issues related to crossing angles Frank Zimmermann
Jan 06, 2016
issues related to crossing angles
Frank Zimmermann
RF Deflector( Crab Cavity )
Head-onCollision
Crossing Angle (11 x 2 m rad.)
Electrons PositronsLERHER
1.41 MV
1.41 MV
1.44 MV
1.44 MV
Super-KEKB crab cavity scheme
2 crab cavities / beam / IP
voltage of crab cavities
12
2/tan
Re
cEV
rf
cbcrab
crfcrab
x
4max
tolerance on IP offset jitter translatesinto tolerance on left-right crab-cavity phase and crab-main-rf phase
R12 & R22(R11) from MAD
nominal LHC optics
|R12,34|~30-45 m
|R22,44|~1 (from crab cavity to IP)
voltage required for Super-LHC
crossing angle 0.3 mrad 1 mrad 8 mrad
800 MHz 2.1 MV 7.0 MV 56 MV
400 MHz 4.2 MV 13.9 MV 111 MV
200 MHz 8.4 MV 27.9 MV 223 MV
crab cavity voltage for different c’s & rf frequencies
tolerance on R22
|60
12
2
2
2
*12
22
*
2
12
22*
12
22
zc
x
x
zc
x
zzc
cc
RR
R
R
zR
Rz
z-dependent additionalcrossing angle
corresponding Piwinskiangle should be small
not a problem
[for c=1 mrad, x=12 mm, R12=30 m, z=7.55 cm]
KEKB crab cavity • Squashed cell operating in TM2-1-0 (x-y-z)
• Coaxial coupler is used as a beam pipe
• Designed 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
K. Ohmi, HHH-2004 ~1.5 MV@500 MHz
longitudinal space required for crab cavities scales roughly linearly with crab voltage; desired crab voltage depends on rf frequency); achievable peak field also depends on rf frequency; 2 MV ~ 1.5 m, 20 MV ~ 15 mfrequency must be compatible with bunch spacing; wavelength must be large compared with bunch length;
1.2 GHz probably too high; 400 MHz reasonable; 800 MHz perhaps ok
longitudinal space & crab frequency
...6
1
22
1)(' 3
2
2
12
z
cz
Rzx
rf
cc
MHz 7752
2
6
z
rf
c
noise
amplitude noise introduces small crossing
angle; e.g., 1% jitter translates into 1%c/2
crossing angle – not critical
phase noise causes beam-beam offset;
→ tight tolerance on left-right crab phase
and on crab-main-rf phase differences
*
2224
revHOrmsIP fxn
t
emittance growth
from turn-by-turnrandom offsets x
requiring less than 10%/hr emittance growth xrms<12 nm ~ 10-3*
<0.012o at c=1 mrad & 500 MHz <0.04o at c=0.3 mrad & 500 MHz
SuperLHC: x,y=0.25 m, nIP=2, HO=0.005,
=7500, =3.75 m
p emittance growth due to random offsets
diffusion rate from strong-strong simulation with BBSS
• x2=x0
2+Dt t: turn
• D~1.4x10-15 x[m]2
z= 0 0.005 0.01
K. Ohmi, HHH-2004
tolerance from Ohmi san’sstrong-strong simulation
• For x=1.6 m (=5 degree) and =100,
D~1.4x10-15 x[m]2, where x2=x0
2+Dt, t: turn.
• Tolerance is x=0.016 m, = 0.05 degree for =100, and x=0.0016 m, 0.005 degree for =1, for luminosity life time ~ 1 day
K. Ohmi, HHH-2004
for 300 rad crossing angleand 400 MHz
slightly worse than my“pessimistic estimate”!?
analytic theory of b-b diffusion (T. Sen et al., PRL77, 1051 (1996)
M.P.Zorzano 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
K. Ohmi, HHH-2004
comparison with the simulation• D(a=1)=<J2>=1.5x10-25 m2/turn• D(sim)=(-0
2)2/2 =10-28 m2/turn Need to check
K. Ohmi, HHH-2004
analytical diffusion rate from Sen-Ellison-Zorzanomodel even much larger!!
} 3 orders ofmagnitudediscrepancy!
impedance of crab cavities
transverse impedance is an issuedue to large beta function
rise time due to 1 crab cavity =
rise time from ~10 normal rf cavities with the same voltage
dispersion correction
if large crossing angles are realized by placing single D1 dipoles first,
and the triplet between D1 and 2, the dispersion correction could be an issue
to be studied
minimum crossing angle from LR b-b
“Irwin scaling”coefficientfrom simulation
note: there is a threshold - a few LR encounters may have no effect! (2nd PRST-AB paper withYannis Papaphilippou)
minimum crossing angle with wirecompensator
*7
c
m75.3
103223
11*bparda
c
N
x
kd
need dynamic apertureof 5-6 and wirecompensation notefficient within 2 from the beam center