Proceedings of the 10th Annual Meeting of Particle Accelerator Society of Japan (August 3-5, 2013, Nagoya, Japan)

Study of Longitudinal Phase Space Distribution Measurement via a LinearFocal Cherenkov Ring Camera
A. Lueangaramwong∗ , F. Hinode, S. Kashiwagi, T. Muto, I. Nagasawa, K. Nanbu,
Y. Shibasaki, S. Takahashi, K. Yanagi, H. Hama
Electron Light Science Centre, Tohoku UniversityAbstract
At Tohoku University, a study of generation of intense coherent THz radiation from sub-picosecond electronbunches has been developing. Initial electron distribution
in the longitudinal phase space produced by an electron
gun is crucial for extreme short electron bunch production.
For relatively lower energy electrons, a novel method formeasurement of electron kinetic energy employing velocity dependence of the opening angle of Cherenkov radiation was proposed. Combined use of a streak camera anda “turtle-back” mirror that confines the Cherenkov light on
to a linear focal line may allow us to observe the longitudinal phase space distribution directly. An experimental
setup was examined with numerical ray tracing, and a radiator placed outside the vacuum chamber was designed toachieve the highest energy resolution. To extract the electron beam from the vacuum, a beryllium thin film was proposed as a beam window. However, a Geant4 Monte Carlosimulation showed that multiple scatterings of the electron
beam in the beryllium window significantly affects the resolution of the Cherenkov angle. Detail of examination will
be presented in this conference.

INTRODUCTION
Intense relativistic electron beam with very short bunch
length is an essential key to coherent radiation in the terahertz frequency region [1]. A test accelerator for the coherent terahertz source (t-ACTS) has been constructed atTohoku University, in which the generation of intense coherent terahertz (THz) radiation from sub-picosecond electron bunches will be demonstrated [2]. The t-ACTS facility
proposed an advanced independently tunable cells (ITC)
thermionic RF gun consisting of two uncoupled cavities.
The electron beam from the RF-gun would be introduced
into an alpha magnet and a linac as the bunch compression system. Proper longitudinal phase space distribution
can be produced by the ITC RF-gun adjusted relative RFphases and field strengths of the two cavities. Since the final electron bunch can be dictated by the longitudinal phasespace distribution at the RF-gun exit, longitudinal phasespace distribution measurement is inevitably significant for
extreme short electron bunch production.
Measurement of electron kinetic energy employing velocity dependence of the opening angle of Cherenkov radiation was proposed as a novel method for relatively lower
energy electrons. By using combination of a streak camera
and a “turtle-back” mirror which confines the Cherenkov∗ anusorn@lns.tohoku.ac.jp

light on to a linear focal line, the longitudinal phase space
distribution could be directly observed [3, 4]. An experimental setup with reflective optics was examined with numerical ray tracing. For the highest energy resolution of
measurement results, a radiator was designed to be placedoutside the vacuum chamber. To extract the electron beamfrom the vacuum, a beryllium thin film was selected as abeam window. However, a Geant4 Monte Carlo simulation
showed that multiple scatterings of non-relativistic electron
beam in the beryllium window significantly degraded theresolution of the Cherenkov angle.

METHODOLOGY
While required a new method, longitudinal phase spacemeasurement of each single micro-pulse of the beam is potentially useful to optimize beam performance and reliability. The method using coherent Cherenkov radiation as adiagnostic tool was proposed, due to the Cherenkov angle
θc corresponding to particle velocity β as shown in Eq. 1,cos θc = 1/n(ω)β,(1)

where n(ω) is the refractive index of the Cherenkov radiator medium at a radiation frequency ω [4]. Since theCherenkov angle contains information of the particle energy, the particular reflective optics is needed to focus thephotons having the same Cherenkov angle on a certain position of a detector, such as a “turtle-back” mirror. Moreover, the “turtle-back” mirror was proposed to focus photons having the different Cherenkov angles on the focal
points aligned as a straight line. Thus the energy distribution of the beam can be observed at once by the streak camera. The mirror surface defined a base position (0, y0 , s0 )can be expressed as Eq. 2.
p
1 2 A 2s + ) = 0 (A ≡ y0 2 + s0 2 + y0 )2A2(2)
At t-ACTS the electron kinetic energy extracted fromITC-RF gun is approximately 1.87 MeV with energy
spread of about 2% [1]. For instance, the Cherenkov ray
from the electron with a kinetic energy of 1.87 MeV strikes
the “turtle-back” mirror at s0 = 47.887 cm (y0 = 10.890 cm, since θc = 0.224 rad). If the entrance slit size of the streak
camera is about 3 mm, electron kinetic energy distribution
in range of 1.870 ± 0.034 MeV can be detected at once.
Moreover, the “turtle-back” mirror has azimuthal symmetry around s-axis, thus 10% of the Cherenkov cone can bedivided to detect by the mirror azimuthal size of 36◦ .

x2 + y 2 − (−- 194 -Proceedings of the 10th Annual Meeting of Particle Accelerator Society of Japan (August 3-5, 2013, Nagoya, Japan)

Assuming no frequency dependences of the refractive
index and the permeability of the Cherenkov radiatormedium in a narrow band, the number of photons N between wavelengths λ1 and λ2 emitted from an electron isshown in Eq. 3,
N = 2παz(11− ) sin2 θc ,
λ1
λ2(3)

where z is radiator thickness and α is the fine structure constant. For example, if an aerogel with refractive index of
1.05 and thickness of 1.0 mm is selected as the radiator, estimated number of the Cherenkov photons produced by 20pC electrons (in micro-pulse) at 1% bandwidth of a wavelength around 555 nm is about 5.07 million for the electron
kinetic energy of 1.87 MeV. In this case, the number ofphotons is obviously above detection threshold of a highresolution streak camera, despite 10% of the Cherenkov
cone split to detect.
Fig. 1 shows the experimental setup. As the “turtleback” mirror gives a focal line on the s-axis, the two offaxis parabolic cylinder mirrors (such as the focal length =10 cm) can be used to transport photons outside the radiator chamber and confine again [3]. The focal line of the 1stand 2nd off-axis parabolic cylinder mirror are the 1st and2nd focal line in Fig. 1 respectively.

Figure 2: (a)Detector screen for point-like beam at various
kinetic energy, (b)spatial profile for horizontal beam size of
4 mm, (c)one for vertical beam size of 0.4 mm, and (d)one
for point-like beam by radiator thickness of 1.0 mm.
resolution. In addition, thickness of radiator also affects on
the energy resolution as shown in Fig. 2(d).
The radiator was intended to be placed outside the vacuum chamber. However, electron beams passing througha dense material lose energy in collisions with the atomic
electrons. For low emittance growth from the multiple scatterings, a beryllium thin film could be chosen as a beam
window to extract the electron beam from the vacuum [5].

MULTIPLE SCATTERINGS OFELECTRON BEAM
Figure 1: Schematic apparatus of the linear focal
Cherenkov ring camera.
By using Eq. 1 and 2, the focal position sf at particle
velocity β can be derived as Eq. 4 [4].
s 21sf (β) = Anβ 1 − 1 −(4)nβThe energy dependence of focal position at the optical detector is about 22.8 keV/mm at electron kinetic energy
around 1.87 MeV. The example result on detector screenfor point-like beam at various kinetic energy is shown inFig. 2(a). Furthermore, if resolution of image intensifier is
20 µm, an energy resolution of detector is 0.457 keV.
To investigate effect of beam size on the energy resolution, spatial profiles on the optical detector for uniform
beam are illustrated as Fig. 2(b) and 2(c), where the spatialsize on the detector is directly proportional to the energy

Electron beam suffers significantly from multiple scatterings. At low energies electrons primarily lose energyby ionization, although other processes (Møller scattering,
Bhabha scattering, e+ annihilation) contribute [6]. Moreover, by multiple scatterings of injected particles throughthe beam window, the root-mean-square deflection angle
θrms is given for an relativistic particle as Eq. 5,
r21MeVt
2 1/2
θrms = hθ i=,(5)EX0where E is the beam energy, t is the thickness of the material, and X0 is the radiation length in the material [5]. If
the minimum thickness of the beryllium thin film that isstrong enough for vacuum is 50 microns, θrms is 0.105 radfor electron kinetic energy of 1.87 MeV.
Geant4 is a free software package composed of tools
which can accurately simulate the passage of particles
through matter by using Monte Carlo methods [7]. To understand multiple scattering effect, Geant4 results, such as
the deflection angle and the longitudinal phase space of the- 195 -Proceedings of the 10th Annual Meeting of Particle Accelerator Society of Japan (August 3-5, 2013, Nagoya, Japan)

electron beam passing through the beam window, can beinvestigated, as shown in Fig 3.

window degrades the energy resolution essentially, sincethe position on the focal line dictates the electron energy.
To extract the electron beam from the vacuum chamber tohit the radiator fails the longitudinal phase space distribution measurement via the linear focal Cherenkov ring camera. The radiator and the reflective optics were suggested to
be placed inside the vacuum, and the Cherenkov light could
be extracted from the vacuum chamber through a quartz
window to the detector.

CONCLUSION AND PROSPECT
Longitudinal phase space distribution measurement via
a linear focal Cherenkov ring camera has been studied.
Due to the numerical ray tracing results combining multiple
scatterings effect of Geant4 results, an experimental setup
with a beryllium thin film to extract the electron beam fromthe vacuum degrades the energy resolution of the measurement. However, the experimental setup, in which the radiator and the reflective optics were placed inside the vacuum
chamber, was proposed, and the Cherenkov light could betransported through a quartz window out of the vacuum tothe detector.
Figure 3: (a)Root-mean-square deflection angle of an injected electron passing through the varied beryllium thinfilm. (b)Transverse and (c)longitudinal phase space ofpoint-like electron beam through 50-micron beryllium thinfilm (incident kinetic energy of electron beam = 1.87MeV).
Fig. 3(a) and 3(b) show that the deflection angle of an
injected electron passing through the 50-micron beryllium
thin film is high significantly according to derivative of
the Cherenkov angle dθc /dβ, which corresponds to energy resolution. However, as shown in Fig. 3(c), time deviates slightly in the longitudinal phase space contrary totime resolution of streak camera, and small energy distribution is also negligible for energy resolution. An experimental setup was examined with numerical ray tracing withthe Geant4 results, in which the point-like electron beam
passes through the beryllium window and the radiator respectively as shown in Fig. 4.

ACKNOWLEDGMENT
Authors would like to thank Drs. N.Y. Huang, R. Yamazaki, M. Miyabe, and H. Kikunaga for technical assistance. Authors acknowledge the support from Electron Light Science Centre, Tohoku University, Monbukagakusho (MEXT) Scholarship, and Japanese Government
Monbukagakusho: MEXT Scholarship, Ministry of Education, Culture, Sports, Science, and Technology, Japan. This
works is partly supported by the Grants-in-Aid of Japan Society for the Promotion of Science, contract no. 24651096
and 25790078.

REFERENCES[1] N.Y. Huang, “Advanced Linear Accelerator System for Generation of Femto-second Electron Beam toward Intense Radiation Sources”, PhD thesis, National Tsing Hua University,
2013.
[2] F. Hinode et al., Proc. of FEL2012, (2012) 137.
[3] K. Nanbu et al., Proc. of FEL2011, (2011) 576.
[4] H. Hama et al., Proc. of BIW10, (2010) 79.
[5] D. Rubin, “Multiple Scattering in Injection Channel”, CON02-01, LEPP, Cornell University, Ithaca, NY 14853, USA.
[6] J. Beringer et al. (Particle Data Group), Phys. Rev. D86,010001 (2012).

Figure 4: Spatial profile for point-like electron beam withthe 50-micron beryllium thin film

[7] The Geant4 Collaboration, Introduction to Geant4, http://geant4.cern.ch/G4UsersDocuments/Welcome/Introd
uctionToGeant4/print/IntroductionToGeant4Merge
d.pdf , 2005.

Contrary to Fig. 2(b), 2(c) and 2(d), Fig. 4 shows thatmultiple scatterings of the electron beam in the beryllium- 196 -