for the Rings of a Neutrino Factory

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15 Νοε 2013 (πριν από 4 χρόνια και 8 μήνες)

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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 &

trains n = 5

Pulse repetition frequency F = 50 Hz

20 GeV

ring circumference C


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.


currents & inductive wall fields



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


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


trains injected in one ring &

in other).

Reactive loading changes as each train is added.

p/p =


inc. to

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.


, the peak current in the bunch, scales as 1 / (FnT)

V, the inductive wall volts/turn, scales as

C / (FnT

Z/m (FFAG chamber walls,
) may be large

5 j

If T=

ns in an 8
20 GeV, FFAG muon accelerator &

n=1, F=15, C= 400 m: I
= 180A, V =



n=5, F=15, C= 400 m: I
= 36 A, V =



n=5, F=50, C=1000 m: I
= 4.5 A, V =



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

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
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
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 (
) mm rad.

Full aperture kickers need low transverse impedance.

Use adjacent, shorted,10

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


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

+ 50 Hz boosters + 2, 25 Hz RCS

180 MeV H

+ 50 Hz booster + 1, 50 Hz NFFAGI


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,
ˉ injection into first FFAG looks difficult.


The change to n =5, F = 50 & C =1000 m, suggested

at the NuFact 05 workshop, is mainly advantageous,

except for


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