1. 26 Nov. 2010 Alexej Grudiev, CLIC DR RF system at 2 GHz. Conceptual design of the CLIC DR RF system at 2 GHz Alexej Grudiev 26.11.2010 CLIC meeting

2. 26 Nov. 2010 Alexej Grudiev, CLIC DR RF system at 2 GHz. Acknowledgements  E. Jensen (CERN)  W. Hofle (CERN)  K. Akai (KEK)

3. 26 Nov. 2010 Alexej Grudiev, CLIC DR RF system at 2 GHz. Outline  Introduction  High stored energy rf system  Normal conducting  Superconducting  Low stored energy rf system  Summary

4. 26 Nov. 2010 Alexej Grudiev, CLIC DR RF system at 2 GHz. Introduction 1 GHz option, current baseline since March 2010 DR DL To RTML DR To RTML 2 GHz option Specs from RTML F. Stulle, CLIC meeting, 2010-06-04 To first order, in steady-state, the energy spread σ E /E will be zero BUT the bunch-to-bunch separation can differ from 0.5 ns due to transient beam loading

5. 26 Nov. 2010 Alexej Grudiev, CLIC DR RF system at 2 GHz. CLIC DR RF parameters CLIC DR*NLC DR + Circumference: C [m]420.56223 Bunch population: N e 4x10 9 7x10 9 Energy : E [GeV]2.86~2 Momentum compaction: α p 7.6x10 -5 ? Energy loss per turn: U 0 [MeV]4.20.635 RF frequency: f rf [GHz]120.714 RF voltage: V rf [MV]4.94.61 Calculated RF parameters Harmonic number: h14022804 Synchronous phase : φ s [ o ]5966 Energy acceptance: ΔE/E [%]2.291.08 Synchrotron frequency: f s [kHz]2.763.36 *from Yannis on 9/07/2010 + from Tor et.al., PAC95

6. 9 March. 2010 Alexej Grudiev, CLIC DR RF. CW klystron power supply LEP klystron power supply 3 phases main 12 phases – 600 Hz ripples 4% filter t t f 600 Hz -40 dB Filter reduce 600 Hz ripples down to 0.04*0.0045 = 2*10 -4 Feedback stabilizes high voltage at lower frequencies to the level of 1-0.1%. Limited mainly by the HV measurement accuracy Information provided by D. Siemaszko

7. 9 March. 2010 Alexej Grudiev, CLIC DR RF. Klystron amplitude and phase stability Beam voltage ~60 kV Low frequency high voltage stability: 0.1 % (0.3 % achieved in Tristan (KEK) DC power supply for 1MW CW klystron, PAC87) -> 60V -> 1.2 kW rf output power stability ~ 0.3 % power stability ~ 0.15 % amplitude stability Or ~ 1.2 degree phase stability This is not sufficient (see RTML specs). Rf slow feedback loop around the klystron is necessary

8. High stored energy option

9. Beam cavity interaction, dV/V << 1 V = V rf + V b = V*e jφ dV = dV b *sinφ s Vdφ = dV b *cosφ s rf phase modulation versus rf amplitude modulation: dφ = dV/(V*tanφ s ) VbVb dV b V rf V φsφs dφ V t Energy los per turn: V0 = V sinφ s

10. Beam cavity interaction, dV/V << 1 T rev tTbTb IbIb 2GHz case1GHz case T rev tTbTb V 2GHz case dV T rev tTbTb φbφb 2GHz case dφ b W = V 2 /2ρω; dW = dV 2V/ρω dW/dt = -P b + n trains *T b /T rev *P b ; dt -> T b dV/V = -P b T b (1-n trains T b /T rev )ρω/V 2 dφ = dV/V*1/tanφ s dφ s V φ V0V0 V 0 = V sinφ s = energy loss per turn = const; dV 0 = dV sinφ s + Vcosφ s dφ s = 0 dφ s = - dV/V*tanφ s dφ b = dφ+dφ s = dV/V*(1/tanφ s - tanφ s ) dφ

11. KEKB RF system K. Akai, et. al, “THE LOW-LEVEL RF SYSTEM FOR KEKB”, EPAC98 dV/V = P b T b (1-T b /T rev )ρω/V 2 ~ 1 % it is consistent with simulation presented in Fig 3 dφ b = dV/V*(1/tanφ s – tanφ s ) ~ 3 o it is consistent with simulation presented in Fig 3 Dominated by direct cavity voltage phase modulation in KEKB case π/2 - φ s

12. THE ARES CAVITY FOR KEKB, Kageyama et al, APAC98 Frequency: f[GHz]0.50912 Normalized shunt impedance (circuit): ρ g =R g /Q [Ω] (~f 0 ) 7.5 Unloaded Q-factor: Q (~ 1/f 1/2 )1100007700055000 Aperture radius: r [mm] (~ 1/f)804020 Max. Gap voltage: V g [MV] (~ 1/f 3/4 ) Nominal 0.50.30.18 Max. Gap voltage: V g [MV] (~ 1/f 3/4 ) High power tested times sqrt(3) 0.850.50.3 Wall loss per cavity: P=V g 2 /2R g [MW] 0.440.220.11 Scaling of the gap voltage is done to keep heat load per meter constant: P/g = V g 2 /2R g g = V g 2 /2ρ g Q g => V g ~1/f 3/4 ~2.5 m

13. CLIC DR parameters for scaled ARES cavity Circumference: C [m]420.56 Energy loss per turn: U 0 [MeV]4.2 RF frequency: f rf [GHz]12 RF voltage: V rf [MV]4.94.6 Beam current I b [A]0.661.3 Train length T b [ns]2 x 156156 Harmonic number: h14022804 Synchronous phase : φ s [ o ]5966 Gap voltage: V g [MV]0.3 – 0.50.18 – 0.3 Wall loss total [MW]1.2 - 2.11.0 - 1.7 Bunch phase spread for scaled ARES cavity: dφ b [ o ] (ρ g =7.5 Ω) 0.7 - 0.49 – 5.3 Specified bunch phase spread: dφ b [ o ]0.050.1 dV/V = -P b T b (1-n trains T b /T rev )ρ g ω/V g V dφ b = dV/V(1/tanφ s -tanφ s ) Specs from RTML F. Stulle, CLIC meeting, 2010-06-04 Assuming parameters of ARES cavity from nominal up to tested (150 - 450 kW) and scaled to 1 or 2 GHz Dominated by cavity voltage modulation

14. Solution 1: Modification of the scaled ARES cavity Frequency: f[GHz]0.50912 Normalized shunt impedance (circuit): ρ g =R g /Q [Ω] (~1/f 3 ) 7.50.950.12 Unloaded Q-factor: Q (~ f 1/2 )110000156000220000 Aperture radius: r [mm] (~ 1/f)804020 Max. Gap voltage: V g [MV] (~ 1/f 5/4 ) Scaled to keep wall loss per cavity constant 0.850.350.15 Wall loss per cavity: [MW]0.44 ρ=V 2 /2ω(W a +W s ); in ARES W s =10W a If we keep the size of the storage cavity the same as for 0.509 GHz when going to 1 or 2 GHz: W s =10W a *(f/0.509) 3 ρ= 1/f 3 In addition, Q-factor improves ~sqrt(f)  This implies that we go to higher order mode in storage cavity from TE015 to whispering- gallery modes like in the BOC-type pulse compressor.  Still, shunt impedance drops and wall losses per cavity increase significantly what requires gap voltage reduction. Scaling of the gap voltage is done to keep heat load per cavity constant: P = V g 2 /2R g = V g 2 /2ρ g Q => V g ~1/f 5/4

15. CLIC DR parameters for modified ARES cavity Circumference: C [m]420.56 Energy loss per turn: U 0 [MeV]4.2 RF frequency: f rf [GHz]12 RF voltage: V rf [MV]4.94.6 Beam current I b [A]0.661.3 Train length T b [ns]2 x 156156 Harmonic number: h14022804 Synchronous phase : φ s [ o ]5966 Gap voltage: V g [MV]0.2 – 0.360.09 – 0.15 Wall loss total [MW]3.5 - 67.9 - 13.4 Bunch phase spread for modified ARES cavities: dφ b [ o ] 0.1- 0.070.28 - 0.17 Specified bunch phase spread: dφ b [ o ]0.050.1 Specs from RTML F. Stulle, CLIC meeting, 2010-06-04 Assuming parameters of ARES cavity in the range from nominal up to tested and modified to 1 or 2 GHz keeping the same storage cavity volume Performance is almost within specs but the power loss in the cavities is big. It is acceptable for 1 GHz but probably too big for 2 GHz

16. BUT the associated voltage reduction δV/V results in bucket reduction and consequently in bunch parameters modification. Radiation damping keeps σ E =const for all bunches in the train so the bunch length varies along the train. The limit from RTML is that RMS{δσ z /σ z } < 1% Solution 2: Mismatch of rf frequency and bunch frequency In the presence of linear phase shift of dφ b over a period of time T b : f b = f rf - dφ b /2πT b ; To compensate dφ b = dV/V (1/tanφ s - tanφ s ) = 1.5 o at 2 GHz, δV/V = -1%, φ s =66 o, df rf /f rf = -1.4e-5, very small ΔE/Δz = σ E /σ z => ΔE σ z = Δz σ E Variation gives δΔE σ z + ΔE δσ z = δΔz σ E + Δz δσ E Which results in δσ z /σ z = δΔz/Δz – δΔE/ΔE σzσz σEσE ΔzΔz ΔE 2 ~ V(cosφ s +(φ s -π/2)sinφ s ) δΔE/ΔE = ½[δV/V+δφ s /(tanφ s +1/(φ s -π/2))] δφ s =- δV/V tanφ s δΔE/ΔE = ½δV/V[1-1/(1+1/(tanφ s (φ s -π/2)))] δV/V = -1%, φ s =66 o => δΔE/ΔE = -8.5% Image from H. Damerau, PhD Thesis, 2005 φ s =73 o Δφ ~ (φ s -π/2) δΔφ/Δφ = δφ s /(φ s -π/2) δφ s = -δV/V tanφ s δΔφ/Δφ = -δV/V tanφ s /(φ s -π/2) δV/V = -1%, φ s =66 o => δΔz/Δz=δΔφ/Δφ = -5.4% δσ z /σ z = δΔz/Δz – δΔE/ΔE = -5.4% + 8.5% = 3.1% (peak-to-peak) ΔEΔE

17. Proposal for conceptual design at 2 GHz based on the ARES-type cavities 1.Fix the value of acceptable bunch length increase from first to the last bunch to δσ z /σ z = 3% 2.This defines allowed voltage reduction δV/V = -1%, which corresponds to dφ b = dV/V (1/tanφ s - tanφ s ) = 1.5 o, φ s = 66 o 3.To assure this voltage reduction the total normalized shunt impedance: ρ = -dV/V *V 2 /(P b T b (1-n trains T b f rev ) ω) = 25 Ω Parameters of the proposed rf system at 2 GHz Q-factor~190000 Total stored energy: W [J]34 Wall loss per cavity: P g [MW]0.11 Number of cavities N=Wω/QP g 20 Normalized shunt impedance per cavity (circuit): ρ g =ρ/N[Ω] 1.25 Gap voltage: V g = sqrt(Wω2ρ g /N)[MV]0.23 Wall loss total [MW]2.2 Average beam power [MW]0.6 Total length of the rf system [m]~40 Bunch phase spread: dφ b [ o ]1.5 Relative rf frequency mismatch: df/f Required for compensation dφ b -1.4e-5 Corresponding mean radius position increase: dR=R*df/f [mm] ~0.7

18. RF station layout ARES type cavities beam Reflections from the cavities go to the load Load HVPS 18 kV AC Klystron 0.3 MW Voltage program input Storage cavity Circulator Storage cavity

19. Superconducting RF option  Making ARES-type cavity superconducting is probably possible but certainly beyond the present state-of-the-art in SC RF technology  Elliptical cavity is an option but it has relatively high normalized shunt impedance. Let’s consider TESLA-like cell: Frequency: f[GHz]1.312 Normalized shunt impedance (circuit): ρ g =R g /Q [Ω] (const) 58 Unloaded Q-factor: Q (~ 1/f 2 )5e98e92e9 Aperture radius: r [mm] (~ 1/f)354623 Max. gradient in CW: G [MV/m] Scaled to keep gradient constant 14 Max. gap voltage: V g [MV]1.621 Stored energy per gap: V g 2 /2ρ g ω [J]2.75.50.7 gap Image and pars from PhysRevSTAB.3.092001 Parameters of SC rf system at 2 GHz Total stored energy [J]34 Gap stored energy: [J]0.7 Number of gaps50 Gap voltage: V g [MV]0.09 Normalized shunt impedance per gap (circuit): ρ g [Ω] 0.5 Q-factor at 2K2e9 Wall loss total [W] at 2K212 Total cryogenic power [MW] at 300K~0.2 Average beam power [MW]0.6 Total length of the rf system [m] Dependent on the # of cells per cavity ~10 for 5 cells per cavity

20. RF station layout for SC cavities beam Reflections from the cavities go to the load Load PS 18 kV AC Klystron or IOT 60 kW Voltage program input Circulator

21. Low stored energy option

22. 26 Nov. 2010 Alexej Grudiev, CLIC DR RF system at 2 GHz. Scaling of NLC DR RF cavity NLC DR RF cavity parametersCLIC DR RF Frequency: f[GHz]0.71421 Shunt impedance: R g [MΩ] (~ 1/√f)31.82.5 Unloaded Q-factor: Q 0 (~ 1/√f)255001540021500 Aperture radius: r [mm] (~ 1/f)311122 Max. Gap voltage: V g [MV] (~ 1/f 3/4 )0.50.230.39 Wall loss per cavity: V g 2 /2R g [MW]0.0420.0150.03 HOM (σ z =3.3mm) Total loss factor: k l [V/pC] (~ f) 1.74.762.38 Fundamental loss factor: k 0 l [V/pC] (~ f) 0.260.720.36 HOM loss factor: k || l [V/pC] (~ f) 1.13.081.54 Transverse HOM kick factor: k T t [V/pC/m] (~ f 2 ) 39.430977.3 From PAC 2001, Chicago AN RF CAVITY FOR THE NLC DAMPING RINGS R.A. Rimmer, et al., LBNL, Berkeley, CA 94720, USA From PAC 1995, Collective effects in the NLC DR designs T. Raubenheimer, et al., Scaling of the gap voltage is done to keep heat load per meter constant: P/g = V g 2 /2R g g = V g 2 /2ρ g Q g => V g ~1/f 3/4

23. 26 Nov. 2010 Alexej Grudiev, CLIC DR RF system at 2 GHz. Cavity parameters Number of cavities: N = V rf /V g = 4.6/0.23 = 20 = 10 x 2-cells cavities Gap voltage: V g = V rf /N = 4.6/20 = 0.23 MV Total wall losses [MW] : P 0 = V rf 2 /2NR = 4.6 2 /(2*20*1.8) = 0.29 MW Peak beam SR power [MW]: P b = U 0 *I b = 4.2*1.3 = 5.46 MW Matching condition: Total power lost in the cavities when the beam is in: P in = P b + P 0 = 5.75 MW Cavity coupling: β = Q 0 /Q ext = P in /P 0 = (P b +P 0 )/P 0 = 20 External Q-factor: Q ext = Q 0 /β = 15400/20 = 770 Filling time: t f = Q l /f = Q ext /(1+1/β)/f = 770/(1+1/20)/2 GHz = 367 ns Klystron bandwidth: ∂f ∂f >> 1/t f = 1 / 367 = 2.7 MHz. AND ∂f >> 1/t gap = 1 / (1402-156) = 0.8 MHz; where t gap – time between the bunch trains RF system total active length: 10 x 1 m = 10 m

24. 26 Nov. 2010 Alexej Grudiev, CLIC DR RF system at 2 GHz. Transient beam loading compensation Transient beam loading compensation with infinite bandwidth klystron Amplitude modulation from 1 to 0.55 is necessary (see V in ) Transient beam loading compensation with 0.5% (10 MHz) bandwidth klystron Amplitude modulation from 1 to 0.35 is necessary (see V in )

25. 26 Nov. 2010 Alexej Grudiev, CLIC DR RF system at 2 GHz. Reflections from the cavities go to the load Basic layout of 2 GHz rf station 2-cells cavity beam Load HVPS 18 kV AC 80 kV DC Klystron 0.6 MW Circulator Voltage program input

26. 26 Nov. 2010 Alexej Grudiev, CLIC DR RF system at 2 GHz. beam Reflections from the cavities go to the load Alternative layout for 2 GHz rf station DR 4-cell cavity Load HVPS 18 kV AC 80 kV DC Klystron 0.6 MW Voltage program input Pulse Compressor Alternative layout doubles peak power for a pulse of ~600 ns Circulator

27. 26 Nov. 2010 Alexej Grudiev, CLIC DR RF system at 2 GHz. Summary table for “a la linac”-type Overall parametersPC-option Total rf power [MW]>6>3 Total length [m]105 Number of HVPS105 Number of klystrons105 High voltage power supply (HVPS) Output voltage [kV]60 Output current [A]20 Voltage stability [%]0.1 Klystron Output power [kW]600 Efficiency [%]50 Bandwidth [MHz]>10 Gain [dB]~40

28. 9 March. 2010 Alexej Grudiev, CLIC DR RF. Klystron bandwidth NLC DR RF system: http://www-project.slac.stanford.edu/lc/local/Reviews/cd1%20nov98/RF%20HighPwr_Schwarz.pdf Klystron High power CW klystrons of 1 MW output power and -3 MHz 1 dB bandwidth at 700 MHz were developed by industry for APT. New requirement for Damping Ring klystron is order of magnitude wider bandwidth: 65 nano-seconds gap in between bunch trains cause variations in accelerating field level during bunch train, resulting in bunch extraction phase variation. This effect can be counteracted by a fast direct feedback loop with about 30 MHz bandwidth. A klystron bandwidth of 20 - 30 MHz is within technical know-how for a 1 MW hiqh power klvstron but will result in lower efficiency. Klystron Dept. Microwave Engineering, H. Schwarz, 1998 http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=01476034 A BROADBAND 500 KW CW KLYSTRON AT S-BAND, Robert H. Giebeler and Jerry Nishida, Varian Associates, Palo Alto, Calif. 1969 klystron amplifier designed for installation ‘on the 210 foot steerable antenna. This paper will describe the development of a 500 kilowatt CW S-band at the JPL/NASA deep space instrumentation facility a€ Goldstone, California. This tube is an improved version of the 450 kilowatt unit developed in 1967. Its features include 1-1/2 percent instantaneous bandwidth, 58 dB nominal gain and 53 percent nominal efficiency. Few percent bandwidth is feasible for 0.5 MW CW klystron Most critical issue is to determine peak power versus bandwidth requirements for the low stored energy option.

29. 9 July 2010 Alexej Grudiev, CLIC DR RF for CDR. Impedance estimate in DR, PDR Calculated RF cavity parameters HOMNLC DRCLIC DRCLIC PDR Frequency: f[GHz]0.7141212 Number of cavities: N = V rf /V g 2 (3)16204048 Total HOM loss factor: k || l * N [V/pC]2.224.661.6 148 Long. HOM energy loss per turn per bunch [μJ]: ΔU = k || l * N * eN e 2 2.810253277 Incoherent long. HOM loss power [kW]: P || incoh = ΔU * N b f/h 22.25.67.719 Coherent long. HOM loss power [kW]: P || coh ~ P || incoh *Q HOM *f/f HOM ( if the mode frequency f HOM is a harmonic of 2 GHz) Careful Design of HOM damping is needed Total HOM kick factor: k T t * N [V/pC/m]78.812406160310014800 Tran. HOM energy loss per turn per bunch [μJ]: ΔU = k T t * 2πf/c * N * eN e 2 * d 2 (d – orbit deviation, 10mm assumed) 0.151.110.53.332 Tran. HOM loss power is not an issue: < [kW]

30. Summary table Low WHigh W: ARESHigh W: SC Train length [ns]156312156312156312 Total stored energy [J]0.334683468 Shunt impedance (circuit) [MΩ]364.82.45000025000 Total rf power [MW]>6360.61.2 Total length [m]~10~40 ~10~20 Klystron bandwidth [%]> 1< 0.1 Voltage modulationStrong: Phase + amplitude No, or very small phase Could be stronger No, or very small phase Could be stronger Strong HOM dampingdemonstrated demonstrated in single cell Transverse impedanceHighestLowerLowest Cryogenic power [MW]00~0.2 Main ChallengeVoltage modulation for transient compensation, Low efficiency Big size Low R/Q, Rf design both for fundamental and for HOM All 3 options seems to be feasible but have different issues summarized below φ s reduction helps a lot here