DESIGN STUDY OF A NEW LARGE APERTURE FLUXCONCENTRATOR∗
L. Zang† , M. Akemoto, K. Furukawa, S. Fukuda, T. Higo, T. Kamitani,K. Kakihara, Y. Ogawa, H. Someya, T. Takatomi
The High Energy Accelerator Research Organization (KEK), Tsukuba, Japan
Abstract

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
consists of primary coil and conductor core. A pulsed current in the primary coil induces an eddy current in the conductor. Due to the skin effect, induced current is directed
into the inner surface through a slit to produce a high magnetic field in small area. A matching device such as flux
concentrator could transform the phase space distribution
from the target so that it is appropriate for the solenoid focusing field in the accelerating section: this improves thecapture efficiency. It works as an important part of adiabatic matching device (AMD) in a positron capture section. The detailed modeling and simulation work could befound in the paper [1]. The spiral slit FC is a preferredchoice because of its small transverse component and relatively high peak field. The detailed comparison between
straight slit FC and spiral slit FC has been discussed in paper [1]. In this paper, I will introduce a new design of FC
which is developed based on the SLAC spiral slit FC design[2]. It could have a much larger aperture with similar levelof peak field accompanying with smaller transverse component. The advantages of using a large aperture FC are:(1) the positron target could be immersed in the FC to improve the capture efficiency and then positron yield, (2) the∗ Work supported by KEK† zang@post.kek.jp

60 mm

100 mm

108 mmINTRODUCTION

Cut-in Cone

80 mm

For high luminosity electron-positron colliders, intense
positron beam production is one of the key issues. Flux
Concentrator (FC) is a pulsed solenoid that can generatehigh magnetic field of several Tesla and is often used forfocusing positrons emerged from a production target. Itworks as an optical matching device in a positron capture section. With this device, high capture efficiency isachieved. In this paper, we will introduce a new design ofa FC for the SuperKEKB positron source. The advantagesof the new design are that the aperture is larger than theprevious design, and the transverse components are muchsmaller. The new FC modeling has been done in CST Studio and we will report the results of new FC field evaluation. In order to calculate the positron yield and capture
efficiency, a tracking simulation to the end of capture section has also been carried out, which is also included in thispaper.

Cut-in Depth
20 mm

Figure 1: CST Model of the new designed Flux concentrator.
positron target could have a larger radius to contain an electron beam with large spot size, which could reduce the peakenergy deposition density to avoid damaging the target, (3)positron beam could benefit from a smaller transverse fieldstrength preventing to be deflected. In the following section, we will perform a detailed field comparison between
spiral slit FC and the new FC. And then apply the field distribution to the tracking code to evaluate positron yield at
the end of the capture section.

NEW FC MODELING AND FIELDEVALUATIONThe new FC has been modeled in CST as shown in Fig.1.
The copper coil length is 100 mm, 11 turns and assuming
a current of 12 kA. The copper core has an outer radius of54 mm and a conical inner radius growing from 7 mm to40 mm. The entrance cone depth is 20 mm with the bottom
radius of 30 mm. The cut-in depth is an important parameter that could influence the field distribution. Fig.2 shows
the peak longitudinal field as a function of cut-in depth.
When the cut-in depth changes from 5 mm to 40 mm, thepeak field increases from 3.7 T to 4.6 T. After that, further
cut can cause a field reduction. Overall, the peak field boost
is about 1 T. However, a deeper cut-in depth is equivalent toa shorter FC, which is end up a steep field ramping up andreduction, so that the energy acceptance is smaller. The detailed discussion regarding FC parameters and acceptancecould be found in the paper [3]. Furthermore, a deeper cutin can also bring challenge to design an immersed positrontarget and its cooling system.

Figure 2: Peak longitudinal field as a function of cut-in
cone depth.

Figure 3: Longitudinal field distribution as a function ofposition z. The black line and red dots represent the newFC and spiral slit FC respectively.

The new FC design research is from all aspects. Other
than the cut-in depth, there are a few parameters couldchange the field distribution. For example, when tungsten
target is immersed in the FC, an eddy current is induced on
the surface of the target, which leads to a field reduction.
The eddy current effect is under investigation, so we willnot go into details in this paper. In general, when the target
size gets larger, the field will be reduced more. And after
taking into account the copper cooling system, the situation
could get even worse. A new target and its cooling systemdesign are undergoing. The goal is to fit the target into thecone shape without reducing peak field too much.

New FC longitudinal Field on Axis
The FC longitudinal field strength is one of the mostimportant figures to judge the performance of a design.
Fig.3 shows the calculated longitudinal magnetic field asa function of longitudinal position on the central axis forthe spiral slit FC and new FC, which are represented by thered curve and the black curve respectively. In this figure,z=0 is where FC has the minimum aperture (for new FC
it means after 20 mm cut-in cone). As we can see, withsame input current of 12 kA and radius of 3.5 mm, new FC
could produce a peak field about 8 T, whereas the spiralslit FC could only do a 5.4 T. The field distribution shape isslightly different. New FC field reduce rapidly after achieving the peak and the spiral slit FC’s field change is gradually. Hence, we could conclude that the new FC can produce higher field but with steep field shape. The adiabatic
condition can be improved by introducing an additional DC
coil around FC. The performance of positron capture has
been investigated by using tracking simulation, which will
be discussed and shown in the later section

New FC Transverse Field on Axis
In previous plot we have compared the field distribution
with same aperture for two FC designs. In this section,a further investigation regarding correlation between field

Figure 4: Longitudinal (left y-axis, green color) and transverse (right y-axis, orange color) peak field as a function ofFC radius. The longitudinal field and the transverse field
are represented by the solid dots and the circles respectively. New FC is shown in red and Spiral slit FC are shownin black.
(longitudinal and transverse) and FC radius will be carriedout. Fig.4 shows the longitudinal and transverse field as afunction of FC radius for both designs. In the figure, soliddots and circles represent the longitudinal peak field valueand transverse peak field value respectively. The red dots
and circles are the results of new FC. The black dots andcircles are calculated from spiral slit FC. First of all, let’s
compare the transverse field between two designs. In fact,with the new design, we do not only get a higher peak longitudinal field, but also get a lower transverse component.
When the radius increase from 4.5 mm to 7 mm, both designs show a similar pattern. The new FC’s transverse fieldstrength is about half of the spiral slit design’s. The transverse component of the magnetic field is crucial to achieve
high capture efficiency, because it could deflect positrons
off the axis causing positron yield reduction.
From Fig.4 we can see that for both designs, the longi-

tudinal field is sensitive to the inner radius changes. The
strength of the longitudinal field along the axis is inversely
proportional to the FC inner radius. But the new FC could
produce the peak field about 1.5 times higher than the spiral slit FC in nearly all radii. If we look into it from another angle, we could keep the same peak field but benefitfrom a larger aperture. For example, the standard spiral slit
FC needs an inner radius of 3.5 cm producing 5.2 T field,
whereas the new FC could achieve same value with a muchlarger inner radius of 5.5 mm. According to Fig.4, spiralslit FC has a 0.118 T transverse field accompanying withthe 5.2 T longitudinal field, and the value for the new FC
with a radius of 5.5 mm is 0.026 T which is about 4.5 times
lower than the spiral slit FC’s. The new FC put us in a very
good position that we could either trade off the aperture toobtain higher field or keep same field strength to have an
immersed target in large aperture FC.
From the calculation results and discussion showing
above we can conclude that the new FC performance ispromising. With the same size as the spiral slit FC, it produces similar level of longitudinal peak field with large FCaperture. On top of that, the transverse component is only
about 1/5 of the spiral slit FC.

TRACKING SIMULATION
The motivation of a tracking simulation is to compare
the capture efficiency of the new FC with the spiral slit
FC. The capture section layout is based on the SuperKEKB
design. Positrons generation simulation is carried out by
GEANT4 assuming a 3.5 GeV electron strike on a 14 mm
thick tungsten target. The generated positrons go throughthe adiabatic matching device consisting of FC and bridgecoil. Downstream of the matching section is the accelerating structures include six 2 m large aperture S-band accelerating units who have apertures of 17.5 mm. The wholeaccelerating structure is surrounded by a 0.4 T solenoid.
Fig.5 shows the positron yield as a function of FC radiusin the end of capture section. The red and black curves
shows the tracking results by using spiral slit FC and new
FC field distribution respectively. As the Fig.5 suggested,when FC radius increases (at the same time field is reduced), the positron yield has a peak at radius of 3.5 mm.
For the case of smaller radius (2.5 mm), although a higher
peak field can be achieve, which can increase the angular
acceptance, the losses due to the reduction of energy acceptance and smaller entrance are greater and vice versa when
the large radius FC is implemented. The results indicatethat a 3.5 mm radius FC may be the best balance amountenergy acceptance, angular acceptance and lateral acceptance. Comparing two FC designs, the red line is above theblack in all radiuses. When the radius is between 2.5 mm
and 4.5 mm, the positron yield for the new FC is improved
about 20%∼30%. After enlarging the radius more than
5.5 mm, the differences start to be smaller and results areconverged. So far the positron yield improvement is basedon the condition of same radius and input current but dif-Figure 5: Positron yield as a function of FC radius in theend of capture section. The red and black line represents
the new FC and spiral slit FC respectively.
ferent peak field. If we compare the new FC with radius of
5.5 mm with the spiral slit FC with radius of 3.5 mm, wewill have some ideas of aperture contribution to yield, because both of them have a peak field about 5 T. When theradius increase by applying new FC, the positron yield increased about 7%. The tracking simulations have returned
promising results indicate that the positron yield could be
benefit from large radius and high peak field new FC configuration.

CONCLUSIONS
Flux Concentrator plays an important role between production and acceleration section. There are several designs
has been proposed such as the straight slit FC and spiral slit
FC. In KEK, we have made a few of similar kind of prototype for test. In this paper, we have introduced anotheralternative option. The new design could either have a 1.5time higher peak field or 1.5 times larger radius than spiralslit FC. Due to the enlarged aperture, the transverse components will be much smaller so that the positrons could
avoid large deflection. Furthermore, the tracking resultsshows the new FC could give a 20%∼30% of yield improvement. In the future, we would like to manufacture a
prototype of the new FC in KEK. A field measurement will
be carried out before installing it into a vacuum chamber
for high voltage operational test.

REFERENCES[1] L. Zang, T. Kamitani, S. Fukuda and Y. Ogawa, “Design Optimization of Flux Concentrator for SuperKEKB”, Proceedings of the IPAC’12, New Orleans, USA, May 20-25, 2012.
[2] A. V. Kulikov, S. D. Ecklund and E. M. Reuter, “SLC
Positron Source Pulsed Flux Concentrator”, SLAC-PUB5473, June, 1991.
[3] R. Chehab, “Positron Sources”, CERN 94-01, 26 January
1994, Vol 2.