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RF Structures

MAX School 1.-2. October 2013 IAP - Frankfurt. RF Structures. Holger J. Podlech Institute for Applied Physics (IAP) University of Frankfurt, Germany. Wave equation and solutions in cylindrical cavities RF parameter RFQ- structures DTL- structures Power consumption.

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RF Structures

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  1. MAX School 1.-2. October 2013 IAP - Frankfurt RF Structures Holger J. Podlech Institute for Applied Physics (IAP) University of Frankfurt, Germany

  2. Wave equation and solutions in cylindricalcavities • RF parameter • RFQ-structures • DTL-structures • Power consumption

  3. b=0.61 SNS, ORNL r.t./s.c. r.t. b=0.82 VENUS ERCIS BNL 4-vane-RFQ, Saclay 4-rod-RFQ, Frankfurt High IntensityHadronen-Linac Typical Layout 40-200 MeV 300-1000 MeV ~0.1 MeV 0.5-5 MeV ECR Ion Source RFQ DTL DTL DTL superconducting elliptical cavities Choice oftechnology (roomtemperature, superconducting) and RF-structuresdepends on: Beam power, accelerationgradients, beam energieanddutyfactor A lotofcavitiesareneeded

  4. Wave Equation for Cylindrical Cavities Numberof Zeros in F-direction Numberofzerosin radial direction Numberof half periodsin z-direction Set ofdiscretewavefunctions (Eigenmodes) whichfulfilltheboundaryconditions

  5. Solutions of Cylindrical Wave Equation: TM

  6. Resonance Frequency The lowestfrequencyhasthe fundamental TM mode (m=0, n=1, p=0) TM010

  7. TM010-Mode: E-Fields m=0 n=1 p=0 0 0 Ez=const. 0 0

  8. TM010-Mode: E-Fields 2R L

  9. TM010-Mode: B-Fields 2R L

  10. Course of E- und B-Fields E B

  11. RF Parameter • Surface Resistance Rs • StoredEnergyW • RF Power LossesPc • Peak-Fields (E,B) • Quality FactorQ0 • (Shunt-) ImpedanceRa • GeometricalFactorG • GeometricalImpedanceRa/Q0 • CryogenicLoadRsRa

  12. Surface Resistance Rs d≈3.5 mm (350 MHz, Cu) RoomTemperature s=Conductivity Skin-Effect

  13. Surface Resistance Rs RoomTemperature Rs≈ mW Copper

  14. Surface Resistance Superconductivity RoomTemperature Superconductivity 1-10 mW 1-100 nW Typically 5 Orders of magnitude lower Resistance

  15. Stored Energy W E=1 MV/m „Homogeneous“ V=1 m3 4.4 J Pillbox-cavity TM010-Mode

  16. RF Power Losses Pc Power lossesforsuperconductingcavitiessignificantlyreducedbecauseofmuchsmallersurfaceresistance Pillbox-cavity TM010-Mode

  17. Quality Factor Q Lorentz-Curve

  18. Quality Factor Q0 NL: 103-105 SL: 107-1011 Q-value: Numberof RF periodsuntilstoredenergyisdissipated Pillbox-cavity TM010-Mode

  19. Quality Factor RoomTemperature f=350 MHz Q0=1.5x104 Df=23 kHz Superconducting f=350 MHz Q0=1x109 Df=0.35 Hz Df=0.35 Hz Df=23 kHz

  20. (Shunt-)-Impedance R Every RF structurecanbedescribedby an oscillatorcircuit Capacitance Inductance

  21. (Shunt-)-Impedance R Resonance

  22. (Shunt-)-Impedance R Rp=L DTL RFQ Pillbox-cavity TM010-Mode

  23. RFQ Structures • Problem • DC Beam fromionsources must bepreparedfordrifttubestructures Bunching, acceleration • Beam transport, focusing Solution Radio FrequencyQuadrupoles (RFQ) Bunching, focussingandaccelerationwithinonecavity

  24. RFQ Structures RFQ structuresusingelectric RF quadrupolfields  Strong electric (velocityindependent) focusing

  25. RFQ Structures Mechanicalmodulation on electrodes  Longitudinal fieldcomponentsforbunchingandacceleration

  26. RFQ Structures

  27. Classification of Drift Tube RF Structures H-Class TEM-Class TM-Class TM010/E010 TEM TE111/211/H111/211 Alvarez DTL EllipticalCavities IH/CH-Structure Multi-Spoke QWR HWR Spoke Additional RF structures: transmissionlineresonators, SCL, CCL,…

  28. Room Temperature RF Structures GSI IAP Frankfurt IAP INFN Legnaro FNAL MPI-HD CERN REX-ISOLDE

  29. Wideröe DTL Celllengthcorresponstotheflight time during half ofthe RF period

  30. ALVAREZ-DTL Alvarez DTL • Cylindricalcavity in TM010-Mode  constantelectricfieldEz • Drift tubesareusedtoshieldthedecelarationfieldfromtheparticles • Drift tubeshousingquadrupollensesfortransversefocusing • Celllengthisbl

  31. ALVAREZ-DTL Alvarez DTL 200 MHz DTL FNAL 108 MHz DTL GSI

  32. H-mode DTL- cavities TE111 TE211 TE211 rt CH E< 100 AMeV 150<f<700 MHz rt IH E< 30 AMeV 30<f<250 MHz sc CH E< 100 AMeV 150<f<700 MHz

  33. RT IH-Structures

  34. RT CH-Structures

  35. Superconducting RF Structures ANL INFN Legnaro ANL IPN, Orsay ANL MSU SNS IAP Frankfurt IPN, Orsay ANL LANL

  36. Power Consumption Pc Power consumption of sc cavities significantly lower (factor 104-105) Geometrical Impedance Impedance

  37. RF Parameter Comparison 2R Pillbox Cavity Fundamental mode TM010 f=1.5 GHz L=10 cm L NC SC

  38. Quarter-Wave-Resonators 50 MHz ≤ f ≤ 200 MHz L ≤ l/4 E-Field B-Field

  39. Half-Wave-Resonators 150 MHz ≤ f ≤ 700 MHz L ≤ l/2 E-Field B-Field

  40. SC CH-Cavities 150 MHz ≤ f ≤ 500 MHz

  41. EllipticalCavities 350 MHz ≤ f ≤ 3000 MHz L BF Ez C Beam axis

  42. EllipticalCavities Spallation-Neutron Source (SNS) f=805 MHz b=0.61 b=0.82 SNS, OakRidge National Laboratory (ORNL)

  43. Power ConsumptionConsiderations Power is a majorissueforaccelerators  Capital and operational costs Plug Power RF Power Gradient Beam Current Shunt Impedance Gradient Beam Current Shunt Impedance DutyFactor Efficiency cryogenics

  44. Power Consumption Pc Without Beam, cw Normal conducting Superconducting Ua=3 MV L=1 m Ra/Q0=2000 W Rs=12.6 nW Q0(BCS)=6·109 Ua=3 MV L=1 m Ra/Q0=2000 W Rs=3.7 mW Q0=2·104 Pc=225000 W Pc= 0.75 W

  45. Power ConsumptionPc Power consumptionofsccavitiessignificantlylower (factor 104-105) BUT: Real lifeismorecomplicated Superconducting Rs=60 nW Additional resistance (magneticfields, material properties, surfacepreparation) Pc= 3.6 W Efficiency ofthecryogenicsystem

  46. Power Consumption (Plug Power Peff) Without Beam, cw Normal conducting Superconducting Pc=225000 W Pc= 3.6 W 15 W staticlosses h = 0.6 (RF amplifier) Ptot= 18.6 W Peff=375000 W h = 0.003 (cryogenicsystem) Peff= 6200 W

  47. Power Consumption (Plug Power Peff) With 20 mA Beam, cw Pbeam=UI Normal conducting Superconducting Pcryo= 6200 W Pc=225000 W h = 0.6 (RF amplifier) Pbeam= 60000 W Pbeam=60000 W Peff= 106200 W Peff=475000 W

  48. Transition Energy NC-SC vsDutyFactor

  49. Choice of Technology (NC-SC) Superconducting Normal Conducting Low Energy High Energy High Beam Power Low Beam Power Low Duty Factor High Duty Factor

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