Deflecting Cavities Rama Calaga, CERN Joint Accelerator School, Japan, 2017 Basics of Deflecting Cavities Practical Aspects Applications
Some General References 1. ICFA Workshop on Deflecting Cavities, I & II 2. CAS, CERN 92-03, USPAS (2013, 2015)
Transverse Force Rev. Sci. Instrum. 27 (1956), p. 967 To exert a transverse force on the charged particle: Integrating the transverse force, Panofsky-Wenzel: Vz and px are 900 out of phase, Vz=0 at x=0
Cylindrical (Pillbox) Cavity Consider TM modes (Hz = 0), variation of long. fields in the trans plane: TM010 Transverse (dipole) modes (m=1) characterized by first order variation around the azimuth TM010 TM110
Pillbox Cavity, TM110 Transverse Cross Section beam beam in/out of the plane TE011 TM210 TM011 TM110 TM110Y TE111 TM010 Deflecting mode is a Higher Order Mode & has it sister polarization freq spectrum
Some Figures of Merit Transverse Voltage: Direct Integral Transverse Shunt Impedance: Stored Energy:
Some Figures of Merit Quality Factor: Geometric Factor: Material Power dissipated: Geometry
TEM (Compact) Deflectors Until recently, RF deflectors were primarily using TM110 type structures for both NC & SC cavities More recently, an emphasis on low frequency compact TEM-like RF deflectors have emerged which was primarily driven by the need for LHC TEM cavities are widely used for acceleration in low velocity applications such as protons & ions and come in many forms and shapes
TEM (Compact) Deflectors Consider the simplest form, l/4 resonator (widely used for low velocity) gap a V0 b ~l/4 Z 0=V 0 / I 0 For a pure transverse kick, a symmetrizing stub is required to cancel the contribution from fringing fields. The next HOM is placed almost 3 times the fundamental (pure l/4)
l/2 TEM Resonator The next order is a l/2 resonator also widely used for low velocity ion acceleration. Proper shaping of beam gaps to achieve magnetic kicks with electrical null, using a HOM ~l/2 I0 V0 By Ex -I0 Drawback is deflecting mode is not lowest order. Z. Li et al., SLAC-PUB-14163
l/2 TEM Resonator An natural l/2 deflector as a fundamental mode is to use two resonators to form a purely dipole cavity (parallel bar). Later optimized to TE-like ridged waveguide pi-mode Frequency separation 0 & pi mode by rounding edges J. Delayen et al., PRSTAB 12, 062002 (2009)
4R (LU-DI-JLAB) Four co-linear l/4 resonators as RF deflector. Four primary eigen-modes Drawback is deflecting mode is not lowest order. 500 MHz CEBAF Separator l/4 = 187.5 mm For the LHC, a SRF version with conical resonators for mechanical stability was proposed and built The deflecting mode is NOT the lowest frequency mode Courtesy G. Burt et al.,
RF Deflector Design Spatial discretization of the 2D (mainly 3D) structures to numerically solve Maxwell's equations Frequency Domain (eigenvalue problem) Time Domain (transient response), Wakefields Different methods: Finite (difference, integration, element) Superfish Mesh,400 MHz Deflector LHC l/4 Crab Cavity 190 mm Generally used (but not comprehensive): 2D: Superfish, SLANS, ABCI 3D: CST, HFSS, ACE3P, GdfidL 300 mm
TEM Deflector Optimization, Example Design evolution of deflecting (RFD) cavities for the LHC Goal is to typically minimize (& balance) surface fields J. Delayen et al. et al., PRSTAB 12 & 16 (2009 & 2013)
Photonic Band-Gaps A different class of resonators that have been study are 2D (or 3D) periodic structures to confine RF fields in specific bands of RF frequencies Create a band-gap in the periodic metallic or metallic-dielectric structures to forbid the wave propagation in the frequency band One shown is an example to trap a dipolar mode with a special arrangement rods or holes to support TM110 like mode Courtesy: Kroll, Smirnova, Shapiro et al.
Practical Aspects Note: Some select topics which useful considerations and with emphasis on deflecting cavities
RF Power & Beam Loading For a pure deflecting mode, there is no longitudinal Ez Recall: Induced Voltage: Beam drives the crabbing (tilting phase) If additional cavity detuning: LHC: R/Q = 300 W, Ib = 0.55 A
Detuning from Lorentz Force Radiation pressure from the very high electro-magnetic fields will distort the cavity shape and therefore the frequency inductive capacitive Deflecting cavities particularly sensitive combined with operation with narrow bandwidth (for example, SRF) can be problematic, mitigation not straightforward RF Dipole Photo Courtesy: Z. Li
Detuning From External Forces External noise can be transferred to cavity via the cryostat (Microphonics) Deflecting (dipole) cavities can be more sensitive (~MHz/mm) Mitigation Tuning system: Mechnical - slow and/or electro-mechanical - moderate RF feedback - fast, BW limited (Dw) M. Liepe, CHECHIA Cryostat
Transverse Impedance Impedance of the deflecting mode: High-Q, the deflecting mode can lead to coupled bunch instabilities In the classical treatment (M-equally spaced bunches), the growth rate: When the w=w0, the positive and negative sidebands cancel each other
Transverse Coupled Bunch Instabilites KEKB example of growth rate vs. cavity detuning Qb = 0.5, so detuning should be kept far from ½ of the frev Instability due to the crabbing mode 10 5 (LER 2A) K. Akai Tuning angle 10 10 4 50 3 Growth rate (1/s) 10 Tuning angle (degree) 0 Q=2E5 (with DRFB @G=3) 2 Q=2E5 10 radiation damping 1-50 Q=1E6 10 0-100 -50 0 Detuning frequency (khz) 50 100 frev
Higher Order Modes Apart from fundamental (deflecting) mode, HOMs contribute to losses induced by the beam excitation and single/multi bunch instabilities Tb = 50 ns LHC example filling scheme (bunch spacing) Non-Resonant Case: P HOM =(Σ k n k 0 ). q. I b Resonant Case: R 2 P HOM =I.Q L. F n Q 2. b Strong damping essential for proper treatment of the HOMs, especially for high currents
HOM Extraction Main goal: Provide high impedance for deflecting mode, high admittance for all HOMs typically made of lumped (LC) elements Ferrites Waveguides Notch filters Double-Notch Band-Pass Broadband: Operating mode typically below cut-off of the guide with a broadband RF load for higher mode damping Narrowband: Typically a resonant circuit(s) to reject the operating mode with a broadband transmission line to a RF load
HOM Couplers, Example A two stage filter (LC filter) concept used for the LHC crab cavities with a rejection notch at the fundamental + transmission at HOMs Transmission Spectrum LHC deflecting cavity HOM Couplers HOM Test Box J. Mitchell et al.
HOM Couplers, Examples Choke-Mode, CLIC crab cavities Cavity-BPM to extract only TM110 power Waveguide Dampers CLIC crab cavities Courtesy: G. Burt et al.
RF Field Measurements Beadpull, standard practice to measure field profiles as benchmark Slaters method: Dw/w µ DU/U (for small perturbations) Bead inside a cavity: LHC Crab Cavity Bead-Pull Vector Network Analyzer S-parameters In deflecting cavities, the kick is a often a combination of electric & magnetic contributions Accurate 2D field uniformity can be very important
Transverse Position Recall, PW-theorem, transverse voltage proportional to offset Scan the integrated voltage as a function of vertical offsets to determine the electrical center Transverse field uniformity in the vicinity of the beam is also important
Field Non-Linearity Cavities w/o azimuthal symmetry can lead to higher order RF multipoles on crest - deflecting 1 0-1 -0.4-0.3-0.2-0.1 0 0.1 0.2 r = 2 mm r = 1 mm 0.3 r = 0 0.4 20 0-20 -0.4-0.3-0.2-0.1 0 0.1 0.2 0.3 0.4 20 0-20 -0.4-0.3-0.2-0.1 0 0.1 0.2 0.3 0.4 500 0-500 -0.4-0.3-0.2-0.1 0 0.1 0.2 0.3 0.4 500 0-500 -0.4-0.3-0.2-0.1 0 z [m] 0.1 0.2 0.3 0.4 {E(2) } [ V /3m] @ 1 V {E(1) } [ V /2m] @ 1 V {E(0) } [ V / m ] @ 1 V acc acc acc A. Grudiev et al., IPAC12 90o off crest - crabing 1 0-1 -0.4-0.3-0.2-0.1 0 0.1 0.2 r = 2 mm r = 0.3 1 mm r = 0 0.4 50-0.3-0.2-0.1 0 0.1 0.2 0.3 0.4 Quadrupole 50 0-50 -0.4-0.3-0.2-0.1 0 0.1 0.2 0.3 0.4-0.3-0.2-0.1 0 0.1 0.2 0.3 0.4-0.3-0.2-0.1 0 z [m] 0.1 0.2 0.3 0.4 2000 Sextupole 0-2000 -0.4 Monopole Dipole 0-50 -0.4 {E(4) } [ V /5m] @ 1 V {E(3) } [ V /4m] @ 1 V acc acc {E(4) } [ V /5m] @ 1 V {E(3) } [ V /4m] @ 1 V {E(2) } [ V /3m] @ 1 V {E(1) } [ V /2m] @ 1 V acc acc acc acc {E(0) } [V /m ] @ 1 V acc Expansion: 2000 0-2000 -0.4 Octupole
Multipacting Electron resonance & multiplication via secondary emission from the cavity surface. Frequency between impacts is N. ½RF (N= Order) Electron avalanche of absorbing all RF power, leading a thermal breakdown It is field, phase and SEY dependent. RF conditioning and/or geometrical shaping to suppress the resonant behavior For deflecting cavities with complex geometries or complicated HOM schemes, it is become a severe limitation.
Multipacting, Dipole Cavities Geometrical suppression techniques typically used with heavy 3D simulations to guide the onset & behavior Some examples of weak multipacting in LHC crab cavities RF tests on these geometries show soft multipacting as predicted in the low to moderate voltages Courtesy: UK-STFC, SLAC
Field Emission Electron emitting site on the cavity surface (due to impurities, surface defects etc..) with a sufficient local field enhancement (10 2 103). FE in LHC Crab Cavities Explained by modified F-N theory (β-enhancement factor) 2. j= 2 3 /2 B Φ βe A.β E e Φ Courtesy: Z. Li Transversely bent by the strong RF field and impact elsewhere on the surface with the typical signature of strong x-rays leading to vacuum and/or thermal breakdown ( hot zones ). Important limitation for field reach
Transverse RF Noise Amplitude and phase jitter of the deflecting mode is a key nuisance for all applications related to RF deflectors (or crab cavities) Amplitude jitter For example, imperfect overlap of colliding bunches from turn-to-turn D VT VT σ *x 1 tan (θ / 2) σ z Amplitude θc=570mrad; DV/V=0.4% σx*=7mm, σx*=7.55cm θerr=1.2mrad Phase jitter θc D x IP = δϕ k RF Phase Dϕ = 0.0050, θc=570mrad DxIP = 0.3mm (5% of σx*)
Applications Note: Not a comprehensive review of applications but represents a good sample to get a general picture of different uses
RF Particle Separators Lengler et al., NIM 164 (1979) Karlsruhe-CERN RF Separator RF separator for 10-40 GeV/c from the SPS Early superconducting RF deflector Unknown heavy particles, baryonic states/exchange, K± & p-bar Velocity separation of different species Separation of different bunches using the RF phase
Particle Separators SW Superconducting RF Separator Assembly into cryostat Freq = 2.865 GHz, Et ~ 1.5-2.0 MV/m Q0~2.2x109, 3m long, 104-cells Still in use at U-70 setup at IHEP
Particle Separators Jefferson Lab 12 GeV Upgrade Deflection of beams from the 5-arcs of the multi-pass linac (11 GeV cw) and transversely displacement the e-bunches using a 499 MHz cavity Normal Conducting Deflector Hall A Superconducting Proposals VT Hall B Hall C Parallel bar Ridge-Waveguide Courtesy: J. Delayen et al.
Particle Separators Project X, Fermilab Also use the principle of fast RF separators for a future proton driver Multii-cell Ridged Waveguides 3 GeV LINAC Mode l TE113 Freq 447 MHz R/Q 500 W Epk 34 MV/m Bpk 74 mt Courtesy M. Champion, Y. Yakovlev
Particle Combiner Recombination of the injected/extracted bunches in the CTF3 delay loop Use pill-box type deflector at 1.5 GHz to reduce the bunch spacing by factor 2 (0.66 ns 0.33 ns) D. Alessini et al., PRST-AB 12, 031301
Beam Manipulations FAIR GSI: Formation of a hollow beam using fast rotation of ion-beam Frequency of operation is 300 MHz, Et = 1.5-2 MV/m Courtesy: S. Minaev et al., NIMA v.620 (2010)
Beam Diagnostics Traveling wave NC X-band (~11 GHz) structures for RF deflection Time resolved beam size measurements (slice emittance) Longitudinal profile diagnostics for plasma wake applications (FACET) Used in FLASH-DESY, ECHO-7 at SLAC, LCLS X-band Prototypes (SLAC) Courtesy J. Wang
Beam Diagnostics Longitudinal diagnostics of ultra-short bunches (FELs) Energy loss scan for measuring x-ray pulse as a function of time The dipole spectrometer translates energy into a transverse coordinate Time jitter & temporal diagnostics for ultra-short bunches
Beam Diagnostics Slice emittance measurement for FEL applications Use RF deflector to induce z-dependent transverse kick Quadrupole scan downstream to change optics as a function of deflector voltage to determine the emittance along the bunch Possible to measure δp/p along the bunch, at dispersive regions normal streaked slices 2 x 2 z σ eff = σ + σ ϕ 2 c Courtesy: M. Rohrs et al., DESY Optical transition radiation screen
Beam Diagnostics Cavity BPM, using TM110 mode for beam position The electrical null (or min voltage signal) corresponds to center Specially polarized waveguides to only pick up only dipole mode Very high resolution (mu-m down to 10 s nm) Main limitations are suppression of parasitic modes
Beam Diagnostics Cornell ERL injector using 4-rod like concept for e-beam diagnostics Characterization of ultra-low emittance beams and reconstruct edistribution coming from the source (Deflector Frequency = 1.3 GHz) Also used for phasing the SC accelerating cavities (TOF) Courtesy: S. Belomestnykh et al.
Beam Diagnostics Direct transverse wakefield measurements (CLIC) for strong HOM damping Wakefield estimated from measured offsets from downstream BPMs Special CLIC-G structure made for the experiment H. Zha et al., PRSTAB 19, 011001 (2016)
Emittance Exchanger Emittance exchange between transverse and longitudinal planes Use RF deflector to give x-dependent energy kick (δp/p ~δx) Particles with dp/p getting position change (δx ~ nδ) Emittance exchange for the right choice of kick = -1/n x-dependent DE Introduce dispersion Emittance exchanged Cornacchia, Emma, PRST AB 5, 084001 (2002), PRST AB 9, 100702 (2006).
Emittance Exchanger Simulations for emittance exchanger for a 200 MeV e-beam Sensitive to initial energy spread & jitter Before exchanger After exchanger Courtesy: V. Dolgashev
Pulse Compression Induce a x-z correlation using RF deflector (phi = crabbing phase) Bunch passing through an undulator has a angle dependent divergence for the emitted x-rays. Passing it through a collimation slit or crystal for x-ray pulse compression A. Zholents et al., NIMA 425, 385 (1999)
Pulse Compression Short x-ray pulse generation from conventional light sources Under development for the Argonne light source upgrade Heavily damped TM110-type Input Coupler / HOM damper Frequency (GHz) 2.815 Deflecting Voltage 4 MV * 2 Qo (2K) 3.8 * 109 G 235 RT / Q ( W m) 37.2 Beam Radius 2.5 cm No. Cavities 12 * 2 Operation CW Beam Current (ma) 100 Esp/Vdefl (1/m) 83.5 Bsp/Vdefl (mt/mv) 244.1 Deflecting cavity LOM/ HOM damper HOM dampers Waveguide damper replaces KEK coaxial coupler Compact single-cell cavity / damper assembly
Crab Crossing for Luminosity R. Palmer, 1988, Linear Collider
Crab Crossing for Luminosity Crab crossing for geometric luminosity (Pwinski angle) compensation Used at KEKB and foreseen for the HL-LHC Bunch length 2 x 2 z 2 Beam size σ eff = σ + σ (θ c /2) e-ion colliders (erhic, JeLIC) with large crossing angles also requiring crab crossing for luminosity
To Recover p - Bump RF Deflector ϕc RF Deflector qv D p x=. sin (ϕ s+ wt ) E ce tan(ϕ c ) 2 sin (p Q) V crab =. w R12 cos (ϕ cc ip p Q)
Crab Crossing for Luminosity Implemented first in the e+e- machine at KEKB (TM110 mode) Squashed elliptical cell to separate the opposite polarization Beam-pipe coaxial coupler for HOM damping + tuning Frequency: 508.9 MHz Power: 50-120 kw (Qext: 2x105, BW: 2.55 khz) Deflecting freq < Cut-off freq < HOMs in the coaxial part beam pipe Notch filter in the coax to account for mis-alignments of the coaxial line
1 st e Crab Cavity ± Long R&D program Used between (2007-2010) Complex HOM Damping Scheme Feb 2007
ILC Crab Cavities ILC crab cavities using TM110 (multi-cell) cavities Compensation of the 7 mrad of crossing angle for luminosity Challenge to damp wakefields to keep vertical offsets below 1.5 nm! G. Burt, L. Bellatoni et al
Crab Crossing for Luminosity HL-LHC will become the first proton collider to host crab cavities Vertical (Double Quarter Wave) & horizontal (RF-Dipole) Ultra compact dipole cavities (TEM-like), on-cell HOM damping RF Dipole Double Quarter Wave 400 MHz, HL-LHC VT = 3.4 MV (Ep, Bp < 40 MV/m, 70 mt) 280 mm 281 mm Already demonstrated Vt > 5 MV (Ep, Bp > 60 MV/m, 120 mt) Two-stage broad band HOM filters
Quarter Wave Crab Cavity Tuner FPC SC cavities require highly complex 2K assembly due to multiple interfaces and strong RF constraints He tank plate (titanium) cavity tuning system HOM coupler internal H-shield (cryoperm) DQW #1 at CERN
3D Printing, Rapid Prototyping Polymer + Cu Coating, Cavity & HOM Couplers Titanium Prototypes HOM Assembly Tool in ISO4 FPC Mock Up Assembly
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Two Cavity Cryomodule 16 cavities (8 Hor, 8 Ver) to be installed in HL-LHC before 2025 1-module with two cavities into the SPS for beam test validation in 2018