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

PASJ2023 TUP16

DESIGN OF A COMBINED-FUNCTION QUADRUPOLE-SEXTUPOLEMAGNET FOR HISOR-II
1

Y. Lu∗ 1,3 , M. Katoh1,2 ,M. Shimada3,1 , H. Miyauchi3,1 ,Hiroshima Synchrotron Radiation Center, Hiroshima University, Higashi-Hiroshima
2
UVSOR Synchrotron Facility, Okazaki
3
High Energy Accelerator Research Organization (KEK), Tsukuba

Abstract

Table 1: Parameters of the Proposed Lattice

HiSOR-II is a low-energy storage ring and is under designing for the future plan at Hiroshima Synchrotron Radiation Center. A compact lattice is desired to reduce thecost and space, which requires combined-function magnet
components. In this paper, a combined-function quadrupolesextupole magnet for the beam focusing and chromaticity
correction is introduced. We proposed two different designs
using auxiliary coil and pole profile adjustment, respectively.
The magnet field is calculated using Poisson and Radia. Bothdesigns have been optimized to meet the magnetic field requirement.

Major Parameters

Proposed Design

Energy [MeV]
Circumference [m]Emittance [nm]Beam current [mA]
RF frequency [MHz]Tune (𝜈𝑥 , 𝜈𝑦 )Number of undulators

500
31.38
17.73
300
191
2.75/2.46
4INTRODUCTIONHiSOR is a small synchrotron light source operated from1996 in Hiroshima University [1]. A new low-energy storage
ring HiSOR-II is under designing for the increasing demandof high-brilliance radiation. A proposed ring lattice layout
is shown in Fig. 1, which only consists of two kinds ofmagnet. The bending magnet and quadrupole magnet areboth combined-function magnets. The bending magnet iscapable of producing quadrupole and sextupole field, andthe quadrupole magnet is capable of producing sextupole
field. The use of combined-function magnet is to reduce
the operation cost, the accelerator size and the amount ofmaterials for the lattice components. The major parametersof the ring are summarized in Table 1.

low energy of the ring, the strengths of the multipole components are relatively small. In addition, the sextupole strength
can be minimised if they are positioned in the quadrupole
magnet where the beta-functions are large.

DESIGN USING AUXILIARY COILThe basic idea is to use two auxiliary coils to generate
sextupole component in a quadrupole magnet [2]. The radiusof the magnet aperture is assumed to be 40 mm.

Preliminary design of a quadrupole magnet
Firstly, a quadrupole magnet is designed using Poisson. A

1model of the quadrupole magnet is shown in Fig. 2. The
8

total current of the coil 𝑁𝐼 is approximately given by𝑁𝐼 =𝑘𝑟 2,2𝜇0(1)where 𝑘 is the gradient of the magnetic field, 𝑟 is the aperture
radius, and 𝜇0 is the magnetic permeability in vacuum.

Figure 1: Layout of HiSOR-II ring.
The design of the quadrupole magnet is reported. We
proposed two different designs using auxiliary coil and pole
profile adjustment, respectively. From the ring lattice, thelength of the magnet is 0.18 m. The quadrupole field is
7.55 T/m, and the sextupole field is 15.20 T/m2 . Due to the∗ yaolu@hiroshima-u.ac.jp- 316 -Figure 2: 1/8 model of the quadrupole magnet.

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

PASJ2023 TUP16

Combined-function magnet using auxiliary coilOnce the geometry of the quadrupole magnet and thecurrent value are decided, two auxiliary coils are added.
The sextupole magnetic field is generated by a sextupole
coil and a dipole correction coil. As shown in Fig. 3 (a),the quadrupole field is generated by the quadrupole coil(red). Figure 3 (b) shows the magnetic field generated by
the sextupole coil (brown) and the dipole correction coil(green). The currents of the sextupole coil and the dipole
correction coil are adjusted to produce a desirable sextupolefield and remove the dipole field at the center. The current
densities of both the sextupole coil and dipole correction
coil are 4 A/mm2 and 0.35 A/mm2 , respectively.
(a)

(b)

Figure 5: Horizontal distributions of 𝐵𝑦 at the magnet center.

Magnetic saturation

Figure 3: (a) Magnetic field generated by the quadrupolecoil. (b) Magnetic field generated by the sextupole and dipole
correction coil.
Then a 3D model magnet is simulated in Radia [3], whichis shown in Fig. 4. The Radia can provide a 3D data ofmagnetic field which will be used for a particle tracking inthe future. The horizontal distributions of 𝐵𝑦 calculated by
Poisson and Radia are shown in Fig. 5. The result of Radia
is well consistent with the result of Poisson.�A parabolic
distribution appears after removing the quadrupole component, which indicates the remaining magnetic field is from a
sextupole component.
In the design, the harmonic analysis gives the strength ofmultipole components, which is more accurate than extracting the polynomial coefficients from the curve fitting of the𝐵𝑦 distribution in Fig. 5.

The magnetic saturation is also evaluated in the simulation. If the magnet is saturated, there will be a risk that thedipole field cannot be eliminated. Because the magnetomotive force is mainly generated by the quadrupole coil, forsimplicity, the current is only supplied in the quadrupole coilin the simulation. Figure 6 shows the magnetic field gradientchanging with the current. The total operation current of
the quadrupole coil is around 5000 A. Therefore, magnetic
saturation will not occur in the magnet operation.

Figure 6: Magnetic field gradient changing with the current.

Dipole correction coil

DESIGN USING POLE PROFILE
ADJUSTMENT

Quadrupole coil

The other method is to adjust the pole profile to generate
a quadrupole and sextupole magnetic field directly [4].
yzBasic method

Sextupole coil

The magnetic field expression of a normal magnet in 2D
case is given by

xFigure 4: Combined-function magnet using auxiliary coil inRadia.

- 317 -∞

𝐵𝑦 + i𝐵𝑥 = ∑ 𝑐𝑛 (𝑥 + 𝑖𝑦)𝑛 ,𝑛=0(2)Proceedings of the 20th Annual Meeting of Particle Accelerator Society of Japan
August 29 - September 1, 2023, Funabashi

PASJ2023 TUP16

where 𝑐𝑛 is called 2(n+1)th multipole coefficients [5]. Thena function of scalar potential can be found. Because thepole face is an equipotential surface. The pole profile is asuperimposition of the quadrupole field and sextupole fieldpotentials, which satisfies
𝜑 = −(𝑘𝑥𝑦 + 𝑠(𝑥 2 𝑦 − 𝑦3 /3))

(3)

Therefore, the pole profiles can be found for a given
quadrupole field 𝑘, sextupole field 𝑠, and magnet aperture.
As shown in Fig. 7, the pole profile of the combined-function
magnet is compared with a pole profile of a quadrupole magnet.
03

Figure 9: Mutipole components optimization by shimming.
It should be noted that the end effect is not considered in
the current work, which may change the 𝑘/𝑠 ratio and also
enlarge higher multipole components. A chamfer at the endof the pole end will be applied for a further optimization
later.

Q magnet pole profile
Q-S magnet pole profile

CONCLUSION AND PROSPECTS

Figure 7: Pole faces of quadrupole magnet and quadrupolesextupole magnet.

Optimization of the pole profile
The pole profile in Fig. 7 was used as a first approximation.
The 𝑘/𝑠 ratio simulated in Poisson/Radia is in good agreement with the designed value but still has a small discrepancy.
The shimming of the pole face should be performed to getproper quadrupole and sextupole components and decrease
another multipole components. After the shimming, themagnet model constructed in Radia is shown in Fig. 8.

Two potential designs of the combined-function
quadrupole-sextupole magnet are introduced. The magnet
using auxiliary coil has a complicated structure. Three
independent power sources should be prepared. The currentdensity of the sextupole coil is relatively high, whichindicates the sextupole coil should be water-cooling. The
advantage is that the quadrupole and sextupole magnetic
field can be adjusted separately. As for the magnet using
pole profile adjustment, it has a simple structure. However,the quadrupole and sextupole magnet field cannot beadjusted separately.
To save energy and get rid of water-cooling system, we areconsidering using permanent magnet material to generate themagnetomotive force. The coil will be kept for a magnetic
field adjustment. The design of vacuum chamber will be
conducted later.

REFERENCES[1] K. Yoshida et al., “Compact Synchrotron Light Source of theHSRC”, J. Synch. Rad. (1998). 5, 345-347.
[2] J. Yamazaki et al., “Lattice Components for Upgrading
UVSOR”, in 13th Symposium on Accelerator Science andTechnology, Suita, Osaka, Japan, October 2001.

Figure 8: Combined-function Magnet using Pole profile
adjustment in Radia.

The multipole components are extracted at 𝑟 = 10 mm.
As shown in Fig. 9, multipole components reduced a lot after
the shimming.

[3] RADIA,
https://www.esrf.fr/Accelerators/Groups/InsertionDevices/Software/Radia[4] Design Report for the MAX II Ring, September 1991.
[5] S. Y. Lee, ”Accelerator Physics”, 2nd Edition, World Scientific,
Hackensack, N.J, 2004.

- 318 -