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Evaluation of 1GHz vs 2GHz RF

frequency in the damping rings

Yannis PAPAPHILIPPOU and Alexej Grudiev

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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.

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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

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New DR parameters

Parameter DR @ 1GHz

DR @ 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

** Using Bane approximation. Piwinski theory gives (400,4.5,5400)

* The ring circumference was shortened after relaxing longitudinal parameters in order to reduce space-charge

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

Scaling of NLC DR RF cavity 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 (~ 1/√f)

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 4 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]

(~ f) 1.1 3.08 1.54

Transverse HOM kick factor: kT

t [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.,

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

Impedance estimate in DR, Impedance estimate in DR, PDRPDR

Calculated RF cavity parameters HOM NLC DR CLIC DR CLIC PDR Frequency: f[GHz] 0.714 1 2 1 2Number of cavities: N = Vrf/Vg 2 (3) 16 20 56 56Total HOM loss factor: k||

l * N [V/pC] 2.2 24.6 61.6 86.2 172.5Long. 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/h2 2.2 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 = kT

t * 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

C L I CC L I CDamping 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)

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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 CLIC@1TeV are not compatible with the 1GHz train structure and need to be re-worked in order to prevent the luminosity reduction

C L I CC L I CDelay 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

Ω-delay lineα-delay line

RF deflector

RF Deflector / kicker

RF deflector

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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

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2ϕ1 −ϕ 2 = 0

C L I CC L I CDelay 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

C L I CC L I CRF 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

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xsep ≥ Nxσ x + Dx

δp

p+ δxrms + dsep

C L I CC L I C1 or 2 GHz, pros and cons

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. 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

RF system @ 1 vs 2GHz

C L I CC L I CSummary

1GHz 2GHzLarger 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 CLIC@1TeV to be reworked

C L I CC L I CConclusions

The choice of 1 or 2GHz is not critical for beam dynamics in the damping rings apart from transient beam loading (some marginal improvement at 1GHz exists)

There is an added complication of train interleaving @ 1GHZ, especially regarding the RF deflector jitter

The parameters for CLIC@1TeV have to be reworked to be compatible with the 1GHz frequency

Frequency choice impacts mostly RF technology and although 1GHz is closer to existing designs (but still not straightforward), RF experts have recommended to focus on 2GHz

A conceptual design for 2GHz RF system will be presented at IWLC2010