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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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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 cylindricalcavities • RF parameter • RFQ-structures • DTL-structures • Power consumption
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
Wave Equation for Cylindrical Cavities Numberof Zeros in F-direction Numberofzerosin radial direction Numberof half periodsin z-direction Set ofdiscretewavefunctions (Eigenmodes) whichfulfilltheboundaryconditions
Resonance Frequency The lowestfrequencyhasthe fundamental TM mode (m=0, n=1, p=0) TM010
TM010-Mode: E-Fields m=0 n=1 p=0 0 0 Ez=const. 0 0
TM010-Mode: E-Fields 2R L
TM010-Mode: B-Fields 2R L
RF Parameter • Surface Resistance Rs • StoredEnergyW • RF Power LossesPc • Peak-Fields (E,B) • Quality FactorQ0 • (Shunt-) ImpedanceRa • GeometricalFactorG • GeometricalImpedanceRa/Q0 • CryogenicLoadRsRa
Surface Resistance Rs d≈3.5 mm (350 MHz, Cu) RoomTemperature s=Conductivity Skin-Effect
Surface Resistance Rs RoomTemperature Rs≈ mW Copper
Surface Resistance Superconductivity RoomTemperature Superconductivity 1-10 mW 1-100 nW Typically 5 Orders of magnitude lower Resistance
Stored Energy W E=1 MV/m „Homogeneous“ V=1 m3 4.4 J Pillbox-cavity TM010-Mode
RF Power Losses Pc Power lossesforsuperconductingcavitiessignificantlyreducedbecauseofmuchsmallersurfaceresistance Pillbox-cavity TM010-Mode
Quality Factor Q Lorentz-Curve
Quality Factor Q0 NL: 103-105 SL: 107-1011 Q-value: Numberof RF periodsuntilstoredenergyisdissipated Pillbox-cavity TM010-Mode
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
(Shunt-)-Impedance R Every RF structurecanbedescribedby an oscillatorcircuit Capacitance Inductance
(Shunt-)-Impedance R Resonance
(Shunt-)-Impedance R Rp=L DTL RFQ Pillbox-cavity TM010-Mode
RFQ Structures • Problem • DC Beam fromionsources must bepreparedfordrifttubestructures Bunching, acceleration • Beam transport, focusing Solution Radio FrequencyQuadrupoles (RFQ) Bunching, focussingandaccelerationwithinonecavity
RFQ Structures RFQ structuresusingelectric RF quadrupolfields Strong electric (velocityindependent) focusing
RFQ Structures Mechanicalmodulation on electrodes Longitudinal fieldcomponentsforbunchingandacceleration
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,…
Room Temperature RF Structures GSI IAP Frankfurt IAP INFN Legnaro FNAL MPI-HD CERN REX-ISOLDE
Wideröe DTL Celllengthcorresponstotheflight time during half ofthe RF period
ALVAREZ-DTL Alvarez DTL • Cylindricalcavity in TM010-Mode constantelectricfieldEz • Drift tubesareusedtoshieldthedecelarationfieldfromtheparticles • Drift tubeshousingquadrupollensesfortransversefocusing • Celllengthisbl
ALVAREZ-DTL Alvarez DTL 200 MHz DTL FNAL 108 MHz DTL GSI
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
Superconducting RF Structures ANL INFN Legnaro ANL IPN, Orsay ANL MSU SNS IAP Frankfurt IPN, Orsay ANL LANL
Power Consumption Pc Power consumption of sc cavities significantly lower (factor 104-105) Geometrical Impedance Impedance
RF Parameter Comparison 2R Pillbox Cavity Fundamental mode TM010 f=1.5 GHz L=10 cm L NC SC
Quarter-Wave-Resonators 50 MHz ≤ f ≤ 200 MHz L ≤ l/4 E-Field B-Field
Half-Wave-Resonators 150 MHz ≤ f ≤ 700 MHz L ≤ l/2 E-Field B-Field
SC CH-Cavities 150 MHz ≤ f ≤ 500 MHz
EllipticalCavities 350 MHz ≤ f ≤ 3000 MHz L BF Ez C Beam axis
EllipticalCavities Spallation-Neutron Source (SNS) f=805 MHz b=0.61 b=0.82 SNS, OakRidge National Laboratory (ORNL)
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
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
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
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
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
Choice of Technology (NC-SC) Superconducting Normal Conducting Low Energy High Energy High Beam Power Low Beam Power Low Duty Factor High Duty Factor