1. RF Power Generation and PETS Design
I. Syratchev

2. 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 = 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 # # #3
Unit length, m
Drive beam, GeV
Drive beam , A
Aperture, mm
Length, m
Power/PETS,MW
Wu/WDS (slotted)
Wt (norm./23mm)
Qt (norm./23 mm)
Layout #2 is the best compromise in terms of power production, beam stability and cost
Module layouts #1 #2 #3

3. 23 mm 12 GHz PETS base line RF design
PETS parameters:
Aperture = 23 mm
Period = 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)

4. 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
Note: this method was developed for the ancient 30 GHz CLIC PETS with ~ 80% Vg and provided efficiency recuperation about 7%

5. 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= 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

6. 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

7. 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

8. 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

9. 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.