1. Evaluation of 1GHz vs 2GHz RF frequency in the damping rings Yannis PAPAPHILIPPOU and Alexej Grudiev

2. Background Baseline: RF frequency of 2GHz, 1 train of 312 bunches spaced by 0.5ns produced and transmitted along injector complex and DRs. But: Power source and RF design needs R&D (high-peak power, short train, transient beam loading) Alternative solution: RF frequency of 1GHz with 2 trains of 156 bunches and bunch spacing of 1ns, separated by half the damping ring circumference minus the length of a train A delay line with an RF deflector is needed downstream of the DRs for recombining the two trains and providing the nominal 2GHz bunch structure.

3. 1 vs. 2GHz in the PDR Larger bunch spacing (1 vs. 0.5 nm) halves harmonic number (1326 vs. 2581), and increases momentum acceptance by 40% (1.7 vs. 1.2%), thereby making the capture efficiency of the positron beam even better For keeping the same momentum acceptance, the RF voltage can be reduced (~10 vs. 6.8MV) All the rest of the parameter changes are the same as for the damping rings

4. New DR parameters ParameterDR @ 1GHz DR @ 2 GHz Circumference [m]420.56* Harmonic number14022805 Energy Loss/turn [MeV]4.20 Damping times [ms](1.88,1.91,0.96) Number of wigglers52 0-current emittances [nm,nm,eVm](280,3.7,4400) 0-current mom. spread/bunch length [%/mm]0.11/1.4 RF Voltage/Stat. phase [MV/deg]4.9/594.4/73 Momentum compaction factor7.6 x 10 -5 Steady state emittances [nm,nm,eVm](480,4.5,5960)** St. state mom. spread/bunch length [%/mm]0.13/1.6 Space charge tune-shift-(0.006,0.12) Peak/Average current [A]0.66/0.1451.3/0.145 Peak/Average power [MW]2.8/0.65.5/0.6 Kicker rise / revolution time [ns]545/14031246/1403 ** Using Bane approximation. Piwinski theory gives (400,4.5,5400) * The ring circumference was shortened after relaxing longitudinal parameters in order to reduce space- charge

5. 9 July 2010 Alexej Grudiev, CLIC DR RF for CDR. Scaling of NLC DR RF cavity NLC DR RF cavity parametersCLIC DR RF Frequency: f[GHz]0.71421 Shunt impedance: R [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 [kV]500180360 Gradient: [MV/m] G ~ V g /4r444 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.,

6. 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)162056 Total HOM loss factor: k || l * N [V/pC]2.224.661.686.2172.5 Long. HOM energy loss per turn per bunch [μJ]: ΔU = k || l * N * eN e 2 2.810253571 Incoherent long. HOM loss power [kW]: P || incoh = ΔU * N b f/h 22.25.68.517 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]78.812406160433017250 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) 0.151.110.53.729.6 Tran. HOM loss power is not an issue: < [kW] The transverse impedance for the 1GHz RF system is 5 times lower than for the 2GHz one The longitudinal impedance is 2.5 times lower

7. Damping rings (I) In the DRs, the harmonic number reduction, raises the equilibrium longitudinal emittance (bunch length). In order to keep it to the same level (IBS effect), the RF voltage should be increased reducing stationary phase (RF bucket becomes more linear). For shorter ring (space charge reduction), stationary phase gets increased (quite big for 2GHz), i.e. voltage should be increased and momentum compaction factor reduced (relaxing arc cell focusing) Extraction kicker rise time becomes smaller but it is still long enough (~550ns). This might eliminate the possibility to use IGBT switches. The 2-train structure may require two separate extraction kicker systems (two pulses of equal size and flat top of 160ns as in the present case) or one kicker with a longer flat top (1μs). RF frequency of 1GHz is closer to existing high-power CW klystron systems used in storage rings or designed for NLC damping rings (714MHz). An extrapolation of this design should be straightforward. Larger bunch spacing reduces peak current and power by a factor of 2 (beam loading reduction)

8. Damping rings (II) The e-cloud production and instability is reduced with the larger bunch spacing. In the e - rings, the fast ion instability will be less pronounced due to the larger bunch spacing by doubling the critical mass above which particles get trapped (not allowing the trapping of H 2 O + and probably CO + ). The reduced number of bunches per train will reduce the central ion density, the induced tune-shift and will double the rise time of the instability, thus relaxing the feedback system requirements. A bunch-by-bunch feedback system is more conventional at 1 than at 2 GHz The parameters corresponding to CLIC@1TeV are not compatible with the 1GHz train structure and need to be re-worked in order to prevent the luminosity reduction

9. Delay line layout Two configurations: an α-shape (as in CTF3) or an Ω-shape In the α-shape the same RF deflector can be used for both injection and extraction (maybe also jitter feedback), whereas the Ω-shape should use 2RF deflectors or a kicker and RF deflector Ω-delay line α-delay line RF deflector RF Deflector / kicker RF deflector

10. Delay line layout II The α-shape has a circumference equal to half the damping ring length (~210m) It can be inserted in between the damping rings in order to be used for both electrons and positrons with a delay of ~1DR revolution time The Ω-shape is larger by the length of the (straight) line between the injection and the extraction point It can be divided in 3 arcs with opposite bending angle satisfying the relationship There is a geometrical relationship imposed to the length of the straight line depending on the bending angles and the arcs radii The optics can be tuned to be isochronous for not perturbing the longitudinal beam characteristics

11. Delay line impact Delay line does not contribute to emittance growth due to incoherent or coherent synchrotron radiation due to low energy and relatively short length Any systematic trajectory errors corrected by orbit correctors and proper choice of optics functions and phase advances. The systematic energy loss will be roughly half of the damping rings (~same energy and bending radius), i.e. 500keV, which is around 0.16% of energy difference. Corrected with RF cavities of a few hundred kV. Can be used for timing jitter feedback if special optics used. Main issue: stability of RF deflector for keeping (horizontal) emittance growth small (<10% of the beam size). Experience with the CTF3 RF deflectors instrumental for determining and achieving the requested tolerances

12. RF deflector stability The angular deflection of the kicker is defined as Large beta functions and π/2 phase advance necessary for minimizing kicks Injected beam position at the septum Typically, injection is dispersion free Number of injected beam sizes set to N x =6-10 The thickness of the septum cannot be smaller than 2-3mm Kicker jitter produces a beam displacement transmitted up to the IP. Typically a tolerance of σ jit ≤0.1σ x is needed Translated in a relative deflection stability requirement as As beam size is around 10 -5 m, position at the septum dominated by septum thickness The tolerance remains typically a few 10 -3 (more relaxed for larger beam sizes and lower septum thickness) Maybe a double RF deflector system can further relax the tolerance

13. 1 or 2 GHz, pros and cons 1 GHz2 GHz Beam loading1 GHz rf system based on over-moded cavities with bigger stored energy can be used to solve the problem in conventional way (has been done before: LEP, KEK-B) Completely different concept must be used. Never been demonstrated before. Higher risk. More studies are needed. Very interesting RF powerRoughly 2 times more powerMore efficient SizeRoughly 2 times longer2 X Shorter (probably can be done even more compact because average cavity wall loss is 4 times lower, if yes it has also impact on HOM power loss) HOMRoughly 3 times lower HOM power loss (incoherent) Higher HOM power loss Rf power source IOTs can be used. There are even R&D on L-band solid state rf system… Only klystrons RF system @ 1 vs 2GHz

14. Summary 1GHz2GHz Larger momentum acceptance in the PDR Simpler RF system (including LLRF for beam loading compensation) RF system (power source and beam loading) very challenging (feasibility item according to ACE) Two stream instability effects reduction Simpler feedback system Delay line for train recombination (cost) RF deflector jitter tolerance (CTF3 tests) Parameters for CLIC@1TeV to be reworked

15. Conclusions The choice of 1 or 2GHz is not critical for beam dynamics in the damping rings apart from transient beam loading (some marginal improvement at 1GHz exists) There is an added complication of train interleaving @ 1GHZ, especially regarding the RF deflector jitter The parameters for CLIC@1TeV have to be reworked to be compatible with the 1GHz frequency Frequency choice impacts mostly RF technology and although 1GHz is closer to existing designs (but still not straightforward), RF experts have recommended to focus on 2GHz A conceptual design for 2GHz RF system will be presented at IWLC2010