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Maximizing Muon Emittance Exchange Using RF Cavities in Particle Acceleration Theory

Discussing the implementation of deflecting/crabbing cavities for effective muon emittance exchange in particle acceleration. Explore design challenges and application examples in different projects. Highlight the Panofsky-Wenzel Theorem and scaling laws of RF deflecting cavities.

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Maximizing Muon Emittance Exchange Using RF Cavities in Particle Acceleration Theory

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  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. • 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=w/c a=off-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 a=u11r/a, u11=3.832, is root of J1, J1/J2 is first/second order of Bessel function. for r0, R/Q=64.16W which is wavelength independent. for a 800MHz cavity, d0=2cm, dc=5cm R/Q= 3091.2W which is wavelength dependent. For a 800 MHz cavity,

  5. d0 dc ~l/2 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, 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).

  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 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.

  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

  9. 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. HOM(TE111) SOM FM LOM Optimize Crab Cavity’s Squash Ratio Crab cavity for LHCs’ squash ratio is chosen tooptimize mode separation Curtsy of L. Xiao and Z. Li of SLAC. Dy Dx Fc=1.2GHz@R_beampipe=70mm

  13. X-rays Slitting  y  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-LBNL’s crab cavity shapes to 800MHz

  16. Elliptical squashed SRF cavity R&D for APS (JLab/LBNL/AL/Tsinghua Univ.) rcav Rarc 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. E E TM110 TM110 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 • M. Cornacchia and P. Emma, Phys. Rev. ST Accel. Beams 5, 084001 (2002). • 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. Magnitude of the magnetic field on the 3-cell cavity. Note the large field enhancement along the iris. 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 SLAC:LHC 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

  24. 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

  25. 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.

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