Simulation of beam-beam induced emittance growth in the HL-LHC with crab cavities
Crab Cavities “from virtual reality to real reality” Cavities “from virtual reality to real...
Transcript of Crab Cavities “from virtual reality to real reality” Cavities “from virtual reality to real...
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LHC
Crab Cavities“ from virtual reality to real reality”R. Calaga, BE-RF, LHC-PW, Chamonix 2012
On behalf of the LHC-CC collaboration
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The Real “ Problem”
Nominal → 4 IRs, 120(+) parasitic encountersSufficiently large crossing angle inevitable (8-12 sep)
Beam-Beam TeamCERN-ATS-2011-217
8 to 16 LR encounters
No collisions or LR
2011 MD: 36 bunches50 ns, 2 Collisions
Reducing crossing angle
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2
Consequence
Φ=σ zσ x
ϕc
σ eff=√σ x2+σ z
2ϕc2
Piwinski angle
Upgrade: reduce * (by factor 2-4)Consequence → approx double the crossing angle (10 sep)
Ineffective Overlap
Note: don't forget hour-glass effect (~15% loss for */z)
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Some Numbers
2011 2012 after LS1 after LS3Energy 3.5 TeV 4 TeV 7 TeV 7 TeV
* [cm] 100 60 55 15
2 [rad] 260 313 247 473
R(z =7.55cm) 0.94 0.85 0.82 0.37
R(z =10.1cm) 0.76 0.74 0.28
2 ϕ≃d.√ϵ/βipAssume:
N = 2.5 m, d=10
very inefficient
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For the Upgrade
12 separation
10 separation
Nb = 2 x 1011 p/bN = 2.5 m* = 15 cm
S. White, LHC-CC11
Lpk < 7 x 1034 (12 sep), little margin for leveling
Note: don't forget synchro-betatron resonances ~2-4BBLRs might alleviate partially
Nominal
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To Recover
Δ p x=qVE. sin (ϕ s+ωt )
c
“ - Bump”
RF Deflector
RF Deflector
V crab=cE tan(ϕc)
ω R12
.2sin (πQ)
cos (ϕ cc−ip−πQ)
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Cavity Voltage
~6MV/ IP-side (2 cavities)
add a cavity
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Why 400 MHzLHC bunches are long
RF non-linearity (longitudinal)
Higher frequency (for example 800 MHz)“ Smaller” cavitiesLess voltage (VT 1/) → Not reallyEasier phase noise control ? (see later)
800 MHz Cavity, K. Ohmi
L∝N b
2
σ2 RΦ FRF
Φ
GUINEA-PIG simulation, Y. Sun
FRF ~ 10-25%Form factor ~1 (* 10-55 cm)
=1
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Pillbox Cavity
beam
Transverse Cross Section, squash
beam in/out of the plane
TM01
0
TE11
1
TM11
0
TE01
1
freq spectrum
TM01
1
TM21
0
TM11
0Y
f res∝1R
R (independent of length)
crabbing mode (HOM)
R: 400 MHz ~ 610mm 800 MHz ~ 305mm
Too big for IR regions
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Lengler et al., NIM 164 (1979)Karlsruhe-CERN RF Separator
“ 1st ” SRF Deflector
Assembly into cryostat
RF separator for 10-40 GeV/c from the SPSUnknown heavy particles, baryonic states/exchange, K± & p-bar
F = 2.865 GHzVT = 2 MV/m (104 cells)
Still in use at U-70 setup at IHEP
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KEK Freq: 508.9 MHzPower: 50-120 kW (Qext: 2x105, BW: 2.55 kHz)
“ 1st” e± Crab Cavity
Feb 2007
LONG R&D, but short lifetime(2007-2010)
Complex HOM Damping Scheme
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THEY WORK!
The real question: will the technology beefficient/transparent for the HL-LHC operation
Real answer: you may have to wait a little while
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The LHC Pillbox
Conceptually simple, but practically difficult (KEKB experience)
Main Constraints:Frequency 800 MHzDamping LOM/SOM/HOM remains a challengeComplexity of multiple frequencies in LHCOnly vertical crossing at both IPs Surface field to kick gradient ratio is poor
1-cell version, CERN, L. Ficcadenti et al.2-cell version, USLARP, L. Xiao et al.
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Pillboxes → TEM Cavities
~4yr of design evolution Exciting development of new concepts(BNL, CERN, CI-DL-LU, FNAL, KEK, ODU/JLAB, SLAC)
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Short History
80yrs latersimilar concepts to be applied
for LHC crab cavities
Concentric Conducting Systemshort for coax
Leading to the telephone etc..
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“ Its strongly reentrant form makes the field pattern at the outer radius predominately TEM with the consequence of only moderate current flow”
E. Haebel
Freq = 100 MHzGap Voltage = 0.5 MVPbeam = 200 kW(1.6 MW @400 MHZ, NC Cavities)
/4
More History
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/4 TEM ResonatorI0
V0
ab
~/4
= 1
87.4
mm
V 0
ab
~/4
~/4
gap
Z 0=V 0/ I 0
Frequency resonator lengthand “ not” the gap or radii of the concentric cylinders
194 mm194 mm
142.5 mm122 mm
BNL: I. Ben-Zvi et al.
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400 MHz LHC Cavity, quasi /4
Z 0 tan(β l)=1
ωC gap
/4 Resonator, HOMs
Note, due to large aperture & residual Ez the LHC cavity will only a quasi /4 resonator
For a pure /4 resonator, next HOM is x3 the fundamental mode
Therefore, damping is a LOT more easier (for example use a high-pass filter)
56 MHz RHIC Prototype
Pedestal to cancel Ez
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V0
I0
-I0
~/2
/2 TEM Resonator
Two /4 resonators → /2➔ Use HOM (TE11 like) for deflection➔ More elegant is to use two /2 resonators
Single /2Two /2
SLAC, Z. Li ODU, J. Delayen
➢ Height of the cavity is symmetric about beam pipe➢ Only compact in dimension, LHC needs both x-y compactness
~/2
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Joint SLAC-ODU Effort
2010
2011
Fill these regions Full design change
SLAC, Z. LiODU, J. Delayen
/2 TEM Resonator
Symmetric Ridges
Also, Initially proposed by F. Caspers (Crab WS 2008)
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/4 = 187.5 mm
Courtesy G. Burt, B. Hall4R (LU-DI-JLAB)
Four co-linear /4 resonators 500 MHz CEBAF Separator
Conical resonators for mechanical stability
Downside is that the deflecting mode is NOT the lowest order mode
4 eigenmodes, mode 2 is our crab mode
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Performance Chart
Double Ridge(ODU-SLAC)
4-Rod(UK)
¼ Wave(BNL)
Cavity Radius [mm] 147.5 143/118 142/122Cavity length [mm] 597 500 380Beam Pipe [mm] 84 84 84Peak E-Field [MV/m] 33 32 47Peak B-Field [mT] 56 60.5 71RT/Q [] 287 915 318Nearest Mode [MHz] 584 371-378 575
Kick Voltage: 3 MV, 400 MHzGeo
met
rical
RF
194 mm
B1 B2
< 60 MV/m
< 100 mT
damping more complicated
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Impedance Thresholds
Longitudinal impedance2.4 M total (7 TeV)
Strongest monopole mode:R/Q=200 → Qe<1x103
Damping → Qe < 100-500
Transverse
Courtesy: Burov, Shaposhnikova
HOM
HOM
HOM
HOM
Crab
Strongest dipole mode:Z < 0.6 M/m (0.58 GHz)(Qext = 500)
Longitudinal
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HOM probe
Input
HOM Broadband
LOM
3-5 stage ChebyshevHigh pass filter
HOM Damping
56 MHz Prototype
(placement not fixed yet)
4 Symmetric couplers on the end caps
(notch/high-pass ?)
4 asymmetric couplers on cavity body
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ODUCAV SRHW KEKCAV UKCAV QWAVER FRSCAV
Vz(x=0) [kV] 0.0 -2.1 - 2.5i -4 +1378i 0.0 0 +85.7i -0.1 -0.2i
Vx [MV] 5 5 5 5 5 5
B(2) [mTm/m] 0 0 -0.04i -32.7 - 0.1i 0.02 + 0i 25 + 0i 0 +108i
B(3) [mTm/m2 ] 1250 + 0i 229 + 0i 250 - 0i 2452 - 0.5i 464 + 0i -233 +1i
B(4) [mTm/m3] 0 0 266 - 5i 0 540 +0i -189 -14209i
RF “ Multipoles”Courtesy: A. Grudiev, R. deMaria, J. Barranco
Linear tune shifts ~ 0.0 -10-3
Non-linear effects (b3, b4) → Negligible
See slide A5 for mitigation
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Cavity Tuning Thoughts
Up/down motion± 2mm → 1 kHz
Push/pull on cavity body
Scissor jack type mechanism
CEBAF TunerDouble lever(Saclay type)
SM
SM
Modified screw/nut(SOLEIL type)
SM
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Low gradient (weak or moderate)
High Field (weak)
Multipacting Courtesy G. Burt, J. Delayan, Z. Li
Medium gradient (strong)beam-pipe region (similar to KEKB)
Not a serious worry, will require RF processing
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RF PowerV b∝QL I b
RT
Q 0
(k Δ x)
50 kW
RF Power ~8kW (VT=3 MV)
Margin
R/Q = 300 Ib = 0.55 A
For Comparison, Main RF 300kW (V=2 MV)
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RF Power Options Courtesy E. Montesinos
2.0m
2.5m
2.0m
Solid State Amplifiers190 kW, 352 MHz
Single tower < 3m
IOTs (TV Transmitter)Light Sources
Tetrode (SPS)400 MHz, ~50kW
Electrosys
2.5 m
50 kW/cavity, moderate powerSimplified (modified) LHC coupler Common platform for 3 cavities designs
Three available choicesFor SPS tests, reuse Tetrodes used in SPS tests
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Crab Cryomodule
Graphic Courtesy: S. Weisz(Space in bypass extremely limited)
RF Distribution
~300m LLRF (Coupled feedback)
P. Baudrenghien
Need ~20-25 m space for amplifiers on each IP-side
Waveguides/Coax
“Preliminary thoughts”
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RF Noise
Δ x IP=θck RF
δϕ
ΔV T
V T≪ 1
tan (θ/2)
σ x*
σ z
For example:c=570rad; V/V=0.4%x*=7m, x*=7.55cm
err=1.2rad
Amplitude jitter
Phase jitterFor example: = 0.0050, c=570radx
IP = 0.3m (5% of x
*)
LHC Main RF, = 0.0050 at 400 MHz (Philippe)(summing noise at all betatron bands from DC→300kHz)
Note: IOTs & SSAs are less noisy + betatron comb (0.001)
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Planning Overview
M2: Compact Validation& Selection (2012-13)
M2: Beam Tests (2015-16)
Prototype Cryomodule
Final Implementation(2022-23?)
Production of Cryomodules
Detailed planning, see E. Jensen (LHC-CC11)
LS1 LS2 LS3
Cavity Testing
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Sheet metal (deep drawing, spinning, hydro-forming)Multiple dies, electron-beam welding
Solid Niobium & machiningMaterial costs & leak tightness
Fabrication Options
{Total 16 cavities (2 IPs, B1 & B2)
With sheet metal (4mm thick)We need approx 500-600 kg Niobium (RRR>300)}
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0 100 200 300 400 500 6000.00E+001.00E+022.00E+023.00E+024.00E+025.00E+026.00E+02
Position [cm]
Ez
[V/m
]
4R Al-Prototype Courtesy G. Burt, B. Hall
Bead-Pull
Niobium cavity to be delivered in March 2012
Nb Cavity from solid Ingot
Al-prototype for field measurements
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Double Ridge FabricationCourtesy:J. Delayan, Niowave
Nov 2011 Jan 2012
NiowaveSTTR, Phase I/II
Testing April 2012
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Real Reality ?
“ If it is real, we believe in it”The Church of Reality
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100% 90% 80% 70%
Leveling with crossing angle
A1: Leveling, X-Angle Courtesy Beam-Beam TeamCERN-ATS-2011-217
Demonstrated in 2011 w/o affecting other IPs and emittancew/o crabs range is extremely limited
To fully exploit leveling with x-angle, an RF cavity is ideal
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A2: Why SC-Cavity
Q0=GR s
Geometrical factor~ 200
Microwave resistanceCopper ~ mNiobium-SC ~ n
With ~6MV/module, NC-RF is not a viable choice
R s=1
σ δ
G=∫ E3dV
∫ H 2dA
Maximize aperture & minimize # of cavities (reduced impedance)
A choice of 2K cryogenic system optimum for crabs (LHC-CC11)
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A3: SPS As a Testbed
Long. Position: 4009 m +/- 5mTotal length: 10.72 mx, y: 30.3m, 76.8m
Cavity validation with beam (field, ramping, RF controls, impedance)
Collimation, machine protection, cavity transparency
RF noise, emittance growth, non-linearities,
Instrumentation & interlocks
Present COLDEX
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4 LHC Cavities in SPS (1998)
RF Power Setup (~50kW, Tetrode)
A4: SPS, BA4 Setup
Y-Chamber like, similar to present COLDEXCourtesy E. Montesinos
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5 db
m/d
iv
500 kHz
500 kHz
A5: RF Noise, LHC with 1-T feedbackP. Baudrenghien
➔ Selective reduction at all frev lines (V=1.5MV, QL=60k)
➔ Using a betatron comb, we can expect ~16dB reduction at selective frequencies
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Courtesy G. Burt, J. Delayan
A6: RF Non-Linearity
Voltage deviation over 5mm:Horizontal: 20% → 5%Vertical: x2 → 10%
Tuning (shaping) to suppress multipoles
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A7: Other Applications
Emittance exchange x-z (P. Emma & others)
Φ=σ zσ x
ϕc
HE-LHC (16.5 TeV)= 0.6, similar to nominal(z = 6.5cm, x = 9m, c = 160mrad)
R = -12% wr.t. to head-on
Compensate offset collisions due to beam loading for LHeC (Zimmermann)May not be needed if phase modulation removes the phase-slip
Momentum cleaning: Qacc = (fcc/f0)(S. Fartoukh)For effective Qacc ~ 0.3 → 8GHz, too high freq (Y. Sun)
x
z
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SRF Deflector10 MV, 366-447 MHz
3 GeV LINAC
Mode l TE113
Freq 447 MHz
R/Q 500
Epk 34 MV/m
Bpk 74 mT
Aperture 75 mm
A8: ProjectX Synergy
LHC Type Concept(s)
Courtesy M. Champion, Y. Yakovlev
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A. Facco, SRF09A9: TEM Resonators
Saclay IPNO
ArgonneNew DelhiINFN LNL-MSUTRIUMF
INFN LNL
Sputtered
INFN LNL
Right here at CERN(HIE-ISOLDE) Cavity reached (ANL 72 MHz)
Ep=70 MV/m, Bp=100 mTQ0 = 1 x 109 at 4.6 K (IPAC10)