Possible size change of LHC as an injector of FCC (HEB)

Possible size change of LHC as an injector of FCC (HEB)

E. Shaposhnikova1.04.2014

Main considerations

• RF frequency and harmonic number• Bunch spacing• Filling of the LHC by the SPS• Filling of the FCC by the LHC

Harmonic number

• Main RF systems: SC 400 MHz and SC 200 MHz under consideration (pile-up, heating, e-cloud, SPS bunch length…). The 200 MHz capture system already exists.

• LHC RF frequency 400.79 MHz & harmonic number h=35640 frf = h * f0 = h βc/CLHC, CLHC = hLrf , where Lrf = βcTrf ;

Lrf = 0.75 m for 400 MHz and Lrf =1.5 m for 200 MHz

=> CLHC = n x 1.5 m

=> minimum ΔCLHC = 1.5 m

Bunch spacing in FCC

• CLHC = nLbb , where Lbb is bunch-to-bunch distance• Possible bunch spacings: 50 ns, 25 ns, 5 ns or 15 m, 7.5 m, 1.5 m • 50 ns spacing: CLHC = 50 ns x Integer = n x 15 m (but 50 ns spacing is not required now)

• 25 ns spacing: CLHC = 25 ns x Integer = n x 7.5 m

=> minimum ΔCLHC = 7.5 m

Minimum change in harmonic number hLHC by Δh=10

=> Possible complications in future LLRF? Diagnostics?Different clocks?

Bunch spacing and harmonic number

• Bunch spacing of 5 ns, 25 ns and 50 ns in SPS, LHC and FCC with the 400 MHz RF system means h = 2x5x2x integer

- additional 125 ns spacing (FHeC?) would require h = 2x5x2x5 x integer (but not possible in injectors)

hLHC = 35640 = 2x5x4x9x9x11

hSPS = 4620x2= 2x5x4x3x7x11

Many different options which change significantly the FCC length1) hFHC = 138600 = 2x5x2x2x7x9x 5x11 => CFCC = 55 CSPS =103.7 km

2) hFHC = 136080 = 2x5x2x2x7x9x9x6 => CFCC = 101.75 km

3) hFHC = 132300 = 2x5x7x9x3x7x10 => CFCC = 98.92 km

4) hFHC = 132930 = 2x5x7x9x211 => C=99.4 km

5) hFHC = 133650 = 2x5x3x5x9x9x11 => CFCC = 100.2 km (N. Mounet)

Harmonic number and ring filling time

Ring synchronisationNow SPS/LHC: hSPS/hLHC =7/27 =>

time for 1 injection to LHC = 7 T0LHC = 27 T0

SPS = 0.6 ms

LHC as HEB of FCC option (2): hLHC/hFHC = 11/ 42

=> time for injection to FCC = 42 T0LHC =3.6 ms

option (5): hLHC/hFHC = 4/ 15

=> time for injection to FCC = 15 T0LHC =1.29 ms


Ring synchronisation: Reduce hlhc by 10 (25 ns spacing) Þ hHEB = 35630 = 2 x 5 x 7 x 509

• hHEB/hSPS = 509/(4x3x11)

=> time for 1 injection to HEB = 509 T0SPS = 11.727 ms

extra filling time of HEB by SPS = 12 x 11.73 ms = 140 ms • hHEB/hFHC = 509/2x2x9x9x6 (option 2) Þ time for 1 injection to FCC = 1944 T0

LHC = 172.76 ms =0.17 s


Ring synchronisation: Increase hlhc by 10 (25 ns spacing) Þ hHEB = 35650 = 2 x 5 x 5 x 713

• hHEB/hSPS = 3565/924


extra filling time of HEB by SPS = 12 x 82.1 ms = 986 ms ~ 1s• hHEB/hFHC = 713/3x9x9x11 (option 5) Þ time for 1 injection to FCC = 2673 T0

LHC = 237.54 ms Þ extra filling time of FCC by HEB = 4 (?) x 0.238 s ~ 1 s


Ring synchronisation: Reduce hlhc by 2 (5 ns spacing) Þ hHEB = 35638 = 2 x 17819

• hHEB/hSPS = 17819/2310


extra filling time of HEB by SPS = 12 x 410.5 ms = 4.93 s • hHEB/hFHC = 17819/68040 (option 2) Þ time for 1 injection to FCC = 68040 T0

LHC = 6.05 s

Similar for increase of hlhc by 2: hHEB = 35642 = 2 x 17821 => hHEB/hSPS = 17821/2310 and hHEB/hFHC = 17821/68040

Choice of RF parameters

RF considerations for FHCfrom FCC meeting on 23.01

Input data: Table 1 from FCC-ACC-SPC-0001 EDMS N 1342402

• Ring parameters:– Circumference: ~99.7 km– Energy loss per turn @50 TeV: U0=4.6 MeV

– Transition energy: γt=120 (Frank Z.)

• Beam parameters:– Bunch spacing(s): 5 ns, 25 ns – Bunch length during physics: 8 cm– Bunch intensity: 1.x1011

Criteria used

• Filling of the RF bucket • maximum momentum filling factor of 0.8 (losses)• minimum filling factor is also important for stability

– threshold ImZ/n ~ (filling factor)5/2 (for φs = π)

• Single bunch longitudinal stability • Threshold for the loss of Landau damping• Longitudinal impedance budget (inductive part ImZ/n) => assumed to be similar to the LHC ImZ/n = 0.1 Ohm (calculated and measured).Factor 2 is taken as a margin (formfactor for particle distribution,…)

RF frequency

• 5 ns spacing => n x 200 MHz => 200, 400, 800,… MHz with bucket length = 5, 2.5, 1.25 ns

• Bucket length in the presence of synchrotron radiation is reduced by Δφ ~ 2(πU0/V)1/2

• Bunch length of 8 cm => τ4σ = 1.07 ns (Table 1 )

=> 200 MHz or 400 MHz

400 MHz RF

Loss of Landau damping Filling factor in momentum

400 MHz or 200 MHz?Longitudinal emittance 400 MHz RF

Bunch length and stability 200 MHz RF

200 MHz RF

Loss of Landau damping Filling factor in momentum

Additional considerations:ring size and harmonic number

• 400.79 MHz and bunch spacings of 5 ns, 25 nshLHC = 35640 = 2x5x4x9x9x11

hSPS = 4620x2= 2x5x4x3x7x11

hFHC = 132930 = 2x5x7x9x211 => C=99.4 km

• For rings synchronisation: hSPS/hLHC =7/27 => 7 Trev (LHC)

hLHC/hFHC = 9x48/(7x211) => Tsync is 211 times longer

hSPS/hFHC = 4x3x11/(9x211) => 132 Trev FCC

=> replace 211 by 216=12x18 (C=101.75 km)?? Or 204?For spacing of 125 ns (FHeC): 211=> 5x(4x11?) => 5% longer ring (103.7 km) or 0.5% shorter for 210=5x2x3x7

Summary400 MHz• The RF system similar to the LHC (frf=400.8 MHz with Vmax=16 MV/beam) is able to provide

at 50 TeV bunches with length of 8 cm (rms) for emittance of 7.0 eVs (2 σ). In this case bucket area is 13.1eVs (qp= 0.77) and ImZ/n for the loss of Landau damping is 0.2 Ohm.

• With Vmax=16 MV injected emittance (at 1.7 TeV) should be less than 3 eVs.• Due to the synchrotron radiation damping a controlled longitudinal emittance blow-up (by

band-limited RF phase noise) will be required not only during the acceleration ramp but also in the coast.

200 MHz • The 200 MHz RF system has certain advantages, however the design of the SC version

doesn't yet exist. • In this RF system for short bunch lengths the longitudinal beam stability will be at the limit

and with RF voltage of 10 MV can be recovered (same margin as for in the 400 MHz RF) only for bunches longer than 12 cm (rms).

• Another possibility to stabilise the beam is to use a double harmonic RF system (the 400 MHz RF system in addition).

Documents

Possible size change of LHC as an injector of FCC (HEB)