Crab cavity option at LHC

K. Ohmi (KEK)HHH04, 8-11, Nov. 2004CERNThanks to K. Akai, K. Hosoyama, T. Sen, F. Zimmermann

Introduction

Half crossing angle 0.15 mrad. Other possibilities are 0.225, 0.5 and 4

mrad.E=7 TeV.Bunch population 1.15x1011

Bunch spacing 25 ns, RF=400.8 MHz.Number of bunch 2808 I = 0.584 AL=26,016m

Crabbing voltage

Deflecting RF voltage, : half crossing angle

*=0.5m =150 m, fRF=500 MHz

V=11.6 MV is required for =0.15 mrad.

*

tan

RF x x

cEV

77 [mrad] MVV

KEKB type crab cavity

TM110 500 MHzTM010 324 MHzV=1.44 MVNeed 8x2 cavities for = 0.15 mrad.Need more cavities 0.225, 0.5 and 4 mr

ad. How is multi-cell cavity? Coupled bunch instability issue.

Original crab cavity Squashed cell operating in TM2-1-0 (x-

y-z)Coaxial coupler is used as a beam

pipeDesigned for B-factories (1〜 2A)

Absorbing materialNotch filter

Absorbing material

Squashed Crab cavity for B-factories

Coaxial beam pipeCooling for inner conductor

(axial view)

inner conductor

"Squashed cell"

(K. Akai et al., Proc. B-factories, SLAC-400 p.181 (1992).) Courtesy K. Akai

~1.5 m

Why squashed cell shape cavity?

TM110 TM010

TM110

TE111

500MHz

500MHz

324MHz

720MHz

Unwanted Mode

TM110 - like Mode

500MHz

TM010 - like Mode

413.3MHz

700MHz

650.5 MHz / 677.6MHz

Unwanted Mode

Crab ModeCrab Mode

E

B

The squashed cell shape cavity scheme was studied extensively at Cornell in 1991 and 1992 for CESR-B under KEK-Cornell collaboration.

Courtesy of K.Hosoyama & K. Akai

Transverse coupling impedance

Courtesy of K. Akai

Zx /cav Zy/cav

f ZL /cav

~1 sec (inj)

~1 hour (inj)

High current type for super KEKB

Courtesy of K. Akai

Damped structure with wave guides.

Impedance~1/10.

Coupled bunch instability caused by the parasitic

modesLongitudinal

f ZL,peak=17.8 / k GHz @injection =152 / k GHz @top　　　　　　　　　　　　　　　　　 : Growth time

(sec)Transverse

Zt,peak=1.37 / [M/m] @injection, =21 / [M/m] @top

0 0 020

( ) ( )2

em s s

s p

MNri pM m Z pM mT

020

( )2

em

p

MNri Z pM m

T

(TOP VIEW)RF Input Coupler

He Vessel

80 K LN2 Shield

Coaxial Line Stub Support

CRYOSTAT FOR KEKB CRAB CAVITY

Bellows

Support

LHe In

GHe Out

LN2 In

LN2 Out

0 1 20.5 1.5 2.5scale ( m )

Cryostat for KEKB Crab Cavity (Top View)

Courtesy of K. Hosoyama

~ 3 m

2003 2004 2005Jan. Jan. Jan.Dec. Dec. Dec.

Beam Test

Crab Cavity #1Design

Road Map to Beam Test (Feb 2004)

Vac.RFCryogenicsControl

Crab Cavity

Cryostat

Coaxial Coupler

E.P.

Cold Test

Assembling

Jan.

Cold TestＣｒｙｏｓｔａｔ　 (Prototype)

Coaxial Coupler (Prototype)

Nb-Cu R&D

Installation

Vac.RFCryogenicsControl

Assembling

Cold Test

Crab Cavity Prototype

Courtesy of K. Hosoyama

Effect on the beam-beam performance

(preliminary)

Noise of RF system. Deviation of RF phase, .

Phase error between two crab cavities.

tanRF

RF

cx

cos( ( *, ))tan tan

2sinx c

c cRF x RF

s sc cx

Fluctuation in collision due to the crab cavity noise

Random fluctuation of beam offset at the collision point.

Example to sketch rough behaviors x=1.6 m for =5 degree (z=1 cm) and =0.15

mrad. Note x=17 m. Correlation of the fluctuation. <x(n) x(n+m)>=e-m/, where n, m are turn. z=1, 0.5, 0.2, 0.1 cm at =1, 100 were examined.

A Strong-strong simulation was executed including the fluctuation.

3D algorithm, Longitudinal slicing

A bunch is divided into some slices which include many macro-particles.

Collision is calculated slice by slice.

Strong bunch is divided into some slices.

Particles in the weak beam is tracked slice by slice.

Weak-strong Strong-strong

Synchro-beam mapping (Hirata)

Weak-strong

Beam envelope of the strong beam slice is transferred to collision point.

Since the interaction depends on z, energy kick occurs.

s1

s2

Extension to strong-strong simulation

Potential is calculated at sf and sb.Potential is interpolated to si between sf and sb.

sf

sbsi

Since the interaction depends on z, energy kick should be taken into account d/dz.We repeat the same procedure exchanging particle and slice.

sf

sbsi

Convergence for the slice number

10x1030

8

6

4

2

0

Lum

inosi

ty/b

unch

[/c

m2/s

ec]

35302520151050

No. of longitudinal slice

All particles in i-th slice are kicked by φcp

Interpolation

How many slices do we need? Disruption parameter of each slice should be smaller than 1.

14

y

y z

Noise free - no diffusion

L x

The beam size with crab is larger, but is pretense, <xx>c=<xx>+2<zz>. Note that the luminosity is higher.

Diffusion due to RF phase error, z

L x

x is raised by dispersion x=z induced by the crab cavity.

Diffusion rate given by the simulation

x2=x0

2+Dt t: turnD~1.4x10-15 x[m]2

z= 0 0.005 0.01

No crab cavity、 RF phase error

Diffusion without crab cavity was weak. Noise of transverse offset is origin of the diffusion.

L x

Diffusion due to phase error of crab cavity

x=1.7 m and dz=1 cm (x =1.7 m) Similar diffusion rate L x

Correlation time,

dx=1.6 m, =100 and dx=0.16 m =1 was similar behavior.

z

x

z

x

z

xn

nn

1

1

111

M.P.Zorzano and T. Sen

Analytic theory of beam-beam diffusion (T. Sen et al., PRL77, 1051 (1996), M.P.Zorz

ano et al., EPAC2000)

2 2 2

0

( ) sinh (2 1) ( )( )

8 4 / cosh cos 2 (2 1)k

xxk

C x k G aD J

k

1 1

1' ' ( 1)k k k k k

aG U U k U kU

a

0 00

1( ) (2 )( 1) ( )

ak w

k k k kU a e I w dww

Diffusion rate due to offset noise. (round beam)

ln(1 1/ )

*

22p p x

p

N r JC a

Comparison with the simulation

D(a=1)=<J2>=1.5x10-25 m2/turnD(sim)=(-0

2)2/2 =10-28 m2/turn Need to check

Tolerance

For x=1.6 m (=5 degree) and =100, 　 D~1.4x10-15 x[m]2, where x

2=x02+Dt,

t: turn.Tolerance is x=0.016 m, = 0.05 degre

e for =100, and x=0.0016 m, 0.005 degree for =1, if luminosity life time ~ 1 day is required.

Crab crossing in e+e- colliders

Flat beam, small y, y<<x<<z .High beam-beam parameter, >0.05.High disruption zy~1.Radiation damping and diffusion.

Symplectic diffusion is caused by crossing angle and lattice errors at collision point

Final beam-beam limit after removing all diffusion sources is determined by the radiation excitation.

Diffusion for various crossing angle

given by the weak-strong simulation (Gauss)

Vertical equilibrium size obtained by the weak-strong simulation and the ratio of the diffusions for the rad. damping.

Diffusion rate

Diffusion due to x-y coupling (Gaussian)X-y coupling is characterized by r1-r4.Diffusion caused by r1 and r2 is shown.

The diffusion rate is proportional to r1 and r2.

Luminosity behavior with x-y coupling in 2D and 3D simulation

X-y coupling seems to affect 2D dynamics. Luminosity behavior depends on 2D or 3D simulation, namely include z or not.

Diffusion due to vertical dispersion

Gaussian beam

Diffusion in the head-on collision

symplectic diffusion is removed Radiation excitation enhances beam enlargement.

In Gaussian model, enlargement is small.

Accuracy of PIC is excellent as far as diffusion.

Gaussian:PICGaussian:Exact solution

Distorted distribution : PIC

Beam-beam parameter for zero and finite crossing angle

Gauss model PIC

* Present KEKB parameter

Strong-strong

Discussions

Do crab cavities contribute luminosity upgrade of LHC?

Is the symplectic diffusion caused by crossing angle dominant? If yes, crab cavity works.

Do diffusion limit the LHC luminosity? What determine the beam-beam limit in LHC?

What is dominant diffusion source in LHC?

Parasitic collision is weakened by large crossing angle.