DESIGN AND PERFORMANCE OF OPTICS FOR MULTI-ENERGYINJECTOR LINAC
Y. Ohnishi∗ ,T. Kamitani, N. Iida, M. Kikuchi, K. Furukawa, M. Satoh, K. Yokoyama, and Y. Ogawa,KEK, Tsukuba, Japan
Abstract
OPTICS
KEK injector linac provides an injection beam for fourstorage rings, KEKB high energy electron ring(HER), lowenergy positron ring(LER), PF-AR electron ring, and PF
electron ring. The injection beams for these rings have different energies and intensities. Recently, a requirement ofsimultaneous injection among these rings arises to make a
top-up injection possible. Magnetic field of the DC magnets to confine the beam to the accelerating structures can
not be changed during a pulse-to-pulse, although the beamenergy can be controlled by fast rf phase shifters of theklystrons. This implies that a common magnetic field of
the bending magnets and the quadrupole magnets should
be utilized to deliver beams having different characteristics. Therefore, we have designed a multi-energy optics for
the KEKB-HER electron ring(8 GeV, 1 nC/pulse), the PF
electron ring(2.5 GeV, 0.1 nC/pulse), and the KEKB-LER
positron ring(3.5 GeV, 0.4 nC/pulse). We present a performance of the multi-energy injector linac for the PF ring andthe KEKB-HER.

INTRODUCTION
A new injection scheme has been developed, which is socalled a pulse-to-pulse injection with multi-energy linac for
the KEKB-HER, the KEKB-LER, the PF ring. The pulseto-pulse injection means that the beam can be switched andinjected to the desired rings within 20 msec at a minimum
duration. However, the beam energy is different among
these rings. Difficulties arise from that most of magnets
can not change the magnetic field by a pulse-to-pulse duration. Therefore, we have developed a new optics to use
a common magnetic field for the different beam energies,
such as 2.5 GeV for the PF and 8 GeV for the KEKB-HER.
The KEKB-LER injection has been still tested and underdevelopment in this scheme, however, the strategy is a similar way of the PF and the KEKB-HER.
The injector linac has 7 sectors, A-sector and B-sector
before 180◦ arc(J-arc) and 1-sector to 5-sector after theJ-arc. The energy of the J-arc is 1.7 GeV and the multienergy scheme focuses on the region from the C-sector tothe 5-sector. A pulse bend is placed in the 5-sector and the2.5 GeV beam is kicked out to the transport line of the PF
ring, while the 8 GeV beam passes through the ECS(theenergy compression system) to the KEKB-HER transportline.
∗ Email: yukiyoshi.onishi@kek.jp

A fundamental block of the linac is an acceleration unitthat consists of an S-band klystron and four 2 m-long accelerating structures. The klystron drives these accelerating structures which have a common phase of the microwaves. The accelerating structures in the acceleration
unit have the same field gradient in principle. Eight acceleration units make a sector, typically. A sub-booster supplies microwaves to each klystron in the sector and adjusts
the phase for a beam passage.
A doublet or a triplet of quadrupole magnets is placedin every one or two acceleration unit and makes a cell ofa periodic lattice. In the case of an electron injection, anelectron beam is accelerated from 1.7 GeV up to 4.8 GeV
between the C-sector and the 3-sector. A positron targetto make a positron beam is placed in the 2-sector. In thecase of a positron injection, a primary electron beam hits
the positron target and positrons are generated by meansof electro-magnetic showers. On the other hand, a smallhall(φ=3 mm) is placed in the vicinity of the target so that
an electron beam can pass through the positron target for
the electron injection. In order to make this possible, it isnecessary to squeeze the beta function at the hall as small
as possible and to make a local bump orbit by using pulse
steerings in the horizontal plane.
The electron beam injected to the PF ring is decelerated
down from 4.8 GeV to 2.5 GeV between the 3-sector andthe 5-sector, while the electron beam is accelerated up to 8
GeV for the KEKB-HER. In the multi-energy region, thephases of the sub-boosters are shifted by 180◦ approximately between the acceleration and the deceleration. In
practice, an off-crest phase typically shifted by 6◦ from thecrest phase is used to compensate the energy difference between the head and the tail of a bunch due to the wake field.
The deceleration phase isφdec = φacc + 180◦ − 2∆φ,(1)where ∆φ is the phase shift from the crest phase. Furthermore, a few klystrons in the 3-sector would be a stand-bymode to adjust the beam energy so as to be 2.5 GeV. The
stand-by mode implies an off-timing trigger for the beam
passage. Both the 2.5 GeV and 8 GeV beam would be adjusted by the energy-feedback system[1] precisely. The energy feedback system consists of a set of two klystrons andadjust the phase. The off-crest phases are used in the opposite side of the crest for each klystron to compensate theenergy spread. Those sub-boosters and the energy feedback system utilize a phase shifter with a solid-sate device
and can change the phase by a pulse-to-pulse duration.

The DC magnets are used in the lattice for thequadrupole and steering magnets. Therefore, the beams
which have a different energy must be transported witha common magnetic field from the 3-sector to the 5sector(multi-energy region). The optics is designed for the2.5 GeV beam as a base line since there is a matching section in the transport line for the KEKB ring and not for
the PF ring. The beta functions and beam energies for the2.5 and the 8 GeV beams are shown in Fig. 1. The betatron phase advance of the cell is 90◦ typically in mostsectors. However, the phase advance in the multi-energy
region should be optimized so as to make the beta function enough small for the the different beam energy. In
the 2.5 GeV optics, the phase advance for each cell is designed to be 108◦ approximately in the 4-sector and the 5sector. While, the phase advance of the cell would become40◦ ∼50◦ for the 8 GeV optics. The optics design would
suppress a large beam size in the multi-energy region forthe both 2.5 and 8 GeV beam.
(a)

(b)

PF 2.5 GeV

Twiss parameters at the entrance of the C-sector are
matched so as to be the design values using the matching
section in the J-arc. The matching procedure is based on
emittance measurements with wire scanners[4]. From theC-sector to the 5-sector, k values correspond to the magnetic field of the quadrupoles are determined so that thebeta functions become the design values by means of a fitting procedure with the SAD code.

CORRECTION OF OPTICS
The optics is corrected by a single-kick method. A
single-kick orbit induced by a steering is measured bybeam position monitors(BPM) which are placed next toeach quadrupole magnet. Since the single-kick orbit is arelative orbit displacement by a single steering, we do nothave to consider an absolute beam position.
The measured orbits are compared with the design orbits
calculated by optical parameters based on the k value ofthe quadrupoles and the calculated beam ebergy describedin the previous section. A fudge factor is introduced tocorrect the k value so that the measured orbits agree withthe design orbits. The definition of the fudge factor, af ,applied to the k value is written by

KEKB-HER 8 GeV

E (GeV)Kps = af · Kd ,
(c)

(2)

where Kps is a k value set to the real magnet and Kd is ak value of the design value. The deviation from the designof the k value of the m-th quadrupole can be estimated bysolving following equations:
(j)

∆xi=M
XRy,im ∆Km

M
XRx,im ∆Km

(j)

(3)

m=1

Figure 1: Optical parameters for (a) 2.5 GeV PF, (b) 8.0
GeV KEKB-HER, and (c) beam energy.

(j)∆yi=(j)(4)

m=1

In the optics calculation, the SAD code[2] is utilized. We
assumed that the beam energy at the exit of the buncher section in the A-sector would be 20 MeV which is measured
by a energy analyzer cosists of a well calibrated bending
magnet and a beam screen monitor. The beam energy iscalculated by using a peak acceleration field of an accelerating structure, a phase, a klystron status[3]. The calculated
energy would have errors due to a characteristic of the accelerating structure and the beam loading. Therefore, theabsolute value of the beam energy should be adjusted tobe the desired energy at the end of linac for each injection.
A normalization factor is used to scale the beam energy to
1.7 GeV at the J-arc, 2.5 GeV for the PF ring, and 8 GeV
for the KEKB-HER. The relative energy among the accelerating structures should be kept since the relartive errorof the energy gain from the accelerating strucure would besmall. Although the normalization factor is an overall factor, the normalization factor of 8 GeV is used for the 2.5
GeV beam in the common energy region which is between
the J-arc and the entrance of the multi-energy region.

(j)

(j)

(j)

(j)

(j)

where ∆xi = xm,i −xd,i , xm,i and xd,i are the measured
and the design orbit at the i-th BPM induced by the j-thsteering in the horizontal plane, and y is the same as x. The
response matrix, Rx,y is calculated by the SAD code. Thefudge factor is a−1f,m = 1 + ∆Km /Kd,m and includes not
only a field gradient error but also an energy error. Here,xy couplings are ignored because it is a higher order effectand it should be small.
In the optics correction, we use 22 kinds of single-kickorbits typically to obtain fudge factors of the quadrupole
magnets and the fudge factors are determined at the 2.5
GeV lattice. During the optics correction, we found a
miss connection of power supplies to quadrupole magnets. In this case, both a large fudge factor and a large
field gradient error are appeared at a specified quadrupole
magnet(QD484, QF484). In this manner, the single-kickmethod is also effective to find a machine error. Thefudge factor after fixing the connection problem is shownin Fig. 2(c). The fudge factors are within 3%. Figure 2

Δy (mm)

Δx (mm)shows a comparison of the measured and the design singlekick orbit for the 2.5 GeV beam before and after the optics correction. Introducing the fudge factors, the measured
single-kick orbit is consistent with the design orbit. Allother single-kick orbits are similar to Fig. 2 and consistent
with each design orbit.
(a)

(b)

af(c)

Figure 2: (a): Horizontal orbits for design(green), measured before correction(red), and measured after correction(blue). (b): The vertical orbits are the same as the horizontal. (c): Fudge factors for quadrupoles.

two steerings can be canceled by adjusting the local bumpheight. The orbits for 2.5 GeV and 8 GeV can be adjusted
by solving a following equation: 
θ1
m11 m1200∆x1
 ∆x2   m21 m2200    θ2  ∆X1  =  n31 n32 n33 n34   h1  , (5)h2∆X2n41 n42 n43 n44
where x and X are a beam position for 2.5 GeV and 8 GeV,
respectively, θ is a kick angle of a steering, and h is a local
bump height. The orbit response matrix, mij and nij , iscalculated by the SAD code. Vertical positions, y and Y ,are adjusted by the similar way of the horizontal positions.
In this procedure, the positions at two BPMs is necessary
at least to adjust the position and the angle. We use two
local bumps and two steerings to control the orbits. Thephase advance between two local bumps is about 90◦ whichcorresponds to two cells of the lattice in the case of 8 GeV.
We consider the orbit feedback system by using thistechnique. This is a slow orbit feedback since the steerings
are DC magnets and beam positions measure by BPMs for
2 sec intervals so far. The slow orbit feedback for the multienergy beam can suppress an orbit drift for a long term .

CONCLUSION
The optics is evaluated by the wire scanner in the 5sector. The measured optical parameters for 2.5 GeV infront of the pulse bend are listed in Table 1. The opticalparameters are well matched to the design values since theBmag parameters are very close to 1.
Table 1: Optical parameters for 2.5 GeV measured by thewire scanner in the 5-sector.
horizontal vertical unit
Beta function
Normalized emittance
Bmag

10.36
288
1.01

13.08
161
1.05

m
µm

ORBIT CORRECTION AND FEEDBACK
Beam orbits are required to be fixed and stable at the endof linac. A position and an angle of the 2.5 GeV beam
should be zero at the pulse bend. At the same time, a position and an angle of the 8 GeV beam should also be zero atthe ECS. We have developed a tuning technique to adjust
both orbits for 2.5 GeV and 8 GeV simultaneously by using a common magnetic field of DC steerings. In order toadjust the orbit for 8 GeV, a local bump method is utilized.
While the local bump is closed at 2.5 GeV, the local bumpis not closed at 8 GeV in general. Therefore, the orbit for 8GeV can be adjusted independent on the 2.5 GeV orbit. On
the other hand, the beam orbit for 2.5 GeV is controlled bytwo steerings. However, these two steerings would affectthe orbit for 8 GeV. In spite of this, the orbit response of

We have present the optics designed for the multi-energy
injector linac. The beams which have the different energies, such as 2.5 GeV and 8 GeV, can be successfully transported to the end of linac with a common magnetic field of
the quadrupoles and steerings. As the next step, the multienergy injector linac together with the positron injection tothe KEKB-LER, the beam energy of 3.5 GeV, is under development.

ACKNOWLEDGMENT
We would like to thank K. Oide and A. Enomoto who
have supported the program for the pulse-to-pulse injection
to the PF and the KEKB rings.

REFERENCES[1] K. Furukawa et al., ICALEPCS ’99, p.248-250.
[2] http://acc-physics.kek.jp/SAD/.
[3] T. Kamitani at al., EPAC 2000, p.1507-1509.
[4] N. Iida et al., EPAC 2000, p.1738-1740.