TM110 Deflecting/Crabbing Cavity for Muon Emittance Exchange ?

1
TM110 Deflecting/Crabbing Cavity for Muon
Emittance Exchange ?

• Haipeng Wang, Robert Rimmer
• Jefferson Lab

2
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.

3
Principle of Deflecting Mode of a RF cavity
Panofsky-Wenzel Theorem
B
E
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.

• Panofskys 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 Panofsys
• Rt/Q??(R///Q)/(ka)2 kw/c
  aoff-axis distance where to assess the R//.
• Deflecting force

Deflecting
B
crabbing
Aberration terms
4
Scaling laws of RF deflecting cavities
Two-rod transmission line
Cylindrical pillbox
d0
a
dc
TM110 mode
TEM dipole mode
l/2
l/2
Reference C. Leemann and C. G. Yao, LINAC 1990,
Albuquerque, NM, p233.
Here au11r/a, u113.832, is root of J1, J1/J2 is
first/second order of Bessel function.
for r??0, R?/Q64.16 W which is wavelength
independent.
for a 800MHz cavity, d02cm, dc5cm R?/Q 3091.2
W which is wavelength dependent.
For a 800 MHz cavity,
5
Scaling laws of RF deflecting cavities
Two-rod transmission line
Cylindrical pillbox
a
l/2
For a 800 MHz cavity with a 50mm beam aperture,
tworod 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).
6
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 RD)
• 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.

7
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, l 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.

8
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
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KEKB Crab Cavity Developments
elliptical squashed shape
10
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.
11
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.

12
Optimize Crab Cavitys Squash Ratio
Crab cavity for LHCs squash ratio is chosen to
optimize mode separation
Curtsy of L. Xiao and Z. Li of SLAC.
Dy
Dx
Fc1.2GHz_at_R_beampipe70mm
13
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.

X-ray pulse compression
A. Zholents, P. Heimann, M. Zolotorev, J. Byrd,
NIM A 425(1999), 385
14
Squashed elliptical cavity shape optimization
MWS ,ANSYS, HFSS and Gdfidl simulation by J. Shi
and G. Waldschmidt
15
Squashed elliptical cavity shape comparison
Scaled KEK and JLab-ANL-LBNLs crab cavity shapes
to 800MHz
16
Elliptical squashed SRF cavity RD for APS
(JLab/LBNL/AL/Tsinghua Univ.)
Rarc
rcav
rcon
Rbp
zcav
First time vertical test achieved design gradient!
Single-cell 2.815GHz Nb crab cavity
17
Waveguide HOM Damped Cavity Structure for APS
R///Q and Rt/Q Calculated from MWS 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.

18
TM110 Cavity Replace Wedge Absorber?

• No gas or liquid to vacuum interface windows.
• No scattering, no straggling

Original from Y. Derbenev and R. P. Johnson EPAC
2006, WEPLS019
19
TM110 cavity used in Trans/Long Emittance Exchange
M in (x, x', z, ?) phase space
a is cavity radius

• ?and ? are dispersion
• and momentum compaction
• Factor respectively

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).

20
Emittance Exchange Simulations and Experiments
?(?x,?y, ?z)
Curtsy of G. Wei and J. Power
21
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)
B field enhancement when operates in pi mode
Curtsey of J. Shi, Tsinghua Univ. Beijing, China
22
Magnetic Field Enhancement at Iris of TM110
Multi-cell Cavity
Thanks K. Tian at JLab
Thanks to G. Waldschmidt
23
Multi-cell TM110 and Loaded Structure of Crabbing
Cavities
Curtsy of Z. Li and L. Xiao from SLACLHC crab
cavity in IP4 GC scheme, 800MHz prototype phase I
with LOM/SOM/SPBM/HOM modes couplers
APS 4-cell crab cavity, 2.815GHz, 0 mode, 8MV
total needed periodic damping LOM/SOM/SPBM/HOM
modes
HOM coupler
200MHz for LHC LC scheme
LOM/SOM coupler
Parallel Bar advanced , 400MHz for LHC, 499MHz
for CEBAF 11GeV.
JLab/Cockcroft Inst./Lancaster Univ. UK
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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 2008s paper.
Parameter O3P Analytical model Unit
Frequency of p-mode 400 400 MHz
?/2 of p-mode 374.7 374.7 mm
Frequency of 0-mode 414.4 400 MHz
Cavity length 374.7 8 mm
Cavity width 500 8 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 mm
Deflecting voltage Vt 0.375 0.375 MV
Ep 4.09 4.28 MV/m
Bp 13.31 14.25 mT
U 0.215 0.209 J
G 96.0 112 ?
Rt/Q 260 268 ?
at Et1MV/m at Et1MV/m at Et1MV/m at Et1MV/m
E field
B field
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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
  absorbers 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.