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					TM110 Deflecting/Crabbing Cavity for Muon
          Emittance Exchange ?

         Haipeng Wang, Robert Rimmer
                 Jefferson Lab




                                    Muon Collider Design
                                   Workshop, 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 Design
                                             Workshop, 12/8~12/2008
                             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.

• 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:                                                                                Deflecting

     Rt/Q(R///Q)/(ka)2 k=w/c a=off-axis
distance where to assess the R//.                                                        B
                                                                                                    crabbing
• Deflecting force:

                                                 Aberration terms
•

                                                                                              Muon Collider Design
                                                                                             Workshop, 12/8~12/2008
                             Scaling laws of RF deflecting cavities

  Cylindrical pillbox                                Two-rod transmission line
    a
                                                      d0
                                                                                       dc

                               TM110 mode                                                   TEM dipole mode
               l/2                                                     ~l/2
                                                    Reference: C. Leemann and C. G. Yao, LINAC 1990,
                                                    Albuquerque, NM, p233.


Here a=u11r/a, u11=3.832, is root of J 1, J 1/J 2
is first/second order of Bessel function.

  for r0, R/Q=64.16 W
  which is wavelength independent.
                                                    for a 800MHz cavity, d0=2cm, d c=5cm R/Q= 3091.2 W
                                                    which is wavelength dependent.



  For a 800 MHz cavity,




                                                                            Muon Collider Design
                                                                           Workshop, 12/8~12/2008
           Scaling laws of RF deflecting cavities

Cylindrical pillbox                                 Two-rod transmission line
    a
                                                     d0
                                                                                   dc


          l/2                                                      ~l/2
                      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).

                                                           Muon Collider Design
                                                          Workshop, 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 Design
                                            Workshop, 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, ~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.
                                         Muon Collider Design
                                        Workshop, 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 Design
                                                                  Workshop, 12/8~12/2008
KEKB Crab Cavity Developments

                           elliptical squashed shape




                             Muon Collider Design
                            Workshop, 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 Design
                                          Workshop, 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 Design
                                                   Workshop, 12/8~12/2008
       Optimize Crab Cavity’s Squash Ratio


                                 Crab cavity for LHCs’ squash
HOM(TE111)                         ratio is chosen to optimize
                                   mode separation
SOM
                                    Curtsy of L. Xiao and Z. Li of SLAC.



FM                                                     Dy


                                                                     Dx
LOM

                                    Fc=1.2GHz@R_beampipe=70mm




                                                 Muon Collider Design
                                                Workshop, 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.




                                                                                                                       a
                                                                            X-ray pulse compression

                                                  Slitting
                                                                                       y
                                                                                                               
A. Zholents, P. Heimann, M. Zolotorev, J. Byrd, NIM A 425(1999), 385


                                                                                       Muon Collider Design
                                                                                      Workshop, 12/8~12/2008
          Squashed elliptical cavity shape optimization




MWS ,ANSYS, HFSS and Gdfidl simulation by J. Shi and G. Waldschmidt




                                                    Muon Collider Design
                                                   Workshop, 12/8~12/2008
      Squashed elliptical cavity shape comparison




Scaled KEK and JLab-ANL-LBNL’s crab cavity shapes to 800MHz




                                               Muon Collider Design
                                              Workshop, 12/8~12/2008
                            Elliptical squashed SRF cavity R&D for APS
                                  (JLab/LBNL/AL/Tsinghua Univ.)
                     rcav     Rarc

Rbp           rcon




                            zcav



  First time vertical test achieved design gradient!          Single-cell 2.815GHz Nb crab cavity




                                                                 Muon Collider Design
                                                                Workshop, 12/8~12/2008
       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.


                                                   Muon Collider Design
                                                  Workshop, 12/8~12/2008
                      TM110 Cavity Replace Wedge Absorber?

• No gas or liquid to vacuum interface windows.            from Y. Derbenev and
                                                  Original E
• No scattering, no straggling                    R. P. Johnson EPAC 2006, WEPLS019




                 E




                                                     TM110




              TM110




                                                               Muon Collider Design
                                                              Workshop, 12/8~12/2008
            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).
                                                                   Muon Collider Design
                                                                  Workshop, 12/8~12/2008
               Emittance Exchange Simulations and Experiments
    (x,y, z)=




Curtsy of G. Wei and J. Power




                                                   Muon Collider Design
                                                  Workshop, 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.
       B field enhancement
                                                   Accel. 42, 123-169. (SLAC-PUB-5783)
       when operates in pi mode




Curtsey of J. Shi, Tsinghua Univ. Beijing, China

                                                                          Muon Collider Design
                                                                         Workshop, 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 Design
                                              Workshop, 12/8~12/2008
              Multi-cell TM110 and Loaded Structure of Crabbing Cavities

    APS 4-cell crab cavity, 2.815GHz,                                Curtsy of Z. Li and L. Xiao from SLAC:LHC
    0 mode, 8MV total needed periodic                                crab cavity in IP4 GC scheme, 800MHz
    damping LOM/SOM/SPBM/HOM modes                                   prototype phase I with
                                                                     LOM/SOM/SPBM/HOM modes couplers




                                                                                         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
                                                                                Muon Collider Design
                                                                               Workshop, 12/8~12/2008
     TEM Parallel Bar (Half-Wave) Deflecting Structure

• recent study for low frequency application
• more efficient J. Delayen, H. Wang, LINAC 2008’s paper.
• more compact
• no LOM but acceleration mode in HOM

                                                                                            Analytical
                                                Parameter                           Ω3P                  Unit
                                                                                             model
                                                Frequency of -mode                 400        400       MHz
                                                λ/2 of -mode                       374.7     374.7      mm
                                                Frequency of 0-mode                 414.4      400       MHz
                                                                                               ∞
      E field                  B field          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        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        Ω
                                                Rt/Q                                260        268        Ω
                                                * at Et=1MV/m


                                                                            Muon Collider Design
                                                                           Workshop, 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.


                                               Muon Collider Design
                                              Workshop, 12/8~12/2008

				
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