensen, M. Donald, B. Graham, R. Gray, E. Guerra, C. Harris, C. Hollosi, T. Jones, J. Jowett, P. Morton, J.M. Paterson, R. Pennacchi, L. Rivkin, T. Taylor, F. Turner and J. Turner, Proc. of the 1987 IEEE Particle Accelerator Conf., Washington, DC, March 16-19, 1987, p. 461. [2] D.W. Rule, Proc. 9th Int. Conf. on Applications of Accelerators in Research and Industry, Denton, TX, 1986, Nucl. Instr. and Meth. B24/25 (1987) 901. [3] M.L. Ter-Mikaelian, High-Energy Electromagnetic Processes in Condensed Media (Wiley, 1972) p. 383. [4] W. Kozanccki (SLAC), private communication.