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Superconducting RF Cavity Design for Accelerators

This course covers the basics of superconducting RF cavity design for accelerators. Topics include cavity types, design principles, gradient and losses, mechanical aspects, couplers/tuners, and cavity performance aspects.

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Superconducting RF Cavity Design for Accelerators

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  1. H. Padamsee SRF Course Topics at Erice(My lectures in red) • Superconductivity, and RF – Larbalastier, Ciovati • General comments on SC cavity design choices for accelerators • Basics of SRF cavities • Structure Types • Basic RF Cavity Design Principles/ Figures of Merit • Gradient, Losses, Q, Shunt Impedance, Peak Fields… • SC/NC comparison for CW application • Design Aspects for Multicells • Higher Order Modes and their importance in cavity design • Mechanical Aspects of Cavity Design • Couplers/Tuners/… • Cavity Performance Aspects/Cavity Technology- Antoine • Multipacting, Breakdown (Quench), Field Emission, Q-Slope • Fundamental critical fields/Ultimate gradient possibilities - Antoine • Cavity Fabrication /Preparation - Singer • Cavity Testing - Reschke • Wide Range of Applications

  2. H. Padamsee Overall Approach Mostly Conceptual with pictures Will go fast through many slides, refer to text books And tons of reviews Some quantitative aspects – references Draw examples from some accelerator applications References: Extensive Literature + 2 Text Books (1998 and 2010) Lots of Review Papers SRF Workshop Proceedings (1980, 83, 85….2001) (including Tutorials) on Jacow CERN website RAST articles (very recent)

  3. H. Padamsee CREATION’S BIRTHDAY A Play about Hubble and Einstein by HasanPadamsee Saturday, 27 April 17:30 Presented by

  4. H. Padamsee General Accelerator Requirements That Drive SC Cavity Design Choices, v/c ~ 1, v/c <1 Voltage needed Storage Rings CESR-III: 7 MV, KEK-B HER: 14 MV, LEP-II: 3 GV Proton Linac: 1 GV SNS, ESS Linac-Based FEL or ERL : 500 MeV - 5 GeV Linear Collider: 500 - 1000 GV Duty Factor (RF on time x Repetition Rate) Storage Rings: CW Linac-Based FEL or ERL CW Proton Linacs: < 10% Linear Collider: 0.01 - 1% Beam Current, Ave. Beam Power, Beam loss allowed Storage Rings: amp, MW Linac-Based FEL or ERL 50 mA - 100 mA Proton Linacs: 10 - 100 mA, 1- 10 MW Linear Collider: few ma, 10 MW

  5. H. Padamsee Low Velocity Accelerators • Transition energies for v< c accelerators

  6. H. Padamsee Cavity Design Choices • Main Choices • Particle velocity, beta = v/c • RF Frequency • Operating Gradient • Operating Temperature • Number of Cells • Cell Shapes • Beam Aperture • Type of Structure, QWR, HWR, Spoike (low velocity) • Optimizations Involve Many Trade-offs • Best Cavity/Accelerator Performance for Least Risk • Minimize Capital + Operating Cost • Discuss parameters/dependencies • But not the trade-offs • Which are particular to each accelerator design

  7. Example Optimizations The criteria/requirements differ depending on application:

  8. H. Padamsee Ideal Cavity • Pill-box shape

  9. /2 Basic Principle, v/c = 1 Multi-Cell Cavity /2 Single Cell Squeezed Cells for v/c = 0.5 H. Padamsee Medium and High Velocity Structures b = v/c = 0.5 -> 1

  10. Structure Examples Structures for Particles at v < c (SNS)For protons at 1 ~ GeV H. Padamsee 1300 MHz Structures for Accelerating Particles at v ~ c TESLA-shape (DESY, TTF) Low-Loss shape (Jlab, KEK…) Re-entrant shape (Cornell)

  11. Niobium Basic Principle Half-Wave Quarter Wave Inter-Digital Split -Ring Spoke Low Velocity Structures, b = v/c = 0.01 -> 0.2 H. Padamsee

  12. H. Padamsee Range of Velocity and Frequency

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  17. Basics for Superconducting Cavities Covered by Ciovati 10 cm E E Vc = One Million Volts Gap = d

  18. H. Padamsee RF accelerator cavitiesFields and Currents

  19. d Enter Exit H. Padamsee Figures of MeritAccelerating Voltage/Field (v = c Particles) • Accelerating voltage then is: • Accelerating field is: T is Transit time factor = 2/p

  20. H. Padamsee Figures of Merit for SC CavityCovered by Ciovati • Accelerating Field and Q: Eacc, Q • Stored Energy, Geometry Factor • Peak Electric and Magnetic Field Ratios • Epk/Eacc, Hpk/Eacc • Shunt Impedance, Geometric Shunt Impedance: Ra, Ra/Q

  21. H. Padamsee Pill-Box Analytical Results

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  23. H. Padamsee Real Single Cell Cavities KEK-B Cavity Electric field high at iris Magnetic field high at equator

  24. Importance of Figures of MeritPeak Fields H. Padamsee • For Eacc important parameter is Epk/Eacc, • Typically 2 - 2.6 • Make as small as possible, to avoid problems with field emission - more later. • Equally important is Hpk/Eacc,to maintain SC • Typically 40 - 50 Oe/MV/m or 4 – 5 mT/MV/m • Hpk/Eacc can lead to premature quench problems (thermal breakdown). • Ratios increase significantly • when beam tubes are added to the cavity • or when aperture is made larger.

  25. H. Padamsee Peak fields for low beta cavities are higher Typical Epk/Eacc = 4 - 6 Hpk/Eacc = 60 - 200 Oe/MV/m Hpk

  26. Define Quality (Q) as which is ~ 2number of cycles it takes to dissipate the energy stored in the cavity Easy way to measure Q • Qnc ≈ 104, Qsc ≈ 1010 = 2 U TrfPc H. Padamsee Figures of Merit Dissipated Power, Stored Energy,Cavity Quality (Q) • Dissipation in the cavity wall given by surface integral: • Stored energy is:

  27. H. Padamsee Galileo, 1600 AD

  28. H. Padamsee Figures of MeritShunt Impedance (Ra) • Shunt impedance (Ra) determines how much acceleration one gets for a given dissipation (analogous to Ohm’s Law)  To maximize acceleration, must maximize shunt impedance. Another important figure of merit is • Ra/Q only depends on the cavity geometry  Cavity design

  29. H. Padamsee Evaluation - Analytic Expressions 1.5 GHz pillbox cavity, R = 7.7 cm, d = 10 cm

  30. H. Padamsee Low Beta Elliptical Cavities • A progression of compressed elliptical cavity shapes at the same rf frequency but for decreasing bvalues

  31. H. Padamsee Current and Voltage for QWRReviews/Tutorials by Delayen and Facco

  32. H. Padamsee Current and Voltage for Half-Wave Resonator (a) (b) (c) (d)

  33. H. Padamsee Spoke is Half-Wave Resonator

  34. H. Padamsee • One-gap (pill-box) transit time factor for low velocity, using two different aperture values 15 mm and 30 mm. Acceleration takes place efficiently above β~2g/λ and it is maximum at β=1. Here g is the gap and b is the aperture.

  35. H. Padamsee Transit Time for Standard QWR • 2-gap transit time factor for the π-mode compared to the 1-gap. Acceleration is maximum for a particular value of b. The transit time factor falls off steeply with b on either side of the optimum

  36. H. Padamsee Transit Time Factor for Low-Velocity • Normalized transit time factor vs. normalized velocity β/β0, for cavities with different number of equal gaps

  37. Adding beam tubes reduces Ra/Q by about x2 => for Cu cavities use a small beam hole. Peak fields also increase. Can be a problem for high gradient cavities Analytic calculations are no longer possible especially if cavity is shaped is to optimize peak fields.  Use numerical codes. H. Padamsee Real Cavities - Codes

  38. RF design tools • Design of elliptical cavities is performed in two steps: 2D and 3D. • 2D codes (Superfish, SLANS/CLANS, …) • faster and allow to design geometry of the cylindrically-symmetric body of the cavity. • 3D codes (MAFIA, Microwave Studio, HFSS, Omega-3P, GdfidL, …) • necessary to complete the design by modeling the cavity equipped with fundamental power couplers, HOM loop couplers, calculating coupling strength, etc.

  39. 2D code example: SLANS/CLANS Peak surface fields • SuperLANS (or SLANS) is a computer program designed to calculate the monopole modes of RF cavities using a finite element method of calculation and a mesh with quadrilateral biquadratic elements. • SLANS has the ability to calculate the mode frequency, quality factor, stored energy, transit time factor, effective impedance, max electric and magnetic field, acceleration, acceleration rate, average field on the axis, force lines for a given mode, and surface fields. • Later versions, SLANS2 and CLANS2, calculate azimuthally asymmetric modes, and CLANS and CLANS2 can include into geometry lossy materials.

  40. H. Padamsee More on 3D EM Codes • Under the SciDAC collaboration, (Scientific Discovery through Advanced Computing), SLAC has developed parallel processing finite element electromagnetic codes to obtain gains in accuracy, problem size and solution speed by harnessing the computing power and exploiting the huge memory of the latest supercomputers, e. g. the IBM/SP (Seaborg) at NERSC and the Cray/X1E (Phoenix) at NLCF. • The suite of electromagnetic codes available are based on un- structured grids for high accuracy, and use parallel processing to enable large-scale simulation. • The new modeling capability supports meshing, solvers, refinement, optimization and visualization. • The code suite to date includes the eigensolver Omega3P, the S-matrix solver S3P, the time-domain solver T3P, and the particle tracking code Track3P. • Direct simulations of the entire cavity with input and HOM couplers have been carried out. • TEM-class drift-tube loaded cavities and Spoke Resonators have been designed using modern 3D simulation codes such as MAFIA, Microwave Studio, SOPRANO

  41. Sample Result from Codes H. Padamsee equator Elliptical cavity (TM-class) Half-wave cavity (TEM-class) 47

  42. H. Padamsee E and H Fields for Multi - Spoke

  43. H. Padamsee Design Cavity Shape Consequences

  44. H. Padamsee Influence of Aperture

  45. H. Padamsee Aperture

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