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

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

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

4. 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,
Very tight !

5. 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

6. 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* = 2*10-4
filter
3 phases main
12 phases – 600 Hz ripples 4% f t t
600 Hz
-40 dB

7. 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

8. High stored energy option

9. 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:

10. 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

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

12. 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

13. 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

14. CLIC DR parameters for scaled ARES cavity
Specs from RTML
F. Stulle, CLIC meeting,
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]
Bunch phase spread for scaled ARES cavity: dφb [o] (ρg =7.5 Ω)
9 – 5.3
Specified bunch phase spread: dφb [o]
0.05
0.1
Assuming parameters of ARES cavity from nominal up to tested ( 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

15. 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 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.

16. CLIC DR parameters for modified ARES cavity
Specs from RTML
F. Stulle, CLIC meeting,
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]
Bunch phase spread for modified ARES cavities: dφb [o]
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

17. 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

18. 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

19. 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

20. 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
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

21. 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

22. Low stored energy option

23. 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: Q (~ 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

24. 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/ = 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 = * = 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)/P = 20
External Q-factor: Qext = Q0/β = 15400/ = 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 / ( ) = 0.8 MHz; where tgap – time between the bunch trains
RF system total active length: 10 x 1 m = 10 m

25. 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)

26. 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

27. 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

28. 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

29. Klystron bandwidth
NLC DR RF system:
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 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
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 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.

30. 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