Muon Collider DesignWorkshop, 12/8~12/2008
TM110 Deflecting/Crabbing Cavity for Muon Emittance Exchange ?
Haipeng Wang, Robert Rimmer
Jefferson Lab
Muon Collider DesignWorkshop, 12/8~12/2008
Talk Outlines
• Motivation: After muon 6D emittance cooling in helix channel, using TM110 mode of RF cavities instead of absorbers combining with dipole chicanes to exchange transverse emittance (too large) to longitudinal emittance (too small) before (pre) acceleration.
• This is an open question to implement this technique.
• Review principle of TM110 mode RF cavity
• Examples of past and present applications of deflecting/crabbing cavities in different projects.
• Design challenge and limitation of practicable cavity.
Muon Collider DesignWorkshop, 12/8~12/2008
Principle of Deflecting Mode of a RF cavity
Panofsky-Wenzel Theorem:
d
z
d
dzEie
dzv
eP
000 BvE
W. K. H. Panofsky and W. A. Wenzel, Review of Scientific Instruments, Nov. 1956, p967.also M. J. Browman, LANL, PAC93, May 17-20, 1993, Washington D.C. USA.
• Panofsky’s theorem implies that for any given RF mode, no matter who (E or B) deflecting the beam, there is must an non-zero transverse gradient of longitudinal component of the electric field.• TM110 is one of such modes. Two rod type, TEM mode is another one. There are also other “exotic” modes, like off-axis TM010 mode, sideway TM012 mode.
• Transverse verses longitudinal impedance based on Panofsy’s: Rt/Q(R///Q)/(ka)2 k=c a=off-axis distance where to assess the R//.• Deflecting force:
•
/2
a
Cylindrical pillbox
TM110 mode
E
B
Deflecting
crabbing
1
01
0 1
2 ( ) cos
0
2( )sin
2 ( )cos
i tz o
r z
i tr
i t
E E J kr e
E E cB
iEcB J kr e
kr
cB iE J kr e
a
c832.3
22 2
0 (1 (3 ) )sin8x z y
kF ev B eE x y t
20
2 2sin
eEd xt
dz mc
Aberration terms
B
Muon Collider DesignWorkshop, 12/8~12/2008
Scaling laws of RF deflecting cavities
2
21
211211
1920
J
J
uJuQ
R
2222112
max
3465.7 muH
U
/2
a
Cylindrical pillbox
Here =u11r/a, u11=3.832, is root of J1, J1/J2 is first/second order of Bessel function.
for r0, R/Q=64.16 which is wavelength independent.
For a 800 MHz cavity,
2
2max
4311759.4816.64 m.H
U
Q
R
Two-rod transmission line
~/2
d0
dc
Reference: C. Leemann and C. G. Yao, LINAC 1990, Albuquerque, NM, p233.
ababb
dd
Q
Rc
22
03
2
ln
ln960
020
2 5.05.0 ddaddb cc
for a 800MHz cavity, d0=2cm, dc=5cm R/Q= 3091.2 which is wavelength dependent.
22
00
032max 11
ln30 m
ddd
dd
H
U
c
c
2
2max
8.636206.02.3091 mH
U
Q
R
TM110 mode TEM dipole mode
Muon Collider DesignWorkshop, 12/8~12/2008
Scaling laws of RF deflecting cavities
/2
a
Cylindrical pillbox Two-rod transmission line
~/2
d0
dc
For a 800 MHz cavity with a 50mm beam aperture, two–rod type is only about 45% in efficiency of pillbox type, and even less than the elliptical cavity. But its transverse dimension is 55% or less than the pillbox type.Squashing elliptical cavity in transverse dimension is in wrong direction for the transverse kick (will give vertical kick instead).
2max0max
1
H
U
Q
R
B
Vdef
0 5 10 15 20 25 300.02
0.025
0.03
0.035
0.04
0.045
Two-Rod, d0=2cmTwo-Rod, d0=5cmPillbox
Pillbox verses Two Rod of 2.8GHz Cavity
Rod Gap Distance dc-d0(mm)
Vde
f / B
max
(M
V/m
T)
0 20 40 60 80 1000
0.0071
0.0143
0.0214
0.0286
0.0357
0.0429
0.05
Two-Rod, dc-d0=2cmTwo-Rod, dc-d0=5cmPillbox
Pillbox verses Two Rod of 2.8GHz Cavity
Rod Diameter d0 (mm)V
def
/ Bm
ax (
MV
/mT
)
Muon Collider DesignWorkshop, 12/8~12/2008
Application Examples of Deflecting/Crabbing Cavities
• Particle separation: (CEBAF separator)
• Temporal beam diagnostics: (injector/gun emittance measurement, BPM, BCM)
• Crab-crossing in colliders (KEK B Factory, LHC, ILC, ELIC, eRHIC…)
• X-ray pulse compression: (APS crab cavity R&D)
• Emittance exchange: (AWA, FELs, Muon pre-acceleration?...)
Most technical challenge to those designs are for high current accelerators (circular) which require heavy damping on parasitic modes (LOM, SOM, HOM, SPBM) and single high-Q deflecting mode CW operation, so SRF structure.
For muon (single pass) EMX, the damping might not required.
Muon Collider DesignWorkshop, 12/8~12/2008
CEBAF Normal Conducting Separator Cavity
Quick fact and number:• Qcu is only ~5000 (structure wise), the stainless steel cylinder only takes less than 5% of total loss.• Each cavity is two-cell, ~ long, can produce 400kV deflecting voltage with 1.5kW input RF power.• The maximum surface magnetic field at the rod ends is ~14.3mT.• Need water cooling on the rods.• Can kick beam into three experiment halls simultaneously.
Muon Collider DesignWorkshop, 12/8~12/2008
Crab Crossing in Linear and Circular Colliders
Robert Palmer invented “Crab crossing” in Feb. 1988 at SLAC to reduce head-on collision luminosity loss due to bremsstrahlung. Just the second day after Peshi Chen reported this possible mechanism. Since then, the first group to use SRF cavities to do the “crab crossing” in a circular collider is KEKB. A global crabbing scheme to increase luminosity has shown a good result recently. Other crab cavities for LHC, ILC are aggressively
Muon Collider DesignWorkshop, 12/8~12/2008
KEKB Crab Cavity Developments elliptical squashed shape
Muon Collider DesignWorkshop, 12/8~12/2008
KEKB Crab Cavity Commissioning
Curtsy of K. Hosoyama: KEK elliptical crab type cavity, 508.9MHz,Started from 1994 Superconducting Nb, one cavity per ring, global crab scheme in KEKB operation.
Muon Collider DesignWorkshop, 12/8~12/2008
ILC Crab Cavity Developments(FNAL/SLAC/Cockcroft Intitutes)
• Collaboration has been worked on this project for many years. So far the 3.9 GHz 9cell, slightly squashed elliptical superconducting cavity has been chosen for the ILC local crabbing scheme.• Cavity VTA test has been done and to be integrated into a cryomodule.• A lot of bead-pulls, simulation of HOM/LOM/SOM work have been done.• All LOM/SOM/LOM damping by coaxial couplers have been designed and simulated. Prototyping in on going.
Muon Collider DesignWorkshop, 12/8~12/2008
Dispersion Curve
5.50E+08
6.00E+08
6.50E+08
7.00E+08
7.50E+08
8.00E+08
8.50E+08
9.00E+08
9.50E+08
1.00E+09
1.05E+09
1.10E+09
0.7 0.75 0.8 0.85 0.9 0.95 1Cross Section Elliptical Ratio
F (H
z)
TM010-1 TM010-2
TM110-1-H (opt.mode) TM110-2-H
TM110-1-V (SOM) TM110-2-V
TE111-1-H TE111-2-H
TE111-1-V TE111-2-V
LOM
HOM(TE111)
SOM
FM
Fc=1.2GHz@R_beampipe=70mm
Crab cavity for LHCs’ squash ratio is chosen to optimize mode separation
Dx
Optimize Crab Cavity’s Squash Ratio
Dy
Curtsy of L. Xiao and Z. Li of SLAC.
Muon Collider DesignWorkshop, 12/8~12/2008
Crab Cavities for Light Sources
• Use transverse-deflecting rf cavities to impose a correlation (“chirp” between the longitudinal position of a particle within the bunch and the vertical momentum.
• The second cavity is placed at a vertical betatron phase advance of n downstream of the first cavity, so as to cancel the chirp.
• With an undulator or bending magnet placed between the cavities, the emitted photons will have a strong correlation among time and vertical slope.
• This can be used for either pulse slicing or pulse compression.
Slitting
y
X-rays
A. Zholents, P. Heimann, M. Zolotorev, J. Byrd, NIM A 425(1999), 385
X-ray pulse compression
Muon Collider DesignWorkshop, 12/8~12/2008
Bmax/Vdef with rbp=23mm, rcon=8mm, Rcav=10mm
150
155
160
165
170
175
180
185
190
38 40 42 44 46 48 50 52
Rarc (mm)
Bm
ax/V
dfe
(mT/
MV
/m))
Bmax/Vdef with rbp=23mm, rcon=8mm, Rcav=10mm
150
155
160
165
170
175
180
185
190
1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2
Racetrack long/short axis ratio
Bm
ax/V
def (
mT/
(MV
/m))
Bmax/Vdef with Rbp=25mm, Rarc=44.74mm, Zcav=53.24mm
170
172
174
176
178
180
182
6 7 8 9 10 11 12
rcon (mm)
Bm
ax/V
def (
mT/
(Mv/
m))
sqrt ( Rt/Q * G ) with Rcav=44.7mm, Rbp=25mm, Zcav=53.28mm
80
82
84
86
88
90
92
94
7 8 9 10 11 12 13
rcon (mm)
sq
rt(R
t/Q
*G)
(Oh
m)
10
11
12
13
14
Rcavmm
Rt/Q with Rcav=44.7mm, Rbp=25mm, Zcav=53.28mm
30
31
32
33
34
35
36
7 8 9 10 11 12 13
rcon (mm)
Rt/
Q=
Vt^
2/P
(O
hm
)
10
11
12
13
14
Rcavmm
Squashed elliptical cavity shape optimization
MWS ,ANSYS, HFSS and Gdfidl simulation by J. Shi and G. Waldschmidt
Muon Collider DesignWorkshop, 12/8~12/2008
Squashed elliptical cavity shape comparison
optimized squashed dimensions scaled to 800MHz KEK crab dimensions scaled to 800MHzmm JLab-ANL-LBNL KEK
racetrack radius Rarc 44 154.9 241.5 153.6beam pipe radius Rbp 25 88.0 94 59.8cavity equator radius rcav 14 49.3 90 57.3cavity iris radius rcon 9 31.7 20 12.7cavity iris-to-iris distance zcav 53.24 187.4 294.5 187.3cavity racetrack half straight length yline 33.66 118.5 191.5 121.8
Scaled KEK and JLab-ANL-LBNL’s crab cavity shapes to 800MHz
Muon Collider DesignWorkshop, 12/8~12/2008
Elliptical squashed SRF cavity R&D for APS (JLab/LBNL/AL/Tsinghua Univ.)
First time vertical test achieved design gradient! Single-cell 2.815GHz Nb crab cavity
Rarc
Rbp
rcav
zcav
rconoptimized squashed dimensions:
Rarc 44 mmRbp 25 mmrcav 14 mmrcon 9 mmzcav 53.24 mmyline 33.66 mm
Crab Cavity Test #1
1.00E+08
1.00E+09
1.00E+10
0 20 40 60 80 100 120
Bpeak [mT]
Qo
RF System unstable
Single-cell structure with beam pipesTM110-y mode frequency MHz 2815.76Rt/Q include TTF (Rt=Vt^2/P) Ohm 35.27Geometry factor G Ohm 232.29sqrt((Rt/Q)*G) Ohm 90.51Bsmax/Vt mT/MV 157.15Esmax/Vt 1/m 75.60Transverse Gradient Et=Vt/dBsmax/Et mT/(MV/m) 8.367Esmax/Et 4.025cavity effective gap d mm 53.24BCS surface resistance Rbcs of Nb at 2K nOhm 51.29Residual resistance R0 nOhm 20.00Q0 at 2K 3.3E+09BCS surface resistance Rbcs of Nb at 4.2K nOhm 2498.33Q0 at 4.2K 9.2E+07
Muon Collider DesignWorkshop, 12/8~12/2008
Waveguide HOM Damped Cavity Structure for APS
R///Q and Rt/QCalculated fromMWS eigen solver
Bench Qext measurement by using• RF absorbers on WG ports• Clamping copper parts (low contact loss)• Weak coupling to VNA• Rotatable antennas to suppress the unwanted modes.
Muon Collider DesignWorkshop, 12/8~12/2008
TM110 Cavity Replace Wedge Absorber?
• No gas or liquid to vacuum interface windows.• No scattering, no straggling
Original from Y. Derbenev andR. P. Johnson EPAC 2006, WEPLS019
E
TM110
E
TM110
Muon Collider DesignWorkshop, 12/8~12/2008
TM110 cavity used in Trans/Long Emittance Exchange
1. M. Cornacchia and P. Emma, Phys. Rev. ST Accel. Beams 5, 084001 (2002).
2. P. Emma, Z. Huang, K.-J. Kim and P. Piot, Phy. Rev. ST Accel. Beams 9, 100702, (2006).
M in (x, x', z, ) phase space
aE
eVk 0
a is cavity radius
and are dispersionand momentum compactionFactor respectively
Muon Collider DesignWorkshop, 12/8~12/2008
Emittance Exchange Simulations and Experiments
Curtsy of G. Wei and J. Power
(x,y, z)=
Muon Collider DesignWorkshop, 12/8~12/2008
TM110/TE111 Modes Cell-to-Cell Coupling and Double-Chain Model
Bane, K. L. & Gluckstern, R. L. (1993), 'The Transverse Wake Field of a Detuned X-band Accelerator Structure', Part. Accel. 42, 123-169. (SLAC-PUB-5783)
dispersion curve
2600
2800
3000
3200
3400
3600
3800
4000
0 30 60 90 120 150 180
phase adv per cell (Deg)
fre
qu
en
cy
Mode1
Mode2
TE11
TM11
TM11
TE11
Dispersion of Dipole
27302740
275027602770
278027902800
28102820
0 50 100 150 200
phase adv / DEG
freq
uenc
y /
MH
z
simulation
single chain
double chain
12
22
22
21
2
22
2
21
21
11
11
cos
kk
kk
Curtsey of J. Shi, Tsinghua Univ. Beijing, China
B field enhancementwhen operates in pi mode
Muon Collider DesignWorkshop, 12/8~12/2008
Magnetic Field Enhancement at Iris of TM110 Multi-cell Cavity
Thanks K. Tian at JLab
Magnitude of the magnetic field on the 3-cell cavity. Note the large field enhancement along the iris.
Thanks to G. Waldschmidt
Muon Collider DesignWorkshop, 12/8~12/2008
Multi-cell TM110 and Loaded Structure of Crabbing Cavities
APS 4-cell crab cavity, 2.815GHz,0 mode, 8MV total needed periodic damping LOM/SOM/SPBM/HOM modes
HOM coupler
LOM/SOM coupler
JLab/Cockcroft Inst./Lancaster Univ. UK
200MHz for LHC LC scheme
Curtsy of Z. Li and L. Xiao from SLAC:LHC crab cavity in IP4 GC scheme, 800MHz prototype phase I with LOM/SOM/SPBM/HOM modes couplers
Parallel Bar advanced , 400MHz for LHC, 499MHz for CEBAF 11GeV.
Muon Collider DesignWorkshop, 12/8~12/2008
TEM Parallel Bar (Half-Wave) Deflecting Structure
• recent study for low frequency application• more efficient• more compact• no LOM but acceleration mode in HOM
J. Delayen, H. Wang, LINAC 2008’s paper.
E field B field
0
1
2
3
4
5
6
7
8
9
10
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
R/
Ep/Et
A/R= 1.6
A/R= 1.8
A/R= 2.0
A/R= 2.2
A/R= 2.4
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
50000
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
2
R/
G*Rt/Q
A/R= 1.6
A/R= 1.8
A/R= 2.0
A/R= 2.2
A/R= 2.4
Parameter Ω3PAnalytical
modelUnit
Frequency of -mode 400 400 MHz
λ/2 of -mode 374.7 374.7 mm
Frequency of 0-mode 414.4 400 MHz
Cavity length 374.7 ∞ mm
Cavity width 500 ∞ mm
Bar length 381.9 374.7 mm
Bar diameter (2R) 100 100 mm
Bar axes separation (2A) 200 200 mm
Aperture diameter 100 0 mmDeflecting voltage Vt * 0.375 0.375 MVEp * 4.09 4.28 MV/mBp * 13.31 14.25 mT
U * 0.215 0.209 J
G 96.0 112 ΩRt/Q 260 268 Ω* at Et=1MV/m
Muon Collider DesignWorkshop, 12/8~12/2008
Summary
• Using crab cavity for muon emittance exchange is an interesting idea. Detail study is just starting. We need simulations with a real field map including fringe field of cavity and dipole magnets.
• If technical feasible, this scheme will solve absorber’s problem and lower cost.
• NC and SC deflecting/crabbing cavity development experience in other projects can be brought in to see the technical limitation.
• Low frequency, larger aperture crab cavity structure without HOM damping is needed for the emittance exchange section.