KEKB LINAC WAKEFIELD STUDIES OF COMPARING THEORETICALCALCULATION, SIMULATION AND EXPERIMENTAL MEASUREMENT*L. Zang† , M. Yoshida, Y. Ogawa, N. Iida, M. Satoh, D. Zhou
High Energy Accelerator Research Organization (KEK)
1-1 Oho, Tsukuba, Ibaraki, 305-0801, Japan
Abstract

SHORT-RANGE WAKEFIELDINTRODUCTIONKEKB [1] was an electron-positron collider with energyof 8 GeV and 3.5 GeV. After a successfully construction
and running, the machine has achieved a peak luminosityof 2.1×10 34 cm2 s−1 . The scientists in KEK have planned amajor upgrade of KEKB to SuperKEKB [2] with the luminosity of 8 × 1035 cm2 s−1 . It is a challenge to improve theluminosity 40 times from the KEKB. In order to achieve
that, a low emittance machine is required so that a nanobeam scheme has been proposed to squeeze the beam as
small as possible (y = 3.2/5.3 nm). The performance ofsuch nano-bean scheme machine highly depends on injection beam characteristics, requiring a low-emittance beam
for the injection linac. When the beam propagates in thelinac, the head particles induce a wakefield, which interacts with tail particles causing the beam instability andemittance growth. The longitudinal wakefield gives rise
to energy spread and the transverse wakefield can lead toincrease of beam emittance. In this paper, we introduce
the trajectory of the bunch when there is an offset injection, and then calculate the emittance growth due to themisalignment of accelerating structure. To reduce the emittance growth caused by wakefield, an investigation of using
offset injection has been carried out. In the final section theresults of beam emittance measurements are presented andcomparing with simulation results.
∗ Work supported by KEK† zang@post.kek.jp

Offset Injection and Trajectory
When a bunch of electron beam travels off-axis along
a perfect aligned accelerating structure, the head particles
in the bunch will interact with the beam pipe and leaves
a wakefield behind the leading particles [3]. The induced
wakefield can deflect the trailing particles further awayfrom the axis. In that case, the projected beam emittancewill increase. In Fig.1, the plot shows the displacement xof a point on the bunch as a function of distance.

Displacement x mmFor SuperKEKB, in order to achieve designed luminosity, the machine needs to run with a small beam emittancein the injection linac. During the beam propagation in thelinac, the short-range wakefield in the accelerating structure will cause the beam instability and emittance growth.
In practice, injecting beam with a certain offset could compensate wakefield effect. In this paper, wakefield theoretical calculation, simulation results will be presented. And
then the wakefield impact to beam emittance and wakefieldcompensation will be discussed. Finally, we will show thecomparison of the results getting from theoretical calculations and experimental measurements.

0.4
0.2
0.0
0.2
0.4
0

100 200 300 400 500
Distance m

Figure 1: The displacement x of a point on the bunch asa function of traveling distance. The blue, green and red
curve corresponds to the position of head, center and tailparticles along the beam respectively.
As we can see in Fig.1, x value depends on the position
along the bunch. The blue line represents the head position,
which vanishes as we expected. And the center and tail ofthe bunch are shown with green and red curves respectively.
The tail particles will suffer a much stronger kick than theparticles located in the center of the bunch. The further
away from head, the stronger the wakefield will be.

Misalignment Effect
In the previous section, calculation is based on the assumption that all the elements are perfect aligned. Thewakefield generated is due to the beam injection with a displacement error. However, in the real world, because of theengineering limitation, there must be some misalignment
along the linac, which could also lead to the beam instabilities even the beam is injected with a perfect precision. Ifwe assume a misalignment error d, the x coordinates squarewill be represented as [4].
(1)2



=xmis


(2)2



=xmis

1  2  r0 L 2 γf 2d () ln( )R1 (z) (1)
2Nc
γf k0
γ0
1  2  r0 L 4 3 γf 2d () ln ( )R2 (z) (2)24Nc
γf k0γ0ΓΕ mm mrad 1/2where d2
is the rms value of the misalignment and thewakefield is assumed to be linear. N c is the number of accelerating unit, r0 is the classical radius of the particle, L is
the total length of accelerating structure, γ 0 and γf are theenergy of the beam at position of entrance and exit. The
expression of R 12 and R22 could be found in [4]. The equations are adopted to calculate the beam emittance growth
due to the wakefield produced by misalignment accelerating structure. In the calculation, we assume a misalignmentof 0.1 mm, with 240 accelerating units in totally length of500 m. The results are shown in Fig.2.

15010050002468103Wake 10 m 
5Figure 2: Emittance growth as a function wakefield. The
red line and green line corresponds to the 1 st and 2nd ordercontribution to beam emittance growth respectively.
Figure 2 shows that for a fixed total acceleration length,
the 2nd order contribution has a much larger effect to theemittance growth when there is a strong wakefield. In otherwords, for a machine whose wakefield is larger than certain critical value, the 2 nd order contribution should be on
the top of priority list to compensate. By considering theKEKB parameters and implement them into the formulaintroduced in [5], we can work out the wakefield is about
4 × 105 m−3 . In that case, the 1 st order and the 2 nd ordercontribution to emittance growth are roughly in the samelevel.

Offset Injection Compensation
The emittance growth due to wakefield effects can beenhanced by both the initial offset errors and the structure
misalignment. In fact, the wakefield induced by misalignment could be cancelled substantially by applying an offset
injection. The compensation could be very helpful to ouremittance preservation. The 1 st order and the 2 nd ordercontribution by an initial offset x 0 could be calculated byequations [4]:(1)

xof f (z, L) =(2)xof f (z, L) =1r0()
(1 + GL)1/2 γ0 k0ln(1 + GL)
R1 (z)
x0 sin k0 L
2G(3)

1r0()
1/2
γ0 k0
(1 + GL)ln2 (1 + GL)
x0 sin k0 L (4)R2 (z)
2G2−

where G is the acceleration gradient and L is the total
length of accelerating unit. The compensation could apply
to either the 1st order or the 2 nd order contribution. Theoffset wakefield effect is represented by Eq.3 and Eq.4, andthe misalignment wakefield effect are represented by Eq.1
and Eq.2. In order to reduce the emittance growth, for instance, in the case of the 1 st order compensation, we need(1)(1)
xmis = −xof f . By solving this equation, the offset injection position x0 could be obtained. Then if we substitutex0 into Eq.2 we can get the emittance growth due to the
2nd order contribution. Similar method could also be used
to cancel the 2nd order and then calculate the 1 st order contribution.
The results have been compared with the one which getsfrom misalignment caused emittance growth without cancellation. The results show us that the emittance could effectively reduce to 1/4 by canceling the 1 st contribution.
On the other hand, the emittance is about 1/3 of the case of
no offset injection if we compensate the 2 nd order contribution. The researches we have done so far implied that an on
purposed offset injection could well control the wakefield
and minimize the emittance growth. In reality, the beamin the accelerator will be far more complicated than what
we have shown in calculations. In the next section, the experimental data taken from KEKB linac has been analysed,
which will help to understand how the emittance changes
in the accelerator due to the wakefield.

KEKB LINAC DATA FOR WAKEFIELD
STUDYExperiment Data Analysis
In reality, the accelerator elements cannot be perfectalignment. Hence, even the beam is injected without offset, the misalignment will induce the wakefield as we introduced in the previous section. In order to reduce the emittance growth, the offset injection compensation method has
been investigated. The purposes are achieved by adjusting
the current of steering coil, then the beam can be injected
into the next section with certain angle and offset. Figure
3 shows the measured emittance as a function of steering
current. From the plot we can observe not only the emittance growth due to the wakefield caused by misalignment,
but also the offset injection compensation of the emittancegrowth.











             

Figure 3: Emittance as a function of steering coil current.
The red and blue dots are the wire scanner measured resultsfor 1 nC, 5 nC beam in KEKB linac. The black lines are thedata parabolic fitting, and the fitting functions have also
been displayed.

Emittance mm mrad    



700
600
500
400
300
200
0.006 0.004 0.002 0.000
SX_A2_1 Angle mrad

0.002

Figure 4: Emittance as a function of kick angle. The red
dots are the emittance value of 5 nC beam. The blue line isthe parabolic data fitting. The KEKB linac lattice file has
been implemented into Elegant, and the components havea random misalignment of 0.5 mm.

SUMMARY AND CONCLUSION
Figure 3 shows the emittance measurement of operating
1 nC and 5 nC electron beam in KEKB linac. The steering
coil current has been changed in order to control the kicking strength, so that the electron beam could go into next
section with an offset and angle. For 1 nC electron beam,
when current changes from -0.5 A to 1.0 A, the maximum
emittance could reach up to 250 mm mrad, and have a minimum value of 115 mm mrad. Regarding the 5 nC electron beam, it is more sensitive to the steering coil current
changes. The emittance could reach up to the 760 mm mrad
when a -0.1 A current is applied. The same as the 1 nC run,the minimum emittance can be obtained at the point of using a current of 0.15 A, which is about 160 mm mrad. It isclearer for the 5 nC beam that when there is an offset compensation, the beam emittance could be 1/3 of the case ofwithout one.
In order to investigate the wakefield effect for imperfectaligned structure, we use Elegant [6] for simulation and results are shown in Fig.4. In simulation, lattice file, changing steering coil and measuring wire scanner are the sameas real experiment. The advantage of simulation is themisalignment magnitude could be known and controlled,
whereas in the experiment there is no way to monitor the
misalignment value. From Fig.3 and Fig.4 we can seethat for both of them, the minimum point has been shifted
off from the origin, which means the emittance is reduced
when the beam is off the axis. In experiment, the 5 nC electron beam has received a kick from steering coil having acurrent of 0.15 A. The 5 nC electron beam inject into thenext unit with a displacement from axis. The displacement
caused the beam instability of inducing wakefield. This
wakefield combines with another wakefield which is generated due to the imperfect structures. They start to cancel each other, which leads to the emittance reduction. To
sum up, both of the simulation and experiment has shown
evidence that the compensation method is valid and wellsufficient to keep a small emittance when electron beam
propagate in the linac.

The emittance growth due to the wakefield effect inthe injection linac appears to be critical to the nano-beamscheme of the SuperKEKB. The structure misalignment
will be the main source of wakefield generation, but thisis something we cannot avoid. In order to minimize the effect of the wakefield, injecting the beam with certain offset
and angle could sufficiently reduce the emittance growth,which has been studied in theory and proved by experiment. With the help of KEKB linac, we have been collecting exciting results of indicating the validation of wakefieldcompensation using offset injection. The latest experimental results show the emittance could be 1/4 of no compensation, which has a well agreement with the theoretical calculation results and simulation output. For SuperKEKB, theexperience we have had so far based on KEKB beam andmachine studies will be valuable to the emittance preservation in the linac.

REFERENCES[1] http://www-kekb.kek.jp[2] SuperKEKB Task Force, “Letter of Intent for KEK Super
B Factory”, KEK Report 2004-4, June 2004, http://wwwkekb.kek.jp/SuperKEKB/home.html[3] K. Bane and M. Sands, “WAKEFIELDS OF VERY SHORTBUNCHES IN AN ACCELERATING CAVITY”, SLACPUB-4441, November 1987
[4] A.W Chao, B. Richter and C.Y. Yao, “BEAM EMITTANCEGROWTH CAUSED BY TRANSVERSE DEFLECTING
FIELDS IN A LINEAR ACCELERATOR”, Nuclear Instruments and Methods, A178(1980), 1-8[5] K. Yokoya, “Short-Range Wake Formulas for Infinite Periodic Pill-Box”, May 13, 1998
[6] M. Borland, “User’s Manual for Elegant”, March 10, 2011,
http://www.aps.anl.gov/Accelerator Systems Division/Accelerator Operations Physics/manuals/elegant latest/elegant.html