INCOHERENT AND COHERENT SYNCHROTRON RADIATION EFFECTS
IN THE SUPERKEKB ELECTRON BEAM TRANSPORTT. Yoshimoto∗ , D. Zhou, Y. Seimiya, N. Iida, and M. Kikuchi
High Energy Accelerator Research Organization (KEK), [3050801] Tsukuba, Japan
Abstract
The delivery of 7-GeV low-emittance electron beams into
the SuperKEKB lepton collider is essential. However, thebeam 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 positron beams [1]. The electron beam
is delivered through the beam transport (BT) following theinjector LINAC, as shown in Fig. 1. The BT which wasconstructed for the previous KEKB project is reused withoutmajor changes. A nominal BT optics is illustrated in Fig. 2.

Figure 2: Nominal 7-GeV electron beam transport optics
with dispersion functions shown in blue and red for thehorizontal and vertical directions, respectively.

RADIATIVE EMITTANCE GROWTHS
Radiative effects on transverse emittances are typicallycaused by synchro-betatron coupling due to beam energychanges in dispersive sections. However, in contrast to theISR effect, the CSR effect depends on the height and widthof the beam ducts (CSR shielding 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 the beam ducts inside the bending magnets
were 32 mm. The evolution of the beam emittances along
the BT for a 2.2-nC beam is shown in Fig. 4.

Figure 1: 7-GeV electron beam transport between the SuperKEKB high-energy ring (HER) and the LINAC. It comprises two achromatic sections of BT1 and BT2. The bending and quadrupole magnets are indicated in blue and green,
respectively.
The BT has several arc sections with large curvature owingto the geometric constraints from existing photon source
facilities. This results in large dispersion functions, as shownin Fig. 2. It is well known that, for multi-GeV low-emittance
lepton beams, both the incoherent synchrotron radiation(ISR) and coherent synchrotron radiation (CSR) play crucial
roles in beam dynamics.
∗ yoshimo@post.kek.jp

Figure 3: Initial beam distribution on the (a) x–x′ , (b) y–y′ ,(c) x–y, and (d) z–𝛿 planes, with normalized histograms in
dark-blue before the 7-GeV electron beam transport. The
color code indicates the density of the beam.

The horizontal emittance growth induced by the CSR
occurred primarily in the first strong 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 the transfer matrix. Hence, strong
CSR wake occurred locally within the beam. The maximum
energy modulation of one bending magnet in the bunch wasestimated at ∼0.6 MeV in the simulation (Fig. 6). Consequently, the energy change that depends on z within thebunch in Arc1, where the horizontal dispersion surpasses 2m, induces emittance growth in the horizontal direction.

Figure 4: Evolution of the normalized horizontal (top)and vertical (bottom) emittances along the beam transport.
The emittances without ISR and CSR, those with ISR, andthose with both ISR and CSR are shown in blue, red, andgreen, respectively. Note that the√︃ horizontal and verticalemittances here are calculated by ⟨x2 ⟩⟨x′ 2 ⟩ − ⟨x · x′ ⟩ 2 and√︃⟨y2 ⟩⟨y′ 2 ⟩ − ⟨y · y′ ⟩ 2 , respectively.

The simulation results indicated no significant verticalemittance growth, regardless of the 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. The measurements and simulations were reasonably consistent only in the horizontal direction, and not inthe 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 and CSR effects, a slighthorizontal emittance growth was observed between BT1 andBT2, which is attributed to high-order dispersions.
Table 1: Normalized rms emittances for a 2.2-nC beam at
BT1 and BT2 in the simulations compared with measured
values presented in parentheses
Simulation condition
No. ISR

123No
Yes
Yes

CSRNoNo
Yes

Location
BT1BT2x/y[µm]x/y[µm]

34/30
54/31
35/30
104/3236/30
132/32(∼30/∼30) (∼120/∼80)

Figure 5: Particle distribution on the (a) x–x′ , (b) y–y′ , (c)x–y, and (d) z–𝛿 planes in Arc 1.

Figure 6: Longitudinal charge profiles (purple) and integrated CSR wake field produced by a bending magnet (orange) in Arc1.

COUNTERMEASURES
Several schemes have been proposed to mitigate the emittance growth due to ISR and CSR effects.

New beam transport line
As evident, a smaller number of arc sections directly reduces the radiation effects. We explored the possibility of anew straight BT line as shown in Fig. 7, which replaces thepresent Arc1 and Arc2. The proposed beam line retains thebeam line at downstream of Arc3. The CSR and ISR effects

were calculated using a preliminary optics of the new BTline (Fig. 8). Figure 9 shows the evolution of the horizontal
emittance along the beam line for the cases 1) without ISRand CSR, 2) with ISR, and 3) with ISR and CSR.

Enhanced CSR shielding
Generally, narrowing the beam ducts is effective to suppress CSR-induced emittance growth. Figure 10 shows anexample of the simulation results of the case with a ductheight of 10 mm for all bends for a 2.2-nC beam. In thissimulation, the CSR effects was underestimated owing to thelack of the transient CSR wake. The simulation results revealed that narrower ducts can effectively suppress the CSReffect. 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 7: New straight beam transport line with two achromatic segments of nBT1 and BT2.

Figure 10: Evolution of the normalized horizontal emittances with narrower beam duct. The normalized horizontal
emittances at the injection point 1) with ISR (blue), 2) with
ISR and CSR (red), and 3) with ISR and CSR and a ductheight of 10 mm (green) are 99, 126, and 100 µm, respectively.

SUMMARY
Figure 8: Optics for the new electron beam transport.

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

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

REFERENCES
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 andCSR are 38, 52, and 66 µm, respectively.
The new BT line shows a significant reduction in the ISR
and CSR effects, although their effects are still not negligible.
Lower dispersion optics, which may be available by adding
more quadrupoles, will contribute to suppress the ISR andCSR effects.

[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 forAccelerator 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 ofcoherent synchrotron radiation by electrons in a bunch compressor”, Phys. Rev. AB vol. 23, 014402, 2020.