Prototyping of the Flux Concentrator for SuperKEKB Positron Capture∗
Lei Zang† A) , Mitsuo AkemotoA), Shigeki FukudaA) , Toshiyasu HigoA) ,Takuya KamitaniA) , Kazuhisa KakiharaA) , Yujiro OgawaA) ,Hirohiko SomeyaA) , Toshikazu TakatomiA) , Shinji UshimotoB),A)The High Energy Accelerator Research Organization (KEK)
1-1 Oho, Tsukuba, Ibaraki, 305-0801
B)
Mitsubishi Electric System & Service Co.Ltd
2-8-8 Umezono, Tsukuba, Ibaraki, 305-0045
Abstract
The SuperKEKB requires higher positron intensity. We
will upgrade the capture system of the injection linac byintroducing a Flux Concentrator type of a pulsed solenoid
that can generate several Tesla solenoid field to focus thepositrons emerged from a conversion target. Due to thehigh temperature environment during brazing, we proposed
to use a high strength copper material (HRSC) for FC
which has a much better mechanical strength than Oxygenfree Copper (OFC). The experiment is designed to measure
and compare the field distribution of two FC prototypes
made of HRSC and OFC to evaluate the possibility of using HRSC for FC. Furthermore, in this paper, we will also
introduce the different FC geometries: a simple straight slit
FC and a SLAC type of spiral slit FC. The measurement results of these two geometries prototypes will be presented
and discussed.

Figure 1: Four flux concentrator prototypes are manufactured and tested in KEK. From left to right: HRSC straightslit FC, OFC straight slit FC, OFC spiral slit FC and HRSC
spiral slit FC.

INTRODUCTION
Flux Concentrator (FC) is a pulsed solenoid that can generate high magnetic field of several Tesla and is often used
for focusing positrons emerged from a production target.
It works as an important part of adiabatic matching device(AMD) in a positron capture section. With the help of thisdevice, high capture efficiency could be achieved. Detailed
modeling of the FC is sufficiently complex that there is significant uncertainty in the results of simulation. The detailed modeling and simulation work could be found in paper [1]. In order to benchmark the simulations, and provide
a solid basis for understanding the issues and optimizingthe design, experimental studies are necessary. Such studies have been performed at KEK, using several full-scale
FC prototypes as shown in Fig.1. And the experimentalstation has been set up as shown in Fig.2. The experimental instruments and control software has been described inpaper [2]. In this paper, experimental results of field measurements for various FC prototypes will be presented andcompared.
∗ Work supported by KEK† zang@post.kek.jp

Figure 2: A straight slit FC made of OFC was set up on theexperimental station.

FC GEOMETRY AND MATERIALFC Geometry: Straight Slit and Spiral Slit
When we manufactured the FC prototypes, there are twokinds of proposed geometries: straight slit and spiral slit.
The straight slit FC is 10 cm long with a cylindrical outsideradius of 4 cm and a conical inside radius growing from
0.35 cm to 2.6 cm. A 0.02 cm straight slit links the inner
and the outer surface as shown in Fig.2. This design is easy
for machining, and it could generate higher longitudinal
field, but the transverse components are large. Whereas thespiral slit design have smaller transverse components dueto the 12 turns of 0.02 cm of spiral cutting. The drawbacksof this geometry are the lower longitudinal peak field andits rather complicated geometry.

Figure 4: Longitudinal magnetic field Bz as a function oflongitudinal position z for four FC prototypes. Black: OFC
straight slit FC, red: HRSC straight slit FC, blue: OFC
spiral slit FC and green: HRSC spiral slit FC.

Figure 3: The comparison of the grain size, tensile strengthand yield strength for HRSC and OFC at various temperature.

A New FC Material: HRSCOther than the geometry, a new material (HRSC) has
been used for FC. The HRSC is a high heat resistance copper alloy [3], which could maintain a fine grain and highstrength during brazing process. Its outstanding physicalproperties in high temperature make it as an excellent candidate material for FC. Actually, after heating at a temperature of 800 ◦ C, the fatigue characteristics of HRSC is about
8 times of the OFC that FC was made initially. During ourHRSC prototype brazing process, 750 ◦ C was applied. The
choice is based on the weight and balance amount grainsize, tensile strength and yiield strength at various temperatures as shown in Fig.3 [4]. The disadvantage of HRSC
is its lower electrical conductivity, which is about 80% ofOFC. One of the goals of the FC prototype experiment isto compare the performance of FC that made of these twomaterials.
Totally there are four FC prototypes, as shown in Fig.2,
have been made with two kinds of material (HRSC andOFC) shaping into two geometries (Straight slit and Spiral slit). In the following section, the results of measuredlongitudinal and transverse field will be presented and compared.

MEASUREMENT OF FIELD PROFILESLongitudinal Field Distribution on Axis
Fig.4 shows the measured longitudinal magnetic fieldBz as a function of longitudinal position z on the central
axis (x = y = 0 mm). There are black, red, blue and green

lines represent the OFC straight slit FC, HRSC straight slit
FC, OFC spiral slit FC and HRSC spiral slit FC respectively. As we can see, with the same input power source,which at this stage is about 6 A, the straight slit FC could
produce a peak field that is about 1.75 times higher than
the spiral slit FC. The field of straight slit FC increases
steeply from 0.5 mT to 3.5 mT in a short distance less than
10 mm, and then reduce to 0.5 mT in distance of 40 mm,
which could be characterized by taper parameter. After arough calculation, the taper parameters for straight slit FC
and spiral slit FC equals to 150 /m and 75 /m respectively.
In fact, taper parameter is an important parameter that determines the energy acceptance. The smaller the taper parameter is, the larger the energy acceptance will be. The
investigation is discussed in paper [1] regarding the distribution that will return higher capture efficiency.
Fig.4 has also shown us that the field distributions are
identical for OFC and HRSC in both geometries. Althoughthe HRSC’s electric conductivity is only 80% of the OFC’s,
the measurement has shown negligible differences.

Transverse Field Distribution on Axis
The transverse component of the magnetic field in FC is
crucial to achieve high capture efficiency. The transverse
magnetic field could flick positrons off the axis causing
positron yield reduction. We have measured the transverse
magnetic field Bx along the central axis (x = y = 0 mm),and the results are presented in Fig.5. There are black, red,
blue and green lines represents the OFC straight slit FC,
HRSC straight slit FC, OFC spiral slit FC and HRSC spiralslit FC respectively.
The effect of the FC shape on the magnetic field profile could be observed. Straight slit FC produced a muchstronger Bx , and it peaked near the FC entrance, then gradually decrease along the longitudinal direction. Whereas
spiral slit FC had a weaker Bx . The peak Bx only maintain a short distance before rapidly reducing to nearly zero.

Figure 5: Transverse magnetic field B x as a function oflongitudinal position z for four FC prototypes. Black: OFC
straight slit FC, red: HRSC straight slit FC, blue: OFC
spiral slit FC and green: HRSC spiral slit FC.

Figure 6: Contour plot of the transverse magnetic field B x
in xz plane for straight slit FC.

The length of relatively high B x region will depend on thelength of cutting-in edge which is a short straight slot before going into spiral cutting trajectory.
Fig.5 has also shown us the field distribution differences
between materials. Both geometries’ field measurement results indicate that HRSC FC produce a stronger B x whichis 1.25 times of OFC’s.

2D FIELD MAPPING AND FIELD OFFSETAs we have discussed in previous sections, the transverse
field could deflect positrons leading to capture efficiency
reduction. In general, a perfect cylindrical axial symmetric geometry should have the field center locate in the center of axis, where has the minimal transverse component.
However, all of the FC prototypes are sort of asymmetry
because of the slit. It is important task to investigate howmuch the slit affects the field center, and find out the ideal
path for positron beam, from where they can suffer the minimal transverse kick.

Straight Slit FC Field Offset
Fig.6 shows the contour plot of the transverse field B x
in the xz plane when y = 0 mm. From the figure we cansee the strong transverse components in front of the FC entrance with opposite polarity, so that the positrons going
through either of them will receive a kick toward to thecentral axis following a cyclotron motion. Positron’s trajectory and radius of cyclotron motion depends on its energy and FC field strength. The transverse field polarity isreversed inside FC, in which case, the transverse field deflects the positron off the central axis. That’s one resourceof capture efficiency reduction. In order to find out the field
center with minimal transverse kick, we integrated the B xmagnitude along z for certain x position. We assumed theposition with lowest integration value should be the newfield center.

Figure 7: Integrated transverse magnetic field B x along z
for straight slit FC.

The integration results for straight slit FC have beenshown in Fig.7. The black curve shows the integration fromentrance of FC to 20 mm inside FC, red curve shows theintegration from 10 mm ahead to FC entrance. There are
few test point have been picked up from x = −1.5 mm tox = 1.5 mm with a step size of 0.5 mm. From the Fig.7
we can see the transverse field in front of the FC provides
strong deflection to a direction pointing to central axis. Inside the FC, the field center is shifted about 1∼2 mm off
the axis due to the straight slit.

Spiral Slit FC Field Offset
The same measurement and analysis has been done forspiral slit FC as well which are shown in Fig.8 and Fig.9.
Fig.7 shows the similar field distribution near FC entrance.
However, inside the FC, thanks to the spiral structure, themagnitude of B x is relatively small even in the region awayfrom axis. There is nearly no field offset. The strong transverse component is associated with the pole face between

The drawback is the relatively low longitudinal field. Secondly, HRSC FC and OFC FC show some identical performance, which let the HRSC be the potential candidate material due to its outstanding physical property in high temperature. And finally, the investigation of the transverse
field distribution on the xz plane has shown us that thefield offset appear inside straight slit FC is about 1∼2 mm.
Comparing to straight slit FC, spiral slit FC’s field offset isnearly zero, which lead to the integrated transverse field on
the central axis is only about 1/4 of the straight slit FC.

REFERENCES[1] L. Zang, T. Kmitani, S. Fukuda and Y. Ogawa, “Design Optimization of Flux Concentrator for SuperKEKB”, Proceedingsof the IPAC’12, New Orleans, USA, May 20-25, 2012.

Figure 8: Contour plot of the transverse magnetic field B x
in xz plane for spiral slit FC.

[2] S. Ushimoto , et al, “Development of Magnet Field Measurement System for Flux Concentrator (2)”, Proceedings of the
8th Annual Meeting of Particle Accelerator Society of Japan,
Tsukuba, Japan, August 1-3, 2011.
[3] http://www.mitsubishi-shindoh.com/en/hrs35.htm[4] S. Fukuda, FC grouping meeting presentation, KEK, Japan,July, 31, 2012

Figure 9: Integrated transverse magnetic field B x along z
for spiral slit FC.

slit gaps near inner surface of FC.
The integrated B x along z in Fig.9 proved the advantages of applying slit cut to FC that the field shift is well
reduced to a negligible level. By comparing the integrated
Bx with the straight slit FC, if the positron beam injects
into FC on the central axis, the results show a reduction
from 1.6 mT·mm to 0.44 mT·mm.

CONCLUSIONS
Four FC prototypes have been successfully manufactured. Each of them represents a unique configuration ofgeometry and material. After a successful field measurement, the longitudinal and transverse field has been evaluated. By comparing the results from each prototype, wecould have a few conclusions. Firstly, straight slit FC produce higher longitudinal field which accompany with highand long lasting transverse field, whereas spiral slit FC’stransverse field is lower and effective in a shorter region.