# Presentation: 719400

## 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 **Δ**p/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. *
*I**b** , the peak current in the bunch, scales as 1 / (FnT)*
*V, the inductive wall volts/turn, scales as **± **C / (FnT**2**)*
*Z/m (FFAG chamber walls, **Ω**) may be large  **≈** 5 j *
*If T=**1⁄3** ns in an 8-20 GeV, FFAG muon accelerator & *
*   **n=1, F=15, C= 400 m:       I**b **= 180A,  V = **± 2.3** MV *
*   **n=5, F=15, C= 400 m:       I**b **=  36 A,  V = **± 0.5** MV  *
*   **n=5, F=50, C=1000 m:      I**b **= 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 (1⁄3 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 **μ**s 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 H**ˉ** 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 H**ˉ **linac** **+ 50 Hz boosters + 2, 25 Hz RCS*
*180 MeV H**ˉ **linac** **+ 50 Hz booster + 1, 50 Hz NFFAGI*
*H**ˉ** 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, **H**ˉ 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*