20 April 2011
!
LINAC
April 20, 2011
Abstract
The European Spallation Source uses a superconducting linac to provide required protons
to the spallation process. The linac will cost around one third of the overall cost of the project
and needs to be optimized on several aspects. Changing one parameter usually demands for a
reoptimization of the whole linac. A new design which reduces the heat load on the cryogenics
system, while allows deliberate segmentation of the linac is studied, compared to the cold
and warm linacs, results are reported here.
Contents
3 Power, Voltage, and Phase Settings 3
3.1 Choice of Accelerating Gradients . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3.2 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.4 Phase Advance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4 Optimizing Criteria 6
5 Studied Structures 6
5.1 Superconducting Quadrupoles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
5.2 Hybrid Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
5.3 Resistive Quadrupoles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Distances between different components of cryo-modules in case of superconducting
quadrupoles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3 Distances between different components of cryo-modules in case of a hybrid design. 7
4 Distances between different components of cryo-modules in case of resistive quadrupoles. 8
5 Optimized values for warm and cold quadrupole designs. The accelerating gradient
varies as a function of βg in the optimization process as in eq. 1. . . . . . . . . . . 9
6 Beam dynamics performance summary for matched beam, as well as an initial beam
with 50% mismatch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
List of Figures
1 Block layout of the ESS Linac 2010 (not to scale). . . . . . . . . . . . . . . . . . 1
2 Simplified diagram of the three cryomodule layouts used in this study. Top: Contin-
uous (C.CQ.DCR), Middle: Hybrid (C.CQ.HCR), Bottom: Segmented (W.SQ.DCR). 2
3 Top: Accelerating gradient along the SC linac, Bottom: Voltage in the cavity along
the SC linac. Green Cross: discontinuous phase advance variation between Spoke
and low β, Blue Rectangle: Continuous phase advance. . . . . . . . . . . . . . . . . 3
4 Required power per cavity along the SC linac, Green Cross: discontinuous phase
advance variation between Spoke and low β, Blue Rectangle: Continuous phase
advance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
5 Synchronous phase along the SC linac, Green Cross: discontinuous phase advance
variation between Spoke and low β, Blue Rectangle: Continuous phase advance. . 5
6 Phase advance per meter along the SC linac, Green Cross: Step, Blue Rectangle:
Smooth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Spokes Low β High βDTLMEBTRFQLEBTSource HEBT & Upgrade Target
1.6 m 4.7 m 1.0 m 19 m 61 m 59 m 169 m 100 m
75 keV 3 MeV 50 MeV 240 MeV 590 MeV 2500 MeV
352.21 MHz 704.42 MHz
Figure 1: Block layout of the ESS Linac 2010 (not to scale).
1 Introduction
The European Spallation Source, ess, planned to built in Lund, south of Sweden, will require
a high current superconducting proton linac to accelerate protons to be used for the spallation
process on which high flux of pulsed neutrons will be generated. The accelerator is a 5.0 MW
linac delivering proton beams of 2.5 GeV to the target in pulses of 2.0 ms long with a repetition
rate of 20.0 Hz. Beam current is 50.0 mA, which at 352.21 MHz is equivalent to 8.86×108 protons
per bunch. The latest design of the linac can be found at ref. [1] and the 2003 Design Update
can be found at ref. [2].
It is foreseen not to exclude the possibility of a potential upgrade of the linac to a higher power
at the fixed energy of 2.5 GeV, by increasing the current. Increasing the beam current implies
that in case of fixed power couplers the energy gain per cavity will decrease, to reach the fixed
energy of 2.5 GeV, extra cryo-modules will be needed to be installed in current High Energy and
Beam Transport line, as illustrated in Fig. 1. This study is an extension of a former study done
on the optimization of superconducting linac [3], for the sake of completeness some of the more
important criteria and information will be mentioned here again.
Table 1: Parameters of the 2010 baseline linac. System Energy Freq. βGeo No. of Length
MeV MHz modules m Source 0.075 – – – 2.5 lebt 0.075 – – – 1.6 rfq 3 352.21 – 1 4.7 mebt 3 352.21 – – 1.0 dtl 50 352.21 – 3 19 Spokes 240∗ 352.21 0.54∗ 15∗ 61∗
Low β 590∗ 704.42 0.67∗ 10∗ 59∗
High β 2500∗ 704.42 0.84∗ 14∗ 169∗
∗ These numbers will be re-optimized in this study for two linacs using cold or warm quadrupoles.
1
2 Superconducting LINAC structures
Two types of superconducting structures will accelerate the beam from 50 MeV, after the normal
conducting dtl, to 2.5 GeV. The first sc accelerating structure is a 352.21 MHz spoke resonator
followed, after a frequency jump to 704.42 MHz, by two families of elliptical multicell cavities.
As can be seen in Table 1 the sc linac is responsible for 98% of the energy gain and covers
around 90% of the Linac length. The purpose of this study is to find the optimum number of
spokes and cells in each of these three families, as well as the best geometric beta, number of
cavities per each period and finally the transition energy between the neighboring structures.
Since all of these parameters are dependent on each other the optimization has to be performed
in the 8 dimensional space, being composed of 3D of βgs, 3D of number of cavities per cryo-module
and 2D of transition energy between spokes to low β and from low β to high β. The number of
spokes in spoke resonators as well as the number of cells in elliptical cavities is fixed to 2 and 5
respectively by a previous study [3].
Hybrid
50
20 2040 45 4540
Figure 2: Simplified diagram of the three cryomodule layouts used in this study. Top: Continuous (C.CQ.DCR), Middle: Hybrid (C.CQ.HCR), Bottom: Segmented (W.SQ.DCR).
2
These parameters will vary depending on the cryo-module geometry, use of resistive or super-
conducting quadrupoles and sectorization of the cold linac, an example of a simple cryomodule
for different used architecture can be found in Fig. 2.
The simplified diagram in Fig. 2 shows the structure, as well as the distanced for the low β
and high β cryomodules. Spoke cryo modules are having the same layout, just the quad length is
250 mm rather than 400 mm in ellipticals, the intercavity distance, from field to field, is 300 mm
rather than 400 mm, and cavity to wall is 300 mm rather than 450 mm. To check the lengths refer
to Table 2-4.
3.1 Choice of Accelerating Gradients
Figure 3: Top: Accelerating gradient along the SC linac, Bottom: Voltage in the cavity along the SC linac. Green Cross: discontinuous phase advance variation between Spoke and low β, Blue Rectangle: Continuous phase advance.
Choosing the right accelerating gradient is of great importance, since an over specified value
which will not be reached will result to a linac which will be shorter on paper, but will not be
able to bring the beam to its final energy, on the other hand an underspecified value may result to
a linac which will be unnecessarily long. The process of finding a reasonable accelerating gradient
3
is explained in [3], resulting to a gradient proportional to βGeo of cavity through:
Eacc.max = Epeak.surface
1.95/βg + 1.15 · βg − 1 , (1)
where Epeak.surface is the peak electric surface field on the cavity surface, being fixed in this study
to 40 MV/m, Fig. 3, based on [4].
3.2 Power
For the ESS beam current, 50 mA, and an accelerating gradient of ≈ 20 MV/m, the required power
to accelerate the beam would be ≈ 1 MW, for a cavity which is almost 1 m long, in case we neglect
the synchronous phase. At such a high power, around 1 MW per coupler, rf windows have to be
designed carefully due to the high thermo-mechanical stresses which they have to tolerate. A pair
of such couplers capable of delivering up to 1.2 MW, at 50 Hz and for a 2 ms pulse have been built
and tested in Saclay, France. [5].
Possibility of feeding a higher power will be helpful for a potential power upgrade scenario. Power
is limited by the maximum power a coupler can deliver to the cavity. In this study the power per
cavity is limited to 900 kW to leave a safety margin 4.
Figure 4: Required power per cavity along the SC linac, Green Cross: discontinuous phase advance variation between Spoke and low β, Blue Rectangle: Continuous phase advance.
3.3 Accelerating rf phase
Acceleration, and bunching, of the continuous beam of particles out of source starts in the rfq at
−90 and then gradually increases to −20 at the end of dtl. Since the frequency stays the same
in the spokes, the accelerating phase, except for the matching cavities, starts at −20 and increases
by 0.18 per cavity reaching to almost −14 at the very last spoke resonators. By not fixing the
maximum synchronous phase to exactly −15 the energy gain along the low beta region could be
enhanced, Fig. 5. However, the possible shrinkage of acceptance due to this little modification
needs to be checked and must not be large. Elliptical cavities will work on twice the frequency, i.e.
704.42 MHz, and if this frequency jump is not handled correctly a loss of longitudinal acceptance in
4
the transition between these two structures may cause excessive emittance increase and/or particle
loss in elliptical cavities. To keep the bucket size the same, accelerating phase as well as the
accelerating gradient are decreased in the first few periods of the elliptical cavities [6]. Later in the
low β region the synchronous phase stays constant at −15, and in the high beta region it starts
from −15 and gradually ramps to −14. Not ramping the phase and keeping it at the constant
value of −15 will reduce the final energy by around 5 MeV.
Figure 5: Synchronous phase along the SC linac, Green Cross: discontinuous phase advance variation between Spoke and low β, Blue Rectangle: Continuous phase advance.
3.4 Phase Advance
Another boundary condition applied to the optimization process is the limit on longitudinal phase
advance per period. The upper limit chosen during this study is 80 per period in all the three
structures, which in case the transverse phase advance in those regions where the longitudinal
phase advance is at its higher value, has the maximum value of 90 per period still the ratio of
transverse to longitudinal phase advance will be 1.125. Due to frequency jump if we do not limit
Figure 6: Phase advance per meter along the SC linac, Green Cross: Step, Blue Rectangle: Smooth.
the phase advance variation between spoke resonators and low β cavities, there will be a step like
discontinuity in average phase advance, phase advance per meter, at that location, which may
decrease the beam dynamics performance of the machine and act as a bottle neck, to avoid this
5
issue the maximum phase advance variation per meter is limited to 0.5 per meter, in the study it
is referred to former case by “STEP” and the latter one by “SMOOTH”, Fig. 6.
4 Optimizing Criteria
Amongst all the choices the total linac length is chosen to be the criteria for the optimization
process. The reasons behind this choice are:
• Since the maximum power per each cavity is fixed, a shorter linac, requires the klystrons to
be working on the more similar power, which will save energy,
• The shorter the linac the more efficiently power is transformed from wall plug to beam
energy, reducing the running cost of linac
• The linac tunnel will cost around 20% of the whole accelerator project [7], a shorter linac
will require less equipment and therefore the overall cost will decrease.
However, in cases where a linac is found to be a few centimeters longer, but required less equip-
ments, the more economic linac is chosen.
5 Studied Structures
5.1 Superconducting Quadrupoles
The reason for choosing cold quadrupoles is that these quadrupoles can be housed inside the
same cryo-module which is housing the cavities, and therefore a large number of cold to warm
transitions will be removed, resulting to lower heat load in the cryogenics system. The lower power
consumption of quadrupoles does not play a significant role in this selection since this can be
somehow compensated by the required cryogenics power.
However, having a long continuous cryo string requires a longer shut down period in case a cryo-
module needs to be repaired. The other disadvantage of cold quadrupoles is their alignment
precision which is limited to 0.5 mm, the effect of such an error in alignment on the beam quality
has to be studied.
5.2 Hybrid Design
A new type of cryomodule architecture is proposed which allows for a transition between cryomod-
ules in the sub-100 K region. The advantages of the new hybrid design are that it will generate
a lower heat load with respect to a fully segmented design - while still providing easy access
to individual cryomodules for maintenance and repair, allows for independent alignment of the
quadrupoles, which are mounted at the two extremities of cryomodule using LHC type alignment
jacks [8]. It has almost all the advantages of a continuous cold design. The fact that such a design
6
Table 2: Distances between different components of cryo-modules in case of superconducting quadrupoles.
Unit Spokes Low β High β Temp Beginning of cryo-module to the quadrupole mm 250 250 250 Cold Quadrupole length mm 250 400 400 Cold Quadrupole to quadrupole mm 400 400 400 Cold Quadrupole to Cavity mm 400 400 400 Cold Cavity to cavity mm 300 400 400 Cold Cavity to the end of cryo-module mm 300 450 450 Cold Cryo-module to cryo-module† mm 100 100 100 Cold † This length can be integrated to either previous or the next cryo-module if needed.
will be longer should not be considered without noting that it has the extra 500 mm area reserved
for utilities, such as beam diagnostics, vacuum gauges, ... . This option is called hybrid, since it
intelligently uses two ranges of cryo temperatures. All the figures in section 3 are plotted for the
c.cq.hcr. linacs.
Table 3: Distances between different components of cryo-modules in case of a hybrid design.
Unit Spokes Low β High β Temp Beginning of cryo-module to the quadrupole mm 250 250 250 Cold Quadrupole length mm 250 400 400 Cold Quadrupole to Cavity mm 400 400 400 Cold Cavity to cavity mm 300 400 400 Cold Cavity to quadrupole mm 400 400 400 Cold Quadrupole to the end of cryo-module mm 250 250 250 Cold Cryo-module to cryo-module† mm 500 500 500 Cold
† This area can have a different temperature from the main cryomodule, and will house the utilities such as diagnostics, vacuum gauges, ... .
5.3 Resistive Quadrupoles
A linac using resistive (warm) quadrupoles is designed in parallel to the superconducting linac.
Such a design is intrinsically segmented to cryo-modules with doublets of quadrupoles in between
them.
The advantages of this linac are the shorter time to repair/change a cryo-module, higher precision
in alignment of the quads, and the accessibility of warm quadrupoles, however the heat load will
increase because of tens of cold to warm transitions. A schematic drawing of this layout is presented
in Fig. 2.
To decrease the radiation due to activation of materials if possible it is better to avoid copper
in favor of other conductors, such as Aluminum which has the same price/mho, for the quadrupole
windings, since copper is the main source of radiation [9].
The spacings defined in Table 2, 3 and 4, though being studied before being chosen, are the
7
Table 4: Distances between different components of cryo-modules in case of resistive quadrupoles.
Unit Spokes Low β High β Temp Beginning of period to the first quadrupole mm 200 200 200 Warm Quadrupole length mm 250 400 400 Warm Quadrupole to quadrupole mm 400 400 400 Warm Quadrupole to beginning of cryo-module mm 200 200 200 Warm Beginning of cryo-module to cavity mm 300 450 450 Cold Cavity to Cavity mm 300 400 400 Cold Cavity to the end of cryo-module mm 300 450 450 Cold
preliminary values and need the feedback from cryogenics, diagnostics, and rf experts not to cause
any extra heat load, lack of enough space for diagnostics or rf coupling between neighbor cavities.
A schematic view of this layout is shown in Fig. 2.
6 Results
6.1 Optimization
For all the three linacs, with superconducting and resistive quadrupoles, two sets of optimizations
are performed, by using equation 1 to calculate the field for each geometric β. The input energy,
after dtl is set to 49.5 MeV, to compensate for a possible lower energy due to matching. In the
spoke resonators an accelerating field of 8 MV/m is chosen, while for the elliptical cavities a surface
peak field of 40 MV/m is used. Accelerating gradient in each cavity for the following designs is
presented in Table 5. Code GenLinWin, [10], from cea France is used to calculate and find the
optimized linac. The results of this study are shown in Table 5.
6.2 Beam Dynamics
To be able to compare the structures from the beam dynamics performance point of view, a
set of preliminary beam dynamics simulations, using code TraceWin [10] was performed. The
Transverse phase advance follows the longitudinal phase advance with a ratio of transverse to
longitudinal being chosen to be 1.125. A beam of 100, 000 multi particles is generated using a
Gaussian distribution cut at three sigma at the entrance to the superconducting linac. The
beam is matched to the structure, and the matching between structures is done using one pair of
quadrupoles, and a maximum of four cavities on each side. The results are reported in Table 6 in
the first seven rows, with a mismatch value of zero.
To check the sensitivity of different designs in a fast (not necessarily precise and exclusive) way,
in initial mismatch is applied to the beam by increasing the Twiss parameters, i.e.
βmismatch = βmatched × 2.25,
αmismatch = αmatch × 2.25,
in all the three planes to have a mismatch of 50% at injection. The beam is then tracked along the
8
Table 5: Optimized values for warm and cold quadrupole designs. The accelerating gradient varies as a function of βg in the optimization process as in eq. 1.
C.CQ.DCR. C.CQ.HCR. W.SQ.DCR. step‡ smooth‡ step‡ smooth‡ step‡ smooth‡
S p o k es
βGeo 0.56 0.56 0.55 0.57 0.56 0.56 βGeo/Eacc(MV/m) 8 8 8 8 8 8 Final energy (MeV) 235 187 234 188 236 188 βT 0.59 0.54 0.595 0.54 0.59 0.54 Cav./Per. ×Nper. 3 × 14 3 × 11 2 × 19 2 × 14 3 × 14 3 × 11 No. of Quads/Cavs. 28 / 42 22 / 33 38 + 1 / 38 28 + 1 / 28 28 / 42 22 / 33 Cavity cntr.2cntr. (m) 1.0150 1.0150 1.0222 1.0278 1.0150 1.0150 Cryo Length (m) 4.5950 4.5950 3.5044 3.5555 3.3450 3.3450 Period Length (m) 4.6950 4.6950 4.0044 4.0555 4.6450 4.6450 Length (m) 65.729 51.645 76.084 + 1.4 56.777 + 1.4 65.029 51.095
L o w
β
βGeo/Eacc(MV/m) 0.71 0.69 0.72 0.70 0.71 0.69 βGeo/Eacc(MV/m) 15.61 15.27 15.77 15.44 15.61 15.27 Final energy (MeV) 609 605 612 606 608 609 βT 0.79 0.79 0.79 0.79 0.79 0.79 Cav./Per. ×Nper. 4 × 10 4 × 15 4 × 10 4 × 16 4 × 10 4 × 15 No. of Quads/Cavs. 20 / 40 30 / 60 20 / 40 32 / 64 20 / 40 30 / 60 Cavity cntr.2cntr. (m) 1.1554 1.1341 1.1661 1.1448 1.1554 1.1341 Cryo Length (m) 6.5217 6.4366 6.3642 6.2791 5.1217 5.0366 Period Length (m) 6.6217 6.5366 6.8642 6.7791 6.7217 6.6366 Length (m) 66.217 98.048 68.642 108.466 67.217 99.548
H ig h
β
βGeo/Eacc(MV/m) 0.90 0.90 0.89 0.90 0.90 0.90 βGeo/Eacc(MV/m) 18.17 18.17 18.06 18.17 18.17 18.17 Final energy (MeV) 2510.3 2504.1 2500.8 2505.6 2508.3 2510.1 Cav./Per. ×Nper. 8 × 15 8 × 15 8 × 15 8 × 15 8 × 15 8 × 15 No. of Quads/Cavs. 30 / 120 30 / 120 30 / 120 30 / 120 30 / 120 30 / 120 Cavity cntr.2cntr. (m) 1.3576 1.3576 1.3469 1.3576 1.3576 1.3576 Cryo Length (m) 12.7606 12.7606 12.4755 12.5606 11.3606 11.3606 Period Length (m) 12.8606 12.8606 12.9755 13.0606 12.9606 12.9606 Length (m) 192.909 192.909 194.632 195.9087 194.409 194.409
T o ta
l No. of Cavities 202 / 39 213 / 41 198 / 44 212 / 45 202 / 39 213 / 41 REG (MeV/m) 7.727 7.309 7.369 6.938 7.679 7.274 Length (m) 324.855 342.602 340.859 362.552 326.655 345.052
‡ c.cq.dcr: Continuous Cold Quadrupoles, Different Cryo-modules, c.cq.hcr: Continous Cold Quadrupoles, Hybrid Cryo-modules, w.sq.dcr: Separated Warm Quadrupoles, Different Cryo-modules, step and smooth indicate the average phase advance variation between spoke and low β,
linac without rematching between the structures, the emittance and halo growth are reported in
Table 6. It worth mentioning that all the losses in all the lossy runs happen in the second doublet
in the line, where beam is transversally very large after going through a waist in the middle of first
period.
9
In the c.cq.hcr cases, to improve the beam dynamics performance a single quadrupole is added
to the beginning of the linac to make the focusing a doublet structure, the extra quadrupole is
added in a way to respect the periodicity of next periods. This fact is indicated in Table 5, by
adding 1 to the number of quadrupoles and 1.4 m to the length of the first SC section, spoke
resonators.
Table 6: Beam dynamics performance summary for matched beam, as well as an initial beam with 50% mismatch.
Mismatch C.CQ.DCR. C.CQ.HCR. W.SQ.DCR. (%) step‡ smooth‡ step‡ smooth‡ step‡ smooth‡
† x (%) 0 20.7 14.6 17.4 14.3 24.2 17.9
y (%) 0 18.3 18.4 22.2 19.4 18.9 15.4 z (%) 0 5.3 6.6 5.0 5.9 2.6 5.3 δH
‡ x 0 0.403 0.287 0.434 0.2913 0.470 0.337
δHy 0 0.373 0.283 0.388 0.2899 0.456 0.322 δHz 0 0.243 0.321 0.250 0.2979 0.179 0.267 Losses (W) 0 0 0 0 0 0 0 x (%) 50 84.0 115.3 118.3 122.2 113.1 102.8 y (%) 50 125.6 105.0 125.8 111.8 146.6 138.0 z (%) 50 79.9 79.3 88.3 85.2 93.1 70.9 δHx 50 2.699 3.149 3.588 3.4161 2.025 2.484 δHy 50 2.803 2.881 3.106 3.3133 3.345 4.475 δHz 50 2.440 2.397 2.348 2.4976 2.043 1.247 Losses (W) 50 200 200 45 0 15 50
† : = (f − i)/i, ‡ : δH = Hf −Hi.
7 Acknowledgements
I would like to thank Hakan Danared and Romuald Duperrier for the fruitful discussions and
suggestions during the preparation of this note.
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Choice of Accelerating Gradients