MOPA107

Incoherent and coherent synchrotron radiation effects
in the superKEKB electron beam transport
T. Yoshimoto∗, Z. Demin, Y. Seimiya, N. Iida, and M. Kikuchi
High Energy Accelerator Research Organization (KEK), [3050801] Oho, Tsukuba, Japan

Abstract

The delivery of 7-GeV low-emittance electron beams into the SuperKEKB lepton collider is essential. However, the beam transport between the linear accelerator (LINAC) andthe High-Energy Ring is plagued by significant transverse emittance growths. In general, both incoherent and coherent synchrotron radiations are crucial in beam dynamics.
This study reported the measured emittance results of a nominal optics along with the results of particle tracking simulations.

INTRODUCTION
The SuperKEKB is a double-ring collider with 7-GeV electron and 4-GeV positronbeams [1]. The electron beam is delivered through the beam transport (BT) following
the injector LINAC, as shown in Fig. 1. The BT which was constructed for the previous
KEKB project is reused without major changes. A nominal BT optics is illustrated in Fig.
2.
The BT has several arc sections with large curvature owing to the geometric constraints
from existing photon source facilities. This results in large dispersion functions, as
shown in Fig. 2. It is well known that, for multi-GeV low-emittance lepton beams, boththe incoherent synchrotron radiation (ISR) and coherent synchrotron radiation (CSR)
play crucial roles in beam dynamics.

The horizontal emittance growth induced by the CSR occurred primarily in the firststrong bending sections following BT1 (Arc1). In this region, the bunch exhibited asteep longitudinal profile, as shown in Fig. 5, owing to nonzero 𝑅56 component of thetransfer matrix. Hence, strong CSR wake occurred locally within the beam. Themaximum energy modulation of one bending magnet in the bunch was estimated at∼0.6 MeV in the simulation (Fig. 6). Consequently, the energy change that depends onz within the bunch in Arc1, where the horizontal dispersion surpasses 2 m, induces
emittance growth in the horizontal direction.

Figure 5: Particle distribution on the (a) x–x′, Figure 6: Longitudinal charge profiles (purple)
and integrated CSR wake field produced by a(b) y–y′, (c) x–y, and (d) z–𝛿 planes in Arc 1.
strong bending magnet (orange) in Arc1.

COUNTERMEASURES

Figure 1: 7-GeV electron beam transport
between the SuperKEKB high-energy ring (HER)
and the LINAC.

Figure 2: The nominal optics of theelectron beam transport.

RADIATIVE EMITTANCE GROWTHS
Radiative effects on transverse emittances are typically caused by synchro-betatron
coupling due to beam energy changes in dispersive sections. However, in contrast tothe ISR effect, the CSR effect depends on the height and width of the beam ducts (CSRshielding effect). This study performed particle tracking simulations using ELEGANT [2]to evaluate the ISR effect and CSR shielding effects on transverse emittances in the BT.
The steady-state parallel-plate CSR model [3] was employed in the simulations
assuming an initial beam distribution, which is shown in Fig. 3. The full heights of thebeam ducts inside the bending magnets were 32 mm. The evolution of the beamemittances along the BT for a 2.2-nC beam is shown in Fig. 4.

⚫ NEW BEAM TRANSPORT LINEAs evident, a smaller number of arc sections directly reduces the radiation effects. We
explored the possibility of a new straight BT line as shown in Fig. 7, which replaces thepresent Arc1 and Arc2. The proposed beam line retains the beam line at downstreamof Arc3. The CSR and ISR effects were calculated using a preliminary optics of the newBT line (Fig. 8). Figure 9 shows the evolution of the horizontal emittance along thebeam line for the cases 1) without ISR and CSR, 2) with ISR, and 3) with ISR and CSR.
The new BT line shows a significant reduction in the ISR and CSR effects, although theireffects are still not negligible. Lower dispersion optics, which may be available byadding more quadrupoles, will contribute to suppress the ISR and CSR effects.

Figure 7:A new straight beam transport line.
Figure 9: Evolution of the normalized
horizontal emittances. The normalized
horizontal emittances at the injection
point 1) without ISR and CSR, 2) with ISR,and 3) with ISR and CSR are 38, 52, and66 µm, respectively.

Figure 3: Initial beam distribution on the (a) x–x′, (b) y–y′, (c) x–y, and (d) z–𝛿 planes, withnormalized histograms in dark-blue before the7-GeV electron beam transport.
Figure 4: Evolution of the normalized horizontal (top) and vertical (bottom) emittances along thebeam transport.

The simulation results indicated no significant vertical emittance growth, regardless ofthe effects of ISR and CSR; however, both the effects increased the horizontal emittance
between BT1 and BT2. Table 1 summarizes the emittance growths with the nominal
measured data. Emittance measurements were performed using four wire monitors at
BT1 and with the quadrupole-scan method using a profile monitor at BT2. Themeasurements and simulations were reasonably consistent only in the horizontal
direction, and not in the vertical direction. The source of the vertical emittance growth
remains unclear. It may be attributed to the 3D-CSR effect [4]. In addition to the ISR andCSR effects, a slight horizontal emittance growth was observed between BT1 and BT2,
which is attributed to high-order dispersions.
Table 1: Normalized rms emittances for a 2.2-nC beam at BT1 and BT2 in simulations withmeasured values in parentheses.

No.

123Simulation condition
ISRCSRNoYes
Yes

NoNo
Yes

2.
3.
4.
5.

⚫ ENHANCED CSR SHIELDING
Generally, narrowing the beam ducts is effective to suppress CSR-induced emittance
growth. Figure 10 shows an example of the simulation results of the case with a ductheight of 10 mm for all bends for a 2.2-nC beam. In this simulation, the CSR effects
was underestimated owing to the lack of the transient CSR wake. The simulation
results revealed that narrower ducts can effectively suppress the CSR effect. However,
the application of this scheme to the BT line necessitates the evaluation of the vacuum
conductance, resistive wall effects, as well as the beam tuning feasibility.
Figure 10: Evolution of the normalized
horizontal emittances with narrower beam
duct. The normalized horizontal emittancesat the injection point 1) with ISR (blue), 2)
with ISR and CSR (red), and 3) with ISR andCSR and a duct height of 10 mm (green) are
99, 126, and 100 µm, respectively.

Location
BT1
x/y
[µm]
34/30
35/30
36/30

BT2x/y[µm]
54/31
104/32
132/32(∼30/∼30)(∼120/∼80)

REFERENCES
1.

Figure 8:
An optics for the new electron beam transport.

[1]
K. Akai et al., “SuperKEKB collider”, Nucl. Inst. Meth. A vol.
907, pp. 188–199, 2018. doi:10.1016/j.nima.2018.08.017[2]
M. Borland, “elegant: A Flexible SDDS-Compliant Code for Accelerator Simulation”, Advanced Photon Source LS-287 2000.
[3]
T. Agoh and K. Yokoya, “Calculation of coherent synchrotron radiation using mesh”, Phys. Rev. ST-AB vol. 7, 054403, 2004.
[4]
Yunhai Cai and Yuantao Ding, “Three-dimensional effects of coherent synchrotron radiation by electrons in a bunch compressor”, Phys. Rev. AB vol. 23, 014402, 2020.

SUMMARY
In the SuperKEKB electron BT line, ISR and CSR play crucial roles in beam dynamics.
Their radiative effects on transverse emittances are a result of the synchro-betatron
coupling due to beam energy modulation within the bunch in dispersive sections.
Based on the numerical simulations in this study, the new BT line which has lessdispersive arcs was proposed. Narrower gap height of the beam duct can also
effectively suppress the CSR effect.

ACKNOWLEDGEMENTS
The authors express their gratitude to all members and operators of the superKEKB
project and KEK injector group.