STATUS REPORT ON STUDIES FOR NEUTRINO FACTORIES AND
MUON COLLIDER
A.M. Lombardi, CERN, Geneva, Switzerland

Abstract
The physical and technical issues will be summarised
and the results from theoretical studies and experimental
activities presented. Possible R&D programmes towards
the realisation of Neutrino Factories and Muon Colliders
will be discussed.

1 INTRODUCTION
The physics interest in neutrino oscillations calls for asource that produces a neutrino beam with a known
flavour composition [1]. Only a machine delivering ahigh flux of single-sign muons can achieve thiscondition. Another important parameter for the neutrino
physics is the energy (minimum 20 GeV, the higher the
better) and the divergence of the muon beam that
produces useful neutrinos (neutrinos flying towards thedetector). The divergence should not exceed the value of
0.1γ (where γ is the relativistic parameter) in order tomaximise the flux at the detector. The number of muons
needed for getting results in a reasonable time isestimated at around 1021 muons/year. The minimum formaking the Neutrino Factory worthwhile is some 1019
muons/year (entry-level Neutrino Factory).
The physics interest for Muon Colliders comes fromthe high energy achievable (absence of bremstrahlung)and the precise energy calibration and thus theopportunity of a precision study of new particles. In
addition, the direct channel Higgs physics makes a µ+µcollider a new frontier Higgs factory [2]. The request on
the muon beam for a Muon Collider is extremely
challenging: some 1021 muons in a 6D emittance of 10-10
m3 at energies up to several TeV.
Muon and neutrino beams with the above-mentioned
qualities are beyond the limit of conventional sources [1]and studies for new dedicated machines are currently
pursued world-wide.

2

phase-space density is increased (phase rotation andcooling). For Neutrino Factories the needed phase-spacecompression is a factor 20 whereas for a Muon Collider afactor 106 is requested. This item is one of the maindifferences between the two facilities.
The muons are accelerated with a linear accelerator to
2 GeV before being injected in a series of re-circulatorsthat bring the beam to the final energy (around 50 GeV
for a Neutrino Factory and up to several TeV for a Muon
Collider). Finally, in a Neutrino Factory the muons are
injected in a decay ring, with straight sections pointing
towards the detectors, where they decay into neutrinos; inthe case of a collider the muons are injected in a collider
ring.
The main challenges for the machine design are theneed of rapid acceleration due to the short muon lifetime,
the need for cooling the beam, and the huge emittanceinvolved.

2.1 Proton Drivers
The proton driver is the first element in the chain ofacceleration for a Neutrino Factory/Muon Collider.
The proton driver must produce a beam suitable for the
production of pions, i.e. a beam with a minimum energyof 1 GeV. The choice of the energy is influenced byseveral factors, amongst which site-dependentconsiderations and “historical” reasons play a big role.
The pion production rate (in a range of pion energy
between 50 and 450 MeV) is weakly dependent on theincoming proton energy as it can be seen in Fig. 1.
However, the number of pions produced is directly
proportional to the power on target. The standardisation
adopted at Nufact99 [3] normalised all Neutrino Factory
designs to 4 MW of beam power.

MACHINE COMPONENTS

The general mechanism for production of highintensity and high-energy muon beams is as follows. A
proton beam bombards a target where pions are produced
and collected in the forward direction. The pion energy
spectrum is peaked around 150 MeV (almost
independently of the energy of the proton beam). Pionsdecay into muons. Muons are captured using a RF
system, their energy spread is reduced, their transverse

Fig. 1: Pion production rate vs incoming proton energy(30 cm long mercury target-FLUKA results).

The proton time structure on target is sketched in Fig.
2. First, the distance between macro-bunches should be
longer than the muon lifetime: this is to assure that abunch of muons has completely decayed before a new one
is injected in the decay ring (this is to avoid stacking in
the ring). Secondly, the length of the macro-pulse should
be such that it fits in the smaller of the rings, again to
avoid stacking. Then comes the internal structure of themacro-pulse: the number of micro-bunches must be
matched to the pion-muon front-end. If the front-end
uses RF cavities [4], the number of micro-bunches/bunchis basically a free parameter whereas the use of an
induction linac [5,6] imposes a reduced number of microbunches/bunch. For a Muon Collider a small number ofbunches is preferred. Finally the length of each micropulse should be of the order of a few ns (very critical fora RF front-end, less critical for an induction linac) tominimise the pion (muon) longitudinal emittance. In
fact, the resulting minimum muon longitudinal emittanceis given by the energy spread at the production and thetime jitters during pion decay (few ns).
Fig. 2: Time structure of the proton beam for a
Lring/c≥µ lifetime

1 ns

Neutrino Factory.
Existing machines around the world which deliver
protons suitable for pion production have an available
power of 0.1-0.2 MW, i.e. more than an order ofmagnitude below what is required. Ways to improve thepresent performance are to increase the number ofprotons per bunch and their energy, and to increase therepetition rate. All these solutions run into limits, inparticular because of space charge, radiation, and thelimit on the magnet cycling rate.
Several new machines have been proposed which candeliver very high-power proton beam. These machines,
generally conceived as drivers for spallation neutron
sources, could very well serve the needs of a Neutrino
Factory/Muon Collider. There are pros and cons between
designing a new machine and upgrading an old one andthe terms of the trade-off are highlighted in Ref. [7].
The two main choices of driver are either a low energy
linac (CERN 2 GeV) followed by an accumulator, or ahigh-energy synchrotron (FNAL 16 GeV, BNL 30 GeV,
Japan 50 GeV). The trade-off between high energy andcycling rate influences the power consumption in themuon part of the accelerator: a slower cycling rate ismore favourable for limiting the power consumption. The

results of a study [8] suggests the optimum balance at 15
GeV, 12.5 Hz.

2.2 Target and transverse capture
The target is a very delicate part of a Neutrino
Factory/Muon Collider: optimising the pion production
within a limited phase-space volume is a difficult task
due to the nature of the production mechanism (nuclear
interaction of the incoming proton with the target
material).
Important parameters in the target design are thechoice of the geometry and material, the type of focusing,but engineering and radiation issues must also be taken
into account.
The choice of the target geometry and target material
strongly influence the production rate: the pions areproduced inside the target and must traverse it to emerge
to the surface. The production itself would be enhanced
in a long target but pions would have a smaller chance toreach the surface due to the higher re-absorption
probability. The optimum choice appears to be a target ofabout two interaction lengths. The choice of the materialis critical: mercury presents the highest cross section forpion production, but it is difficult to handle whereas
carbon presents a production rate of almost a factor two
smaller for a proton energy above 10 GeV. The
advantage of mercury is that it can be made into a jet,thus allowing for a new target at each proton shot. R&D
is going on at CERN and BNL on the interaction of astatic liquid mercury target with a proton beam and the
behaviour of a mercury jet in a high field solenoid. Pion
production cross sections at different energies (2-16
GeV) will be measured by HARP [9]. The results of theseexperiments will provide fundamental design input to a
Neutrino Factory/Muon Collider.
Pions come out of the target almost isotropically,hence the target itself must be immersed in a focusing
system in order to have a significant collection ofparticles in the forward direction. Two types of focusing
system have been considered and studied: a magnetic
horn and a solenoid.
The magnetic horn (Fig. 3) is a system where current
flows in the axial direction along a conductor thus
generating a toroidal field that bends the particles which
traverse the horn surface. Changing the design of thesurface influences the horn focusing. As it can be seen in
Fig. 3 the horn is the best focusing system for point-liketargets, due to the point-to-parallel type of focusing it
provides. The advantage of the horn is that it can beradiation-hardened. The technical problem with the hornis the high current requested (300 kA for the CERN
design) together with a high pulsing rate (about 50 Hz).
With a careful design of the horn it is estimated that arepetition rate of 50 Hz could be achieved [10] with aloss in acceptance with respect to an ideal horn of 40%.
R&D is continuing at CERN to go beyond this limit.

Presently, the solution of choice for pion capture is ahigh-field solenoid (20 T). The solenoidal field is thenadiabatically tapered down to values of a few T, value
typically used to confine the pions to a radius of some 30
cm along the decay channel. The design of special coils,
which can tolerate radiation as well as leave the space forthe mercury trough is under way at MIT.

Fig. 3: Sketch of a magnetic horn, showing the target
position and a few rays

implies the use of high-gradient RF cavities in a highradiation area. For example the PJK scenario [12] calls
for cavities at 30-90 MHz, 5 MV/m at few meters fromthe target. R&D on the behaviour of cavities in highradiation areas has been started [13] and so far the
results are positive. Other efforts are planned at BNL.
Another approach is to allow most of the pions to decay(this requires a drift of tens of metres) before the muons
enter a RF cavity with moderate gradients. This approach
does not enhance polarisation and has a lower efficiency
than the first one but it does not call for high gradientcavities in a high-radiation area. Frequencies of the orderof the tens of MHz are needed, due to the length of themuon beam after decay. The CERN reference scenario[4] has adopted this approach, and phase rotation isaccomplished with 30 cavities at 44 MHz with a gradientof 2 MV/m. R&D is needed also for this approach:cavities at 44 MHz exist [14] but with a considerably
smaller bore radius than required. As well as the RF
design, some clever engineering solution must be foundto fit a solenoid around the beam pipe. A preliminary
proposal is shown in Fig 5. As it can be seen from thesketch it would be quite cumbersome to fit a solenoid
around an object of more than 2 m diameter.

With these systems, a yield of few percent pion/proton
GeV in the phase space acceptable by the subsequent
accelerator can be produced.
Another interesting possibility , at the moment studied
only theoretically, is a pulsed target. In this case, current
would run through the target itself thus confining thepions immediately at production. This system would
provide the same number of pions in a smaller phasespace [11].

2.3 Preparing the muons for acceleration:phase rotation and cooling
After production the pions occupy a phase spacevolume that is much bigger than the acceptance of any
conventional accelerator. A typical phase space portrait
at production is shown in Fig. 4. In particular the energy
spread of the pions is quite large and only a small
percentage of them are within a few percent. The energy
spread will further increase during the decay process(jitter of 50 MeV). In order to keep the longitudinal
structure of the beam, it is necessary to reduce its energy
spread by applying a time-dependent electric field todecelerate faster particles and accelerate slower particles.
This operation is commonly called "phase rotation".
There are nonetheless three approaches to phase rotation,and their difference relies on the degree of time-energy
correlation that is allowed in the beam.
A first approach consists in applying a RF electricfield to the pions just after the target. This allows the full
benefit of the defined time structure of the pions, andenhances polarisation of the resulting muon beam, but it

Fig. 4: Pion longitudinal phase space at production(FLUKA , 26 mm mercury target, 2.2 GeV beam)

Fig. 5: Preliminary design of a 44 MHz cavity forphase rotation

Fig. 6: Muon longitudinal phase space during phaserotation using an induction linac (from [5])A third approach is to allow the pions to decay and let
the muons drift for some hundreds of meters in order tobuild up a strong correlation between time and energy
and then match the energy spread with a quasi-dc device(e.g. an induction linac). This method is very effective
for reducing the energy spread (Fig. 6), but the drawback
is the resulting pulse length at the end of the process(order of µs): re-bunching is required, and the efficiency
using careful adiabatic processes is of the order of 60%.
Special attention should be paid to minimising distortion
caused by relativistic effects. For this purpose a
combination of three induction linacs and a hydrogen
absorber has been chosen as reference for the feasibility
study II [6]. Existing induction linacs do not yet meet therequirements assumed in the study and some R&D wasstarted during feasibility study I [5].
Phase rotation is not needed if a large acceptancemachine like an FFAG is used for the first stage ofacceleration after the target [15].
Cooling, i.e. the increase of phase space density, is thenext operation needed before accelerating the muons.
Cooling is needed in the neutrino factory as well as in the
Muon Collider but to a different degree. To increase thenumber of neutrinos arriving at the detector, thedivergence of the muon beam in the straight section
should be 10 times smaller than the opening of the conein which the neutrinos are emitted (1/γ). This condition
imposes a divergence of 0.2 mrad on a 50 GeV muon
beam. In order to have muon beams with a reasonableradius, the useful muons must fit in an acceptance of
0.015 m⋅rad (normalised). There is no physics limitation
to longitudinal emittance in a Neutrino Factory but thelongitudinal acceptance of the RF system used foracceleration: this value ranges from 0.15 to 0.3 m,
depending on the frequency. The overall 6D acceptanceturns out to be 5×10-5 m3. In a Muon Collider, however,the necessary luminosity at the interaction point imposesa limit on the 6D emittance at 10-10 m3. The difference
between the two cases is dramatic: assuming a 4 MW

beam on target a cooling factor of 20 is needed for the
Neutrino Factory whereas a factor of 106 is needed in the
Muon Collider scenario. Additionally, for the Neutrino
Factory longitudinal cooling can be an asset but is notneeded, whereas it is imperative for a muon collider.
It is envisaged to cool the beam transversally byionisation cooling, although other types of cooling (e.g.
frictional [16]) are being considered. The principle ofionisation cooling is as follows: the muon beam traverses
a material (absorber) and loses energy (by ionisation)
along the direction of motion. Then energy is restored in
the longitudinal direction by re-acceleration. This
process results in a net reduction of the transverse
velocity, i.e. in an increased transverse phase-spacedensity. When traversing the absorber, the muons also
scatter off the nucleii thus increasing their transverse
velocity (heating). A cooling cell is thus a system where
the overall effect of these competing mechanisms is areduction of the transverse velocity. Fig. 7 shows thethree processes. The energy loss as a function of energy
is given by the Bethe-Bloch formula and the r.m.s.
scattering angle by the Moliere theory. From theexpression in Fig. 7 the choice of a low-Z material (i.e.
higher radiation length) is clear: liquid hydrogen is thematerial proposed in all designs. Liquid hydrogen vessel
tests will be shortly performed at FNAL. The amount ofcooling per cell depends strongly on the energy loss/gain
per cell. Basically it depends on the energy that the RF
cavity is able to restore (as the absorber can in principle
be made as long as needed). This has been calculated inseveral theoretical studies [17,18]. The emittance
reduction is a few percent in each fundamental coolingcell, and a cooling channel using several tens of cells
must be used for a Neutrino Factory. The cooling canideally be applied till the divergence of the muon beamreaches the limit of the divergence that the beam acquires
due to multiple scattering (equilibrium emittance).
The choice of frequency is fundamental for the designof a cooling channel: the first condition is that the beam
must stay bunched all along the channel. This condition
favours the choice of lower frequencies, for the broader
acceptance of energy spread. Another competingargument is the cooling rate (emittance reduction/metre):
the higher the gradient the better, which argues in favourof a higher frequency. But the transverse dimension of
the cavity is inversely proportional to the frequency. A
trade-off is thus necessary, and the present proposals are
the following: either use low frequency cavities (below
100 MHz) and accept higher energy spread and a slower
cooling rate, or use high-frequency cavities (above
100 MHz) closed with beryllium windows. The
advantage of the latter choice is a faster cooling rate, but
the disadvantage is the scattering in the windows (whose
thickness should be minimised). Tests on beryllium
windows are documented in Ref. [19].

θ0 =13.6 MeVβ ⋅c ⋅ p( )zz
1 + 0.0038 ⋅ ln
X0
X0

z= distance travelled in the absorber
X0 = radiation lengthp = particle momentum

Fig. 7: The ionisation cooling principle (top), the energy loss in different material as function of muon momentum(bottom left) and the r.m.s. scattering angle (bottom right)
The study of the focusing is of great importance in thedesign of a cooling channel. The magnetic field must
keep the beam confined, but it should also provide a
waist in the middle of the absorber whenever the multiple
scattering becomes important (a high-divergence beam
will be less spoiled by scattering). Ionisation cooling is asystem that reduces the divergence of the beam, leaving
the transverse dimension almost unchanged. It is thennecessary periodically to trade divergence with positionin order to be able to continue cooling. This is achievedby a strong radial component as, for example, generated
by two adjacent solenoids with opposite polarity (Fig. 8)

Fig. 8: Single particle dynamics during rematching(field-flip)

Longitudinal cooling cannot be performed directly ona muon beam: the mechanism is to create a dispersion inorder to exchange longitudinal and transverse emittanceand then use ionisation cooling to reduce the transverse
emittance. Several mechanisms to perform the exchange
are under study, amongst which are a bent solenoid
system, an RF cavity and a wedge absorber [20].
The ionisation cooling principle has never been
applied and although there is the general agreement thatthe "ingredients" (Bethe-Bloch energy curve, Moliere
scattering theory and electromagnetic fields) are wellunderstood, nevertheless the community feels the needfor a cooling experiment. The results should not be a
proof-of-principle but a demonstration that the coolingcell works in less than ideal conditions (e.g. non-perfectsolenoidal and RF field). The purpose of the experimentshould be to demonstrate that cooling can be achieved
and that the mechanisms influencing the delicate
equilibrium of cooling-heating are completely mastered.
The results of an ideal cooling experiment should look
like Fig. 9. There is agreement that a cooling experimentshould be a small section of the final cooling channel.
Debate is still open on the precision of the measurement
needed to extrapolate from a few stages to several coolingstages. Another debate is open on the necessary
diagnostics: a few cooling stages reduce the emittance byonly a few percent and a single particle measurement
device seems to be the preferred diagnostics for suchsmall effect [21]. Cooling experiments have been
proposed in the US [22] and are under study at CERN.

Fig. 9: Emittance out vs emittance in: results from an
ideal ionisation cooling experiment

2.4 Muon acceleration
After phase rotation and cooling the muon beam isready to be accelerated to the final energy of 50 GeV(Neutrino Factory) or higher (70-100 GeV for Higgs
Factory, several TeV for a high-energy Frontier
Collider). Due to the finite muon lifetime, theacceleration must be rapid.
The first stage of acceleration (from 300 MeV to few
GeV) is done with a linac, generally at the same
frequency as the cooling channel. A solenoidal focusing
system is necessary till at least 1 GeV if low frequencies
are used. Only from that energy a quadrupolar focusing
can be used. At an energy of a few GeV the beam is
injected into a multi-pass accelerator like a Recirculating

Linac (RLA) or a Fixed Field Alternating Gradient(FFAG). There are two possible set-ups for the RLA: theso-called “dogbone” where the beam is recirculated
through the same linac and at each pass is re-injected in
the linac via a fixed-field separate path, and the“racetrack” where there are two parallel linacs connectedby semicircular arcs. The arcs for a racetrack system all
fit in the same tunnel, contrary to the "dogbone" system,and tunnel cost is the main reason (together with easierlongitudinal dynamics) for the choice of the "racetrack"[4,5,12].
Only a few (4) passes are possible through an RLA due
to the difficulty of separating large beams in the arcs.
After a few turns (at energies of ∼10-20 GeV) the beam
is injected in a second RLA where the final energy for a
Neutrino Factory is reached. The RLAs are the biggest
component of a Neutrino Factory, as shown in Figs. 10(CERN scenario RLAs at 352 MHz, 7 MV/m) and 11(Feasibility study I RLAs at 200/400 MHz, 15 MV/m).
In order to limit power consumption superconducting
cavities are used in the RLAs. R&D on 200 MHz superconducting cavities is going on at Cornell and at CERN.
The main issues are the maximum achievable gradientand the behaviour in pulsed mode. A Rapid Cycling
Synchrotron (RCS) [23,16] performs acceleration beyond
70 GeV.
A completely different scheme based on FFAG is
proposed in Japan [15]. The beam produced from a 50
GeV proton beam on the target is directly accelerated by
4 FFAGs. The large transverse and longitudinal
acceptance of these machines allows for avoiding, at leastin a first stage, both phase rotation as well as cooling.

Figure 10: Layout of the CERN reference scenario for a Neutrino factory.

Figure 11: Layout of the Feasibilit study I scenario for a Neutrino factory

2.5 Muon storage rings
After acceleration to the final energy muons are
injected into the storage ring where they decay into
neutrinos. The optimisation of the storage ring geometry,
together with the choice of the detector locations
determines the number of neutrinos which reach them.
The discussion on the detector location goes beyond thescope of this paper. The consensus amongst neutrino
physicists seems to be for two detectors at about 1000 and3000 km from the neutrino source. The storage ringshould then contain two straight sections pointing
towards the detectors. The length of the straight sections
should be maximised. Two main geometries have been
considered: the triangular and the bow-tie. The choice ofthe geometry is strongly site-dependent due to different
geodesic constraints. The main issue in the storage ringis the heat deposition from the decay electrons:
measurements to deal with this problem have beenenvisaged [5, 4].

2.6 Muon colliders
The design of the ring where µ+ and µ- beams interact
at collision points depends on the final beam energy.
Designs have been proposed for different energies[23,16]. The fundamental issue is the low-beta-functionneeded at the interaction points. The beams are spacecharge dominated giving rise to coherent instabilities,
although only instabilities with a growth rate comparable
to the muon lifetime can be destructive.

4 CONCLUSIONSThe effort towards the feasibility and the constructionof a Neutrino Factory and Muon Collider is spread overthree continents and involves many people. The need fortheoretical studies and R&D is important and the task isbeing shared amongst all the laboratories involved.
The most important R&D issues for the feasibility ofsuch machines are the target area and the coolingchannel.

5 ACKNOWLEDGEMENTS
The work reported in this paper is an attempt tosummarise the effort on Neutrino Factories and Muon
Colliders. Many people have kindly provided me withmaterial and information: to all of them go my thanks.

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