Proceedings of the 20th Annual Meeting of Particle Accelerator Society of Japan
August 29 - September 1, 2023, Funabashi

PASJ2023 WEP48

A STUDY FOR ENVELOPE MATCHING OF ELECTRON BUNCH FOR
EMITTANCE REPARTITIONING EXPERIMENT IN KEK-STF
Sayantan Mukherjee†,1, Masao Kuriki1, Keisuke Date1, Zachary J. Liptak1, Hitoshi Hayano2,Kirk Yamamoto2, Naoto Yamamoto2, Masafumi Fukuda2, Xiuguang Jin2, Masakazu Kurata2,Kazuyuki Sakaue3
1
Hiroshima University, Hiroshima, Japan2
KEK Accelerator laboratory, Tsukuba, Japan
3
University of Tokyo, Tokyo, JapanAbstract
The International Linear collider (ILC) is a e+ e- linear
collider at centre of mass energy up to 1 TeV. At the interaction point, the beam shape must be flat in the transverse
space to maximize the luminosity, compensating the energy spread by beamstrahlung. The flat beam is obtainedby asymmetric emittance in x and y made up by radiation
damping with a 3 km damping ring. We propose a new
method to make the asymmetric emittance based on emittance exchange techniques using the two beamlines called
as Round to Flat beam transformation (RFBT) and Transverse to Longitudinal Emittance exchange (TLEX). In
KEK Superconducting Test facility (STF) the RFBT experiment has been performed but the results are not as expected due to a significant emittance growth due to thespace charge effect. We studied the emittance growth compensation by space charge effect by the envelope matchingin the STF injector. We report the results of our study here.

INTRODUCTION
The purpose of flat beam generation is to increase theluminosity of the linear collider and to reduce the beamstrahlung effect. The beam luminosity is inversely proportional to beam sizes, i.e., 𝐿𝐿 =𝑓𝑓𝑛𝑛𝑏𝑏 𝑁𝑁24𝜋𝜋𝜎𝜎𝑥𝑥 𝜎𝜎𝑦𝑦, whereas the beam-strahlung is proportional to (𝜎𝜎𝑥𝑥 + 𝜎𝜎𝑦𝑦 )−2 . Thus, to simultaneously increase luminosity and reduce beamstrahlung weshould have an asymmetric flat beam (𝜎𝜎𝑥𝑥 ≫ 𝜎𝜎𝑦𝑦 ) [1]. Generation of such flat beams is usually carried out by damping
rings. However, the emittance exchange techniques RFBTand TLEX have a much simpler beamline design which
could reduce the maintenance cost as well. In this paper thedescription of RFBT experiment and its implementation atthe STF beamline of KEK is given. The concept of RFBT
[2] was previously studied by several groups. The flat beam
generation for KEK-STF had been studied and experiments
were performed by M. Kuriki and S. Aramoto et al. [1], but
the flat beam generation was not confirmed due to the emittance growth of the beam. In this article, we report the results of studies of the emittance growth and its compensation due to the space charge effect in the STF injector part.
Simulations were performed with ASTRA.
___________________________________________† d223836@hiroshima-u.ac.jp

ROUND TO FLAT BEAM TRANSFORMATIONThe RFBT involves transformation of an angular momentum dominated beam into a flat beam after passing
through three skew quadrupoles. The solenoid provides thenecessary magnetic field for generating an angular momentum dominated beam according to the equation:𝑒𝑒ℒ = 𝛾𝛾𝑚𝑚𝑟𝑟2 𝜑𝜑̇ +𝛷𝛷 = 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐.,
2𝜋𝜋
where ℒ is the angular momentum and 𝛷𝛷 is the magnetic flux. After passing through the solenoid field, theelectron trace space coordinate transforms as:
𝑦𝑦𝑥𝑥𝑒𝑒𝑒𝑒
𝑋𝑋 = �𝑥𝑥 ′ − 𝑘𝑘𝑘𝑘�, 𝑌𝑌 = �𝑦𝑦 ′ + 𝑘𝑘𝑘𝑘 � where 𝑘𝑘 = .
2𝑃𝑃𝑧𝑧
As a result, the beam matrix becomes: [3]𝜎𝜎 200𝑘𝑘𝜎𝜎 22 2′22𝑘𝑘 𝜎𝜎 + 𝜎𝜎−𝑘𝑘𝜎𝜎0𝛴𝛴 = � 0
�
𝜎𝜎 200−𝑘𝑘𝜎𝜎 200𝑘𝑘 2 𝜎𝜎 2 + 𝜎𝜎 ′2𝑘𝑘𝜎𝜎 2where𝜎𝜎 2 =< 𝑥𝑥 2 >=< 𝑦𝑦 2 >, 𝜎𝜎′2 =< 𝑥𝑥′2 >=< 𝑦𝑦′2 >and ℒ = 𝑘𝑘𝜎𝜎 2 is the angular momentum. If the Twiss parameters are matched, i.e., 𝛼𝛼𝑥𝑥 = 𝛼𝛼𝑦𝑦 and 𝛽𝛽𝑥𝑥 = 𝛽𝛽𝑦𝑦 just before the skew quadrupoles then the x-y correlation can beremoved and the flat beam can be obtained which has
asymmetric emittances 𝜀𝜀𝑥𝑥 = �𝜀𝜀𝑢𝑢2 + ℒ 2 + ℒ and 𝜀𝜀𝑦𝑦 =�𝜀𝜀𝑢𝑢2 + ℒ 2 − ℒ, giving its ratio as 𝜀𝜀𝑥𝑥 /𝜀𝜀𝑦𝑦 ~4ℒ 2 /𝜀𝜀𝑢𝑢2 .

KEK-STF

KEK-STF is a linear accelerator based on the superconducting accelerator model. The beamline consists of a
1.3 GHz L-band normal conducting RF gun [4] with Cs2Te
photocathode and two cryomodules as shown in Fig. 1. The
first module is referred to as CCM (Capture Cryomodule)

Figure 1: Block diagram for the STF beamline at KEK- 628 -Proceedings of the 20th Annual Meeting of Particle Accelerator Society of Japan
August 29 - September 1, 2023, Funabashi

PASJ2023 WEP48

which accommodates two super-conducting cavities. The
second is referred to as CM (Cryomodule) which accommodates 12 superconducting cavities. The CM section consists of CM-1a and CM-2a which are also cryomodules. In
CM-1a and CM-2a, there are 9 TESLA cavities with
40 MV/m gradient.
The RF gun has a peak field of 44 MV/m with 3.5 MW
RF input [5]. The cathode is Cs2Te semiconductor formed
on a molybdenum block by evaporation in vacuum. The laser spot size is 2 mm in radius and the thermal emittance is0.80 π mrad mm. A solenoid magnet is placed for focusing.
There is a bucking coil whose purpose is to cancel the magnetic field on the cathode generating angular momentum.
The angular momentum spoils the 2D emittance in x-x’ andy-y’ plane. For performing the RFBT experiment only weneed angular momentum. A B-field on cathode can be obtained by switching the bucking coil polarity.
The chicane is placed at downstream of the RF gun, followed by CCM. The chicane, shown in Fig. 2 consists offour dipole magnets of length 0.114 m each. The bending
angle and strength of the dipole magnets are 16.2𝑜𝑜 and
0.048 T respectively. The bending magnets bend the beamin a horizontal direction whereas the beam is focused on
the vertical direction due to the edge-focusing effect. The
focal length is estimated as 1.04 m based on linear dynamics. Between CCM and CM, a beam diagnostic section isplaced where emittance can be measured by Q-scanmethod. There is a momentum analyser with a bending
magnet in the middle which is not shown in the figure.
Downstream of CM-2a is the RFBT section composedof two Q-magnets, three skew Q-magnets, two Q-magnets,
and RPM06 (screen). The two Q-magnets match the Twiss
parameters before the skew Q-magnets for generating flatbeam.
Table 1: Simulation Parameters
Parameter
value
Unit
Charge0.06
nC
Laser pulse duration
12Ps
Laser rms spot size
1.0mm
Thermal emittance
0.80
π mrad mmBunch size (RMS)
0.77mm
RF gun gradient on-43.5MV/mcathodeRF gun frequency
1.3GHzBeam energy before
5.474
MeVCCM

main and bucking solenoid coils are adjusted to provide
zero magnetic field at the cathode.

Figure 2: Beam trajectory in horizontal and vertical plane
after passing through the chicane.

Figure 3: Gaussian beam generated in ASTRA with rms
laser spot size 1.0 m.

Space charge effect

SIMULATION STUDY
Figure 3 shows the initial beam distribution in the x-zand y-z planes. 10,000 macro particles are generated inGaussian distribution. The initial beam parameters aresummarized in Table 1 together with other simulation parameters. To investigate the space charge in emittance
growth, we used a non-magnetized beam. Therefore, theOur goal at the injector region of STF beamline is tocompensate the emittance growth by space charge to obtainsufficiently good emittance to perform the RFBT experiment. Because the space charge effect is highly suppressedby acceleration, the emittance is conserved after acceleration. We expected the emittance growth in the injector region due to 1) Slice deformation and mismatch in transverse space by the transverse space charge effect, 2) Slicemismatch in transverse space by combination of longitudinal space charge effect and the transverse dispersion in chicane. 1) and 2) are occurred in x, but only 1) in y becauseof no dispersion in y.
The space charge force is non-linear effect because of
the Gaussian distribution, and it rotates at different angles
on the beam due to which we get slice mismatches. As aresult, both the area of each slice and the area of the projected slice are increased.

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Proceedings of the 20th Annual Meeting of Particle Accelerator Society of Japan
August 29 - September 1, 2023, Funabashi

PASJ2023 WEP48

The solenoid gives focusing in both x and y direction andcan reduce the space charge effect in the transverse directions by envelope matching. In our case, the chicane provides additional focusing in y as the edge focusing whichcauses the beam size to shrink and thus increase the spacecharge effect in the y direction. For this reason, we have theQi magnet at the downstream of chicane to compensate byfocusing in the x direction and de-focusing in y to achieve
quasi-symmetric focusing.
The chicane gives another emittance growth effect. The
longitudinal space charge effect gives energy spread between the bunch head and tail. If the effect exists wherever
there is dispersion, the emittance is increased due to thehorizontal slice shift according to the slice energy. Thisemittance growth by the longitudinal space charge cannot
be compensated by solenoid focusing in x. We varied thesolenoid strength and observed asymmetric emittances in x
and y at s=4.5 m and the results are shown in Fig. 4. The xemittance is minimized with 0.18 T solenoid field, but theevolution of y emittance is quite different. The chicane
gives edge focus in y direction which disturbs the emittancecompensation by the solenoid. The minimum emittance in
x is, however, 2.2 π mrad mm which is larger than the thermal emittance at the cathode. Because the emittance
growth by the longitudinal space charge effect with dispersion in chicane could not be compensated by solenoid focusing, it remains even if the emittance growth by the slice
mismatch is compensated.

Figure 5: Ellipse of longitudinal bunch slice in x phasespace giving 2.0 π mrad mm emittance at s=2.15 m.

Figure 6: Ellipse of longitudinal bunch slice in y phasespace giving 2.0 π mrad mm emittance at s=2.15 m.

Figure 4: Transverse emittance as a function of solenoid
field. Due to the chicane, we have asymmetric focusing on
x and y and thus the emittances could not be simultaneously optimized.
To confirm this speculation, the slice motion was observed in the STF injector with and without chicane. The
solenoid field is applied in both cases. The longitudinalphase ellipse is observed at s=2.15.
Figure 5 and 6 show the longitudinal slice ellipse intransverse phase space x and y, respectively without thechicane. The slice deformation and angle mismatch are observed as an imperfection of the emittance compensation
by solenoid, but Fig. 5 in x and 6 in y are symmetric because the system is symmetric in x and y.

Figure 7: Ellipse of longitudinal bunch slice in x at s=2.15
m with chicane giving 2.2 π mrad mm.
Figure 7 and 8 show the same plot, but with the chicane.
Figure 7 shows that slices are shifted in x direction whichis consistent with the speculation that the emittance is increased by slice shift due to dispersion with the longitudinal space charge effect. Figure 8 shows slice rotation mismatch which is also consistent to the envelope matchingwith solenoid is disturbed by the edge focus effect of chicane.
The phase space distribution of particles in x without chicane is shown in Fig. 9. In this condition, the solenoid field
is adjusted to compensate the emittance growth, but the- 630 -Proceedings of the 20th Annual Meeting of Particle Accelerator Society of Japan
August 29 - September 1, 2023, Funabashi

PASJ2023 WEP48

non-linear deformation is observed which is evidence of
non-linear contribution in the emittance growth.

[2] P. Piot, Y.-E Sun, and K.-J. Kim, “Photoinjector generation of a flat electron beam with transverse emittance ratio of 100”, Phys. Rev. Accel. Beams, vol. 9,p.031001, 2006. doi:10.1103/PhysRevSTAB.9.031001[3] Yin-E Sun, “Angular-momentum dominated electron
beams and flat-beam generation”, Ph. D thesis, The
University of Chicago, 2005.
[4] H Sugiyama et al., “L-band Photocathode RF Gun atKEK-STF”, J. Phys.: Conf. Ser., vol. 298, p. 012015,
2011. doi:10.1088/1742-6596/298/1/012015[5] M. Kuriki, “1 ms pulse beam generation and acceleration by photocathode Radio Frequency Gun and Superconducting accelerator”, Jpn. J. Appl. Phys., vol.
52, p. 056401, 2013. doi:10.7567/JJAP.52.056401

Figure 8: Slice ellipse at 2.15 m with chicane. The y emittance is 3.4 π mrad mm.

Figure 9: Nonlinear space charge effect in x phase space.
At 4.5 m, the emittance has increased to 3.1 π mrad mmwithout chicane.

CONCLUSION
We attempted to optimize the STF injector to perform
RFBT experiment. A simulation study with ASTRA wascarried out and we found that the chicane causes asymmetric emittance growth in x and y. In the horizontal direction,
the emittance is increased by a combination of the longitudinal space charge effect in chicane where dispersion exists.
In the vertical direction, the emittance is increased because
the edge focus of the chicane disturbs the emittance compensation by the solenoid. We could not find the best condition of the injector because the horizontal and verticalemittances are not able to be optimized simultaneously. We
will evaluate the expected RFBT experiment performancewith this condition.

REFERENCES[1] M. Kuriki et al., “Flat Beam Generation with the Phase
Space Rotation Technique at KEK-STF”, in Proc.
IPAC'22, Bangkok, Thailand, Jun. 2022, pp. 18971900. doi:10.18429/JACoW-IPAC2022-WEPOPT025- 631 -