Crab crossing at KEKB

K. Ohmi, KEK

Beam-beam workshop

2-4, July, 2007, SLAC

T. Abe, T. Agho, K. Akai, M. Akemoto, A. Akiyama, M. Arinaga, K. Ebihara, K. Egawa, A. Enomoto, J. Flanagan, S. Fukuda, H. Fukuma, Y. Funakoshi, K. Furukawa, T. Furuya, K. Hara, T. Higo, S. Hiramatsu, H. Hisamatsu, H. Honma, T. Honma, K. Hosoyama, T. Ieiri, N. Iida,

H. Ikeda, M. Ikeda, S. Inagaki, S. Isagawa, H. Ishii, A. Kabe, E. Kadokura, T. Kageyama,K. Kakihara, E. Kako, S. Kamada, T. Kamitani, K. Kanazawa, H. Katagiri, S. Kato, T. Kawamoto, S. Kazakov, M. Kikuchi, E. Kikutani, K. Kitagawa, H. Koiso,

Y. Kojima, I. Komada, T. Kubo, K. Kudo, N. Kudo, K. Marutsuka, M. Masuzawa, S. Matsumoto, T. Matsumoto, S. Michizono, K. Mikawa,

T. Mimashi, S. Mitsunobu, K. Mori, A. Morita, Y. Morita, H. Nakai, H. Nakajima, T. T. Nakamura, H. Nakanishi, K. Nakanishi, K. Nakao, S. Ninomiya, Y. Ogawa, K. Ohmi, S. Ohsawa, Y. Ohsawa, Y. Ohnishi,

N. Ohuchi, K. Oide, M. Ono, T. Ozaki, K. Saito, H. Sakai, Y. Sakamoto, M. Sato, M. Satoh, K. Shibata, T. Shidara, M. Shirai, A. Shirakawa,

T. Sueno,M. Suetake, Y. Suetsugu, R. Sugahara, T. Sugimura, T. Suwada, O. Tajima, S. Takano, S. Takasaki, T. Takenaka, Y. Takeuchi, M. Tawada, M. Tejima, M. Tobiyama, N. Tokuda,

S. Uehara, S. Uno, Y. Yamamoto, Y. Yano, K. Yokoyama, Ma. Yoshida, Mi. Yoshida, S. Yoshimoto, K. Yoshino,

KEK, Oho, Tsukuba, Ibaraki 305-0801, JapanE. Perevedentsev, D. N. Shatilov, BINP, Novosibirsk, Russia

Input Coupler Liq. Helium Vessel

Stub Support

Coaxial Coupler

Copper Bellows80 K Liq. Nitrogen Shield

Notch Filter

RF Absorber

Aluminum End Plate

Aluminum End Plate

SUS Support Pipe

Crab Crossing @ KEKB

Crossing angle 22 mrad

Head-on (crab)(Strong-strong simulation)

Crab Crossing can boot the beam-beam parameter higher than 0.15 !

Crab cavities were successfully produced and beam study has started

in Feb. 2007.

K. Ohmi

K. Hosoyama, et al

Crab Cavities in the KEKB Rings

LER

HER

1 cavity per ring

Single Crab Cavity Scheme

1 crab cavity per ring.

saves the cost of the cavity and cryogenics.

avoids synchrotron radiation hitting the cavity.

•Beam tilts all around the ring.

•z-dependent horizontal closed orbit.

•tilt at the IP:

Crab cavity creates a dispersion, (x,px)=(’)z

• Periodic solution at crab cavity.

• Synchrotron radiation damping realizes an equilibrium orbit (closed orbit) and beam size with periodic condition.

• (,') is transferred as

• (,') is matched at IP as follow

€

ς (s)

ς '(s)

⎛

⎝ ⎜

⎞

⎠ ⎟= M0

ς (s)

ς '(s)

⎛

⎝ ⎜

⎞

⎠ ⎟+

0

edVcrb dz

⎛

⎝ ⎜

⎞

⎠ ⎟

€

ς (s2)

ς '(s2)

⎛

⎝ ⎜

⎞

⎠ ⎟= M21

ς (s1)

ς '(s1)

⎛

⎝ ⎜

⎞

⎠ ⎟

€

ς (s*)

ς '(s*)

⎛

⎝ ⎜

⎞

⎠ ⎟=θcrs0

⎛

⎝ ⎜

⎞

⎠ ⎟

Remember the ordinary dispersion, (x,px)=(’)

Parameterization of 6x6 revolution matrix

€

x 2 xpx xy xpy xz xδ

px2 pxz px py pxz pxδ

y 2 ypy yz yδ

py2 pyz pyδ

z2 zδ

δ 2

⎛

⎝

⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟

= HRB

εx 0 0 0 0 0

0 εx 0 0 0 0

0 0 εy 0 0 0

0 0 0 εy 0 0

0 0 0 0 εz 0

0 0 0 0 0 εz

⎛

⎝

⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟

B tR tH t

€

V = HRB

€

M =VUV −1

€

U =

cosμ x sinμ x 0 0 0 0

-sinμ x cosμ x 0 0 0 0

0 0 cosμ y sinμ y 0 0

0 0 -sinμ y cosμ y 0 0

0 0 0 0 cosμ z sinμ z0 0 0 0 -sinμ z cosμ z

⎛

⎝

⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟

€

R =

μ 0 R4 −R2 0 0

0 μ −R3 R1 0 0

−R1 −R2 μ 0 0 0

−R3 −R4 0 μ 0 0

0 0 0 0 1 0

0 0 0 0 0 1

⎛

⎝

⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟

€

H =

1− ax ζ x η x1− ax ζ 'x η 'x

1− ay ζ y η y1− ay ζ 'y η 'y

−η 'x η x −η 'y η y 1 0

ζ 'x −ζ x ζ 'y −ζ y 0 1

⎛

⎝

⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟

€

B =

β x 0 0 0 0 0

−α x β x 1 β x 0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

⎛

⎝

⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟

K. Ohmi, K. Hirata, K.Oide, PRE 54, 751, 1994

Crab Phase Scan (LER)

Horizontal orbit distortion by a crab kick measured with 453 BPMs.

Dependence of the horizontal kick the crab cavity of the rf phase. The kick angles estimated from the orbit response agree well those from the setting voltage of the crab cavity by 3.6%.

crab

V(z=0) gives a dipole kick.

Beams has indeed tilted!

LER HER

inside of the rings

outside of the rings

- Observation with Streak Cameras (H. Ikeda et al, FRPMN035)

The streak camera

longitudinal

horizontal

Vcrab Scan (HER)

3.6 mrad

Luminosity Ratio

Vertical beam size

Beam lifetime

design

H. Koiso

HERHER

LERLER

Warmupto 300K

Crab cav.detuned

IHER = 0.7 A, ILER = 1.3

A, L > 1034 with

crab crossing.

Working Point of Tunes

K. Ohmi, et al.Phys. Rev. ST Accel. Beams 7, 104401(2004)

We are here.

Simulations give good guidelines.

Head-on 22 mrad crossing

LER

HER

Achievable luminosity for various emittance cases

x=18/24nm (3/14)x=24/24nm

(4/1)x=24/29nm (6/14)

achieved scaled achieved scaled achieved scaled

# of bunches 51 1389 51 1389 100 1389

ILER

(mA)61 1661 75 2043 125 1736

IHER

(mA)34 924 30 817 74 1028

Luminosity

(/nb/sec) 0.594 16.5 0.611 17.0 1.03 14.3

Luminosity with/without crab cavityx=18/24nm

With Crab

x=18/24nm

No Crab (achieved)

achieved(2007/3/14)

scaled scaled acheived(2007/11/15)

achieved(2005/12/25)

# of bunches 51 1389 1585 1389 1585

ILER

(mA)61 1661 1933 1662 1800

IHER

(mA)34 924 1078 1340 1360

Luminosity

(/nb/sec) 0.594 16.5 18.8 17.1 15.2

Ecloud?Ecloud?

Specific Luminosity

L18 H24 (3/11, 4/3)

L18 H24(4/10, 4/19)

L24 H24 (3/29, 4/1)

L24 H29(6/14)

H. Koiso

No crab

What we expect crab cavity?• Establish symmetry of the collision

• Degree of freedom of the collision system is decreased to one for x->+0.5.

• Vertical motion is decoupled, therefore vertical emittance growth become weak.

• Motion in one degree of freedom is confined in KAM surface.

Symmetry breaking source• Optimization with a large number of parame

ters

• Offset x, y, x’, y’

• Twiss parameters, (waist), Ri=1,4, x,y, ’ x,y of each beam.

Tolerance for twiss parameters• Tolerance of all parameters are individually

in controllable range.

0.E+00

1.E+31

2.E+31

3.E+31

4.E+31

0 0.05 0.1 0.15 0.2 0.25

r4

L

LLgeo

1 unit for KEKB tuning: r4=0.021, =0.00016

0.E+00

1.E+31

2.E+31

3.E+31

4.E+31

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012

etay (m)

L

LLgeo

Difficulty for multi-parameters optimization

Crossing Angle and Horizontal Offset

The luminosity should be significantly degraded by small errors in the crab crossing mode. Therefore it is important to keep both the crossing angle and the horizontal offset between two beams sufficiently small. The crossing angle was optimized by adjusting the crab kick voltage. The horizontal offset must be less than 20 m. The offset was maintained by an orbit feedback to keep the canonical beam-beam kick constant. The target position was determined by the offset scan.

Lum

inosi

ty

Effect on the beam-beam performance of the phase jitter of RF’s

0

0.5

1

1.5

2

2.5

0 0.02 0.04 0.06 0.08 0.1 0.12

x/ σx

σx/σx0

e-

e+

e-

e+

• Luminosity and beam size as functions of x.

• Correlation time of the jitter, 1 or 10 turns, is important for the degradation.

• Since Q=200,000 and H=5120, the correlation time will be larger than 10 turns.

• Tolerance is 0.05 degree.

0

0.2

0.4

0.6

0.8

1

1.2

0 0.02 0.04 0.06 0.08 0.1 0.12

x/ σx

L/L0

Tcor=10

Tcor=1

LER HER

RF Phase Stability

Phase stability of the crab mode was better than the requirement with the rf feedback.

Slow stability below 1 Hz is shown above.

Independent measurement by a spectrum analyzer shows better than 0.01 deg for f > 2 kHz, 0.1 deg for 2 Hz < f < 2 kHz.

Backlash or friction exists in the coaxial tuner for the LER.

LER x, y tune dependence

x -x =integer

x +s =integer These resonances have to be eliminated.

Succeeded in some lattices, but not in some others.

Most serious issue in the crab operation • Asymmetry for the horizontal offset• Beam life time is very short in a region of a horizontal offset.• This asymmetry can not be reproduced by the simulation.

• We had a similar experience. Remember “egure”.• Banana shape of beam (D. Shatilov), or nonlinear?

Short life time

Long life time e+e-

Horizontal offset scan

• The (HER) beam current seems to be limited by the short life time of the LER beam.

• The (LER) beamlifetime is very asymmetric with respect to H offset.

Collision center given by the beam-beam kick

LER lifetime

Beam-beam halo in simulation• Long term simulation by Gaussian weak-strong model.

500x106 particle turn

Head-on 11 mrad

Life time can be improved due to the crab cavity.

Beam-Beam Simulation with lattice non-linearity

• Luminosity drops (beam loss) abruptly at threshold strengths.

• However, the threshold strengths are about 2 order higher than expected values.

Summary• Crab cavity operation starts from Feb. 2007.• High current operation was succeeded, 1.3 A

(e+) and 0.7 A(e-).• RF Phase fluctuation (20 sec period) was see

n at high current operation due to the backlash in the coaxial tuner. The fluctuation is seen only in collision mode. Related to beam-beam?

• Luminosity gain is not yet. • It seems to be essential for me to solve the as

ymmetry.