Machine aspects for the ECFA report

Bruno Autin

Global layout

The size and shape of a muon complex are dominated by the fast acceleration needed to increase the muon life time in the laboratory. It has also to comply with the various peculiarities of an existing site. These constrainst will first be reviewed and the integration of the various machines will then be described qualitatively. More technical aspects will be discussed in sections 2.2, 3.1 and 4.2.

Muon life-time

The muon life-time at rest is 2.2 ms and its decay length (D) 660 m. High energy collisions may nevertheless be contemplated because of the dilation of the lifetime in the laboratory by the Lorentz factor g. When the acceleration is linear and characterized by a gradient g', expressed as a function of the energy gradient dE/ds and of the rest energy E0 by


the evolution of the number of particles N with the distance s is determined by the differential equation


whose solution is


Typical parameters for the acceleration of muons from 250 MeV to 2.5 TeV are
dE/ds = 1 MeV/m
particle loss = 75%
acceleration length = 2500 km
acceleration time: 8 ms.

The variation of the particle loss with the distance is shown in Figure 1. It is at the beginning of the acceleration that the losses are the most severe. This makes the first stages (momentum spread reduction, cooling) particularly critical.

Figure 1: Surviving muons at distance s.

Site considerations

The presence on the CERN site of the largest machine in the world makes very tempting, at least in a first analysis, to use the SPS and LHC tunnels for accommodating the accelerators which drive the muons to their top energy. It has also to be noted that the American study envisages circular accelerators to attain the final energy. Up to the Higgs factory energy, a linear structure prevails whether it is made of pure linacs or of re-circulators. The line has to point towards the Gran Sasso laboratory where the next generation of neutrino experiments is foreseen to take place in Europe. Moreover, a linear proton driver is the machine which has the best yield in terms of pions per watt and the lowest losses for high intensity beams. This linac would also have other important applications: radio-active beams (ISOLDE), neutron spallation in conjunction with the present booster synchrotron and accelerator driven systems (ADS) such as an energy amplifier or a nuclear waste burner. For these reasons, the proton linac should be in the neighborhood of the CERN Proton Synchrotron.


The general layout shown in Figure 1 illustrates the three-step scenario. Its first part is stretched along a line which is approximately at the border of the Meyrin and Prevessin sites and oriented towards the Gran Sasso laboratory. It starts with a 1 km proton linac. The proton beam bombards a target from which pions and muons are collected in the transverse phase plane by a powerful focusing system and in the longitudinal phase plane by a linac which reduces the energy spread of the beam without changing the mean energy. The beam is then pre-accelerated (n factory) or cooled (colliders) before entering a re-circulator whose shape recalls the one of a "neck-tie". The muons are accelerated along a 500 m linac which provides 5 GeV at each passage and are sent back to the linac in arcs located at both ends. Each arc has a fixed field and there is thus one arc per energy increment. After the forth arc (20 GeV), the beam is deflected towards a storage ring in which the muons decay along the two long straight sections and emit the two flavor (e and m) neutrino beam towards the detector. In the collider mode, the beams remain longer in the re-circulator to reach the maximum energy of 50 GeV at the end of tenth passage in the linac and is directed to the "Higgs factory" which roughly occupies the location of an eleventh arc at the north-west end of the re-circulator near the SPS. From the Higgs factory, the beams are ejected into a fast accelerator located in the SPS tunnel up to an energy of 400 GeV, then to a second fast accelerator in the LHC tunnel up to 2.5 TeV and finally stored in a large muon collider where they can achieve about 1000 collisions at a center of mass energy of 5 TeV. Other experiments can be envisaged on the way to the highest energy such as an intermediate collider to study the A boson or deep inelastic scattering using high energy neutrinos.


Figure 2: A muon complex on the CERN site.

Special features of a neutrino factory

Neutrinos impose less constraints to the beam than the colliders and are thus an ideal first step in a muon complex. The time structure is arbitrary and, at least for first experiments, one charge is sufficient. With a primary beam of protons, it is the p+ and therefore the m+ which is produced in greater abundance. The whole design is greatly dependent on a study of super-conducting proton linac using LEP cavities [1]. This study has been oriented towards the injection of very bright beams into LHC but can be adapted to a different regime pertinent to neutrinos.

In that case, the linac works continuously and takes full advantage of the superconducting cavities. The bunches are 24 ps long and spaced by 1 m (3 ns). The maximum current is 10 mA; in other terms, the proton flux is 6 10 16 p/s and the beam power is 20 MW for a proton energy of 2 GeV. These parameters, although quite uncommon in present machines, are rather typical of the new accelerator driven systems (ADS) contemplated for hybrid reactors or new neutron spallation sources.

The next step is to make a target which can stand the deposited energy over a long enough period. This is a subject of research and development of top priority. The model which can be investigated at the beginning is inspired of existing technology (NGS beam) where the target is segmented into disks. Moreover, it is important not to dilute the phase-space beam density DE-Dt at least in the time dimension. The length of a disk must then be about equal to the bunch length, here 8 mm and the disk spacing equal to the bunch spacing (1 m). As 20 cm of matter is near the optimum distance for p production, the target length would be 24 m. Over such a distance, the beams have to be focused. The definition of the beam sizes can be sketched. The proton and pion beams have different momenta: 2.8 GeV/c for protons against .25 GeV/c typically for pions. The focusing channel is then designed for the low energy beam and it can consist of a solenoid of a few Tesla or, better, of a series of FODO cells which are likely to improve the distribution of collected particles in the transverse phase space as already discussed for the antiprotons in the context of a long single piece target. Preliminary calculations show that 1.4 m FODO periods made of 20 cm long quadrupoles with field gradients slightly smaller than 10 T/m would confine the pion beam within a radius of 10 cm and with a normalized emittance of 7 10-3 m. Such an emittance is consistent with the acceptance of the CERN antiproton collector and validates the feasibility of the optics of the neutrino factory. It is also the emittance adopted for PILAC, a study of pion linac performed at Los Alamos [2].

The choice of the target material is important for the production of p-. Simulations made with MARS showed that the p-/p+ could be as large as 60 % for 2 GeV protons impinging a lead target. In case of a scarce production of p-, one could resort to an isoscalar beam made of a particles. The presence of neutrons in the beam may have the extra advantage of reducing the energy deposited in the target since they are not slowed down by ionization. For a 2 GeV linac, the energy per nucleon drops to 1 GeV and it has to be checked that there will be enough pions produced in the forward direction.

After the target, the proton beam should be dumped. Since there is roughly a factor 10 between pion and proton momenta, the magnetic separation of the two beams is easy. The target area is nevertheless non trivial for Megawatt beams. In the absence of any engineering study, this part has not been represented in Figure 3.

The distance at which the maximum number of muons is produced is of the order of 50 m (Figure 4) and coincides with the entrance to the bunch rotator. This device is also assumed to work at 350 MHz but with normal cavities which can deliver 0.1 MW/m and an energy gradient of 0.7 MeV/m for an iris radius of 10 cm and a shunt impedance of 5 MW/m. The muons are collected within an energy interval of 150 MeV reduced to ± 10 MeV after bunch rotation while the bunch is dilated from 24 to 180 ps. The linac length is 107 m and the longitudinal emittance 0.0036 eV.s. At the end of the bunch rotator, 300 m can be occupied by an ionisation cooling system but, in a first approach, the neutrino factory would not rely on a cooler and this space could be used by a pre-accelerator.

The beam is injected vertically into a small arc of the recirculator. Each arc has the shape of a "petal". It starts with an arc of circle a1 which has a bending angle equal to -p/3 and continues with a series of arcs: a2 tangent to a1 and of angle p/3, a3 is a half circle tangent to a2, a4 and a5 are symmetric of a2 and a1 with respect to the axis of the re-circulator. The radius of curvature is proportional to the momentum of the particle and corresponds to an average field of 1.2 T. The first arc used for injection is just made of the S-shape sequence (a1, a2). The linac which occupies the 500 m straight section has an energy gradient of 10 MeV/m, it could operate at 700 MHz and be similar in design to the one developed at Fermilab for the cooling experiment [3]. In order for the bunches to be in phase with the RF wave at each passage, the arc lengths must be such that the transit time through the arc be a multiple of the RF period. There may be an extra tolerance for off-momentum particles which forces the arcs to be isochronous. It has to be noted that the beam flows continuously in the recirculator without any pulsed magnet such as kickers. The field being fixed for dipoles and quadrupoles as well, the focusing strength is different in the straight section at each passage and, in particular, it is opposite between a forward and a backward passage. The focusing of an arc must therefore begin with an F-quadrupole and end with a D-quadrupole to maintain the global alternating gradient structure. More generally, the optics of a re-circulator is not new and has already been succesfully addressed in a machines like CEBAF [4] or ELFE [5].

Last comes the muon storage ring. Here, the race-track shape is prefered to the neck-tie because it optimizes the neutrino yield which is proportional to the ratio of the straight section length to the overall length (~ 40%). In order to eliminate any overlap between the neutrinos coming from the pion beam with those resulting from the muon decay, the plane of the muon storage ring is tilted with respect to the horizontal plane of the other machines and the dedicated straight section points towards the detector. Another detector could use the opposite straight section but should be located at a relatively short distance since the first detector is at the end of a long base line. The focusing of the long straight section is such that the beam divergence is small with respect to the divergence of the neutrino beam. This means a rather loose focusing (high b inserts) in contrast with the packed focusing of the re-circulator and it is possible because the beam emittance has decreased by the factor 1/bg with respect to the beam emittance at injection into the re-circulator. Last point, the decay time in the muon storage ring at 20 GeV is 440 ms and exceeds by far the revolution time (~ 3.5 ms). An accumulation system has then to be designed. The techniques of momentum (CERN ISR), betatron (PS booster) and/or azimuthal stacking (CLIC) have to be investigated and there is ample room for ingenuity.


Figure 3: The neutrino factory as a front end of muon collider.


Figure 4: Muons (blue curve) produced by decaying pions (red curve) .

Higgs factory

The Higgs factory could be built once the light Higgs will have been discovered and its mass more precisely known. The present assumptions are a mass near 100 GeV and a width of the order of 1 MeV. The basic interest of a muon collider is the possibility of producing the Higgs in the s-channel and to measure its width with precision. This opportunity can turn to reality if one can achieve sufficient luminosities for beams of tiny momentum spread (10-5). Here, three differences manifest themselves with respect to a neutrino factory. First, the beam has to be bunched; second, the two charges have to be manipulated simultaneously and third, 6D cooling is mandatory.

In the present scheme, the muon beam has a time structure which is roughly the image of the proton beam structure. The bunching is thus produced at the level of the protons by an ingenious fast bunch rotation near the transition energy of a synchrotron. A preliminary experiment performed at BNL [6] has proved the feasibility of the scheme but on a limited number of protons in the bunch. Dedicated work has to be continued to show that it is indeed possible to compress 1014 protons in a 1 ns bunch. Within the context of the neutrino factory, the linac would work in the regime of a synchrotron injector [1] and, using the PS as a buncher, the proton energy would be near 6 GeV.

The target length has to match the bunch length, 20 cm about as in the case of the neutrino factory but in a single piece and no longer distributed. This is the realm of the targetry experiment proposed at BNL [7]. The bunch rotator would be a new linac operating at lower frequency (~ 70 MHz). The pre-accelerator of the neutrino factory would be replaced by the cooler for which one relies heavily on the Fermilab proposal of cooling experiment [3]. It is especially important to design the cooler in such a way that the accelerating system of the re-circulator will still be valid.

Once the beam has been cooled, it is accelerated in the re-circulator up to 50 GeV per beam, the bunches of opposite charges being phase shifted by pon the RF wave and circulate in opposite directions in the arcs. In Figure 5, the arcs are represented with the same average field as for the neutrino factory. It is likely that they will be shorter using super ferric magnets (3 T) fed by a superconducting cable [8]. The last three loops would thus be located in the same tunnel and some civil engineering would be saved. The same technology might be appropriate for the Higgs factory itself.

As far as the collider is concerned, the study of the American collaboration is resumed. A weak point in this study is the low repetition frequency, 15 Hz, which is well adapted to a large collider but not as well to a low energy collider where the particles decay 50 times faster. The luminosity is indeed proportional to the repetition frequency and some innovation is required to improve it.

Another innovation may be worth some investigation. If the muons were bunched downstream of the recirculator, the only modification to the neutrino factory would be the replacement of the pre-accelerator by the cooler. The technique of "frequency multiplication" used for the drive beam of CLIC [9] addresses the problem of the azimuthal bunch stacking and would have to be generalized.

Figure 5. The Higgs factory.

Final acceleration and large collider

To reach the final energy of several TeV is more an economical than a technical problem. It is indeed rather straightforward to apply all the developments of linear colliders to muon colliders. Assuming that 40 MV/m superconducting cavities will be available in 20 years from now, a 60 km linac could feed a storage ring with both m+ and m-. The present approach tries to minimize the cost of civil engineering and RF investment by re-using the accelerating field over several passages. We have seen that re-circulators have precisely this function but it is not desirable to multiply the number of arcs excessively. Recent studies try to resurrect the concept of the fixed field alternating gradient (FFAG) accelerators [10] or to adapt achromats to a large range of momenta. The common feature of these techniques is to achieve a substantial part of the bending strength with quadrupoles: at some nominal energy, the orbit is centered in the quadrupole and the bending strength is only determined by the dipole field, at lower energy, the negative field of the quadrupole would reduce the integrated bending strength and at higher energy the positive field of the quadrupole would increase the total bending strength. Alternatively, the bending strength modulation produced by the quadrupoles might be replaced by a fast modulation of the dipole field using pulsed coils. This type of accelerators should be accommodated in circular tunnels like the SPS and LHC tunnels. In brief, the problem of ultimate energy for a muon collider resorts more to optics than to acceleration.

The high energy muon collider has been thoroughly studied by the American colaboration [11] and the most important issues (detector background, final focus, isochronicity, beam stability, polarisation, ...) have been addressed yet not fully solved. On the CERN site, the center of mass energy should not exceed 5 TeV to maintain the collider at the depth of the LHC. Any hope to get rid of the neutrino radiation lies in a reduction of the intensity. To maintain the luminosity with a lower current is at the cost of a reduced emittance which makes sense only if the beam-beam interaction is in some way counteracted by a special device. A lower emittance means more cooling and optical stochastic cooling has been proposed [12]. Beam-beam passivation has been discussed for a long time and is based on electromagnetic shielding produced by the electrons of a plasma or, at the charge density of a TeV collider, by the free electrons of a metal which could be here a jet of lithium. The theory of these effects exists but no experimental application has been performed up to now. This kind of research has to be vigorously stimulated.

Conclusions and Request


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