crab cavity option at lhc
DESCRIPTION
Crab cavity option at LHC. K. Ohmi (KEK) HHH04, 8-11, Nov. 2004 CERN. Thanks 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 1.15x10 11 - PowerPoint PPT PresentationTRANSCRIPT
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.