Muon Accelerator for the Neutrino Factory
D. Douglas, L. Harwood, V. A. Lebedev#, Jefferson Lab, Newport News, VA
A concept for a neutrino factory muon accelerator driver is presented. Such
acceleration of a muon beam is a challenging task because of a large source phase space
and short species lifetime. In the design concept presented here, acceleration starts after
ionization cooling at 190 MeV/c, and proceeds to 50 GeV where the beam is injected into
a neutrino factory storage ring. The proposed driver consists of a 3 GeV linac and two
consecutive recirculating linear accelerators. A choice of accelerator technology, the
machine layout and its main parameters are discussed.
System Requirements
A neutrino factory [1] is a facility that forms a narrow neutrino beam via decay of
muons in a storage ring with long straight sections. This article is drawn from work
supporting a Fermilab study [2] carried out to investigate the feasibility of such a system.
It describes a concept for the acceleration of muons after ionization cooling at 190 MeV/c
to the 50 GeV storage ring injection energy. A parameter set for such a muon accelerator
driver (MAD) has been established by Fermilab and is presented in Table 1.
The key technical
Table 1:Main Parameters of the Muon Accelerator Driver
requirements, beyond the
190/112 MeV
basic physics parameters Injection momentum/Kinetic energy
Final energy
50 GeV
of Table 1, are 1) muon
Initial rms normalized emittance,
1500 mmmrad
survival, 2) the choice of Initial rms energy spread
acceleration technology Initial rms bunch length
12 cm
and frequency, 3) the Number of bunches per pulse
4 batches of 30 bunches
acceleration, Batch duration
150 ns
250 ns
transport and preservation Time between batches
2.51010 / 31012
of the large source phase
space of the unstable Bunch frequency/Accelerating frequency 200/200 MHz
15 Hz
4) Repetition
Peak power transferred to the beam
40 GV
accelerator performance Average beam power
360 kW
issues such as potential
collective effects (e.g., cumulative beam breakup) resulting from the high peak current
The first requirement is a consequence of the character of the muon source itself. As
the species is unstable, acceleration must occur at high average gradient in order to
ensure survival rates, and thus flux into the storage ring, are adequate. Estimates suggest
that a “real estate average” RF gradient of 15 MV/m will allow survival of in excess of
80% of source muons to the storage ring injection point [3]. The second and third issues
also stem from the nature of the source. As muons are generated as a secondary beam of
nuclear reaction products and ionization cooled to a volume that may most optimistically
be described as “impressive”, the MAD must provide high average gradient acceleration
while maintaining very large transverse and longitudinal accelerator acceptances. This
circumstance drives the design to low RF frequency, particularly in the early stages of
acceleration. Were normal-conducting cavities used, the required high gradients would
demand unachievably high peak RF sources. Superconducting RF (SRF) cavities are a
much more attractive solution. RF power can then be delivered to the cavities over an
extended time, and thus RF source peak power can be reduced. Peak power is then
determined by microphonics [4] leading to a choice of long pulse operation of the RF
cavities and reducing total power consumption for both RF and cryogenics. The final,
fourth, issue represents the traditional beam dynamics concerns associated with any high
brightness accelerator. A very preliminary study suggests that the beam stability is not
expected to be a severe problem [5] and with not be further discussed in this article.
Machine Architecture
Muon survival demands either a high-gradient conventional or recirculating linac.
While recirculation provides significant cost savings over a single linac, it cannot be
utilzed at low energy for two reasons. First, at low energy the beam is not sufficiently
relativistic and will therefore cause a phase slip for beams in higher passes, thus
significantly reducing acceleration efficiency for subsequent passes. Secondly, there are
major difficulties associated with injection of a beam with the large emittance and energy
spread associated with a muon source. Beam pre-acceleration in a linear accelerator to
about 3 GeV makes the beam sufficiently relativistic and adiabatically decreases the
phase space volume so that further acceleration in recirculating linacs is possible.
Cost considerations favor multiple passes per stage, but practical experience
commissioning and operating recirculating linacs dictates prudence. Experience at
Jefferson Lab suggests that for given large initial emittance and energy spread, a ratio of
final-to-injected energy well below 10-to-1 is deemed prudent [6] and number of passes
should be limited to about 5. We therefore propose a machine architecture (see Figure 1)
featuring a 0.2-to-3 GeV straight “preaccelerator” linac, a 3-to-11 GeV four pass
recirculating “compressor” linac (RLA1), and a 11-to-50 GeV five pass recirculating
“primary” linac (RLA2). The preaccelerator captures the large phase space coming from
the cooling channel and accelerates it to relativistic energies. At this point, the increased
muon lifetime () allows use of a compressor (RLA1). During compression, the
longitudinal and transverse phase spaces are shaped (while further raising the energy) for
injection into the high-energy primary (RLA2), which then generates the 50 GeV beam
for the storage ring.
4 pass
p=190 MeV
2.8 GeV
11 GeV
3.4 GeV
200 MHz
1.23 GeV
1.23 GeV
200 MHz
5 pass
50 GeV
4.25 GeV
400 MHz
4.25 GeV
Figure 1. The layout of the MAD
The large acceptances (longitudinal and transverse) determined by muon cooling,
combined with the fact that the source beam is bunched at 200 MHz, imposes a minimum
RF-frequency requirement of 200 MHz for both the preaccelerator and the compressor.
This choice also provides adequate stored energy to accelerate multiple passes of a
single-pulse bunch train without need to refill the extracted energy between turns. The
choice of frequency is less obvious for RLA2, inasmuch as the phase space is smaller and
rather more manageable. Preliminary studies suggest that the second harmonic, 400
MHz, may provide adequate aperture, acceptance and the stored energy. If so, the higher
frequency is desirable in that it provides significant cost savings for construction and
operation. Detailed calculations affirm that although acceleration at 400 MHz yields
larger energy spread due to the smaller stored energy and the shorter RF wavelength, the
energy spread is still adequate at 50 GeV. However, it is not clear that the 400 MHz
scenario can meet the performance requirement for transverse phase space conservation.
Because of significant cost savings, it is however our baseline frequency choice for
RLA2. If further studies indicate that 400 MHz will not provide an adequate
performance, the 200 MHz solution used in the preaccelerator and compressor will be
used for the primary as well.
Accelerator System Design
The initial longitudinal acceptance of the linear accelerator is chosen to be 2.5, i.e.
p/p=27% and RF phase =72 deg. To perform adiabatic bunching, the RF phase of
the cavities is shifted by 75 deg at the beginning of the preaccelerator and gradually
changed to zero by the linac end. In the first half of the linac, when the beam is still not
sufficiently relativistic, the offset causes synchrotron motion, allowing bunch
compression in both length and momentum spread to p/p=6.6% and =19 deg. The
synchrotron motion also suppresses the sag in acceleration for the bunch head and tail.
The first frame in Figure 1 shows how the initially elliptical boundary of the bunch
longitudinal phase space will be transformed by the end of the linac. To perform a further
bunch compression in RLA1 (see Fig. 2) the beam is again accelerated off-crest with
phase offsets in the range of 22 – 45 deg for different passes and M56 in the range of 50 to
60 cm for different arcs. Similar RF gymnastics for RLA2 yields the final total energy
Recirculator entrance
Arc1 entrance
Arc3 entrance
Recirculator exit
Arc7 entrance
Arc5 entrance
Arc6 entrance
Arc4 entrance
Arc2 entrance
Figure 2. Longitudinal phase space through RLA1 for 400 MHz scenario; axis: horizontal
– RF phase in deg, vertical - p/p0.
spread of 1%. The synchrotron motion in the
Main recirculator exit
recirculators also strongly suppresses the beam
loading effect. At 400 MHz a single pass of the
beam takes away about 2.4% of the energy
stored in cavities, thus reducing the accelerating
gradient for the last bunch in the train by 1.2%.
Fortunately, that imposes only about 0.3%
energy drop on the last bunch, because bunches
with smaller energy arrive earlier and
experience larger acceleration due to the RF
phase offset. The longitudinal phase space for
Figure 3. Longitudinal phase space
the first and last bunches at the exit of RLA2 is at the RLA2 exit for the first () and
depicted in Figure 3.
last (+) bunches; axis: horizontal –
The initial transverse acceptance of the
RF phase in deg, vertical - p/p0.
linear accelerator is also chosen to be 2.5,
which corresponds to 5200 mmmrad at injection energy. To keep the beam radius below
the 200 MHz cavity radial aperture of about 20 cm, the beta-functions should be below 8
m. Small beta-functions also suppress a harmful effect of beam focusing due to cavity
accelerating fields. To achieve such small beam envelopes, short 5 m cryomodules (2
two-cell cavities at 200 MHz) are used at the beginning of the linac. As the beam energy
increases, a transition to 8 m cryomodules (8 two-cell 200 MHz cavities) occurs. Note
that this RF building block is used through the remainder of the preaccelerator and
throughout RLA1. The beta-functions and horizontal dispersion in the preaccelerator and
RLA1 injection chicane are shown in Figure 4. Solenoid focusing is considered to be
most appropriate to handle the huge initial emittance. At approximately 1.5 GeV energy
the magnetic field of 50 cm SC solenoids achieves 5 T and their further use would not be
prudent. Fortunately, at this point the beam radius is sufficiently small (~ ½ the initial
beam size) and long cryomodules are introduced, thus reducing the fraction of the
accelerator taken by the cavities. Quad triplets then become a preferable choice for the
beam focusing. This combination of solenoidal and triplet focusing makes a smooth
focusing structure and avoids chromatic growth of the beam envelopes. Despite the large
initial energy spread, particle tracking through the linac and the injection chicane exhibits
only a few percent emittance growth with 0.5% beam loss from particles at the phase
space boundary. One family of four sextupoles is used in the injection chicane to correct
its non-linear dispersion.
OptiM - MAIN: - E:\Optics\NeutrinoSource\Linac\Linac.opt
Tue Mar 28 11:43:36 2000
Figure 4: The beta-functions and dispersion in the preaccelerator and RLA1 injection chicane
12 deg.
4.843 deg. 1.6 deg.
12 deg.
8.039 deg.
3.2 deg.
6.045 deg.
10 m
Figure 5. Spreader (recombiner) layout
The RLA1 beam transport system uses a horizontal separation of beams at the end of
the linacs to allow independent recirculation of each pass. Individual recirculation arcs
are based on a periodic triplet focusing structure, which allows use of longer straight
sections (cryomodules as much as 10 m long), simplifies spreader/recombiner design (by
easing beam envelop matching from linac to recirculation arc) and reducing vertical beam
envelopes and chromatic effects. The required large momentum acceptance necessitates
introduction of a three-sextupole family chromatic correction of the off-momentum orbit
and path length. As in other recirculating linacs, and unlike storage rings and
synchrotrons, correction of betatron “tunes” or beam envelopes is unnecessary. Figure 5
shows a spreader (recombiner) layout. Optics for a few first arcs has been built and
tracking studies exhibited an acceptable emittance growth.
Design of RLA2 is similar to that of RLA1. As discussed above, the optional use of
200 MHz or 400 MHz SRF systems remains open; longitudinal matching scenarios have
been developed for both cases. As in RLA1, some longitudinal matching is still required
and is provided by a proper choice of recirculator momentum compactions and linac RF
phase profile. The 400 MHz option requires somewhat greater recirculator momentum
acceptance, which may well lie within the realm of possibility and will be resolved as
detailed design of the transport system progresses. Present RLA2 designs utilize
horizontal beam separation, periodic arc focusing, and sextupole correction of appropriate
aberrations, as in RLA1.
Results of this study suggest there are no obvious physical and technical limitations
precluding construction of an accelerator-recirculator for muons. The use of 200 MHz
accelerating frequency and SRF technology looks well justified. The use of 400 MHz in
second RLA is desirable but a machine design should be developed to verify that the
required performance (in particular, recirculator acceptance) can be achieved.
[1] See, for example, the Fermilab site at
N. Holtkamp and D. Finley, editors, “A Feasibility Study of a Neutrino Source Based on a Muon
Storage Ring”, Fermilab Report, 31 March 2000.
J. Delayen, private communication.
J. Delayen et al., “Design of a Muon Accelerator Driver for a Neutrino Factory”, JLAB-TN-00-009,
29 March 2000.
For a discussion of linac dynamic range (injected-to-final energy ratio) see, e.g. D. Douglas, “Lattice
Design Principles for a Recirculated, High Energy, SRF Electron Accelerator”, Proceedings of the
1993 Particle Accelerator Conference, IEEE Catalog No. 93CH3279-7, p. 584 (1993).