RF Power Generation and PETS Design I. Syratchev

Fixed input parameters for the CLIC 12 GHz PETS design: - Power production: Power/WDS = 76 MW WDS length (physical)=0.246 m Power limit/PETS ~ WDS ? Drive beam frequency = 12 GHz (first harmonic) Module layout: Quad + BPM length = 0.35 m PETS specific: Extractor length = 0.075 m Drive beam energy < 2.5 GeV Beam stability: Quad spacing  1 m PETS slotted configuration bring ~ 30% Wu enchantment. About 10% can be played back with optimizing the iris profile Module layouts #1 #2 #3 Unit length, m 1.0 Drive beam, GeV 2.25 Drive beam , A 93 Aperture, mm 15.7 23 30.8 Length, m 0.10 23 56.4 Power/PETS,MW 79 160 317 Wu/WDS (slotted) 0.46 1.0 1.37 Wt (norm./23mm) 3.1 1.0 0.42 Qt (norm./23 mm) 1.65 1.0 0.8 Layout #2 is the best compromise in terms of power production, beam stability and cost Module layouts #1 #2 #3

23 mm 12 GHz PETS base line RF design PETS parameters: Aperture = 23 mm Period = 6.253 mm (900/cell) Iris thickness = 2 mm R/Q = 2258 Ω V group= 0.453 Q = 7200 E surf. (160 MW)= 61 MV/m H surf. (160 MW) = 0.1 MA/m (ΔT max (140 ns, Cu) = 2.0 C0)

Power production efficiency In a structure with a high group velocity, the tail of the single bunch get the stronger deceleration. This effect can be compensated with a slight detuning of the structure synchronous mode frequency (Daniel). In general: the longer the structure and shorter the bunch, the less detuning detuning reduces beam stability ΔF, MHz Eff., % E0, GeV I,A 0 85.9 2.259 97.43 125 84 2.361 95.32 Note: this method was developed for the ancient 30 GHz CLIC PETS with ~ 80% Vg and provided efficiency recuperation about 7%

GDFIDL/HFSS/Wake model/PLACET: PETS Transverse wake Wake expression for the structure with high group velocity. Structure length – Ls. PLACET Loads Beta=0.702 C F=14.707 GHz Q=285 Kt=0.89 HFSS data Moderate damping Wt, V/pC/m/mm (log) Reflected wave |Ez| |E| Wake (single mode model) Wake (GDFIDL) Distance, m (log) Wt vs. aperture Heavy damping No damping EH Transverse wakes spectra, GDFIDL Moderate damping 23 mm 16 mm In a presence of the damping slots, the two competing transverse modes appear. The optimal balance between them should be found to provide stable beam transportation. Re (Zt) V/A/m/mm (log) 30 mm HE 12 Frequency, GHz Frequency, GHz

First and second harmonic, detuning and beam stability. For the given aperture and chosen method of damping, the wake amplitude and Q-factor can be estimated quite accurately. The draft PLCET simulations (W,Q f(Freq)) for the transverse frequency scan, Wake amplitude and Q scaling where done using layout #2. Drive beam frequency 12 GHz Drive beam frequency 6 GHz 84.% 80.1% 85.9% 86.1% For the CLIC PETS operating at a first harmonic the situation with the beam stability is rather critical (no safe margins) because of the natural frequency of the dominant transverse mode ~ 15 GHz. The detuning make the situation even worse and should be seriously discussed. The same time, operating at the second harmonic, the bunches sit close to the wake zero crossing providing a good stability

The control of the transverse modes frequencies and damping #1. Phase advance Radial #3. Damping slot configuration Inclined Iris 2.0 mm 900 1200 Impedance Impedance Frequency, GHz Flat #2. Iris thickness 3.5 mm 2.0 mm Phase/cell 1200 Impedance Frequency, GHz Wake integral at the punches center position Wt Frequency, GHz The lower phase advances and thinner irises favor the beam stability The damping slot configuration can be used for the fine tuning of the dangerous modes balance Distance, m Bunch number

GDFIDL & 9 modes model PETS with radial slots Beam envelope along decelerator simulated with PLACET (9 modes). Erik Adli Initial beam offset ~ Without detuning Q nominal Q nominal x 1.5 Frequency, GHz Q nominal x 1.5 With detuning Distance, m Q nominal Wt Q F

Further study towards 12 GHz CLIC PETS Power production: Optimization of the iris profile to reduce the surface peak power plow. Beam stability: Low frequencies HOM. Optimization of the damping slots and loads configuration. High frequencies HOM. Frequency detuning if necessary (phase advance). ON/OF capability: Integration of the detuning wedges. Minimization of their impact on the beam stability. Conclusion: Unit layout with 2 WDS/PETS and 2 PETS/ Quad is recommended as a baseline for configuration 12 GHz CLIC. Unit length 1.0 m, girder length 2.0 m. The PETS with 23 mm aperture, 900 phase advance per cell and iris thickness 2 mm is considered.