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Superconducting RF Cavities for Particle Accelerators: An Introduction Ilan Ben-Zvi Brookhaven National Laboratory

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In a word: Superconducting RF (SRF) provides efficient, high-gradient accelerators at high duty-factor. SRF accelerator cavities are a success story. Large variety of SRF cavities, depending on: – Type of accelerator – Particle velocity – Current and Duty factor – Gradient – Acceleration or deflecting mode

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What is a resonant cavity and how do we accelerate beams? A resonant cavity is the high- frequency analog of a LCR resonant circuit. RF power at resonance builds up high electric fields used to accelerate charged particles. Energy is stored in the electric & magnetic fields.

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Pill-box cavity Q=G/R s G=257 R s is the surface resistivity.

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Some important figures of merit U=PQ/ A cavity is characterized by its quality factor Q and the geometric factors R/Q and G Dissipated power per cavity depends on voltage, surface resistivity and geometry factors. V 2 =P·Q·R/Q For a pillbox cavity R/Q=196 Per cavity: P = V 2 · R s · 1/G · Q/R Other quantities of interest for a pillbox cavity: E peak /E acceleration =1.6 (~2 in elliptical) H peak /E acceleration = 30.5 Gauss / MV/m (~40 in elliptical cavities)

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RF Superconductivity Superconducting electrons are paired in a coherent quantum state, for DC resistivity disappears bellow the critical field. In RF, there is the BCS resistivity, arising from the unpaired electrons. H c (T)=H c (0)·[1-(T/T c ) 2 ] For copper = 5.8·10 7 -1 m -1 so at 1.5 GHz, R s = 10 m For superconducting niobium R s = R BCS + R residul and at 1.8K, 1.5 GHz, R BCS = 6 n R residual ~ 1 to 10 n

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Various SRF materials – only one practical and commonly used MaterialT c (K)H c1 (kGauss)H c2 (kGauss) Lead7.70.8 Niobium9.21.74 Nb 3 Sn180.5300 MgB 2 400.335 “Superheating” field for niobium at 0 K is 2.4 kGauss

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Design Considerations Residual resistivity: R actual R BCS +R residual Dependence on field – shape, material, preparation – “Q slope” Electropolishing, baking – Field emission- cleanliness, chemical processing – Thermal conductivity, thermal breakdown – High RRR Multipacting – cavity shape, cleanliness, processing Higher Order Modes – loss factor, couplers Mechanical modes– stiffening, isolation, feedback

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Measure of performance: The Q vs. accelerating field plot Magnetic fields of 1.7 kGauss (multi-cell) to 1.9 kGauss (single cell) Can be achieved, and recently 2.09 kGauss achieved at Cornell.

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Limit on fields Field emission – clean assembly Magnetic field breakdown (ultimate limit) - good welds, reduce surface fields Thermal conductivity – high RRR material Local heating due to defects Fields of 20 to 25 MV/m at Q of over 10 10 is routine

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Choice of material and preparation High “RRR” material (300 and above) Large grain material is an old – new approach Buffered Chemical Polishing (BCP) (HF – HNO 3 – H 2 PO 4, say 1:1:2) Electropolishing (HF – H 2 SO 4 ) UHV baking (~800C) Low temperature (~120C). High pressure rinsing Clean room assembly

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Multipacting Multipacting is a resonant, low field conduction in vacuum due to secondary emission Easily avoided in elliptical cavities with clean surfaces May show up in couplers! Multipacting in Stanford SCA cavity, 1973 PAC

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Higher Order Modes (HOM) Energy lost by charge q to cavity modes: Longitudinal and Transverse Energy is transferred from beam to cavity modes The power can be very high and must be dumped safely Transverse modes can cause beam breakup Solution: Strong damping of all HOM, Remove power from all HOM to loads Isolated from liquid helium environment.

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Electromechanical issues Lorentz detuning Pondermotive instabilities Pressure and acoustic noise Solutions include – broadening resonance curve – feedback control – good mechanical design of cavity and cryostat

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Miscellaneous hardware Fundamental mode couplers Pick-up couplers Higher-Order Mode couplers Cryostats (including magnetic shields, thermal shields) Helium refrigerators (1 watt at 2 K is ~900 watt from plug) RF power amplifiers (very large for non energy recovered elements

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Some Examples Low velocity High acceleration gradient Particle deflection High current / Storage rings High current / Energy Recovery Linac RF electron gun

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Low Resonators Quarter Wave Resonator Radio Frequency Quadrupole Elliptical Split Loop ResonatorSpoke cavityMulti-spoke Critical applications: Heavy ion accelerators, e.g. RIA High power protons, e.g. SNS, Project-X

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High acceleration gradient Critical applications: Linear colliders e.g. ILC X-ray FELs e.g. DESY XFEL

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Deflecting Cavities Critical applications: Crab crossing (luminosity) e.g. KEK-B, LHC Short X-ray pulses from light sources

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Energy Recovery Linac: A transform to a boosted frame Energy needed for acceleration is “borrowed” then returned to cavity. Little power for field. Energy taken from cavity Energy returned to cavity JLab ERL Demo

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High current ERL cavities Multi-ampere current possible in ERL Critical applications: High average power FELs (e.g. Jlab) High brightness light sources (e.g. Cornell) High luminosity e-P colliders (e.g. eRHIC)

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High current SRF photo-injector Low emittance at high average current is required for FEL. The high fields (over 20 MV/m) and large acceleration (2 MV) provide good emittance. High current (0.5 ampere) is possible thanks to 1 MW power delivered to the beam. Starting point for ERL’s beam.

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Summary SRF cavities serve in a large variety of purposes with many shapes. The future of particle accelerators is in SRF acceleration elements – light sources, colliders, linacs, ERLs and more. While there is a lot of confidence in the technology, there is still a lot of science to be done.

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