Proceedings of the 15th Annual Meeting of Particle Accelerator Society of Japan
August 7-10, 2018, Nagaoka, Japan

PASJ2018 THOM07

HIGH LUMINOSITY FLAT BEAM GENERATION WITH PHASE-SPACEROTATION FOR LINEAR COLLIDERS
Masao Kuriki∗ A) , Hitoshi HayanoB) , Naoto YamamotoB) , Yuji SeimiyaB) ,Xiuguang JinB) , Taro KonomiB) , Shigeru KashiwagiC) , Kazuyuki SakaueD) ,Masakazu WashioD) , Philippe PiotE) , John PowerF)
A
Hiroshima University, Higashihiroshima, JapanB
KEK Accelerator Laboratory, Tsukuba, JapanCTohoku University, Sendai, Japan
DWaseda University, Tokyo, JapanENorthern Illinois University, Illinois, USAF
Argonne National Laboratory, Illinois, USAAbstract

large energy spread by Beamstrahlung asElectron Positron Linear Collider is the only way to realize
annihilation of elementary particles with more than 350
GeV center of mass energy in the current technology. InLinear Collider, the beam spot should be flat, i.e. tiny in one
axis and moderate in another axis to maximize luminosity
suppressing beam-beam effect. Instead of radiation dampingwith a storage ring, we propose to generate the flat beam withphase-space rotation technique in the injector. We plan tocarry out beam tests at STF(Superconducting Test Facility)KEK and WFA (Wake Field Accelerator)-ANL(ArgonneNational Laboratory). According to our simulation, the flat
beam required at IP in ILC can be made with this technique.

INTRODUCTION
Electron Positron Collider is the only way to realize annihilation of elementary particles with controlled conditions
with the current technology. Because there has been no
any significant evidence of Super-symmetry in LHC experiments, the significance of detail studies of Higgs boson and searching inconsistency in the standard model withelectron positron collider is maximized. ILC (InternationalLinear Collider) [1] is an e+e- linear collider based on superconducting accelerator with CME from 250 to 1000 GeV. It
would be constructed in Iwate, Japan, as the main project ofHigh energy physics.
Luminosity L is the index showing the performance ofcolliders. It can be expressed asf nb N 2
L=,4πσx σy(1)where f is repetition of pulse, nb is number of bunches in apulse, N is number of particles in a bunch, σx,y is transverse
beam size. The numerator can’t be too large, because it
increases the wall plug power asPwall = ηeE f nb N,(3)A practical way to enhance the luminosity and suppress
Beamstrahlung simultaneously is squeezing the beam in oneof the transverse direction, e.g. σx  σy . For ILC, Thebeam size at IP is 640 nm in horizontal direction and 5.7
nm in vertical direction. Emittances are 10 and 0.04 mm
mrad in horizontal and vertical directions, respectively. Thisasymmetric emittance beam is made by radiation damping ina storage ring in the current design. We propose to generatethe flat beam for ILC only with the injector by employing
the emittance exchange technique.
As the phase-space rotation technique, there are two methods. One is RFBT (Round to Flat Beam Transformation) [2]generating the flat beam from an angular-momentum dominated beam produced by beam emission in a solenoid field.
Another is TLEX (Transverse to Longitudinal EmittanceeXchange) exchanging the phase-spaces between longitudinal and transverse directions by dipole mode cavity in adispersive beam line [3].

EMITTANCE EXCHANGE TECHNIQUESIn this section, RFBT and TLEX are briefly explained.

RFBT
RFBT generates the asymmetric emittance beam between
two transverse directions from an angular momentum dominated beam. A proof of principle experiment of RFBT
was performed demonstrating 100 emittance ratio [4]. The
angular momentum dominated beam is made by the beamemission in a solenoid field. Vector potential of the solenoid
field A makes a canonical angular momentum Pc asPc = P − eA,(2)where η is power efficiency and eE is beam energy. One way
to enhance the luminosity is minimize σx,y , but it causes a∗ mkuriki@hiroshima-u.ac.jp

212
∆E ∝.
σz σx + σywhere P is kinematic momentum, because eB0 yA=,2 −x- 135 -(4)(5)

Proceedings of the 15th Annual Meeting of Particle Accelerator Society of Japan
August 7-10, 2018, Nagaoka, JapanPASJ2018 THOM07

where e is elementary charge and B0 is the solenoid magneticfield. The correlation between x, y and Py, Px makes nondiagonal components of sigma matrix Σ0 as
εT0 L JΣ0 =,(6)
−L J εT0
where ε is the intrinsic emittance, T0 is sigma matrix components for the intrinsic emittance by Twiss parameters as!
β−α2 ,
T0 =(7)−α 1+αβ
L is dimension less angular momentum
L=eB0 σ,pz

(8)where σ is the beam size, pz is longitudinal momentum, and

0 1
J=,
(9)
−1 0
RFBT can be made with a linear beam transformation
with three skew quadrupoles. The channel of the three skew
quadrupoles can be expressed as
1 A+ A−M = R−1 NQ R =,(10)
2 A− A+
where R is π/4 rotation matrix, NQ is transfer matrix ofthree quadrupoles in normal coordinate asA 0
NQ =,(11)0 B
and A± is A ± B. The sigma matrix transformed with Mcan beε T0Σ = MΣ0 M̃ = − −,(12)0
ε+T+ifA− = A+ S,
(13)
where
S = ±JT0 .
−1(14)

Analytic solution for M is expressed as [5]r−D1 s11 + s12 + D1 Dt s21 + Dt s22
q1 = ±(15)
D1 Dt s12
s12 + Dt s22
q2 = −(16)D1 D2 (1 + q1 s12−q1 − q2 − D1 q1 q2 s11 − s21q3 =.
1 + (Dt q1 + D2 q2 )s11 + D1 D2 q2 (q1 + s21 )(17)
where D1 and D2 are drift space between the first and second,
and the second and third skew quadrupoles, respectively. Dt
is sum of D1 and D2 . After the skew channel, the normalized
emittance in transverse coordinate is
q2 + (γ βL)2 ± γ βL,
εn± = εn0(18)giving the emittance ratio as
2εn+εn0∼.
εn−2γ βL

(19)

TLEX
TLEX is implemented with a couple of doglegs and adipole mode cavity. TLEX was experimentally demonstratedby showing transformation of the transverse intensity modulation to the longitudinal modulation [6]. The transfer matrix
of a dogleg section Md and dipole mode cavity Mc are expressed as
1 L 0 η©
ª­0 1 0 0®
Md = ­(20)®,­0 η 1 ξ ®
«0 0 0 1¬
and
1 0 0 η©
ª
­ 0 1 k 0®
Mc = ­(21)®,­ 0 0 1 0®
« k 0 0 1¬
where k = eV0 /(aE0 ) with V0 (cavity voltage at iris), a(cavityiris size), and E0 (beam energy).
The dipole mode cavity is placed between the dogleg
sections giving the transfer matrix of TLEX section MT as
MT = M d M c M d0©
­ 0= ­­ ξ­− η1«− η00
η − Lξ
η− ηL− ηL− f rac1η
00

η − Lξ
η ª− ηξ ®®
,0 ®®
0 ¬(22)where a matching condition of 1 + ηk = 0 is assumed. Aseasily recognized in this equation, the phase-space of x andz are exchanged with TLEX section.

FLAT BEAM GENERATION FOR LINEAR
COLLIDERS
As explained in the introduction, the flat beam is essentialto enhance the beam luminosity for linear colliders. In theILC current design, the emittance at IP are 10 mm mrad forhorizontal direction, 0.04 mm mrad for vertical direction,and 8.4×105 mm mrad for longitudinal direction. This beamis made up with radiation damping in 3 km DR. Figure 1
shows the schematic drawing of the injector with DR.
By employing the emittance exchange techniques (RFBTand TLEX), the ILC compatible beam can be generated onlywith an injector lilac as shown in Fig. 2. 3.1 km DR can beomitted. The emittance budget is summarized in Table 1.
The first row is required emittance at IP for ILC. The second
row is emittance at Gun when we employ only RFBT. InRFBT, the product of εx and εy is conserved. To make 10mm mrad and 0.04 mm mrad with RFBT, the emittance from
Gun should be 0.6 mm mrad. This small emittance cause
several problems. One is emission density. To make thissmall emittance from the gun, the beam spot should be also
small, cause a high density beam emission from the cathodesurface. Including 50% margin of the bunch charge, 4.8 nCbunch charge should be extracted from the small spot. Thebunch length can be large and a careful design for bunching- 136 -

Proceedings of the 15th Annual Meeting of Particle Accelerator Society of Japan
August 7-10, 2018, Nagaoka, JapanPASJ2018 THOM07

Table 2: Parameters of the simulation. G1,2,3 are field gradient of skew quadrupoles, α is bending angle of dogleg,ηand ξ are dispersion and momentum compaction of dogleg.
RF voltage of dipole mode cavity is defined at λ from thecavity center.

To Main LinacDamping Ring
Circumference 3.1km
DC Buncher
Gun CavitiesBooster Linac

Figure 1: The conventional design of the injector for Linear
colliders. The beam is stored in DR to make asymmetricbeam emittance in horizontal and vertical directions by radiation damping.
ToMain Linac
Dipole Mode RF
Skew quarupoles

Gun

Booster Linac

Injector Linac

Figure 2: The injector design employing the emittance exchange techniques. The asymmetric emittance beam in horizontal and vertical directions are made by RFBT and TLEX.

section is required. Another problem is emittance growthby space charge effect. The small beam size cause a strong
non-linear space charge increase the beam emittance. If theemittance growth of the space charge is significant, the ILC
compatible beam can’t be generated with RFBT because theproduct is not conserved anymore.
The third row shows the emittance at gun when we employ RFBT and TLEX. If we employ RFBT and TLEX, theproduct of three emittance (x, y, and z) can be conserved
and therefore, εx and εy can be large to avoid the problem
at the gun emission and the space charge emittance growth.
The fourth row shows the expected emittance with the sameparameter at IP. εx and εy are compatible to the ILC requirement at IP. εz is still less than the requirement.

SIMULATION
A simulation is performed by assuming a beam test at
KEK-STF. KEK-STF is a test facility to demonstrate theTable 1: Emittance budget for ILC at IP (TDR), case 1 (only
RFBT, gun), case 2 (RFBT and TLEX, gun), and case 2(RFBT and TLEX, IP). Emittance is in mm mrad.
Designεxεyεz

ILC at IP (TDR)
Case 1 (RFBT, gun)Case 2 (RFBT+TLEX, gun)Case 2 (RFBT+TLEX, IP)

100.645100.04
0.6
450.04

2.5 × 105
2.5 × 105105.1 × 104

Parameters
Solenoid field
Initial emittance (x,y)
Bunch length
Beam size
Lorentz γ after acceleration
G1G2G3αηξRF voltage

Value
0.1
1.5
12
1.6
49
-0.503
0.926
2.058
0.3
0.355
0.106
1.29

unit
Tmm mradps (full width)
mm (rms)
T/m
T/m
T/m
radmm
MV at λTable 3: Emittance evolution in the simulation. Emittanceis in mm mrad.
Position
CathodeAfter RFBT
After TLEX

εx
1.5160
8.5εy
1.5
0.045
0.045

εz8.5
8.5
160

beam acceleration with super-conducting accelerator. It consists from 1.3 GHz L-band RF Gun which is compatible toXFEL/FLASH, a super-conducting accelerator module withtwo 1 m TESLA type cavities. The STF is now upgrading
to increase number of accelerator module from one to two.
The second accelerator module has 12 1 m cavities.
To implement RFBT, solenoid field should be on the cathode surface. Usually, the gun is designed to vanish solenoid
field to avoid emittance growth by the angular momentum.
The solenoid field can be induced on the cathode by changing the polarity of bucking coil. According to the solenoid
design, up to 0.15 T field can be made. In the simulation, 0.1
T field is assumed. The parameters are summarized in Table
2. G1,2,3 are field gradient of skew quadrupoles, α is bending angle of dogleg,η and ξ are dispersion and momentum
compaction of dogleg. RF voltage of dipole mode cavity isdefined at λ from the cavity center.
The simulation was performed with GPT. The optimization of skew Q setting was made to minimize the sum of
non-diagonal components of Σ matrix, i.e. < xy >, < x y 0 >,< x 0 y >, and < x 0 y 0 > by steepest descent method. The
result of the simulation is shown in Fig. 3. The horizontal
axis show the distance from the cathode surface. εx , εy ,and εz are drawn with solid line, dashed line, and dottedline, respectively. The emittance evolution is summarizedin Table 3. By comparing these numbers with them in Table
1, ILC requirements are almost satisfied.

- 137 -

Proceedings of the 15th Annual Meeting of Particle Accelerator Society of Japan
August 7-10, 2018, Nagaoka, Japann. emittance(m)PASJ2018 THOM07

the feasibility of the method with these beam tests. If the experiment showed a good performance, a full demonstration
should be made by introducing a dipole mode RF cavity in
STF as a future plan.

−31010−4SUMMARY
We propose the flat beam generation for linear colliders
by employing the emittance exchange techniques. By using
RFBT and TLEX, the flat beam compatible to ILC parametercan be made with a large initial x and y emittance fromthe cathode. The large emittance from the gun relaxes thecondition for the beam emission density and space charge
emittance growth. Beam tests will be carried out at KEKSTF and ANL-WFA for further investigations.

10−510−6

10−710−834567891011

ACKNOWLEDGMENT

12s(m)

Figure 3: Emittance evolution of the simulation. The horizontal axis shows the distance from the cathode, and thevertical axis shows the normalized emittance in m. εx , εy ,and εz are drawn with solid line, dashed line, and dottedline, respectively.

This work is partly supported by Grant-in-Aid for Scientific Research (B) and US-Japan Science and Technology
Cooperation Program in High Energy Physics.

REFERENCES[1] ILC Technical Design Report, KEK-Report 2013-1, 2013.

Please note that the simulation does not include spacecharge effect, yet. Next, we perform a simulation with alarger beam emittance at the cathode with space-charge effectto confirm the feasibility of the method.

[2] R. Brinkmann, Y. Derbenev, and K. Flöttmann, Phys. Rev. STAccel. Beams,4, 053501(2001).
[3] M. Cornacchia and P. Emma, Phys. Rev. ST Accel. Beams 5,084001(2002).
[4] P. Piot, Y.-E Sun, and K.-J. Kim, hys. Rev. ST Accel. Beams
9, 031001(2006).

FUTURE PLAN
We schedule beam test at KEK-STF and ANL(ArgonneNational Laboratory) WFA(Wake Field Accelerator). In
STF, an experiment for RFBT will be performed. In ANLWFA, RFBT and TLEX will be performed. We will examine[5] Yin-E Sun, PhD Thesis, Fermi-lab(2005).
[6] Y.-E Sun, P. Piot, A. Johnson, A. H. Lumpkin, T. J.
Maxwell, J. Ruan, and R. Thurman-Keup, Phys. Rev. Lett.
105, 234801(2010).

- 138 -