1. Evaluation of 1GHz vs 2GHz RF frequency in the damping rings
Yannis PAPAPHILIPPOU and Alexej Grudiev
April 16th, 2010

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 3

4. New DR parameters
Parameter
1GHz
2 GHz
Circumference [m]
420.56*
Harmonic number
1402
2805
Energy Loss/turn [MeV]
4.20
Damping times [ms]
(1.88,1.91,0.96)
Number of wigglers 52
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]
4.9/59
4.4/73
Momentum compaction factor
7.6 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]
0.66/0.145
1.3/0.145
Peak/Average power [MW]
2.8/0.6
5.5/0.6
Kicker rise / revolution time [ns]
545/1403
1246/1403
* The ring circumference was shortened after relaxing longitudinal parameters in order to reduce space-charge
** Using Bane approximation. Piwinski theory gives (400,4.5,5400) 4

5. Scaling of NLC DR RF cavity
NLC DR RF cavity parameters
CLIC DR RF
Frequency: f[GHz]
0.714 2 1
Shunt impedance: R [MΩ]
(~ 1/√f) 3
1.8
2.5
Unloaded Q-factor: Q0
25500
15400
21500
Aperture radius: r [mm]
(~ 1/f) 31 11 22
Max. Gap voltage: Vg [kV]
500
180
360
Gradient: [MV/m] G ~ Vg/4r 4
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.,

6. Impedance estimate in DR, PDR
Calculated RF cavity parameters HOM
NLC DR
CLIC DR
CLIC PDR
Frequency: f[GHz]
0.714 1 2
Number of cavities: N = Vrf/Vg
2 (3) 16 20 56
Total HOM loss factor: k||l * N [V/pC]
2.2
24.6
61.6
86.2
172.5
Long. HOM energy loss per turn per bunch [μJ]:
ΔU = k||l * N * eNe2
2.8 10 25 35 71
Incoherent long. HOM loss power [kW]:
P||incoh= ΔU * Nbf/h
5.6
8.5 17
Coherent long. HOM loss power [kW]:
P||coh~ P||incoh*QHOM *f/fHOM
(if the mode frequency fHOM is a harmonic of 2 GHz)
Careful Design of HOM damping is needed
Total HOM kick factor: kTt * N [V/pC/m]
78.8
1240
6160
4330
17250
Tran. HOM energy loss per turn per bunch [μJ]:
ΔU = kTt * 2πf/c * N * eNe2 * d2
(d – orbit deviation , 10mm assumed)
0.15
1.1
10.5
3.7
29.6
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) 7

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 H2O+ 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 are not compatible with the 1GHz train structure and need to be re-worked in order to prevent the luminosity reduction 8

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
α-delay line
Ω-delay line
RF deflector
RF deflector
RF Deflector / kicker 9

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 10

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 11

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 Nx=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 σjit ≤0.1σx 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 RF system @ 1 vs 2GHz 1 GHz 2 GHz
Beam loading
1 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 (see next slide). Never been demonstrated before. Higher risk. More studies are needed.
Very interesting
RF power
Roughly 2 times more power
More efficient
Size
Roughly 2 times longer
2 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)
HOM
Roughly 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

14. Summary 1GHz 2GHz 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 to be reworked

15. Recommendation
The 1GHz frequency in the damping rings is easing beam dynamics in the CLIC DR and drives the RF system to more conventional parameters
The added complication of the train interleaving regarding the RF deflector jitter does not seem a show-stopper as:
A conceptual design of the delay loop has been already worked and will be further refined for the CDR
Typically the RF deflector power source in CTF3 have shown stability of around 10-3
The jitter in beam position can be further studied in CTF3 and measurements can back up this choice for the CLIC CDR
The parameters for have to be reworked to be compatible with the 1GHz frequency
It is recommended thus to choose as baseline in the CLIC DR an RF frequency of 1GHz
A conceptual design for the 2GHz RF system has to be undertaken in parallel as a back-up solution