Conceptual design of the CLIC DR RF system at 2 GHz Alexej Grudiev (CERN) 15.09.2010, ALERT2016, Trieste (first time presented at the CLIC meeting, 26.11.2010)

Acknowledgements E. Jensen (CERN) W. Hofle (CERN) K. Akai (KEK)

Outline Introduction High stored energy rf system Normal conducting Superconducting Low stored energy rf system Summary

Introduction 1 GHz option, current baseline since March 2010 DR To first order, in steady-state, the energy spread σE/E will be zero BUT the bunch-to-bunch separation can differ from 0.5 ns due to transient beam loading DL To RTML DR To RTML 2 GHz option Specs from RTML F. Stulle, CLIC meeting, 2010-06-04 Very tight !

Calculated RF parameters CLIC DR RF parameters CLIC DR* NLC DR+ Circumference: C [m] 420.56 223 Bunch population: Ne 4x109 7x109 Energy : E [GeV] 2.86 ~2 Momentum compaction: αp 7.6x10-5 ? Energy loss per turn: U0 [MeV] 4.2 0.635 RF frequency: frf [GHz] 1 2 0.714 RF voltage: Vrf [MV] 4.9 4.6 Calculated RF parameters Harmonic number: h 1402 2804 Synchronous phase : φs [o] 59 66 Energy acceptance: ΔE/E [%] 2.29 1.08 Synchrotron frequency: fs [kHz] 2.76 3.36 *from Yannis on 9/07/2010 + from Tor et.al., PAC95

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

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). Slow RF feedback loop around the klystron is necessary

High stored energy option

Beam loading effect (1/3) 2GHz case 1GHz case Variation of the stored energy and rf voltage due to beam loading (δVC/VC << 1): IB TB TR t VC 1GHz case δVC VA Condition to keep RF voltage variation small in an RF system with constant input rf power:

Beam loading effect (2/3) Variation of the bunch phase due to rf voltage variation (δVC/VC << 1): Im{V} δVB VC δV1 δVC δV2 δφ1 δφ2 φ Re{V} VA

Beam loading effect (3/3) Variation of the bunch length due to rf voltage variation (σE<< ΔE): σZ σE σZ + δσZ

KEKB RF system K. Akai, et. al, “THE LOW-LEVEL RF SYSTEM FOR KEKB”, EPAC98 π/2 - φs dV/V = PbTb(1-Tb/Trev)ρω/V2 ~ 1 % it is consistent with simulation presented in Fig 3 dφb = dV/V*(1/tanφs + tanφs) ~ 3o it is consistent with simulation presented in Fig 3 Dominated by direct cavity voltage phase modulation in KEKB case

THE ARES CAVITY FOR KEKB, Kageyama et al, APAC98 Frequency: f[GHz] 0.509 1 2 Normalized shunt impedance (circuit): ρg=Rg/Q [Ω] (~f0) 7.5 Unloaded Q-factor: Q (~ 1/f1/2) 110000 77000 55000 Aperture radius: r [mm] (~ 1/f) 80 40 20 Max. Gap voltage: Vg [MV] (~ 1/f3/4) Nominal 0.5 0.3 0.18 High power tested times sqrt(3) 0.85 Wall loss per cavity: P=Vg2/2Rg [MW] 0.44 0.22 0.11 Scaling of the gap voltage is done to keep heat load per meter constant: P/g = Vg2/2Rgg = Vg2/2ρgQ g => Vg ~1/f3/4 ~2.5 m

CLIC DR parameters for scaled ARES cavity Specs from RTML F. Stulle, CLIC meeting, 2010-06-04 Circumference: C [m] 420.56 Energy loss per turn: U0 [MeV] 4.2 RF frequency: frf [GHz] 1 2 RF voltage: Vrf [MV] 4.9 4.6 Beam current Ib [A] 0.66 1.3 Train length Tb [ns] 2 x 156 156 Harmonic number: h 1402 2804 Synchronous phase : φs [o] 59 66 Gap voltage: Vg [MV] 0.3 – 0.5 0.18 – 0.3 Wall loss total [MW] 1.2 - 2.1 1.0 - 1.7 Bunch phase spread for scaled ARES cavity: dφb [o] (ρg =7.5 Ω) 0.7 - 0.4 9 – 5.3 Specified bunch phase spread: dφb [o] 0.05 0.1 Assuming parameters of ARES cavity from nominal up to tested (150 - 450 kW) and scaled to 1 or 2 GHz dV/V = -PbTb(1-ntrainsTb/Trev)ρgω/VgV dφb = dV/V(1/tanφs+tanφs) Dominated by cavity voltage modulation

Solution 1: Modification of the scaled ARES cavity ρ=V2/2ω(Wa+Ws); in ARES Ws=10Wa If we keep the size of the storage cavity the same as for 0.509 GHz when going to 1 or 2 GHz: Ws=10Wa*(f/0.509)3 ρ= 1/f3 In addition, Q-factor improves ~sqrt(f) Frequency: f[GHz] 0.509 1 2 Normalized shunt impedance (circuit): ρg=Rg/Q [Ω] (~1/f3) 7.5 0.95 0.12 Unloaded Q-factor: Q (~ f1/2) 110000 156000 220000 Aperture radius: r [mm] (~ 1/f) 80 40 20 Max. Gap voltage: Vg [MV] (~ 1/f5/4) Scaled to keep wall loss per cavity constant 0.85 0.35 0.15 Wall loss per cavity: [MW] 0.44 Scaling of the gap voltage is done to keep heat load per cavity constant: P = Vg2/2Rg = Vg2/2ρgQ => Vg ~1/f5/4 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.

CLIC DR parameters for modified ARES cavity Specs from RTML F. Stulle, CLIC meeting, 2010-06-04 Circumference: C [m] 420.56 Energy loss per turn: U0 [MeV] 4.2 RF frequency: frf [GHz] 1 2 RF voltage: Vrf [MV] 4.9 4.6 Beam current Ib [A] 0.66 1.3 Train length Tb [ns] 2 x 156 156 Harmonic number: h 1402 2804 Synchronous phase : φs [o] 59 66 Gap voltage: Vg [MV] 0.2 – 0.36 0.09 – 0.15 Wall loss total [MW] 3.5 - 6 7.9 - 13.4 Bunch phase spread for modified ARES cavities: dφb [o] 0.1- 0.07 0.28 - 0.17 Specified bunch phase spread: dφb [o] 0.05 0.1 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

Solutions 2: mismatch of rf frequency and bunch frequency RF frequency is close to 2 GHz It is designed in a way that the stored energy is intermediately high, so that the rf voltage variation is kept small to minimize the transient effect to be below the specifications for the bunch length only The remaining variation of the bunch phase is above the specification but it is linear and is compensated by reducing the rf frequency VC VA Trf dTb < Trf

Proposal for conceptual design at 2 GHz based on the ARES-type cavities Fix the value of acceptable bunch length increase from first to the last bunch to δσz /σz = 3% This defines allowed voltage reduction δV/V = -1%, which corresponds to dφb= dV/V (1/tanφs+ tanφs) = 1.5o, φs = 66o To assure this voltage reduction the total normalized shunt impedance: ρ = -dV/V *V2/(PbTb(1-ntrainsTbfrev) 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: Pg [MW] 0.11 Number of cavities N=Wω/QPg 20 Normalized shunt impedance per cavity (circuit): ρg =ρ/N[Ω] 1.25 Gap voltage: Vg = sqrt(Wω2ρg/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: dφb [o] 1.5 Relative rf frequency mismatch: df/f Required for compensation dφb -1.4e-5 Corresponding mean radius position increase: dR=R*df/f [mm] ~0.7

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

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: 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 gaps 50 Gap voltage: Vg [MV] 0.09 Normalized shunt impedance per gap (circuit): ρg [Ω] 0.5 Q-factor at 2K 2e9 Wall loss total [W] at 2K 212 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 gap Frequency: f[GHz] 1.3 1 2 Normalized shunt impedance (circuit): ρg=Rg/Q [Ω] (const) 58 Unloaded Q-factor: Q (~ 1/f2) 5e9 8e9 2e9 Aperture radius: r [mm] (~ 1/f) 35 46 23 Max. gradient in CW: G [MV/m] Scaled to keep gradient constant 14 Max. gap voltage: Vg [MV] 1.6 Stored energy per gap: Vg2/2ρgω [J] 2.7 5.5 0.7

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

Low stored energy option

Scaling of NLC DR RF cavity NLC DR RF cavity parameters CLIC DR RF Frequency: f[GHz] 0.714 2 1 Shunt impedance: Rg [MΩ] (~ 1/√f) 3 1.8 2.5 Unloaded Q-factor: Q0 (~ 1/√f) 25500 15400 21500 Aperture radius: r [mm] (~ 1/f) 31 11 22 Max. Gap voltage: Vg [MV] (~ 1/f3/4) 0.5 0.23 0.39 Wall loss per cavity: Vg2/2Rg [MW] 0.042 0.015 0.03 HOM (σz=3.3mm) Total loss factor: kl [V/pC] (~ f) 1.7 4.76 2.38 Fundamental loss factor: k0l [V/pC] (~ f) 0.26 0.72 0.36 HOM loss factor: k||l [V/pC] 1.1 3.08 1.54 Transverse HOM kick factor: kTt [V/pC/m] (~ f2) 39.4 309 77.3 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 = Vg2/2Rgg = Vg2/2ρgQ g => Vg ~1/f3/4

Cavity parameters Number of cavities: N = Vrf/Vg = 4.6/0.23 = 20 = 10 x 2-cells cavities Gap voltage: Vg = Vrf/N = 4.6/20 = 0.23 MV Total wall losses [MW] : P0 = Vrf2/2NR = 4.62/(2*20*1.8) = 0.29 MW Peak beam SR power [MW]: Pb = U0*Ib = 4.2*1.3 = 5.46 MW Matching condition: Total power lost in the cavities when the beam is in: Pin = Pb + P0 = 5.75 MW Cavity coupling: β = Q0/Qext = Pin/P0 = (Pb+P0)/P0 = 20 External Q-factor: Qext = Q0/β = 15400/20 = 770 Filling time: tf = Ql/f = Qext/(1+1/β)/f = 770/(1+1/20)/2 GHz = 367 ns Klystron bandwidth: ∂f ∂f >> 1/tf = 1 / 367 = 2.7 MHz. AND ∂f >> 1/tgap = 1 / (1402-156) = 0.8 MHz; where tgap – time between the bunch trains RF system total active length: 10 x 1 m = 10 m

Transient beam loading compensation Transient beam loading compensation with infinite bandwidth klystron Amplitude modulation from 1 to 0.55 is necessary (see Vin) Transient beam loading compensation with 0.5% (10 MHz) bandwidth klystron Amplitude modulation from 1 to 0.35 is necessary (see Vin)

Basic layout of 2 GHz rf station 2-cells cavity beam Reflections from the cavities go to the load Circulator Load Klystron 0.6 MW HVPS 80 kV DC Voltage program input 18 kV AC

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

Summary table for “a la linac”-type Overall parameters PC-option Total rf power [MW] >6 >3 Total length [m] 10 5 Number of HVPS Number of klystrons 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

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.

Summary table See more detail in CLIC–Note–879 1 GHz 2 GHz, no train interleaving after DR Classical RF system based on the NC ARES-type cavities Baseline PRF = 3.8 MW; L = 32 m; Cavity design: OK Alternative 2.0 PRF = 5.9 MW; L = 48 m; Cavity design: ok? Classical RF system based on the SCC cavities Alternative 1.1 PRF = 0.6 MW; L = 108 m; Alternative 2.1 PRF = 0.6 MW; L = 800 m; Cavity design: NOT OK RF system with RF frequency mismatch Alternative 1.2 PRF = 1.3 MW; L = 16 m; Alternative 2.2 PRF = 2.1 MW; L = 24 m; “A-la-linac” RF system with strong input power modulations Alternative 1.3 PRF = 3.3 MW; L = 8 m; Alternative 2.3 PRF = 5.8 MW; L = 12 m; Baseline solution is safe Alternative with a RF frequency mismatch is very attractive both at 1 GHz and 2 GHz. Alternative 2.2 certainly can be taken as a baseline at 2 GHz. Why not? See more detail in CLIC–Note–879