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Proton / Muon Bunch Numbers, Repetition Rate, RF and Kicker Systems and Inductive Wall Fields for the Rings of a Neutrino Factory. G H Rees, RAL. Parameters Suggested at NuFact 05. 4 MW, proton driver energy T = 10 GeV No. of p bunches & μ ± trains n = 5

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## G H Rees, RAL

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**Proton / Muon Bunch Numbers, Repetition Rate, RF and Kicker**Systems and Inductive Wall Fields for the Rings of a Neutrino Factory G H Rees, RAL**Parameters Suggested at NuFact 05**4 MW, proton driver energy T = 10 GeV No. of p bunches & μ± trains n = 5 Pulse repetition frequency F = 50 Hz 20 GeV μ± ring circumference C ≈ 1000 Increase in products, (nF, nFC) x ≈ 17, 41 Previously: n = 1, F = 15, C ≈ 400, T = 8-26 GeV Why? Bunch compression & Muon beam loading**Reasons behind Suggested Changes**• Allows adiab. p-bunch comp. to 1 ns rms at 10 GeV • Lower peak & av. μ±currents & inductive wall fields • μ±beam loading compensation becomes feasible • Lower costs for the RF systems despite higher F • Injection and ejection systems are much easier • Lower reactive cavity loading in μ±storage rings • Thermal shock effects less in high power pion target (But, there is increased muon decay in acceleration)**Parameters for an 8-20 GeV Muon Ring**Peak power needed to compensate the fundamental beam loading is reduced from ~2000 MW to ~48 MW. If just stored energy limits the voltage drop in former, the muon output energies will be intensity dependent. If n = 5 only is changed, and just one bunch train is in ring at any time, the ~2000 MW reduces to ~400 MW.**Number of RF Systems for 8-20 GeV Ring**Muons are in the ring for five times as long if n = 5. Without BLC, all 5 trains will vary in output energy. Assuming 2 x 1 MW couplers per cavity system, the number of systems for compensation reduces from: N = 200 (for 400 MW) to 24 for (48 MW) Power for cavity switch-on depends on both N and F. Large C (same tunnel) also used for a 3.2-8 GeV ring.**Parameters for the 20 GeV Storage Rings**The number of muons per ring changes by n/2 (n, μ+ trains injected in one ring & n, μ-in other). Reactive loading changes as each train is added. If Δp/p = ± 0.019, Δφ inc. to ±90º,88 MV needed. Cavities on tune & reactive beam compensation. Reflected power is dissipated in circulator loads. 24 cavities per ring for 47 MW at 15 Hz 7 cavities per ring for 14 MW at 50 Hz**Inductive Wall Effects**T is the time duration (sec) of a (parabolic) bunch. Ib , the peak current in the bunch, scales as 1 / (FnT) V, the inductive wall volts/turn, scales as ± C / (FnT2) Z/m (FFAG chamber walls, Ω) may be large ≈ 5 j If T=⅓ ns in an 8-20 GeV, FFAG muon accelerator & n=1, F=15, C= 400 m: Ib = 180A, V = ± 2.3 MV n=5, F=15, C= 400 m: Ib = 36 A, V = ± 0.5 MV n=5, F=50, C=1000 m: Ib = 4.5 A, V = ± 0.3 MV**Effect of Z/m on Longitudinal Motion**Estimates are for volts/turn at bunch extremities. Easy to scale for other (T, Z/m) than (⅓ ns, 5j Ω). Focusing largest near crest of the accelerating field. Field effects ~10% for n = 1, F = 15 & C = 400 m. Longitudinal cooling would increase the effects. Effects have been neglected in the studies to date, but need to be included in the ring tracking codes. For IFFAGs, partial φ-shift compensation is possible or a higher harmonic RF system may be introduced.**Effects on Injection and Ejection Kickers**1 km ring, ~5 m long straights, ~3 μs kicker rise times: Two 2m,~12 kA kickers,~ 50 kV PFN/system/beam (8) (Cryostat end geometry will affect these parameters.) Kickers for 400 m ring would be a major design issue. Kickers for decay rings become too complex if n > 5 or if C < 1170 m, or for beam emittance > 30 (π) mm rad. Full aperture kickers need low transverse impedance. Use adjacent, shorted,10 Ω delay line, push-pull units.**Proton Driver Considerations**Favoured energy range for muon yields is 5-10 GeV (possibly higher), and favoured F range is 15-50 Hz. Adiabatic bunch compression to 1ns rms in the driver for these ranges is best with n = 5 at 10 GeV, 50 Hz. This is because of long. & transv. space charge limits in the RCS booster ring(s) after 180 MeV Hˉ injection. Another advantage is that longitudinal space charge and inductive wall fields approxim. cancel at 10 GeV. RAL rule of thumb for MW beam lines 10 M£/100 m.**10 GeV, 50 Hz Proton Driver Options**180 MeV Hˉ linac+ 50 Hz boosters + 2, 25 Hz RCS 180 MeV Hˉ linac+ 50 Hz booster + 1, 50 Hz NFFAGI Hˉ linac + 50 Hz FFAG + 50 Hz FFAG + 50 Hz FFAG 8 GeV linac + accumulator + compressor is not listed as it seems incompatible with the muon bunch trains. The cost of the proton driver must be around ~ 2 B$ A slower cycling RCS requires more difficult boosters. An electron model is required for the NFFAGI option. In option 3, Hˉ injection into first FFAG looks difficult.**Summary**The change to n =5, F = 50 & C =1000 m, suggested at the NuFact 05 workshop, is mainly advantageous, except for μ± decay losses and storage ring kickers. Lower peak, average currents & inductive wall fields Fewer RF cavities for beam loading compensation The beam loading compensation becomes feasible Easier injection & ejection in the muon accelerators Space for loss collimators in the muon accelerators Less holding time of intense beams in proton driver Feasible driver at 10 GeV, instead of higher energy

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