26 Nov. 2010 Alexej Grudiev, CLIC DR RF system at 2 GHz. Conceptual design of the CLIC DR RF system...

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26 Nov. 2010Alexej Grudiev, CLIC DR RF system at 2 GHz.

Conceptual design of theCLIC DR RF system at 2 GHz

Alexej Grudiev

26.11.2010CLIC meeting

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Acknowledgements

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

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Outline

Introduction High stored energy rf system

Normal conducting Superconducting

Low stored energy rf system Summary

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Introduction

1 GHz option, current baseline since March 2010

DR

DLTo RTML

DR

To RTML

2 GHz option

Specs from RTML F. Stulle, CLIC meeting, 2010-06-04

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

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CLIC DR RF parameters

E

Veh

Rp

Veh

V

U

h

EVe

h

EVeE

EE

srfp

rev

srfrevs

rf

s

p

rfrf

sss

2

cosˆ

2

cosˆ

ˆsin

ˆ2ˆ2

sin)2(cos

1

0

1

2

0

0

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 1

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

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9 March. 2010Alexej Grudiev, CLIC DR RF.

CW klystron power supply

LEP klystron power supply

3 phases main 12 phases – 600 Hz ripples

4%

filter

t t

f

600 Hz-40 dB

Filter reduce 600 Hz ripples down to

0.04*0.0045 = 2*10-

4

Feedback stabilizes high voltage at lower frequencies to the level of 1-0.1%. Limited mainly by the HV measurement accuracy

Information provided by D. Siemaszko

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Klystron amplitude and phase stability

Beam voltage ~60 kVLow 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 stabilityOr~ 1.2 degree phase stability

This is not sufficient (see RTML specs). Rf slow feedback loop around the klystron is necessary

High stored energy option

Beam cavity interaction, dV/V << 1V = Vrf + Vb = V*ejφ

dV = dVb*sinφs

Vdφ = dVb*cosφs

rf phase modulation versus rf amplitude modulation:

dφ = dV/(V*tanφs)

Vb

dVb

dVb

Vrf

V

φs

dφ

V

t

Energy los per turn: V0 = V sinφs

Beam cavity interaction, dV/V << 1

Trev tTb

Ib

2GHz case 1GHz case

Trev tTb

V 2GHz case

dV

Trev tTb

φb2GHz case

dφb

W = V2/2ρω; dW = dV 2V/ρωdW/dt = -Pb + ntrains*Tb/Trev*Pb ; dt -> Tb

dV/V = -PbTb(1-ntrainsTb/Trev)ρω/V2

dφ = dV/V*1/tanφs

dφs

V

φ

V0

V0 = V sinφs = energy loss per turn = const; dV0 = dV sinφs + Vcosφs dφs = 0dφs = - dV/V*tanφs

dφb = dφ+dφs = dV/V*(1/tanφs- tanφs)

dφ

KEKB RF systemK. Akai, et. al, “THE LOW-LEVEL RF SYSTEM FOR KEKB”, EPAC98

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

π/2 - φs

THE ARES CAVITY FOR KEKB, Kageyama et al, APAC98Frequency: f[GHz] 0.509 1 2

Normalized shunt impedance (circuit): ρg=Rg/Q [Ω] (~f0)

7.5 7.5 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

Max. Gap voltage: Vg [MV] (~ 1/f3/4)High power tested times sqrt(3)

0.85 0.5 0.3

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 = Vg

2/2Rgg = Vg2/2ρgQ g => Vg ~1/f3/4

~2.5 m

CLIC DR parameters for scaled ARES cavity

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



Gap voltage: Vg [MV] 0.3 – 0.5 0.18 – 0.3

Wall loss total [MW] 1.2 - 2.1 1.0 - 1.7

Bunch phase spread for scaled ARES cavity: dφb [o] (ρg =7.5 Ω)

0.7 - 0.4 9 – 5.3

Specified bunch phase spread: dφb [o] 0.05 0.1

dV/V = -PbTb(1-ntrainsTb/Trev)ρgω/VgV

dφb = dV/V(1/tanφs-tanφs)

Specs from RTMLF. Stulle, CLIC meeting, 2010-06-04

Assuming parameters of ARES cavity from nominal up to tested (150 - 450 kW) and scaled to 1 or 2 GHz

Dominated by cavity voltage modulation

Solution 1: Modification of the scaled ARES cavity

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


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 0.44 0.44

ρ=V2/2ω(Wa+Ws); in ARES Ws=10Wa

If we keep the size of the storage cavity the same as for 0.509 GHz when going to 1 or 2 GHz: Ws=10Wa*(f/0.509)3

ρ= 1/f3

In addition, Q-factor improves ~sqrt(f)

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.

Scaling of the gap voltage is done to keep heat load per cavity constant: P = Vg

2/2Rg = Vg2/2ρgQ => Vg ~1/f5/4

CLIC DR parameters for modified ARES cavity

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



Gap voltage: Vg [MV] 0.2 – 0.36 0.09 – 0.15

Wall loss total [MW] 3.5 - 6 7.9 - 13.4

Bunch phase spread for modified ARES cavities: dφb [o]

0.1- 0.07 0.28 - 0.17

Specified bunch phase spread: dφb [o] 0.05 0.1

Specs from RTMLF. Stulle, CLIC meeting, 2010-06-04

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

BUT the associated voltage reduction δV/V results in bucket reduction and consequently in bunch parameters modification. Radiation damping keeps σE=const for all bunches in the train so the bunch length varies along the train. The limit from RTML is that RMS{δσz /σz} < 1%

Solution 2: Mismatch of rf frequency and bunch frequency In the presence of linear phase shift of dφb over a period of time Tb : fb = frf - dφb/2πTb; To compensate dφb= dV/V (1/tanφs- tanφs) = 1.5o at 2 GHz, δV/V = -1%, φs=66o, dfrf/frf = -1.4e-5, very small

ΔE/Δz = σE/σz => ΔE σz = Δz σE Variation gives δΔE σz + ΔE δσz = δΔz σE+ Δz δσE

Which results in δσz /σz = δΔz/Δz – δΔE/ΔEσz

σE Δz

ΔE2 ~ V(cosφs+(φs-π/2)sinφs)δΔE/ΔE = ½[δV/V+δφs/(tanφs +1/(φs-π/2))]δφs=- δV/V tanφs

δΔE/ΔE = ½δV/V[1-1/(1+1/(tanφs(φs-π/2)))]δV/V = -1%, φs=66o => δΔE/ΔE = -8.5%

Image from H. Damerau, PhD Thesis, 2005

φs=73o

Δφ ~ (φs-π/2)δΔφ/Δφ = δφs/(φs-π/2)δφs= -δV/V tanφs

δΔφ/Δφ = -δV/V tanφs/(φs-π/2)δV/V = -1%, φs=66o => δΔz/Δz=δΔφ/Δφ = -5.4%δσz /σz = δΔz/Δz – δΔE/ΔE = -5.4% + 8.5% = 3.1% (peak-to-peak)

ΔE

Proposal for conceptual design at 2 GHz based on the ARES-type cavities

1. Fix the value of acceptable bunch length increase from first to the last bunch to δσz /σz = 3%

2. This defines allowed voltage reduction δV/V = -1%, which corresponds to dφb= dV/V (1/tanφs- tanφs) = 1.5o, φs = 66o

3. 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/fRequired for compensation dφb

-1.4e-5

Corresponding mean radius position increase: dR=R*df/f [mm]

~0.7

RF station layout ARES type cavities

beam

Reflections from the cavities go to the load

Load

HVPS

18 kV AC

Klystron0.3 MW

Voltage program input

Storage cavity

Circulator

Storage cavity

Superconducting RF optionMaking ARES-type cavity superconducting is probably possible but certainly

beyond the present state-of-the-art in SC RF technologyElliptical cavity is an option but it has relatively high normalized shunt

impedance. Let’s consider TESLA-like cell:


Normalized shunt impedance (circuit): ρg=Rg/Q [Ω] (const)

58 58 58

Unloaded Q-factor: Q (~ 1/f2) 5e9 8e9 2e9


Max. gradient in CW: G [MV/m] Scaled to keep gradient constant

14 14 14

Max. gap voltage: Vg [MV] 1.6 2 1

Stored energy per gap: Vg2/2ρgω [J] 2.7 5.5 0.7

gap

Image and pars from PhysRevSTAB.3.092001 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

RF station layout for SC cavities

beam


Load

PS

18 kV AC

Klystron or IOT

60 kW


Circulator

Low stored energy option

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Scaling of NLC DR RF cavity

NLC DR RF cavity parameters CLIC DR RF


Shunt impedance: Rg [MΩ] (~ 1/√f)

3 1.8 2.5

Unloaded Q-factor: Q0 (~ 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]

(~ f) 1.1 3.08 1.54

Transverse HOM kick factor: kTt

[V/pC/m] (~ f2) 39.4 309 77.3

From PAC 2001, ChicagoAN RF CAVITY FOR THE NLC DAMPING RINGSR.A. Rimmer, et al., LBNL, Berkeley, CA 94720, USA

From PAC 1995,Collective effects in the NLC DR designsT. Raubenheimer, et al.,

Scaling of the gap voltage is done to keep heat load per meter constant: P/g = Vg

2/2Rgg = Vg2/2ρgQ g => Vg

~1/f3/4

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Cavity parameters

Number of cavities: N = Vrf/Vg = 4.6/0.23 = 20 = 10 x 2-cells cavities

Gap voltage: Vg = Vrf/N = 4.6/20 = 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 = 4.2*1.3 = 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)/P0 = 20

External Q-factor: Qext = Q0/β = 15400/20 = 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 / (1402-156) = 0.8 MHz; where tgap – time between the bunch trains

RF system total active length: 10 x 1 m = 10 m

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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)

0 1000 2000 3000 4000 5000 6000 7000 8000 90000

0.2

0.4

0.6

0.8

1

1.2

1.4

rev

/2

V/V

in; /

Ib

Vin

Vout

Vrf

Vb

0 1000 2000 3000 4000 5000 6000 7000 8000 90000

0.2

0.4

0.6

0.8

1

1.2

1.4

rev

/2

V/V

in; /

Ib

Vin

Vout

Vrf

Vb

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Basic layout of 2 GHz rf station

2-cells cavity

beam

Load

HVPS

18 kV AC

80 kV DCKlystro

n0.6

MW

Circulator


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beam


Alternative layout for 2 GHz rf station DR

4-cell cavity

Load

HVPS

18 kV AC

80 kV DCKlystro

n0.6

MW


Pulse

Compressor

Alternative layout doubles peak power for a pulse of ~600 ns

0 2000 4000 6000 8000 10000 12000 14000 16000 180000

0.5

1

1.5

2

2.5

3

rev

/2

V/V

in; /

V

in

Vout

Circulator

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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 10 5

Number of klystrons 10 5

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

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Klystron bandwidth

NLC DR RF system:http://www-project.slac.stanford.edu/lc/local/Reviews/cd1%20nov98/RF%20HighPwr_Schwarz.pdfKlystron• 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 20 - 30 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

http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=01476034

A BROADBAND 500 KW CW KLYSTRON AT S-BAND, Robert H. Giebeler and Jerry Nishida, Varian Associates, Palo Alto, Calif. 1969klystron 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 1967. 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.

http://www-project.slac.stanford.edu/lc/local/Reviews/cd1%20nov98/RF%20HighPwr_Schwarz.pdf

http://www-project.slac.stanford.edu/lc/local/Reviews/cd1%20nov98/RF%20HighPwr_Schwarz.pdf

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9 July 2010Alexej Grudiev, CLIC DR RF for CDR.

Impedance estimate in DR, PDR

Calculated RF cavity parameters HOM NLC DR CLIC DR CLIC PDR

Frequency: f[GHz] 0.714 1 2 1 2

Number of cavities: N = Vrf/Vg 2 (3) 16 20 40 48

Total HOM loss factor: k||l * N [V/pC] 2.2 24.6 61.6 61.6 148

Long. HOM energy loss per turn per bunch [μJ]: ΔU = k||

l * N * eNe2

2.8 10 25 32 77

Incoherent long. HOM loss power [kW]: P||

incoh= ΔU * Nbf/h2 2.2 5.6 7.7 19

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 3100

14800

Tran. HOM energy loss per turn per bunch [μJ]: ΔU = kT

t * 2πf/c * N * eNe2 * d2

(d – orbit deviation , 10mm assumed)

0.15 1.1 10.5 3.3 32

Tran. HOM loss power is not an issue: < [kW]

Summary tableLow W High W: ARES High W: SC

Train length [ns] 156 312 156 312 156 312

Total stored energy [J] 0.3 34 68 34 68

Shunt impedance (circuit) [MΩ] 36 4.8 2.4 50000 25000

Total rf power [MW] >6 3 6 0.6 1.2

Total length [m] ~10 ~40 ~40 ~10 ~20

Klystron bandwidth [%] > 1 < 0.1 < 0.1

Voltage modulation Strong:Phase + amplitude

No, or very small phase

Could be stronger

No, or very small phase

Could be stronger

Strong HOM damping demonstrated demonstrated demonstrated in single cell

Transverse impedance Highest Lower Lowest

Cryogenic power [MW] 0 0 ~0.2

Main Challenge Voltage modulation for transient

compensation,Low efficiency

Low efficiency Big size

Low R/Q,Rf design both for

fundamental and for HOM

All 3 options seems to be feasible but have different issues summarized below

φs reduction helps a lot here

26 Nov. 2010 Alexej Grudiev, CLIC DR RF system at 2 GHz. Conceptual design of the CLIC DR RF system...

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