Task 12: Beta-Beam Aspects
Conceptual Design Report
(Published on CD only)

November 2009

PROJECT RIDS 51576

Project funded by European Community under the “Structuring the European Research Area”  
Specific Programme Research Infrastructures Action  within the 6th Framework Program (2002‐2006) 

Conceptual Design Report for a Beta-Beam Facility

A. Bechtold1, M. Benedikt2, F. Borgnolutti2, E. Bouquerel2, L. Bozyk3, J. Bruer2, A.
Chancé4, P. Delahaye2,5, A. Fabich2, S. Hancock2, C. Hansen2, E. Jensen2, A. Källberg6,
M. Kirk3, A. Lachaize7, M. Lindroos2,8, M. Magistris2, A. Mueller7, J. Payet4, H. Podlech1, P.
Puppel3, M. Silari2, A. Simonsson6, P. Spiller3, S. Stadlmann3, A. Tkatchenko7, S. Trovati2,
V. Vlachoudis2, and E. Wildner2
1
2
3
4
5
6
7
8

IAP, University of Frankfurt
CERN, Geneva
GSI, Darmstadt
CEA Saclay
GANIL, Caen
MSL, Stockholm
IPN Orsay
ESS-S, Lund

Beta-Beam task leader: M. Benedikt, CERN

Project funded by European Community under the “Structuring the European Research Area”
Specific Programme Research Infrastructures Action within the 6th Framework Program (20022006)

Contents
Conceptual Design Report for a Beta-Beam Facility........................................................................... 1
I. Introduction .................................................................................................................................. 3
Comments on the 6He and 18Ne production and ionization methods............................................... 3
II. The Beta-Beam database .............................................................................................................. 4
Production ........................................................................................................................................ 4
ECR source ...................................................................................................................................... 4
Linac and rapid cycling synchrotron ................................................................................................ 4
PS and SPS acceleration to high energy .......................................................................................... 5
Decay ring ........................................................................................................................................ 5
Transverse emittance and tune shift ................................................................................................. 5
Results .............................................................................................................................................. 5
III.
Post-accelerating LINAC .......................................................................................................... 6
RFQ design ...................................................................................................................................... 6
DTL design....................................................................................................................................... 7
IV.
Accumulation Ring ................................................................................................................... 8
V. Design of the Rapid Cycling Synchrotron ................................................................................. 10
RCS general parameters ................................................................................................................. 10
Optical design ................................................................................................................................ 11
Injection ......................................................................................................................................... 12
Acceleration ................................................................................................................................... 13
Other beam optics aspects .............................................................................................................. 14
Vacuum System Requirements for the RCS .................................................................................. 14
RCS radioprotection studies........................................................................................................... 19
VI. Ion acceleration scenarios in PS and SPS ............................................................................... 22
PS - RF considerations ................................................................................................................... 23
Vacuum System Requirements for the PS...................................................................................... 23
PS Radioprotection studies ............................................................................................................ 26
SPS - RF simulations ..................................................................................................................... 28
Vacuum System Requirements for the SPS ................................................................................... 32
Identification of limitations in PS and SPS.................................................................................... 36
VII. Design of Decay ring .............................................................................................................. 37
Optics ............................................................................................................................................. 37
Injection ......................................................................................................................................... 38
Asymmetric bunch merging ........................................................................................................... 40
RF system ....................................................................................................................................... 40
Momentum collimation .................................................................................................................. 44
Losses by β decay .......................................................................................................................... 47
Dynamic aperture ........................................................................................................................... 50
Decay ring radioprotection studies ................................................................................................ 51
Decay losses ............................................................................................................................... 52
Collimation section .................................................................................................................... 52
Air activation.............................................................................................................................. 53
Vacuum System Requirements for the Decay Ring ....................................................................... 53
VIII.
Conclusion ........................................................................................................................... 58
IX. References ............................................................................................................................... 59

2

I.

Introduction

The Beta-Beam [1] is a concept of large scale facility that aims at providing pure electronic neutrino
and antrineutrino beams for the measurement of νeνµ oscillations, with unprecedented sensitivity
for detection of the θ13 mixing angle and CP violating phase. In the scenario presented in different
publications[2][3][4], a Beta-Beam facility could be advantageously placed at CERN making use of
the PS and SPS for accelerating the beta-decaying, neutrino-emitting beams to a Lorentz gamma of
100. Intense beams of 6He and 18Ne would be produced using the so-called “isotope-separation on
line” ISOL method in a facility of the scale of EURISOL. The synergy between the two projects
was pointed out in [5]. The task 12 of the EURISOL design study aimed at producing a conceptual
design report for the accelerator chain of a EURISOL/CERN-baseline Beta-Beam facility (Figure
1). CERN was leading the task. This document summarizes the achievements made during the time
of the study and constitutes the final conceptual report of the beta-beam facility.

Figure 1: Overview of the CERN-baseline Beta-Beam.
Comments on the 6He and 18Ne production and ionization methods
For an optimal sensitivity of the Beta-Beam facility to the θ13 angle and CP violating phase, a total
throughput of 1.1 1019 neutrinos and 2.9 1019 antineutrinos was generally assumed over a running
period of 10 years. In turn, a top-down approach results in the need for production of about 3.3 1013
6
He radioactive atoms and 2.1 101318Ne atoms per second, with efficiencies along the accelerator
chain as quoted in the next section. While the 6He production rate appeared to be possible from a
“standard” 200kW EURISOL target [6], the 18Ne production was found more problematic. The
cyclotron laboratory from Louvain-La-Neuve conducted some promising tests for using the reaction
16
O(3He,n)18Ne on large size oxide targets. The production rates do not seem out of reach now and
the envisaged production methods are briefly summarized in Table 1.

3

Isotope
6
He
18

Ne

Primary beam and target
Reaction
2GeV p (200kW) on a neutron converter 9Be(n,α)6He
surrounding a BeO target[6]
16
60 cm diameter target MgO
O(3He,n)18Ne
3
2MW He beam (14.8MeV, 130mA)

Yields
2.1013/s
1013/s

Table 1: Envisaged production methods for 6He and 18Ne.
A 60 GHz ECRIS is under study for the multi-ionization and bunching of the 6He and 18Ne ions into
10Hz 50µs pulses. A first design was done within the task 9 of EURISOL, and a prototype should
be built and tested at LPSC Grenoble within FP7 [7]. Alternative neutrino emitters have been
proposed in the frame of FP7, 8B and 8Li that could possibly be produced in copious amounts using
the concept of ionization cooling ring [8].

II.

The Beta-Beam database

The flux out of the Beta-beam facility is determined by the number of ions that can be produced, by
the number remaining after acceleration and by the total accumulated in the decay ring. A first
“bottom-up” analysis of the ion intensities along the accelerator chain and of the neutrino and
antineutrino flux out of the decay ring was realized by CERN, starting with the rate at which atoms
are transported out of the target [9] [10]. It was lately updated and turned into a “top-down” analysis
[11], for which it was assumed that the required 2.9×1018 antineutrinos/year and 1.1×1018
neutrinos/year [3] could be obtained. We recall here the main arguments which served to the
constitution of the database.
A full description of the Beta-Beam can be found in e.g. [2][4]. Figure 1 represents the Beta-Beam
facility as described in these articles.
Production
In the Beta-beam baseline it was first assumed that one could produce and transport 2×1013 6He
atoms/s and 8×1011 18Ne atoms/s out of the target with a proton driver beam current of 100 µA
impinging on the target at 2.2 GeV. These numbers are based on an evaluation of suitable isotopes
and their production rates at ISOL facilities and have been presented as part of the Beta-beam
contribution to NuFact02. The full write-up of this presentation could not be published as part of
the proceedings, but it exists as a CERN internal note [2]. During the course of the study, alternative
production methods were envisaged (see Comments on the 6He and 18Ne production and ionization
methods, in the previous section). It is now assumed that 6He and 18Ne can be produced in sufficient
quantities, which are derived from the required neutrinos and antineutrinos throughput of BetaBeam.
ECR source
Efficient bunching and stripping of the high intensity beam are achieved using a high-frequency
ECR source [12]. We assume the efficiency of such a source to be 50% both for 6He in the
2+ charge state and 50% for 18Ne ions in one (e.g., 6+) of several charge states being extracted. We
further assume that the ECR operates at 10 Hz with an accumulation time of 97.5 ms, that the
source is at a potential of 50 kV relative to the linac, and that the ions are ejected in 50 µs long
bunches with a physical transverse emittance of about 50 π.mm.mrad.
Linac and rapid cycling synchrotron
The linac accelerates the ions to 100 MeV/nucleon, after which they are multi-turn injected into a
4

rapid cycling synchrotron (RCS). We assume an injection efficiency of 80%. Both ion species are
accelerated to a magnetic rigidity of 14.47 Tm in a time dictated by the 10 Hz repetition rate of the
ECR source. Each cycle provides a single bunch.
PS and SPS acceleration to high energy
The PS waits for 20 shots from the RCS then accelerates the 20 bunches to a magnetic rigidity of
86.7 Tm. Then they are transferred to the SPS and accelerated to γ=100 and ejected off momentum
into the decay ring for stacking. The cycle time of the SPS is a multiple of the 1.2 s basic period of
the CERN machines. The extra acceleration required for the 6He results in a 6 s cycle compared
with only 3.6 s for 18Ne.
Decay ring
The 20 incoming bunches are combined with the 20 circulating ones of the stack by an asymmetric
merging process in the decay ring (see section Decay Ring). The number of times this process can
be repeated is constrained by the 1 eVs longitudinal emittance of each bunch delivered by the SPS.
Simulations for 6He show that such bunches can be stacked up to 15 times. At given relativistic γ,
the aperture of the decay ring defines a longitudinal acceptance limit which scales with ion
momentum. Consequently, the more advantageous charge-to- mass ratio of 18Ne ions should allow
the number of merging steps to fill the decay ring to be increased by something approaching a
factor of 3 with respect to the stacking procedure established for 6He involving 15 merges.
However, the sensitivity of the process to phase errors between the two rf components employed in
the merging puts an upper limit of about 20 on the number of merges that can realistically be
achieved. We therefore assume that the extra acceptance available for 18Ne in the upstream PS and
SPS is exploited to stabilize the beam and consider 2 eVs per bunch (cf., 1 eVs for 6He) injected
into the decay ring, giving 40 eVs in the stack.
The resultant relative momentum spread of the stack is ±2.5×10-3 at the start of merging for both ion
species and, applying the full 20+20 MV of the 40+80 MHz rf systems in the decay ring, the
duration of each bunch is 5.2 and 4.5 ns for 6He and 18Ne, respectively.
The annual integrated flux of potentially useful neutrinos and antineutrinos emanating from the
decay ring is linearly dependent on the relative length of the straight section that points towards the
detector. This is taken to be 36% of the decay ring circumference [2].
Transverse emittance and tune shift
The transverse emittance and tune shift evaluations were reported in [10][11].
Results
The above parameters result in the numbers of ions at each stage of the CERN Beta-beam facility
quoted in Table 2. The decay losses are properly accounted for, but the transfer efficiencies
between the different machines are assumed to be 100% except for the multi-turn injection into the
RCS (80% efficiency). The figures “Decay Ring accumulated” correspond to 10.7 effective
merging steps for helium and to 17.4 for neon and are based on idealized stacking but with betadecay taken into account between the 15 or 20 shots that fill the machine. Detailed simulations
indicate that the stacking efficiency is in excess of 80% of the idealized one in both cases [13],[14].

5

6He2+

18Ne10+

RCS injected

8.5 × 1011

2.6 × 1011

RCS ejected

8.3 × 1011

2.6 × 1011

PS accumulated

1.1 × 1013

4.5 × 1012

SPS injected

9.5 × 1012

4.3 × 1012

SPS ejected

9.0 × 1012

4.3 × 1012

Decay Ring injected

1.8 × 1014

8.5 × 1013

Decay Ring accumulated

9.7 × 1013

7.4 × 1013

Table 2: Ion intensities in the EURISOL baseline scenario
From the number of ions at RCS injection, the intensities required from the production chain can be
estimated. It is assumed that 50% or the ions extracted from the ECR source have the desired charge
state and that the linac transmission efficiency is 80% and the RCS injection efficiency is 80%.
This results in an average of 2.6 × 1013 6He ions per second or 8.1 × 1012 18Ne ions per second to be
extracted from the source, pulsed in 10 bunches spaced by 100 ms.

III.

Post-accelerating LINAC

It was originally believed that the design of the EURISOL post-accelerator could be replicated for
the injector into the Rapid Cycling Synchrotron of the beta-beam facility. It turned out in the middle
of the study that the superconducting LINAC of EURISOL would not be suited to the postacceleration of the intense pulses of 6He and 18Ne. For this reason, a separate study was done by
IAP Frankfurt for delivering specifications of a normal-conducting LINAC that would fulfill the
Beta-Beam requirements (Table 3).
Due to the low duty cycle of 0.05% and the high pulse beam current up to 13 mA as required by
Beta-Beam, the use of normal conducting NC-RF-structures instead of superconducting cavities
even up to the intended final energy of 100 MeV/u seems more favorable. Even at accelerating
gradients between 3 and 6 MV/m the thermal load on the cavities is very moderate. For the desired
maximum mass to charge ratio of A/q = 3 an operating frequency of 175 MHz at energies up to 10
MeV/u is well adapted, which then would be changed to 352 MHz for further acceleration [15].
β-BEAM LINAC BENCHMARK
mass to charge ratio A/q
<3
duty cycle
0.05%
beam current
≤13 mA
input energy Win
8 keV/u
output energy Wout
100 MeV/u
input emittance εin,rms,normalized
0.2 π mm mrad

Table 3: Beta-Beam requirements for the post-accelerating LINAC.
RFQ design
First accelerating stage behind the ECR ion source would be a 4-rod-type RFQ [15]. This resonator
type has proven its reliability at many instances and is well suited for this field of application here.
The 4-rod type provides very comfortable rf-tuning possibilities compared to other resonator
structures like IH- or four vane type RFQs. The frequency tuning during operation is accomplished
by an inductively operating tuning plunger, which has an only marginal effect on the rf-efficiency of
the device. Some preliminary design calculations have been executed [16]; main RFQ parameters
6

are listed in Table 4. The transition energy between RFQ and DTL has been chosen to be 1 MeV/u,
which can be adapted to DTL requirements during further optimization procedures. The RFQ
design provides transmission above 90% even with beam currents up to 50 mA.

MAIN RFQ PARAMETERS
length l
275 cm
frequency f0
176 MHz
mass to charge ratio A/q
≤3
input energy Win
8 keV/u
output energy Wout
1 MeV/u
max. electrode voltage at A/q = 3 Vel
95 kV
input emittance εin,rms,normalized
0.2 π mm mrad
transmission T (≤50 mA)
>90%
max. pulsed power consumption P f
350 kW

Table 4: A possible NC-RFQ concept for β-beam application.
The 4-rod structure is basically a chain of strong coupled λ/4 resonators oscillating in fundamental
0-mode (Figure 2). One resonating ground cell is accomplished by two neighbouring stems
mounted on a ground plate forming a short circuit and a capacitive load represented by the
electrodes. Frequency and field tuning can easily be done by adjusting additional movable tuning
plates. The thermal situation is with 175 W thermal load very relaxed, no extensive cooling system
is required.

Figure 2: Scheme of the 4-rod-RFQ on the left and - as an example - the SARAF 176 MHz
4-rod RFQ built by NTG Company on the right

DTL design
Possible candidates for NC-DTLs are H-mode cavities (IH-, CH-DTL). In general, H-mode cavities
have high shunt impedance. IH-structures are operated in the low energy regime between
0.1 MeV/u and 10 MeV/u with RF-frequencies between 36 and 250 MHz. The IH-DTL structure
has no competitor with respect to rf-efficiency. The first DTL part could consist of three IHstructures operated at 176 MHz. The input energy is 1 MeV/u and the output energy 8 MeV/u. The
total voltage gain is 22 MV with a length of about 7 m. The total required power per cavity
including the beam loading is between 600 and 750 kW. The following DTL section from 8 MeV/u
to 100 MeV/u could consist of NC-CH-cavities. CH-cavities are operated in the H21-mode. The CH7

section would be operated at 352 MHz. For this frequency cost efficient klystrons in the MW-range
are available. To cover the voltage gain of 276 MV about 46 CH-structures are necessary. The
effective voltage per cavity varies between 5 and 7 MV. The total power per cavity is kept below
1 MW including the beam loading. The length of the CH-DTL is about 100 m. Figure 3 shows a
prototype of a NC-CH cavity which is being developed for the new proton injector for FAIR [17].
This 70 MeV, 70 mA p-linac will use 11 NC-CH-structures. Figure 4 shows the schematic layout of
a possible H-mode linac for β-beam applications. The total length is about 110 m. This corresponds
to a real estate gradient of 2.73 MV/m.

Figure 3: A 217 MHz medicine IH-DTL and the 350 MHz CH-prototype cavity for GSI.

Figure 4: Schematic layout of an IH/CH-DTL for the production of β-beams.

IV.

Accumulation Ring

The possibility to use an accumulation ring using electron cooling between the LINAC and the RCS
was studied as a non-baseline option by MSL. Its layout is shown on Figure 5 and its lattice
functions on Figure 6. It includes a long section with large β-functions for fast electron cooling, as:
1/cooling time ~ 1/Θ3 ~ (ß/ε)1.5

with Θ the angle between the electrons and the ions.

Figure 5 : Schematic layout of an accumulator ring.
8

Figure 6 : Lattice functions for a quarter of the cooler ring. The electron cooler would be in the
right part of the diagram.
The electron cooling over repetition times of 100ms has been shown to be feasible for 18Ne10+ as
long as εx is less than 65 π mm mrad, as can be seen in Fig. 3. In the simulations the following
parameters were assumed for the electron cooler: 2.5 A electron current, 29 mm electron beam
radius and a 0.1 T longitudinal magnetic field. Applying such electron cooling for 6He2+ seems more
problematic because of the longer time needed for transverse emittance cooling (cooling rate ~
Q1.7/A [18]).

Figure 7 : Simulation of horizontal, vertical, and longitudinal profiles of an 18Ne10+ beam before
(above) and after (below) 0.1 s cooling. Initially all ions have the same emittances,
εx=65 π mm mrad and εy=30 π mm mrad. Intrabeam scattering is not included so after cooling the
central peak becomes unrealistically high.
Such accumulator ring could make beneficial use of the ramping time of the PS for accumulating
Ne10+ ions, which lost in the case of the baseline scenario (see Figure 8). This way it would permit
a more flexible mode of operation where bunches could be stored at injection energy in the SPS

18

9

rather than in the PS (as shown in Figure 8) for limiting decay losses.
Ramp time
PS

Ramp
time SPS

Reset
time SPS
Decay
ring
SPS
PS
Production

Wasted time

3.6

0

Time (s)

Figure 8 : A complete cycle for the baseline beta-beam complex consists of injection into the PS,
storage of bunches at PS injection energy, acceleration in the PS and SPS and finally injection into
the decay ring.
Assuming that 10 bunches are stored within the SPS, an optimum of 23 ECR bunches accumulated
in the ring has been found for optimizing the throughput of Beta-Beam for neutrinos arising from
the decay of 18Ne (Figure 9). In such conditions, the 18Ne in-target yield required for achieving the
annual rate of 1018 neutrinos would be reduced by a factor of 4 compared to the baseline scenario.
Anart
nulae

1 e
8N

17

1 5 0
. 1
1 2  017
.5 1
17
1
1 0
7 5  016
. 1
5 016
1
2 5  016
. 1
5
0

10
0

10
5

20
0

erace
cbths

Figure 9 : The annual rate of neutrinos along one straight section of the decay ring as a function of
the number of pulses from the linac that are accumulated in the accumulator ring. A total of 10
bunches from the accumulator ring is stored in the SPS before further acceleration and injection
into the decay ring. The discontinuities in the curve are due to a requirement that the PS and SPS
cycle time must be a multiple of 1.2 seconds.
The accumulation ring is presented with more details and a cost estimate in [16].

V.

Design of the Rapid Cycling Synchrotron

The RCS is described in detail in [19] (IPNO, CNRS/IN2P3). Its preliminary design was presented
in [20]. We recall here the main elements of its conceptual design report [19], [21]. A dedicated
Radio-Protection study was performed at CERN, showing no showstopper for the RCS. It is
reported here and in [16] together with dynamic vacuum studies performed by GSI.
RCS general parameters
The RCS accelerates He and Ne ion beams from 100 MeV/u to a maximum magnetic rigidity of
10

14.47 T.m (that is the rigidity of 3.5 GeV protons) with a repetition rate of 10 Hz. The threefold
symmetry lattice proposed is based on FODO cells with missing magnets providing three
achromatic arcs and three sufficiently long straight sections for accommodating the injection
system, the high energy fast extraction system and the accelerating cavities. According to the first
design, the number of dipoles has been increased to obtain a transition energy allowing acceleration
of protons up to 3.5GeV. These latters have been split into two parts separated by a drift space for
inserting absorbers to intercept the decay products. Finally the physical radius has been adjusted to
40m in order to facilitate the synchronization between the CERN PS and the RCS and therefore the
transfer of bunches from one ring to the other. As a consequence, the ring is composed of 60 short
dipoles and 48 quadrupoles. A schematic view of the RCS layout is shown in Figure 10 and the
main parameters are summarized in Table 5.

Figure 10: Schematic layout of the RCS
Circumference

251.32 m

Superperiodicity

3

Physical radius

40 m

Injection energy

100 MeV/u

Maximum magnetic rigidity

14.47 T.m

Repetition rate

10 Hz

Number of dipoles

60

Number of quadrupoles

48

Table 5: Main parameters of the ring
Optical design
The RCS is partitioned into 24 FODO cells, 6 in arcs and 2 in a straight section. The betatron phase
advance per cell (i.e quadrupole strength) and the length of the 2 sections without dipoles in the arcs
have been adjusted so as to cancel the dispersion function in long straight sections and to obtain,
with only two quadrupoles families, a working point located in a region of the tune diagram which
is free of systematic resonances up to the fourth order. Lattices function of one period calculated
11

with BETA [22] are shown in Figure 11. Dipoles are only 1.4m long in order to obtain a maximum
magnetic field of 1.08T and therefore to avoid a large ramping rate for the 10Hz operation.
Quadrupoles have a length of 0.4 m and a maximum gradient of less than 11 T/m. The diluted
transverse emittances in the RCS after multi-turn injection are calculated from the emittances
required in the PS at the transfer energy with a possible blow-up of 20 %

Figure 11: Optical functions for one superperiod
.
Injection
It is assumed that the ion source delivers a beam pulse of 50 µs. The revolution period of ions at
100 MeV/u being 1.96µs, the injection process takes place over several (26) turns in the machine
and is therefore referred to as multi-turn injection. Ions are injected into one of the long straight
section by means of an electrostatic septum and at least 2 pulsed kickers producing a local closed
orbit bump which places the distorted orbit near the septum for the first injected turn and which
moves it away from the septum on subsequent turns until it has collapsed and which moves it away
from the septum on subsequent turns until it has collapsed. The aim of the injection process is to
maximise the number of injected ions within the specified transverse emittance. Optimum filling in
the horizontal phase space is achieved when incoming ions are injected with a position and a slope
which minimize their Courant and Snyder invariant. In the vertical phase space the dilution is
obtained by a betatron function mismatch and a beam position offset. The Figure 12 shows the
diluted emittances in transverse phase spaces after multiturn injection, obtained with the Winagile
code. We obtain an injection efficiency of 80% after optimization.

12

Figure 12: Phase space distributions of the multi-turn injected beam (left : horizontal plane, right :
vertical plane)
Acceleration
The Programs for RF voltage and synchronous phase are determined by the following requirements:
- In order to maintain the central trajectory on the reference orbit, the energy gain per turn must be
related to the variation of the magnetic field.
- The voltage must provide a sufficient bucket area to enclose all the longitudinal emittance.
- The trapping process must be optimized to minimize the beam losses.
- At extraction the bunch must be matched to the bucket of the next machine.
After injection the circulating beam is continuous and occupies a rectangle in the longitudinal phase
space. To capture the injected beam, one stationary bucket is created. During trapping, the magnetic
field is clamped at is minimum value for a period of few ms and the synchronous phase is zero. The
RF voltage is optimized to obtain a beam rotation of about 90° and a momentum spread as small as
possible before the acceleration phase.
When the magnetic field starts to ramp, the synchronous phase is shifted and the beam is
accelerated. The program of the rise of the RF voltage and the synchronous phase variation are
defined to obtain a sufficiently large bucket area and to minimize losses. Finally, at the end of the
cycle, the bunch is manipulated so as to be matched to one of the PS RF buckets. The RF cycle has
been simulated and optimized with the code ACCSIM developed at TRIUMF [23]. The Figure 13
shows the variation of the synchronous phase and voltage during cycle for He ions.

13

Figure 13: Synchronous phase and voltage evolution during cycle for He ions
Other beam optics aspects
Several beam dynamics studies have been investigated in order to assess the feasibility of the RCS,
in addition to the results presented here. Unavoidable magnets misalignments and dipole field errors
can affect the RCS closed orbit. Distortions to be expected have been statistically estimated
assuming standard error tolerances and a correction system has been defined. In fast ramping
machines such as the Beta-Beam RCS, eddy currents induced in metallic vacuum chamber walls by
the time varying magnetic field produce various field components acting on the beam. In dipoles
vacuum chambers, one important component is a sextupole which modifies the natural chromaticity
of the ring. The associated effects have been estimated and it has been shown that they could be
compensated for so that they do not pose problems from the point of view of beam dynamics.
Finally, after injection , ions beams are extracted in a single turn and directed towards the CERN
PS. A fast extraction system consisting of fast kickers and septum magnets has been defined to
produce the deflection angle required to eject the beam from the ring. All the beam dynamics
studies made on the RCS have shown that there are no showstoppers on this ring. It can be realized
with the present technology.
Vacuum System Requirements for the RCS
The parameters used for the simulations of the dynamic pressure are listed in Table 6 and Table 7.
The data in Table 6 were taken from “The EURISOL Beta-beam Facility Parameter and Intensity
Values” generated at 12. March 2009.
The loss distribution for both 6He2+ and 18Ne10+ ions are shown in Figure 14. The losses are
dominated by radioactive decay. Losses due to charge exchange are negligible, as the cross sections
for electron capture are very small. The 6He2+ ions which decay within the straight sections hit the
vacuum chamber within the first and second dipole doublet. Due to their higher magnetic rigidity
the decayed 18Ne10+ ions hit the chamber between the first and second dipole doublet and the
corresponding quadrupole magnets, while some ions hit the magnets themselves.

14

Table 6: Beam parameters used with StrahlSim.

Table 7: Vacuum parameters used with StrahlSim.
The transmission is almost independent of the pumping speed and the residual gas pressure. This is
due to the low cross sections for electron capture. Beam losses at injection are crucial for the
transmission. Figure 15 shows the number of particles in the RCS ring and the accumulation of
particles in the PS. This calculation assumes a beam loss at injection of 20 %. This assumption
leads to 6.58×1011 ejected 6He2+ ions and 2.07×1011 18Ne10+ ions per cycle. The number of
accumulated particles within the PS after 20 injections from the RCS considering ongoing decay is
about 8.12×1012 for 6He2+ and 3.39×1012 for 18Ne10+. This is less than the designated numbers of
1.1×1013 and 4.51×101 for 6He2+ and 18Ne10+ respectively.
One possibility to increase the number of particles accumulated within the PS is to reduce the losses
at injection. Figure 16 shows the dependence of the number of ejected particles on the losses at
injection. In order to eject more than 8×1011 6He2+ ions or 2.5×1011 18Ne10+ ions per cycle one has to
reduce the losses to about 3 %.

15

Figure 14: Loss distribution for 6He2+→6Li3+ (top) and 18Ne10+→18F9+ (bottom) at injection energy.
Dipole magnets are shown in light blue, quadrupole magnets in red and blue.
In the following, the required pumping speed of the vacuum system in order to maintain a residual
gas pressure below 1×10-8 mbar is investigated. Figure 17 shows the pressure within the RCS over
20 cycles for effective pumping speeds varying between 2 and 10 m3/s. Using 18Ne10+ as projectile
ion the pressure stays below 1×10-8 mbar for pumping speeds greater than 2 m3/s, reaching a
maximum for Seff=5 m3/s of about 6.5×10-9 mbar. The situation for 6He2+ is different. For pumping
speeds less than 10 m3/s the pressure goes up exceeding the 1×10-8 mbar limit. This is due to beam
losses at injection. The pumping speed is not sufficient to remove enough of the gas desorbed at
injection before the next cycle starts.

16

Figure 15: Number of particles over twenty cycles for 6He2+ (left) and 18Ne10+ (right). The blue line
shows the accumulation of the particles within the PS.

Figure 16: Number of ejected particles against beam losses at injection for an effective pumping
speed of Seff=5 m3/s for 6He2+ (left) and 18Ne10+ (right).
As it is desirable to have a conventional pumping system1 installed in the RCS, the best way to
work around this problem would be to reduce the beam losses at injection. If it is possible to reduce
the losses to about 10% an effective pumping speed of 5m3/s would be sufficient to stay below the
1×10-8 mbar limit. This is visualized in Figure 18. If the injection losses cannot be reduced one has
to consider an increase of the pumping speeds for example by applying NEG-coating to a part of the
vacuum chamber. This analysis was done for 6He2+ only, since the pressure evolution for 18Ne10+ is
not critical. Because most beam losses occur within or close to the dipole magnets, it is best to
apply an eventually needed NEG-coating to these. Figure 19 shows the pressure in case of NEG17

coated dipole chambers for 6He2+. The number of NEG-coated dipole chambers was varied between
8 and 20 per arc. For all calculations the maximum residual gas pressure is 5×10-9 mbar, while the
effective pumping speed due to the NEG ranges from about 310 to 650 m3/s for 8 and 20 coated
dipoles respectively.

Figure 17: Pressure evolution over 20 cycles for different effective pumping speeds (2 to 10 m3/s)
for 6He2+ (left) and 18Ne10+ (right).

Figure 18: Pressure evolution for different losses at injection ranging from 2.5 to 20 %. The
pumping speed for the calculations is Seff=5m3/s.
Of course one has to consider an ongoing saturation effect, which reduces the pumping speed of the
NEG coating over time. If NEG-coating is needed all dipole magnets should be treated with NEG to
ensure a stable residual pressure over the whole operation time. It is important to remark, that only
beam losses inside the RCS ring are relevant for the calculation of the pressure bump at injection. In
18

this sense a beam loss of 20% means that all particles are lost inside the machine. Losses outside the
machine, e.g. inside a drift line just before injection do not contribute to the pressure rise and must
be subtracted. In general it is hard to distinguish these two effects.

Figure 19: Pressure evolution with NEG-coated dipole chambers. The projectile ion is 6He2+ and
the pumping speed is Seff=5 m3/s. The number of NEG-coated dipole doublets per arc was altered in
the range from 4 to 10 for the different lines.
The beam losses and their effects on the residual gas pressure have been investigated using the
program StrahlSim. Concerning the required effective pumping speed, 5 m3/s is sufficient to stay
below 1×10-8 mbar when using 18Ne10+ as the projectile ion. The maximum pressure for this
scenario is 6.51×10-9 mbar. In case of 6He2+ an effective pumping speed of 5 m3/s would not be
enough if there are 20% beam losses at injection inside the RCS ring. Reducing the beam losses by
a factor of two and therefore reducing the pressure bump induced by desorbed gases, would lead to
a maximum pressure slightly below the 1×10-8 mbar limit.
If the losses at injection cannot be reduced, an effective pumping speed of more than 10 m3/s would
be needed. This is to our best knowledge not achievable by using conventional pumping techniques.
If such a pumping speed is required one has to consider applying a NEG-coating to the vacuum
chambers of the dipole magnets. It was shown that NEG-coating leads to a maximum residual gas
pressure of 5×10-9 mbar.
RCS radioprotection studies
Detailed radioprotection studies were realized according to the different loss mechanisms within the
RCS. They permitted to define the shielding required by the machine operation, the classification of
the area and eventual limits on the release of airborne activity.

19

Figure 20 : Layout of the RCS. The different kinds of losses and their locations in the ring are
shown.
Beam losses can be divided into injection, decay and RF capture-acceleration losses. At injection
30% of the beam is lost on the septum. Decay losses are uniformly distributed in the dipoles and in
the short straight sections in the arcs during all the magnetic cycle. RF capture-acceleration losses
are point losses that occur in the families of quadrupoles in the arcs as indicated in Figure 20 (QP).
All the percentages of beam lost in the RCS are summarized in Table 1: they are given for 3
energies in the machine energy range. For injection loss percentages are referred to the incoming
beam, for decay and RF-acceleration losses to circulating beam.
Energy (MeV/u)

Injection

Decay

RF capture - acceleration

100

30%

0.10 (0.45) %

5.70 (9.40) %

400 (640)

-

0.80 (0.20) %

2.85 (8.50) %

787 (1650)

-

1.80 (0.70) %

4.75 (5.05) %

Table 8 : Beam loss percentages for 6He (18Ne)
The areas around the RCS tunnel will probably be classified as supervised radiation areas during
operation, with a dose rate constraint of 3 µSv h-1: the respect of this value would require concrete
shielding thicknesses ranging from 3 to 5 m, depending on the position in the tunnel. In these places
where different kinds of losses occur, the thickness imposed by the dominating mechanism was
considered.
In the released airborne activity study a constant rate of 10000 m3 h-1 was chosen for the ventilation
system in the RCS tunnel. In this condition, the effective dose given to the reference population in
one year of operation was estimated to be in the order of 0.7µSv for the worst ion, i.e. 18Ne. It is
well below the reference value for CERN emission and could be further decreased enlarging the
ventilation outlet dimensions. Figure 21 presents the contributions of the main radionuclides to the
annual effective dose.

20

Figure 21 : Annual effective dose to the reference population: contributions from the main
radionuclides.
For the inhalation dose to workers that could access the tunnel during shutdown periods a
conservative assumption was made: the ventilation system is not operating. The intervention time
depends on dose rates and on whether or not the ventilation system is on. For a 1-hour intervention
the integrated dose does not exceed the constraints, much less than 1 µSv even without waiting time
(see Table 9). Furthermore, if the ventilation system is working a waiting time before access of
nearly 20 minutes is enough to completely change the air in the tunnel.
tirr

twait

tint

Inhalation Dose (µSv)

24 hours

0

1 hour

1.41E-01

24 hours

1 hour

1 hour

6.48E-02

1 week

0

1 hour

2.56E-01

1 week

1 hour

1 hour

1.80E-01

3 months

1 hour

1 hour

9.30E-01

Table 9 : Inhalation dose to workers for various irradiation times tirr and waiting times twait. tint is
the intervention time.
Dose rates from material activation were calculated for a 3-month continuous operation and 3
different waiting times of 1 hour, 1 day and 1 week (Figure 22). The results show that, according to
CERN area classification, the RCS tunnel is likely to be classified as a limited stay area, accessible
1 week after the shutdown. The doses do not decrease much after 1 week because the residual
radionuclides that mostly contribute to the total dose have half-lives longer than 1 week. The high
activation of the machine elements that remains after 1 week may require a remote handling system
for the maintenance.

21

Figure 22 : Residual dose rates for a 3-month irradiation and 1-week waiting times for septum,
quadrupoles and dipoles in the arcs for 6He ions. Left: top view. Right: front view.

VI.

Ion acceleration scenarios in PS and SPS

Ion acceleration in the PS and SPS is a routine operation since many years. Different ion types from
light ions such as sulfur up to heavy ions such as lead have been accelerated. We summarize here
the results of the study realized by CERN within FP6 for the acceleration of the Beta-Beam
nuclides 6He and 18Ne [24]. Dynamics vacuum studies were in addition performed by GSI. They are
reported in [16]. An acceleration in the PS2 is being followed at CERN as a non-baseline option.
Finally dedicated studies for protecting the PS magnets from too high power deposition, and RadioProtection studies were initiated at GSI with the help of CERN [16].
22

PS - RF considerations
Since the beta-decay lifetime at injection in the PS is much longer than the cycle time of the RCS, it
pays to operate the PS at the rf harmonic consistent with the 10 MHz upper frequency limit of the
accelerating cavities and to transfer the maximum number of batches from the RCS. Thus, the PS
harmonic of choice becomes h=21 and 20 bunches are accumulated one by one leaving one rf
bucket empty to accommodate the extraction kicker risetime.
Figure 23 shows how beta-decay diminishes the number of helium ions accumulated on the PS
injection plateau. Figure 24 shows the corresponding relative intensity along the bunch train. As
little as 40% of the first helium bunch remains when the last one arrives.

Figure 23: Number of helium ions accumulated in the PS versus RCS batches.

Figure 24: Relative helium intensity along the bunch train in the PS.
The situation is better in the neon case due to its longer half-life and more advantageous charge-tomass ratio, but the PS extraction kicker gap must still be established at a different position within
the bunch train from batch to batch in order to even out the bunches that are ultimately stored in the
decay ring.
The longitudinal emittance that the PS must deliver is 0.80 eVs in the case of helium ions and
1.8 eVs for neon. This implies matching voltages of ~30 kV and ~10 kV, respectively, in order to
provide the requisite bunch length of 20 ns at ejection. No bunch shortening gymnastics are
required due to the addition of a 40 MHz rf system in the receiving SPS (see next section).
Vacuum System Requirements for the PS
The parameters used for the simulations of the dynamic pressure are listed in Table 10 and Table 11.
The data in Table 10 were taken from “The EURISOL Beta-beam Facility Parameter and Intensity
Values” generated at 12. March 2009.

23

Table 10: Beam parameters used with StrahlSim.

Table 11: Vacuum parameters used with StrahlSim.
The loss distributions for both 6He2++and 18Ne10+ ions are shown in Figure 25 for one section of the
PS. The losses are dominated by radioactive decay. Losses due to charge exchange are negligible,
as the cross sections for electron capture are very small. For both 6He2+ and 18Ne10+ the losses are
spread over the whole ring.
The transmission was checked by using an ideal cycle assuming the maximum number of particles
coming from the RCS. The numbers were taken from”The EURISOL Beta-beam Facility Parameter
and Intensity Values”. A graphical representation is given in Figure 26.
For 6He2+ there are 20 injections from the RCS with 8.29×1011 ions per injection, which
accumulates to 1.06×1013 particles before the acceleration starts. This leads to 9.37×1012 ejected
ions. This number is close to the desired number of 9.53×1012. For 18Ne10+ there are 20 injections
with 2.59×1011 particles each. The number of accumulated particles is 4.51×1012. Given these
numbers there were 4.29×1012 particles ejected. This is again very close to the desired number of
4.31×1012.

24

Figure 25: Loss distribution for 6He2+→6Li3+ (top) and 18Ne10+→18F9+ (bottom) at injection energy.
The combined function magnets are shown in light blue/magenta.
The effective pumping speed is essential for the simulation with StrahlSim to get a reliable pressure
evolution. The effective pumping speed used in the simulations was estimated as follows. There are
147 vacuum pumps along the PS ring, which were assumed to be equally distributed. Together with
the given total pumping speed of 38 m3/s, StrahlSim calculates an effective pumping speed of about
11.5 m3/s.
The pressure evolution over one and five cycles for 6He2+ and 18Ne10+ is shown in Figure 27. The
pressure stays well below 1×10-8 mbar for both 6He2+ and 18Ne10+, when a pumping speed of
11.5 m3/s is assumed. The maximum pressure is 5.8×10-9 mbar and 3.2×10-9 mbar for 6He2+ and
18
Ne10+ respectively. The minimum effective pumping speed required in order to stay below 1×108
mbar was estimated to be about 9 m3/s (dashed lines in Figure 27). If the pumping speed is less
and 6He2+ is used as the projectile ion, the pressure limit will be exceeded. Operating the PS with
18
Ne10+ the minimum pumping speed is about 7 m3/s.

25

Figure 26: Number of particles over one cycle for 6He2+ and 18Ne10+.

Figure 27: Pressure over one and five cycles for different effective pumping speeds (11.5 and
9.0m3/s) for 6He2+ and 18Ne10+.
The beam losses and their effects on the residual gas pressure have been investigated using the
program StrahlSim. At an accelerator operation with 6He2+ and 18Ne10+ as projectile ions an effective
pumping speed of 11.5 m3/s in the PS ring is sufficient. This pumping speed is delivered by the
existing vacuum system of the PS. The minimum effective pumping speeds needed for a stable
operation were estimated to be 9 m3/s and 7 m3/s for 6He2+ and 18Ne10+ respectively.
PS Radioprotection studies
A preliminary study has focused on two radiation protection aspects related to the operation of PS
as part of a Beta-Beam facility, namely the induced radioactivity in the magnets and the air
activation. A complete study would also include an analysis of the existing shielding (in particular
26

with respect to those points, like the PS bridge, where the shielding is relatively thin), the prediction
of induced radioactivity in hot components like septum magnets and the activation of the cooling
water of the magnets. At this stage it is not possible to perform such a detailed study because of the
lack of information on the operation conditions and on the exact particle loss distribution.
Nevertheless, during this study it was possible to assess the impact that the Beta-Beam operation
would have on the radiation level expected during maintenance and on the release of radioactivity
to the environment.

Figure 28 :From top to bottom: ambient dose equivalent rate after 3 month irradiation followed by
27

1 hour, 1 day and 1 week waiting time. Left: 6He case. Right: 18Ne case.
At the beginning of the annual shutdown period in 2008, radiation survey measurements of ambient
dose equivalent rate were performed to gain information about the present radiation levels in the
CERN PS [25]. The survey measurements are done at 40 cm distance from the object of concern,
usually the vacuum chamber. The average dose rate along the PS ring is about 250 µSv h-1, with
40% of the measured points below 100 µSv h-1 and only 5% above 1 mSv h-1.
FLUKA [26][27] simulations with 3-month continuous irradiation of 6Li and 18F and 1-week
waiting (Figure 28) show that the dose rate at 40 cm distance from a PS magnet would range
between 60 µSv h-1 and 2 mSv-1 which is relatively high compared to the present level of induced
radioactivity. This indicates that the tunnel would remain accessible with limited stay during
maintenance – as long as the maintenance operations are well planned and optimized in order to
reduce doses to workers. These values also suggest that there might be magnets whose levels of
induced radioactivity require remote handling. This eventuality can only be confirmed or ruled out
by a detailed study with precise and realistic scenarios of beam losses and with the implementation
of the exact material composition (including traces).
The effective dose given to the reference population in a 1-year operation of the PS, due to the air
release in the environment, is 0.37 µSv for the He-operation and 0.35 µSv for the Ne-operation.
Table 12 shows the contribution of the main radionuclides to the effective dose. As the total
effective dose given to the population by all CERN installations must not exceed 10 µSv, the
contribution from the PS only is within this value.
Contributions to the effective dose from the main radionuclides (µSv
per year)
6

He

18

Ne

13

N

0.171

0.156

15

O

0.078

0.073

11

C

0.078

0.074

14

O

0.011

0.010

Ar

0.020

0.020

41

Table 12 : Contributions to the effective dose from the main radionuclides (µSv per year).
SPS - RF simulations
Rather than consider another new machine, the space charge bottleneck at SPS injection has been
addressed by adding a “modest” 40 MHz rf system to the existing infrastructure. This would allow
much longer bunches to be transferred from the PS, the matching voltage for 20 ns bunches being
~120 kV and ~5 kV for helium and neon, respectively. Then, near transition when the bunches are
short enough, the standard 200 MHz system of the SPS would take over for the bulk of the
acceleration. Conceptually this is fine, but the baton must be passed between buckets of very
different aspect ratio so mismatching the bunches is unavoidable.
1 MV at 40 MHz is at the limit of what might be considered as “modest” and constrains the
maximum ramp rate to around 0.1 T/s in the early part of the cycle. Even so, the ramp rate must be
slowed down still further for the rebucketing because even a small ramp rate reduces the 200 MHz
bucket length and buying this back with voltage is costly in terms of mismatch. Assuming a ramp
rate of 0.02 T/s and that the emittance the SPS is supposed to deliver is already established before
28

transition, Figure 29 shows how proximity to transition (γtr=23) reduces the 200 MHz voltage that is
required to accommodate the bunch length accelerated in the proposed new 40 MHz bucket.
Performing rf gymnastics close to transition is bound to be a delicate matter, but it incurs no penalty
in mismatch because the aspect ratios of the two buckets scale identically with γ.

Figure 29:Ratio of 40 MHz bunch length to 200 MHz bucket length versus 200 MHz voltage for
helium ions at γ=19, 20, 21, 22 (from top to bottom) and a ramp rate of 0.02 T/s in the SPS.
Figure 30 and Figure 31 show ESME simulations of rebucketing at γ=21.5 from 1 MV at 40 MHz
to 1.75 MV at 200 MHz for helium ions. The bunch is mismatched at 200 MHz, but one quarter of
a synchrotron period later (Figure 32) it can be rematched by a step in voltage to 7.9 MV (Figure
33). Thereafter, the ramp rate can be increased and acceleration can proceed normally.

Figure 30: 1.0 eVs bunch of helium ions in a 1 MV, 40 MHz
bucket at γ=21.5 and a ramp rate of 0.02 T/s in the SPS.

29

Figure 31: The bunch of Fig. 9 after the 40 MHz bucket is
superseded by a 1.75 MV, 200 MHz one.

Figure 32: The bunch of Fig. 10 after rotation during a
quarter of a synchrotron period.

30

Figure 33: The bunch of Fig. 11 after a step in 200 MHz
voltage to 7.9 MV. A small fraction of the bunch population
remains at large amplitude.
Despite a larger emittance, the situation is easier in the neon case due to its advantageous charge-tomass ratio. Although rebucketing must still be performed at the same miniscule ramp rate of
0.02 T/s, proximity to transition can be decreased to γ=20 and still have 1 MV at 40 MHz passing
the baton to 1.75 MV at 200 MHz. 7.8 MV at 200 MHz is needed to rematch.
1 MV is very much the minimum 40 MHz voltage required. It also costs cycle time because of the
need to slow the ramp rate down to permit rebucketing. However, since the 40MHz system sees
almost all the frequency swing during acceleration, more voltage would be expensive.
Alternatively, one could consider rebucketing at zero ramp rate as this reduces slightly the problem
of matching.
The longitudinal emittance that the SPS must deliver is 1.0 eVs in the case of helium ions and
2.2 eVs for neon. These values are derived from the known performance for protons and, allowing
an emittance budget of some 25% for blow-up during each acceleration stage, they also fix those in
all the upstream machines. The novel injection scheme proposed for the decay ring requires the
beam to be delivered off-momentum into the non-linear region of the receiving bucket.
Consequently, the bunch is deliberately mismatched before extraction from the SPS by a step down
in 200 MHz voltage (see Figure 34). This bunch tilting is a first-order attempt to increase the
capture efficiency at the end of a quarter of a synchrotron turn in the decay ring. The fine detail of
capture will depend on the large-amplitude distribution created in the SPS.

31

Figure 34: An SPS bunch of helium ions (green) is delivered tilted (following a step down in rf
voltage from 2 to 0.5 MV) and 5‰ off-momentum with respect to the stack (red) in the decay ring.
Vacuum System Requirements for the SPS
The parameters used for the simulations of the dynamic pressure are listed in Table 13 and Table 14.
The data in Table 13 were taken from”The EURISOL Beta-beam Facility Parameter and Intensity
Values” generated at 12. March 2009.

Table 13: Beam parameters used with StrahlSim.

Table 14: Vacuum parameters used with StrahlSim.
The loss distribution for both 6He2+ and 18Ne10+ ions are shown in Figure 35 for one section of the
32

SPS. The losses are dominated by radioactive decay. Losses due to charge exchange are negligible,
as the cross sections for electron capture are very small. For both 6He2+ and 18Ne10+ the losses are
peaked behind the quadrupole magnets.

Figure 35: Loss distribution 6He2+→6Li3+ (top) and 18Ne10+→18F9+ (bottom) at injection energy.
Dipole magnets are shown in light blue, quadrupole magnets in red and blue.
The transmission was checked by using the proposed cycle assuming the maximum number of
particles coming from the PS. The numbers were taken from “The EURISOL Beta-beam Facility
Parameter and Intensity Values”. For 6He2+ there are 9.53×1012 ions injected coming from the PS.
This leads to 8.99×1012 ejected ions. For 18Ne10+ there are 4.31×1012 injected and 4.25×1012 ejected
particles. These numbers are arguably identical with the desired numbers of 9.0×1012 and 4.26×1012
for 6He2+ and 18Ne10+ respectively.
The effective pumping speed used in the simulations was estimated as follows. Every SPS magnet
has an ion pump with a pumping speed of 20 l/s. Considering the MBA, MBB, QF and QD magnets
only, StrahlSim calculates a conductance corrected effective pumping speed of Seff=2.6 m3/s.
Placing pumps at the positions were are no dipoles in the ring, leads to Seff=2.8 m3/s. This is close to
the value of Seff=2.28 m3/s. given in the “Parameter and Intensity Values” document. All
simulations carried out for the SPS assuming Seff=2.8 m3/s (differing values are given explicitly).
During the simulations it turned out, that ionization of residual gas particles by the revolving beam,
called target ionization, is the dominant effect that causes a pressure rise in the SPS during Beta
33

Beam operation. The cross sections for target ionization are given by a scaled Bethe formula [28].
The ionized gas particles are accelerated away from the beam by its space charge potential. When
these particles hit the vacuum chamber a low energy desorption process takes place. The desorption
rate η for this process is considered to be in the range between 1 and 10 desorbed particles per
ionized gas particle hitting the vacuum chamber [29], while the ”Parameter and Intensity Values”
document states a value of 10.
Figure 36 shows the pressure evolution for the proposed cycles using 6He2+ and 18Ne10+ as projectile
ions. The pressure evolution strongly depends on the assumed desorption rate. For 6He2+ the
residual gas pressure is not stable when a desorption rate greater than 5 is assumed, while for
18
Ne10+ even in case of η=1 the pumping speed is not sufficient to stabilize the pressure. For
comparison Figure 36.shows the pressure evolution for 18Ne10+ with an effective pumping of
7.5 m3/s and η=1.

Figure 36: Pressure evolution over several cycles for 6He2+ (left) and 18Ne10+ (right) for different
desorption rates using the proposed cycle. For 18Ne10+ there is one simulation with an increased
effective pumping speed of 7.5 m3/s.
One possibility to reduce the pressure build up is to reduce the acceleration time within the SPS.
The acceleration time can be shortened from 2.54 s to 1.58 s for 6He2+ and from 1.42 s to 0.90 s for
18
Ne10+, when using the maximal available ramping rate of the SPS of 0.74 T/s. Furthermore the
cycle time of the 18Ne10+ cycle was extended to 6 s in order to give the vacuum more time to relax.

34

Figure 37 shows that this measurement would slow down the pressure rise for 6He2+ operation with
η=10 and stabilize the 18Ne10+ operation with η=1. In this scenario accelerating 18Ne10+ ions with
η>1 is still not feasible. In the following paragraph the effect of an increased effective pumping
speed will be discussed.

Figure 37: Pressure evolution over several cycles for 6He2+ (left) and 18Ne10+ (right) for different
desorption rates using the maximal available ramping rate and extending the 18Ne10+ cycle to 6 s.
As shown before the operation with 6He2+ is stable for η=5. In Figure 38 the pressure evolution for
6
He2+ operation with the increased ramping rate and η=10 is shown for several effective pumping
speeds. At a pumping speed of 4 m3/s the pressure is stabilized below 1×10-8 mbar. For 18Ne10+
various combinations of η and Seff have been calculated assuming the maximal ramping rate and an
extended cycle time of 6 s. Figure 13 shows a selection of the obtained results. For each η=1, 3
and 5 the required pumping speeds were estimated to be 2.8 m3/s, 7.5 m3/s and 12.0 m3/s
respectively.
35

Figure 38: Pressure evolution over several cycles for 6He2+ (left) and 18Ne10+ (right) for different
effective pumping speeds. For both projectiles the maximal available ramping rate of the SPS was
assumed and for 18Ne10+ the cycle time was extended to 6 s. The desorption rate used for 6He2+ was
η=10. The rates for 18Ne10+ are given in the legend.
The interactions of the beam with residual gas particles and their effect on the pressure evolution
inside the SPS ring have been investigated using the program StrahlSim. The simulations show, that
during SPS operation with 6He2+ or 18Ne10+ as the projectile ions, there is a massive pressure build
up due to ionization of residual gas particles induced by the circulating beam.
It could be shown, that an operation with 6He2+ ions is possible, if the desorption rate for ionized gas
particles hitting the vacuum chamber is less or equal to five. In this case the residual gas pressure
stays below 1×10-8 mbar. Should the desorption rate be greater than five, the pressure can be
stabilized by reducing the acceleration time from 2.54 s to 1.58 s by using the maximal available
ramping rate of 0.74 T/s and increasing the total effective pumping speed to approximately 4 m3/s.
An operation using 18Ne10+ ions with the proposed cycle is not possible without adjusting the cycle
or the pumping speed. In case of a desorption rate η=1 either the effective pumping speed has to be
increased to about 7.5 m3/s or the acceleration time has to be minimized by using the maximal
available ramping rate of the SPS, while the cycle has to be extended to 6 s in order to give the
vacuum enough time to relax. The increased ramping rate reduces the acceleration time from 1.42 s
to 0.90 s. If the desorption rate is greater than one, the higher ramping rate and the extended cycle
of 6 s have to be combined with a higher effective pumping speed. For desorption rates η=1, 3
and 5 effective pumping speeds of 2.8 m3/s, 7.5 m3/s and 12.0 m3/s have to be applied.
Identification of limitations in PS and SPS
The budget of decay losses within PS and SPS was estimated and compared to CNGS operation by
CERN in [30]. From that study, it turned out that the power losses occurring for the Beta-Beam
operation are in the same order of magnitude than CNGS for nominal intensities of 6He and 18Ne
and are therefore not a showstopper for the project.

36

VII.

Design of Decay ring

The design of the decay ring of the beta-beam facility was performed by CEA Saclay [31],[32]
using a stacking mechanism as was originally proposed by CERN [13],[14]. CERN has conducted a
preliminary design of the collimation section starting from the optics proposed by CEA, and a study
of the dipoles of the arcs for protecting them from high energy deposition using FLUKA and
ACCSIM softwares. The RF was studied by CERN and an original solution was proposed (see
section RF system, also presented in [31]).

Optics
The decay ring is a 6911.5 m-long racetrack-shaped-ring with two 2468-m-long straight sections, of
which one is directed toward the detector situated in the Fréjus tunnel [33]. The useful section is
around 36 % of the circumference. Table 15 presents the lattice parameters of the decay ring.
The parameters of the beam are given in Table 16. A first consequence to store high intensity beams
is that the tune spread due to the space charge effects may not be negligible. The tune shift was
calculated for 6He2+ and 18Ne10+ and is given in Table 16. With nominal parameters, the space charge
effects can be neglected in 6He2+ case contrary to 18Ne10+ case. A solution to decrease the space
charge effect would be to increase the rms emittance of the stored beam by injecting a mismatched
beam. To have a manageable tune shift for 18Ne10+ of -0.063 in the horizontal plane and -0.055 in
the vertical one, the rms emittance must then be enlarged up to 0.22 π mm.mrad in both planes. In
the following, we assume this rms emittance for 18Ne10+ to neglect space charge effects.

Total length
Radius
Straight section length
Arc length
Qx
Qz
Q’x
Q’z
Α
Η

M
M
M
M
10-3
10-3

Angle
1/ρ

Rad
m-1

Total number
Kmax
Gmax

m-2
T/m

Family number
Total number
SmaxL
HmaxL

6911.5
1100
2468
988
22.226
12.161
-1.717
-2.351
1.512
1.412

m-2
T/m

ARC DIPOLES

π/86
6.43 x 10-3

QUADRIPOLES
176
+4.848 x 10-2
+45.326

SEXTUPOLES
6
44
0.151
141.174

Table 15: Lattice parameters of the Beta-Beam decay ring.

37

γ
Bρ
Bdipole
τ at rest
Ninjected (ions/batch)
Nstored (ions/batch)
Bunch number
rms εx
rms εy
∆νx
∆νy

Units
T.m
T
S
π mm.mrad
π mm.mrad
-

6He2+
100
938
6
0.8
9.05×1012
9.71×1013
20
0.11
0.06
-0.015
-0.024

18Ne10+
100
563
3.6
1.67
4.26×1012
7.40×1013
20
0.11
0.06
-0.127
-0.201

Table 16: Nominal parameters for the decay ring.
The arcs are 2π insertions of which the optics is given on Figure 39. Four functional parts were
distinguished in the arcs [32]: a regular FODO lattice in the arc, a matching section between the
long straight section and the FODO lattice, which is used to extract the decay products coming from
the long straight section too, a low β − high dispersion insertion for the injection and a matching
section between the regular FODO lattice and the insertion. Moreover, large betatron functions are
needed in the FODO lattices of the long straight sections to maximize the neutrino flux going to the
detector.

Figure 39: Optical functions in the arcs (left) and in the energy collimation section (right). In red,
horizontal betatron functions, in blue vertical betatron function and in green horizontal dispersion.
Injection
The number of injected ions from the SPS is limited by the space charge effects in the PS and the
source [9]- [11]. In order to increase the number of stored ions in the decay ring and reach the
required neutrino flux, the injection has to enable an accumulation of the ions in the decay ring in
presence of the circulating beam. An insertion in the arcs for an off-momentum injection was then
designed following the principle presented in Figure 40. The injection insertion is presented in
detail in [31] and [34], we recall here only its basic principles. The natural dispersion present in the
arcs and the need to keep the long straight sections safe make the arcs the natural location to put the
injection insertion. Moreover, the arc and thus the insertion for the injection are symmetric and
present a waist at the centre of the insertion. During injection the kickers are on, and the injection
septum deflects the incoming beam without perturbing the stored beam. The closed orbit of both
38

beams are forming a bump, with the injected beam running above the septum blade and the
circulating one still running below. The fast kickers are then switched off before the fresh beam has
made a turn, and both beams circulate under the blade. The injection is realized in a high dispersion
- low βx area. For both 6He and 18Ne, an off-momentum injection at δ = 5×10−3 was assumed. The
optics of the injection section was realized with the code BETA [22] and is presented on Figure 41.
The beam sizes in the injection insertion are represented on Figure 42. A specific RF program with
two variable cavity families, of which one is at double frequency, is then used to merge both beams.
It is summarized in the next section.

Figure 40: Injection principle. In blue, injected beam and in red, stored beam. In dashed, central
axes of both beams one turn after injection (kickers off).

Figure 41: Optical functions in the injection section. In red/blue, horizontal/vertical betatron
function and in green horizontal dispersion.

Figure 42: On left, sizes of the stored beam at 6 sigma in the injection insertion. On right, sizes of
the injected beam at 5 sigma in the injection insertion. In red, beam sizes in the horizontal plan and
39

in blue in the vertical one.
Asymmetric bunch merging
After injection, the stored and fresh bunches are horizontally separated and circulating both under
the septum blade. The merging is realized using 2 RF cavities at 40 and 80 MHz. It consists of four
phases terminated with the insertion of the new fresh bunch in the center of the circulating one, as
described on Figure 43 for 6He. The corresponding RF program is detailed in [13][14] and [31].

B)

A)

D)

C)

Figure 43 : The four phases of the bunch merging for 6He as simulated by ESME. A) off-momentum
injection. B) rotation in the longitudinal phase space (synchrotron motion). C) asymmetric bunch
merging. D) symmetric merging leading to the insertion of the fresh bunch into the center of the
stored one.
RF system
This section presents a method to cope with the heavy transient beam loading in the decay ring. The
beam in the decay ring with few but very high intensity bunches leads to heavy transient beam
loading, which is a potential issue for the RF system. The problem is that, with a large beam current
in quadrature to the gap voltage, the cavity will be effectively detuned. In order for the final
amplifier to remain matched, this reactive beam current must be compensated with another reactive
40

element – the tuner. While this may be still feasible for a constant beam current, such a tuner would
become impracticable for a partially filled machine, since it would have to act very fast.
In the following, we will use the existing PS 40 MHz RF system as a reference: it is designed for
𝑅𝑅
bunching of the LHC beam, has a moderate 𝑄𝑄 = 33 Ω and a relatively high 𝑄𝑄 of 18000. More

details can be found in Chapter 8 of Reference [35]. The system is designed for a nominal gap
voltage of 0.3 MV and can cope with 1.2 A of RF beam current. However, a beam current of around
𝑅𝑅
100 A would induce an unacceptably high voltage of 30 MV in a single gap. An even lower 𝑄𝑄 could

mitigate this, but at the expense of proportionally higher installed RF power. We will show in the
following how one could conceive to use a similar RF system in spite of this extremely high beam
current. For a total required gap voltage of 20 MV, about 50 of these cavities would be required.
For illustration, we consider the case of a stationary bucket in a partially filled circular machine.
This is simplifying the situation of the decay ring with its double harmonic RF system somewhat,
but the findings can be generalized. Stationary bucket implies no acceleration, i.e. there is no net
power transfer necessary between the RF system and the beam. Power from the final amplifier will
just have to compensate for ohmic losses in the cavity. Partially filled machine implies a special
class of transient beam loading – i.e. there is either beam or no beam at all (cf. Figure 45).
For a synchrotron above transition and with the bunched beam in the stable phase, the beam
represents an inductive current, which will tune the cavity “up”. For steady state (constant beam
current and gap voltage), the beam could be replaced in the equivalent circuit (Figure 44) by an
𝑉𝑉𝑔𝑔 𝑔𝑔𝑔𝑔
inductivity 𝜔𝜔 |𝐼𝐼 |.
𝐵𝐵

Figure 44: Equivalent circuit of a cavity including beam loading.

To compensate for this inductive beam current, the cavity should be tuned “down” to a
𝜔𝜔
1
𝑔𝑔
𝑅𝑅 |𝐼𝐼 |
frequency 𝜔𝜔0 < 𝜔𝜔, given by 𝜔𝜔0 = 2 ��4 + 𝑔𝑔2 − 𝑔𝑔� ≈ 1 − 2 , where 𝑔𝑔 = 𝑄𝑄 𝑉𝑉 𝐵𝐵 , ω is the operation
𝑔𝑔 𝑔𝑔𝑔𝑔

frequency and ω0 resonance frequency of the cavity. Assuming that the cavity was tuned to the
frequency 𝜔𝜔 initially, this could for example be achieved by adding a parallel capacitor of
2 𝑔𝑔 𝑄𝑄
approximately 𝜔𝜔 𝑅𝑅 (Figure 44).

As an example, we calculate the necessary detuning for the existing PS 40 MHz cavity � 𝑄𝑄𝑆𝑆 =
𝑅𝑅

33 Ω�, for a nominal gap voltage of 300 kV and an RF current of 100 A; in this case, 𝑔𝑔 = 0.011
41

and 𝜔𝜔0 = 0.9945, i.e. the empty cavity should be tuned to 39.78 MHz for operation at 40 MHz. In
the stationary case (constant beam current), this could be implemented for example by adding a
𝑄𝑄
(tuner) capacitor of 2.6 pF in parallel to the existing 𝜔𝜔 𝑅𝑅 = 120 pF.
As mentioned above, a practicable tuner with this relatively large tuning range (0.5 %) would not be
fast enough in the case of transient beam loading implied by a partially filled machine. The
amplifier would consequently have to remain mismatched either in the presence of beam or in the
absence of beam.
In the following, we will describe a concept of how the problem of heavy transient beam loading
could be overcome; the approach is based on the assumption that one may choose any gap voltage
while the beam current is zero. For example, the frequency can be chosen such that the final
amplifier remains matched also in the absence of the beam, while keeping the gap voltage and thus
the stored energy constant.
Let us assume that a circular machine with revolution period T is partly filled: there is full beam
current 𝐼𝐼 𝐵𝐵 for 0 < 𝑡𝑡 < 𝑇𝑇𝐵𝐵 , followed by zero beam current in the interval 𝑇𝑇𝐵𝐵 < 𝑡𝑡 < 𝑇𝑇 (see Figure
45). In order for the RF fields in the cavity to be correct in amplitude and phase again at the next
passage of the beam, the frequency offset must however satisfy the condition that Δ𝜔𝜔(𝑇𝑇 − 𝑇𝑇𝐵𝐵 ) is an
integer multiple of 2𝜋𝜋.
𝜔𝜔

If we can allow to drive the amplifier in this latter interval at 𝜔𝜔0 rather than 𝜔𝜔, it will remain
2𝜋𝜋
permanently matched. With the RF on harmonic ℎ equal to 𝜔𝜔 = ℎ 𝑇𝑇 , this additional phase
Figure 45: Transient beam current in a partially filled machine.

condition now reads: −ℎ 𝑔𝑔 � 𝑇𝑇 𝐵𝐵 � ≈ 𝑇𝑇 ��4 + 𝑔𝑔2 − 𝑔𝑔 − 2�(𝑇𝑇 − 𝑇𝑇𝐵𝐵 ) = 2𝑁𝑁, where 𝑁𝑁 is an arbitrary
integer. For the non-trivial case 𝑁𝑁 ≠ 0 and small 𝑔𝑔, this condition can only be met if both ℎ and
𝑇𝑇 − 𝑇𝑇𝐵𝐵 are large enough; for the value of 𝑔𝑔 from the above example and 𝑇𝑇𝐵𝐵 ≪ 𝑇𝑇, one would require
a harmonic of at least 181 for the phase slip to be −2𝜋𝜋 (𝑁𝑁 = −1). For larger harmonics, this
condition still results in discrete possible values of 𝑔𝑔 for which it can be satisfied exactly; Figure 46
𝑇𝑇
shows these discrete possible values for 𝑔𝑔 plotted over the parameter 𝑇𝑇𝐵𝐵 for a harmonic of 924
(corresponding to the 23.1 μs of the decay ring). With given beam current and cavity parameters,
each of those discrete values corresponds to a gap voltage for which the matching condition is
2
satisfied. For the limiting case 𝑇𝑇𝐵𝐵 → 0, the increment in 𝑔𝑔 would become ∆𝑔𝑔 = ℎ , corresponding
with the above parameters to acceptable gap voltage increments of below 15 kV for a bandwidth of
1 % of the RF system. Since the decay ring will have several tens of these RF systems (with a gap
voltage per cavity of 400 kV, e.g., the number of systems would be 50), any total gap voltage could
be programmed using different voltages in different cavities. This would result in a more
complicated low level RF system, in which different phase programs would have to be programmed
𝑇𝑇
for different cavities, each as function of beam current, the overall voltage and the parameter 𝑇𝑇𝐵𝐵 , but
this is not a conceptual difficulty.
𝑇𝑇−𝑇𝑇

ℎ

42

For illustration, we look again at a single cavity with the above parameters. For 𝑇𝑇 − 𝑇𝑇𝐵𝐵 = 21 μs
𝑇𝑇
( 𝑇𝑇𝐵𝐵 = 0.0866), e.g., one could chose 𝑁𝑁 = −5, resulting in 𝑔𝑔 = 0.01158, very close in fact to the
optimum 𝑔𝑔 = 0.011. Without changing any other parameters, the matching would again be perfect
for a gap voltage of 278.5 kV (instead of the nominal 300 kV). Figure 47 shows the simulation of
this case. The generator current is 0.85 A, constant in amplitude and always in phase with the gap
voltage, i.e. the generator has to deliver around 65 kW in CW (The unloaded shunt impedance is
600 kΩ). Note small ratio of generator current to beam current of below 1%!
The situation in the beta beam decay ring is slightly more complicated since it is using a double
harmonic RF system, the basic idea of the above is however still applicable, since there is no
significant net energy transfer for acceleration. For stability reasons, the RF systems would
certainly have to be dimensioned for higher power than the number given in the above example.
Also the voltages on the 80 MHz system (ℎ = 1848) could be produced using the same principle. A
more thorough analysis is required to determine the needs and possible implementations of the lowlevel RF system.
Figure 46: Discrete values of g as function of TB/T for harmonic 924.

1

0.5

5 -6
10

0.00001

0.000015

0.00002

-0.5

-1

Figure 47: Mathematica simulation of one revolution period with heavy transient beam loading,
assuming a period of 23 µs and a beam current of 100 A over 2 µs. Total current (beam +
generator) in units of 100 A (red); phase of this current in units of π (blue); the resulting gap
voltage in units of 300 kV (green).
43

Momentum collimation
Two loss sources were identified by simulating the injection and stacking processes as described in
the former sections . The first one comes from the fresh ions which are not captured at the injection.
The second one is due to the blow-up in the space (l,δ ) injection after injection. On Figure 48, the
survival of a beam injected at t = 0 is represented as a function of the number of injection cycles.
After around 15-20 injections, most ions are not accepted anymore. When the steady state is
reached, the loss amount between two injections is compensated by the injection itself. About 50 %
(Helium) and 20 % (Neon) of the losses which occurred between two cycles are due to the β decay.
The mean power to collimate in the ring can then be evaluated to 74 kW for 6He2+ and 248 kW for
18
Ne10+. Therefore, a two-step collimation system is needed and was designed to collimate in energy
at δ = 2.5×10−3 (Figure 49). It is located in the long straight section which is not directed toward the
detector.

Figure 48: Loss amount as a function of time for Helium (left) and Neon (right).
A 6D simulation of the collimation section has been done with FLUKA with losses generated by
ACCSIM. At the end of the symmetric bunch merging, the collimation rate can be controlled by
increasing the second harmonic, which shortens the time spread and widens the energy spread. The
energy spread is limited cutting negative energy shifts Es-E0 beyond 2.5‰, as shown on Figure 49.
After a few synchrotron periods, the bunch phase space is homogeneously cut. Such an asymmetric
collimation permits the off-momentum, positive energy shift injection while limiting the
longitudinal phase-space blow-up of the bunches.

Figure 49: 6He bunch phase space stretching after the ramping up of the second harmonic, as
calculated by ESME.

44

D'
α
= − [32][36]. The secondary
D
β
collimators are placed on the beam envelope of a beam with maximum negative dispersion of
2.5‰, alternatively on one side and the other from the collimation section (Figure 50). The energy
distribution of the collimated halo, as estimated in 2D by ESME, could be satisfactorily reproduced
using ACCSIM for calculating the actual evolution of the full 6D phase space of the bunches during
the ramping up of the second harmonic (Figure 51). The loss map as generated by ACCSIM was
then used as an input to FLUKA for simulating secondary particle showers and energy deposition
within the collimation section.
The primary collimator is placed to fulfill the condition:

Figure 50 : Placement of the primary and secondary collimators along the collimation section. The
x and z axis are in meters, and the blue and green lines are the limits of the beam envelope for a
beam emittance of 2.6pi.mm.mrad and maximum δ=2.5‰.

Figure 51 : Left: energy spread of the collimated 6He halo as estimated by ESME. Right: energy
spread of the merged bunch before the ramping up (in black) energy spread of the collimated 6He
halo as after the ramping up (in red), as calculated by ACCSIM.
The size and materials of the collimators were optimized with respect to deposited power and
activation. Graphite collimators of thickness 30 cm were found suitable for the primary and
45

secondary collimators. The deposited power for those should below 10kW, which is commonly
accepted as the limit beyond which deformation issues appear [37]. The use of graphite absorbers
after the collimators and before the second bump of the collimation section decreases considerably
the power losses in the magnet coils [31]. Table 17 and Table 18 present the doses absorbed in the
coils per year for the different magnets of the collimation section when graphite absorbers are used
and placed according to Figure 52. The lifetime of warm magnets is commonly assumed to
correspond to a dose of 10 MGy, beyond which the magnet components such as the resins of the
coils start to deteriorate [37]. For some of the quadrupoles following the primary collimator and for
a running period of 10 years, the doses are still above this limit. This preliminary design of the
collimation section (dipole and quadrupole magnets details, collimators and absorbers) is therefore
being further refined using FLUKA to obtain compatible magnet lifetimes with the 10 years
operation of Beta-Beam.
Dose absorbed in the coils (MGy/Year)
Beam
1st
2nd
3rd
Qdrupole
Qdrupole
Qdrupole
6
2+
He
2.3
1.9
0.4
18
Ne10+
3.0
2.9
1.3

4th
Qdrupole
0.4
1.08

Table 17 : Dose absorbed in the coils of the quadrupoles located after the Primary Collimator
Dose absorbed in the coils (MGy/Year)
Beam
1st Dipole
2nd Dipole 3rd Dipole
6
2+
He
0.9
0.7
0.6
18
Ne10+
1.0
0.8
0.7
Table 18 : Dose absorbed in the coils of the dipoles located in the 2nd bump

Absorbers

Primary
collimator

Secondary
collimator
Beam
Quadrupoles

Figure 52 : Placement of graphite absorbers in the collimation section. (SimpleGeo view [38])
46

Losses by β decay
The decay of the stored ions implies a continuous power loss with a mean value of 10.8 W/m for
6
He2+ and 11.8 W/m for 18Ne10+[32]. The relative rigidity difference between the decay products and
the reference one is around -33% for 6He2+ and +11% for 18Ne10+. In turn, the decay products are
lost after the dipoles. Two principal issues can be underlined. After the long straight sections, the
deposition is equal to several tens of kilowatts: a dedicated extraction section at the arc entry is
needed. Moreover, the deposition in the superconducting magnet coils must be low enough to avoid
quenching. A solution to this problem is to insert absorbing elements between the magnets. For this
layout, a model of a large aperture dipole for the decay ring is needed and it was shown that an 80
mm magnet aperture could be envisaged for the case absorbers between the magnets were needed
[39]. From energy deposition studies of this layout it was concluded that open mid plane dipoles,
which are dipoles without coils around the horizontal plane, could be a better choice. In this case,
absorbers are not necessary which would make the arcs more compact. The required field could
then be 5T instead of 6T and the minimal dipole aperture required would be reduced (±50 mm
against ±80 mm). In addition the structure changes would then be simpler if other ions have to be
used.
To evaluate the power deposition of the decay products in the vacuum chamber, a simple 1D model
was implemented in BETA [22]. It does not take into account any interaction with the walls. It was
applied to the case where absorbers are inserted between the arc dipoles. To improve this study, a 3D
simulation was run, including particle tracking in matter (FLUKA). Particle maps were generated by
ACCSIM. The 1D simulation in BETA and the FLUKA simulation both showed that the average
value deposited in the dipoles is then less than 10 W/m. However, peaks in power deposition exceed
the recommended limit for LHC like magnets (4.3 mW/cm3) for both dipoles and quadrupoles. The
power deposition along an arc cell as calculated with FLUKA using the 6Li3+ ions loss map from
ACCSIM is presented in Figure 53. As an example, the loss profile of the peak heat along D2 is
presented in Figure 54. The maximum deposited peak power was found to be in the order of 30
mW/cm3.
[cm]
Q1

D1
D2
Q2
D3

A1
A2

D4
A3
Q3
A4
[cm]

47

Figure 53 : Overview picture of the energy deposition in an arc cell (including one extra
quadrupole for checking) projected on the horizontal plane for the Li 3+ ions (averaged). Q stands
for Quadrupole and D stands for Dipole. The absorbers (A) are placed after the dipole magnets.

Figure 54 : Peak energy deposition in each longitudinal bin along the superconducting cable on the
dipole D2 in the lattice cell. Recommended limit value for quenching is 4.3 mW/cm3. The bars
represent statistical errors.
Figure 55 shows that the peak energy deposition is situated on the bending plane of the magnets.
The first calculations permitted to estimate the opening angle that could reduce sufficiently the peak
power deposition in the magnet coils. A study of cosθ-design solutions for open mid plane dipole
design [40] shows that this technology is a possible approach. Complementary studies including
energy deposition should follow, to tune the magnet and shielding design in the decay ring.

Figure 55 : Overview of the energy distribution in the superconducting cable on the dipole 3 in the
lattice cell. The superconducting cable is modeled, for simplicity, as a cylinder. Transverse
projection, averaged over the length of the magnet.
Different options of open mid-plane dipoles were studied. From first estimations, based on energy
deposition calculations on large aperture magnets for the solution with absorbers, magnets having
48

5° half-opening angle of the coils in the mid-plane (see Figure 57) were assumed to reduce the
deposited peak power by a factor 10. At 1.9K, open midplane magnets of aperture radius up to
90mm reaching the required field of 6T are feasible. At 4.2K, the radius has to be reduced, coil
layers have to be added and the yoke thickness enlarged (see Figure 56 and Table 19).

Figure 57 : Transverse cross-section of the coil of an open mid-plane dipole magnets for the betabeam decay ring.

Figure 58: Possible open mid-plane magnet designs for the decay ring.
Design

1

2

3

Aperture radius (mm)

60

90

60

Bss at 1.9 K (T)

6.5

6.8

8.7

Operational field at 1.9 K (T)

5.2

5.5

7.0

Bss at 4.2 K (T)

4.9

5.3

6.7

Operational field at 4.2 K (T)

4.0

4.2

5.4

Gap in midplane (mm)

8.9

12.5

8.7

Yoke (mm)

180

270

240

Table 19 : Parameters and performances of the possible open mid-plane magnets presented in
Figure 58.
49

Parametric studies of the open midplane quadrupoles [41] permit to choose an optimum solution
(field, length, aperture). Needed opening angles were estimated from energy deposition calculations
[42] to be less than 6 ° (see Figure 59).
0º
2º
4º
6º

Nominal gradient (T/m

120
100
80

openning
openning
openning
openning

60
40
20
0
100

150
200
Aperture diameter (mm)

250

Figure 59 : Parametric dependence of quadrupole gradient on aperture for different midplane
opening angles.
Dynamic aperture
The study of the dynamic aperture is presented in detail in [31]. We recall here the main results.
The natural normalised chromaticity in the decay ring is respectively Q’x= -1.72 and Q’z= -2.35 in the
horizontal and vertical planes. In order to accept the injected beam at δ=5‰, the natural chromaticity must
be corrected by sextupole families in the dispersive areas. Normally, only two sextupole families situated in
the regular FODO lattices are necessary. We obtain then the blue curve on Figure 60. The dynamic aperture
is large enough. Nevertheless, the coupling resonances are not corrected and the transfer between the two
planes is not negligible. Therefore, other sextupole families were added in order to correct the sextupole
resonances. After correction, we obtain the red curve on Figure 60. The dynamic aperture is much larger and
the beam keeps an elliptic shape during its transport in the structure by assuming all magnetic elements
perfect. The variation of the dynamic aperture with the momentum is plotted on Figure 61 assuming that the
chromaticity is corrected with six sextupole families. In the energy range of the stored beam (±2.5‰), the
dynamic aperture stays large enough to accept the whole beam.

Figure 60: Dynamic aperture for 10,000 turns at the middle of the injection insertion. In red, with 6
sextupole families and in blue with 2 sextupole families.
50

Figure 61: Dynamic aperture around the chromatic orbit for 10,000 turns at the middle of the
injection insertion. In black, at δ=0, in red at δ=2.5 ‰ and in blue at δ=-2.5 ‰.
The impact of defects in the magnetic elements was in addition studied. The large aperture of the
dipoles implies unavoidable multipole components. Until now, only systematic multipole
components were considered. The assumed systematic multipole components in the dipoles are b3 =
−1.68×10−4, b5 = 33.02×10−4, b7 = −50.12×10−4 and b9 = 29.58×10−4 at the reference radius 60 mm
[39]. A direct consequence is a reduction of the dynamic aperture. In order to identify the main
multipole effects, Figure 62 gives the dynamic aperture calculated for each alone multipole
component for the same reference structure. The strongest contribution comes from the fifth and the
seventh order multipole components. In order to decrease their effects, different working points
were considered and an automatic enlargement program of the dynamic aperture was added in
BETA, which enabled to obtain a dynamic aperture of more than 6 σ [43].

Figure 62: Dynamic aperture for 1,000 turns without optimization and after applying the fifth order
(red), the seventh order (blue), the ninth order (green) or every (black) multipole component.
Decay ring radioprotection studies
Losses are present all over the DR and can be subdivided into:
- Injection and merging losses
- Decay losses
- Collimation losses
The decay losses and collimation losses were described in previous sections. Preliminary
radioprotection studies were performed for these two types of losses, while the study of injection
and merging losses remains to be done. The main results of these studies are summarized here.
51

All calculations are performed with the Monte Carlo code FLUKA [26][27]: realistic geometries
are implemented to calculate the residual dose rates during the machine maintenance due to the
activation of the materials and the activation induced in the air in the tunnel. For both types of
losses the loss maps were provided from ACCSIM.
DECAY LOSSES
Recoils from decay are lost after the dispersive elements of the ring. The activation of magnet
materials was therefore estimated both in the arcs and in the collimation section where respectively
superconducting and warm magnets are used. In the collimation section the geometry of typical
warm magnets [44] using typical materials was implemented. In the arcs, both open mid-plane and
standard magnets with absorbers were implemented with geometries consistent with those used for
the study described in section “Losses by β decay”. The losses at the entrance of the arcs or bumps
are assumed to be sent to appropriate beam dumps [31]. An example of residual dose rate map is
shown on Figure 63 for the first bump of the collimation section. For the arcs as well as for the
collimation section, the residual dose rate after 3 month of irradiation and 1 week waiting time is a
few mSv (5-10 mSv·h-1), which corresponds to a “high radiation area” according to CERN rules
(>2mSv·h-1 and <100mSv·h-1).

Figure 63: Residual dose in the 2nd quadrupole of the first bump of the collimation section after 3
month of irradiation and 1 week waiting time. The upper picture represents the magnets
arrangement within the first bump. Left bottom: residual dose map for 6He, right bottom: residual
dose map for 18Ne.
COLLIMATION SECTION
The procedure discussed in section “Momentum collimation” was used for generating the
collimation loss map. After 3 months of irradiation and 1 week of waiting time, the area around the
primary collimator exhibits a peak value above 100mSv·h-1 (prohibited area, see Figure 64) whilst
the entrance of the second bump shows a maximum dose rate of 50mSv·h-1 compatible with a high
radiation area. Remote handling would therefore be highly recommended for the maintenance of the
primary collimator.
52

µSv h-1

Figure 64: Residual dose rate in the straight section of the collimation section, after 1 week waiting
time and 3-month 18Ne irradiation.
AIR ACTIVATION
Using the same approach and parameters as for the RCS, a very preliminary calculation has shown
that the annual effective dose given to the reference population exceeds the 10µSv limit value for both the
ion cases. This latter could certainly be efficiently reduced by optimizing the tunnel-ventilation parameters
on which they are known to be highly depending. Ad-hoc solutions can be found to reduce the emissions,
like e.g. high efficiency filters, different ventilation rates in different segments of the tunnel, etc.

Vacuum System Requirements for the Decay Ring
The parameters used for the simulations of the dynamic pressure are listed in Tables 20 and 21. The
data in Table 20 were taken from ''The EURISOL Beta-beam Facility Parameter and Intensity
Values'' generated at 12. March 2009.

Table 20 : Beam parameters used with StrahlSim.

Table 21 : Vacuum parameters used with StrahlSim.
The loss distribution for both 6He2+ and 18Ne10+ ions are shown in Figure 65 for a part of one of the
53

arcs. The figures distinguish between lost particles hitting the vacuum chamber and particles hitting
the ion catcher. The ion catcher were positioned at a distance of 4 cm from the beam axis. The
extraction of the decayed particles at the end of the straight lines is modeled using an ion catcher,
because StrahlSim is only capable of simulating an extraction at the end of a cycle. The desorption
from this ion catcher, which is very small at the ion energies in the Decay Ring, can be considered
to be ejection losses, which will occur anyway. The simulation furthermore assumes that all lost
ions hitting an ion catcher are stopped inside the catcher. Fragmentation effects are not considered.
The losses shown are dominated by radioactive decay. Losses due to charge exchange are
negligible, as the cross sections for electron capture are very small. For both 6He2+ and 18Ne10+ the
losses are peaked at the positions of the ion catchers. Unfortunately it was only possible to perform
tracking simulations with a relatively low number of ions due to the size of the decay ring. This
leads to the peaked structure of the longitudinal distribution of ions hitting the vacuum chamber. In
reality this should be a continuous distribution. This does not affect the simulations of the pressure
evolution, which will be discussed later.

Figure 65: Loss distribution for 6He2+ → 6Li3+ (top) and 18Ne10+ → 18F9+ (bottom) at injection
energy. Dipole magnets are shown in light blue, quadrupole magnets in red and blue and ion
catchers as gray lines. The peaked distribution of ions hitting the vacuum chamber is due to the low
number of tracked particles (see text). Note that the intensities are scaled logarithmically.
54

The number of particles accumulated in the Decay Ring are 9.66×1013 for 6He2+ and 7.42×1013 for
18
Ne10+. In the 6He2+ cycle there is a reinjection every 6 s and every 3.6 s for an operation with
18
Ne10+, which brings the number of particles back to the desired numbers.
The simulations done with StrahlSim start with the maximal number of particles and inject the
number of lost particles due to radioactive decay after 6 s and 3.6 s respectively. For 6He2+ there are
4.82×1012 and for 18Ne10+ 1.10× 1012 particles reinjected.
The main mechanism for a pressure build up in the Decay Ring is the ionization of residual gas
particles by the circulating beam, called target ionization. The cross sections for target ionization
are given by a scaled Bethe formula [28]. This effect was already observed in the simulations for
the SPS. The ionized particles are accelerated towards the vacuum chamber due to the space charge
potential of the revolving beam. When these particles hit the vacuum chamber a low energy
desorption process takes place. The desorption rate η for this process is considered to be in the
range between 1 and 10 desorbed particles per ionized gas particle hitting the vacuum chamber [29],
while desorption rates less than 1 have been observed [45]. Additionally the re-emission coefficient
has to be considered. This coefficient describes the probability that an incidenting particle is
reflected from the surface of the vacuum chamber. The value of this coefficient was measured for
15
N2 to be less than 0.1 [45] at energies of 2 keV. The simulations for 6He2+ were taken out with an
re-emission coefficient of 1, which is a worst case approximation. Due to the strong dependence of
the pressure evolution on the target ionization in case of 18Ne10+ as projectile ion, re-emission
coefficients of 0 and 1 have been used.
Obviously the starting pressure is a crucial parameter for the simulations. At higher starting
pressures there are more particles that can be ionized by the beam. For the simulations three
different pressures have been used, namely 10-10, 10-11 and 10-12 mbar. As the Decay Ring is a cold
machine 10-10 mbar is already very high. A starting pressure below 10-11 mbar is more realistic.
Nevertheless the value of 10-10 mbar was used to show an upper limit for 6He2+.
The ionization of residual gas particles creates free electrons. Effects caused by these electrons like
electron multipacting are not considered in the StrahlSim code. It has to be ensured, that such
effects do not affect the Decay Ring operation.
The conventional effective pumping speed of the Decay Ring was estimated by using the value of
the SPS of 2.8 m3/s. Compared to the pumping speed delivered by the cold surfaces of the
cryogenic arcs of the machine this value is very small and contributes very little to the total
effective pumping speed. The pumping speed of the cold surfaces depends on their temperature.
The temperature of the arcs was assumed to be 10 K, while simulations for 15 K and 20 K have
been taken out as well. For sufficiently cold vacuum chambers, with a temperature below 16 K (see
text below), the pumping speed of the cold surfaces was calculated by StrahlSim to be about
1000 m3/s. As the whole arcs are cold the vacuum conductance is very high, and the total and the
effective pumping speed is the same. It should be pointed out, that the model used by StrahlSim
assumes that the pressure in the machine is everywhere the same. This means, that the pressure in
the arcs and the straight lines are averaged. But in the Decay Ring the arcs and the lines are going to
have very different pressures due to the completely different pumping techniques used to maintain
the vacuum. In reality the pressure in the arcs will be lower and the pressure in the straight sections
will be higher than the average pressure used by StrahlSim. As StrahlSim cannot calculate a
dynamic longitudinal pressure profile at the moment, this effect is not reflected in the results
presented in this report.

55

Figure 66: The figures show the pressure evolution over several cycles for 6He2+. In the left figure
the temperature of the arcs was set to 10 K, while the starting pressure P0 was varied in the range
from 10-12 to 10-10 mbar. In the right figure the starting pressure for all simulations was 10-11 mbar
and the temperature was varied from 10 K to 20 K. Please note that the lines for T = 10 K and
T = 15 K are almost on top of each other.
All simulations show a very steep pressure rise at the beginning of the simulation. This is, because
the simulations start with the maximal number of particles which is supposed to be stored in the
Decay Ring. The accumulation phase is neglected. This can be justified, as it is only relevant
whether the pressure inside the Decay Ring stabilizes at a value that is low enough for a stable
operation.
For 6He2+ here was a desorption rate for perpendicular incidents of η = 10 and a re-emission
coefficient of 1 assumed. Simulations were taken out for different starting pressures in the rage
from 10-12 to 10-10 mbar and for different temperatures of the cold surfaces between 10 and 20 K.
Figure 66 shows the results. For all reasonable starting pressures and a temperature of 10 K the
pressure evolution stabilizes at sufficiently low values. For temperatures above 15 K the pumping
speed is not sufficient any more to maintain a residual gas pressure below 10-8 mbar. Above this
temperature the residual gas particles do not freeze out any more on the cold surfaces. For
temperatures less than approximately 16 K the pumping speed is almost constant what can be seen
in the right plot in figure 66. The starting pressure of 10-10 mbar gives the upper limit of an
acceptable starting pressure, which should be easily achieved by a cold machine.
The operation of the decay ring with 6He2+ as the projectile ion is feasible according to the
simulation results obtained using StrahlSim.

56

Figure 67: This figure shows the pressure evolution for 18Ne10+ in the Decay Ring for a reemmission coefficient of 1 (left) and 0 (right). The desorption rates were varied from 0.5 to 1 and
2.0 to 3.0 respectively. All simulations were done with a starting pressure of P0 = 10-11 mbar and a
temperature of the cold surfaces of T = 10 K.
For 18Ne10+ the situation is different. Like in the SPS the operation with 18Ne10+ is subject to an
enormous amount of residual gas ionization. Figure 67 shows the pressure evolution for a starting
pressure of 10-11 mbar and a temperature of the cold surfaces of 10 K. The simulations have been
taken out for a re-emission coefficient of 0 (left plot in Fig. 67) and 1 (right plot in Fig. 67).
For a re-emission coefficient of 1 the pressure exceeds acceptable values already for desorption
rates η < 1. For a re-emission coefficient of 0 η can be larger than 2 and the vacuum is still stable.
The real coefficient should be closer to 0 according to [45]. Due to special surface treatments of the
vacuum chambers very low desorption rates η can be achieved. The Beta Beam Operation with
18
Ne10+ ions in the Decay Ring could be feasible when the low energy desorption rates can be
reduced accordingly.
Assuming a desorption rate η = 2.7, Figure 68 shows the dependence of the pressure evolution on
the starting pressure. Under this condition the residual pressure in the Decay Ring stabilizes at
sufficiently low pressure values, as long as the surface temperature of the cold arcs stays below
16 K. The temperature dependence is identical to the dependence observed for 6He2+.

57

Figure 68: The figure shows the pressure evolution for 18Ne10+ assuming a desorption rate of η =
2.7 and a re-emission coefficient of 0. The temperature was set to T = 10 K.
The interactions of the beam with residual gas particles and their effect on the pressure evolution
inside the Decay Ring have been investigated using the program StrahlSim. The simulations show,
that during Decay Ring operation with 6He2+ the pressure does not exceed critical values as long as
the temperature of the cold surfaces in the arcs is less than approximately 16 K. The dependence on
the starting pressure is rather weak. For all considered values of 10-12, 10-11 and 10-10 mbar the
equilibrium pressure stays below 10-8 mbar.
For 18Ne10+ there is a massive pressure build up due to ionization of residual gas particles induced
by the circulating beam. This effect was already observed in the simulations done for the SPS. Only
for small values of the desorption rate of about η < 3 combined with a re-emission coefficient close
to~0, the residual gas pressure in the Decay Ring stabilizes at sufficient pressure values below 108
mbar, as long as the surface temperature of the cold arcs stays below 16 K. Low desorption rates,
even below 1, have been observed and can be achieved by special surface treatments [45]. For Beta
Beam operation such low values have to be assured.

VIII.

Conclusion

A summary has been made of a conceptual design report on a CERN/EURISOL baseline scenario
for the Beta-beam facility. The study focused on the accelerator chain, which incorporates some of
the existing CERN infrastructure. Particular attention was paid to the RCS and Decay Ring
machines that are not part of the latter. An original stacking mechanism has been proposed in the
Decay Ring involving off-momentum injection and novel rf gymnastics to accumulate ions in
longitudinal phase space with minimal emittance dilution. The resultant high stack intensities
present their own problems and detailed studies have been made of momentum collimation in the
Decay Ring and of beam loss, dynamic vacuum and radiation protection issues throughout the
accelerator chain. In addition, since the stack comprises only a small number of bunches, transient
beam loading is a major issue for the rf systems of the Decay Ring. A conceptual approach to
counteract this has been proposed, but further study is required. Even with stacking there remains
pressure on ion production rates and methods to improve these have been investigated within other
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tasks of the EURISOL design study.
From the outset, this study has been based as far as possible on known technology. Nevertheless,
the challenge of unprecedented neutrino production rates has produced, for example, a new stacking
process and an open-midplane superconducting magnet design. The combination of the novel with
the tried-and-tested - underscored by the use of existing CERN machines - has allowed that
challenge to be met without compromising the chances of converting the conceptual design into a
technical one.

IX.

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