muon collider design workshop, 12/8~12/2008 tm110 deflecting/crabbing cavity for muon emittance...

Muon Collider DesignWorkshop, 12/8~12/2008

TM110 Deflecting/Crabbing Cavity for Muon Emittance Exchange ?

Haipeng Wang, Robert Rimmer

Jefferson Lab


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.


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


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


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

)


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.


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.


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


KEKB Crab Cavity Developments elliptical squashed shape


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.


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.


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.


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


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


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


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


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.


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


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


Emittance Exchange Simulations and Experiments

Curtsy of G. Wei and J. Power

(x,y, z)=


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


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


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.


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


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.

muon collider design workshop, 12/8~12/2008 tm110 deflecting/crabbing cavity for muon emittance...

Documents