1. The Post-linac Collimation System of CLIC: Machine Protection Aspects
Javier Resta Lopez
IFIC (CSIC-UV), Valencia, Spain
In collaboration with J. L. Fernandez-Hernando,
A. Latina and R. Tomas
Machine Protection workshop
6-8 June 2012, CERN, Geneva

2. Introduction
The main functions of collimation systems for high energy colliders:
Reducing detector background at the interaction point
Protecting the machine by minimising the activation and damage of sensitive components
In the BDS of the future linear colliders (ILC and CLIC) there are two collimation sections:
Betatron collimation: transverse halo cleaning
E collimation: collimation of particles with high energy deviation
In this presentation we focus on the machine protection function of the CLIC collimation system

3. Introduction Machine protection in BDS usually relies on:
Emergency extraction kickers and dumps (fast abort systems)
BPMs and BLMs for abnormal operation detection, and interlock systems
Passive protection: collimation system, masks
The CLIC E collimation system is conceived to fulfil a function of passive protection of the BDS against miss-steered beams
Energy collimation depth determined by failure modes in the linac
The conventional collimation systems are based on mechanical collimation using spoilers (scrapers) and absorbers. It could include several stages
The machine protection strategy of the BDS relies on Fast Abort System using fast kickers and dumps for the fast extraction of the beam at the beginning of the BDS in case of emergency.
And detection systems of miss-steered beams based on beam position monitors and beam loss monitors. This allows interlock of the machine in case of abnormal operation.
On the other hand to deal with fast faults we have passive protection based on collimation systems and additional masks protecting sensitive components of the beamline.
In CLIC, the energy collimation system fulfils an important function of passive protection of the BDS against miss-steered beams due to failure modes in the main linac. These failure modes determine the energy collimation depth.
The conventional collimation systems are based on mechanical collimation using spoilers and absorbers. It could include several stages.
Here you can see a schematic of a spoiler used to increase the angular divergence of the beam by multiple Coulomb scattering, thus increasing the beam spot size at the downstream absorber.

4. Beam delivery system CLIC BDS vs ILC BDS
3 TeV CM
ILC BDS
0.5 TeV CM
[Deepa Angal-Kalinin/James Jones]
The layout of the CLIC BDS at 3 TeV CM energy is as follows:
First we have a section dedicated to beam diagnostics,
Downstream this section we have the energy collimation system with a spoiler and an absorber and several bending magnets to generate the necessary horizontal dispersion.
Downstream of the energy collimation section we find a section for transverse or betatron collimation
And finally the called Final Focus system to focus the beam to the interaction point with the necessary small transverse beam sizes
It is worth comparing this BDS structure with ILC BDS. Unlike the ILC BDS, for the CLIC BDS the energy collimation system is upstream of the betatron one. The main reason for choosing this is because errors generated by failure modes in the CLIC main linac are expected to be much more frequent than large betatron oscillations with small emittance beams
In CLIC BDS the E collimation system is upstream of the betatron one. The main reason for choosing this is because energy errors generated by failure modes in the CLIC main linac are expected to be much more frequent than large betatron oscillations with small emittance beams

5. CLIC baseline BDS Optics
The corresponding betatron functions and first order dispersion for the CLIC baseline BDS are shown here.
Energy collimation: Protection against miss-steered or
errant beams with energy errors ~> 1.3%. E-spoiler half-gap: ax=Dxδ=3.51mm
4 pairs of spoilers and absorbers in x,y plane to collimate at IP/FD phases

6. Collimator parameters
Energy colllimators
The collimator parameters that we can find in the conceptual design report of CLIC are summarised in this table.
The betatron collimators and absorbers are made of Titanium alloy.
However, the energy spoiler is made of beryllium. This material has been selected for the energy spoiler due to is thermal and electrical properties. In comparison with other metals it is robust and has high electrical conductivity (which reduces the wakefield effects).
Betatron collimators
Beryllium has been considered as a good material candidate for the E-spoiler. Its high
electrical and thermal conductivity with a large radiation length compared with other
metals makes Be an optimal candidate.

7. Failure modes
Investigation of failure modes in the CLIC main linac which could generate significant energy deviation, in such a way that the beam hits the energy spoiler
For example: Injection phase error, RF breakdown, missing drive beam, beam charge error
Tracking simulations LINAC + BDS assuming failures between two pulses. Assuming nominal beam parameters and a perfect linac lattice (no additional lattice imperfections)
Thermo-mechanical characterisation of the energy collimators using the output beam distribution from tracking simulations, and the codes FLUKA (energy deposition and temperature rise) and ANSYS (mechanical stress)
After this brief introduction on the baseline design of the CLIC collimation system, I will talk about the studies on failure modes in the CLIC main linac, which are relevant for machine protection studies.
The goal is to identify possible failure modes in the CLIC main linac which could lead to significant energy deviation, in such a way that the beam hits the energy spoiler. Possible failure modes are, for example: injection phase errors, cavity fails due to RF breakdown or missing drive beam, and beam charge errors.
For this study we have performed beam tracking simulations through the linac and the BDS introducing failures between two pulses in the main linac. In these simulations we assume the nominal CLIC beam parameters and a perfect linac, i.e. no additional (static or dynamic) lattice imperfections.
Then we use the resulting beam distribution at the energy spoiler as an input for the thermo-mechanical study of the spoiler. The thermo-mechanical analysis of the spoiler is performed using the codes FLUKA and ANSYS.

8. Failure modes Injection phase error:
Beam centroid trajectory in the BDS for different injection phase errors
Here I show you some results for the case of injection phase errors. You can see here the beam centroid trajectory in the CLIC BDS for different injection phase errors. The beam pipe aperture is also represented as well as the collimator apertures.
For phase errors bigger than + 5 degrees and smaller than -3 degrees the beam hits the energy spoiler.
For phase error ~> +5o and <~ -3o the beam hits the energy spoiler (ESP)

9. Failure modes Injection phase error (example 1):
Temperature increase
along the spoiler
For -5o phase error, transverse
beam distribution at ESP
ΔTpeak=210 K
FLUKA
Beryllium spoiler model
ANSYS
σx= μm
σy=26.45 μm
Emean= GeV
≈1% full energy spread
Equivalent stress
If we consider a critical case where the beam impinges on the spoiler, for instance for -5 degrees, we obtain the following transverse beam distribution. In FLUKA simulations we consider this distribution hits our beryllium spoiler model. It results the following temperature increase along the spoiler. A peak temperature increment of 210 K has been obtained, which is well below of the temperature melting point for the beryllium.
The outputs from FLUKA are introduced as inputs for ANSYS and the mechanical stress build-up due to thermal shock is evaluated. In this study the figure of merit is the equivalent stress. For this case, the result shows that the equivalent stress reaches a peak 300 microseconds after the beam impact which surpasses the fracture limit. Evidently this is not so good for the survivability of the spoiler!
The equivalent stress reaches a peak (300 μs after the
beam impact) which surpasses the fracture limit (> 370 MPa)

10. Failure modes RF cavity fail:
Beam centroid trajectory for different number of RF structures switched off
in the last section of the main linac
Considering now other type of failure scenario, for instance the fail of several RF cavities. For simplicity in the simulations we switched off a different number of cavities and check the beam trajectory in the BDS.

11. Failure modes RF cavity fail (example 2):
Temperature increase
along the spoiler
1500 cavities switched off in the
last section of the main linac.
Transverse beam distribution at ESP
ΔTpeak=35 K
FLUKA
Beryllium spoiler model
ANSYS
σx=1 mm
σy=25.4 μm
Emean=1471 GeV
≈1% full energy spread
Equivalent stress
Following the same procedure as before, we select a critical case where the beam hits the energy spoiler. For example, if 1500 cavities are switched off in the last section of the main linac the transverse beam distribution at the energy spoiler position is as follows (figure). Then we evaluate the temperature increment and the equivalent stress using FLUKA and ANSYS (as before).
In this case, the equivalent stress is below the fracture limit, but it stabilises near the deformation limit.
In this case, the equivalent stress is below the fracture limit,
but it stabilises near the tensile yield strength (deformation
limit, 240 MPa)

12. Failure modes
Results show that, considering the previous failure scenarios and the nominal beam parameters, it may be difficult to avoid the spoiler fracture or a permanent deformation of the spoiler surface
In order to reduce the risk of damage to the spoiler, we are considering the following alternatives:
Alternative materials
Alternative geometric structure
Alternative optics: nonlinear passive protection

13. Alternative spoiler design
“Hollow” spoilers
Beampipe wall or spoiler support
Ti-alloy or Be
Vacuum
Beam axis L
We have started studies to redesign the spoiler. One alternative is to make “hollow” spoilers with an empty inner body. A schematic of the longitudinal sectional view of this type of spoiler is shown here. The thickness of the walls facing the incoming beam should be enough to get the necessary angular divergence by multiple Coulomb scattering and to increase the spot size for the survival of the downstream absorber.
This empty inner part of the spoiler would allow to accommodate a cooling system.
2L is the minimum length of material that the beam has to see in order to obtain the
necessary angular divergence Θ by MCS. In this way the beam spot size is increased
at the downstream absorber position in order to avoid its damage or fracture.
The empty inner part of the spoiler could accommodate a water cooling circuit or
some other kind of cooling system

14. Alternative spoiler design
“Semi-hollow” spoilers
Beam axis
SiC foam
Ti-alloy or Be
Beampipe wall or spoiler support Cu
Another alternative is a “semi-hollow” spoiler, where the inner part is filled with a material such as Silicon-carbide foam, which is practically transparent for a relativistic beam.
We plan to perform similar simulations for these two collimator models as we did before with the baseline spoiler design.
Suggestions about how to improve the models are welcome.
We plan to study the thermo-mechanical characteristics of these spoiler designs
using the codes FLUKA and ANSYS (following the same procedure as
for examples 1 and 2).

15. Nonlinear passive protection Basic concept
collimators
Sextupole 1
Sextupole 2 S1 S2
R (s1→ s2)
Use a nonlinear magnet (e.g. sextupole, octupole), which somehow plays the role of a spoiler (or primary collimator), to increase the beam spot size at the downstream collimators for a beam with mean energy offset ~> energy collimation depth
Cancellation of optical aberrations using a second nonlinear element
For CLIC we have studied an E collimation system based on a pair of skew sextupoles of relatively moderate strength
Let us now to talk about the nonlinear passive protection scheme that could be another alternative to reduce the risk of damage to the spoiler.
The basic concept is based on the use of nonlinear magnets (e.g. sextupole, octupole), which somehow plays the role of a spoiler, to increase the beam spot size at the collimator position
The cancellation of optical aberrations is done using a second nonlinear element placed at the right phase space
For CLIC we have studied an E collimation system based on a pair of skew sextupoles.

16. Nonlinear passive protection
In the past …
Concept of Magnetic Energy Spoiler (MES) for TESLA
[R. Brinkmann et al., TESLA (2001)]
The concept of nonlinear magnetic system for machine protection is not a novel one. For example, for TESLA a magnetic energy spoiler was designed which, according to tracking simulations could allow to increase the beam area at momentum spoiler by a factor 6 with respect to the linear one. The MES was located downstream of the betatron collimation system of TESLA, and it also includes an octupole at a high dispersion point in between of two skew sextupoles. The octupole introduces third order
dispersion at the second skew sextupole position, which contributes to significantly increase the
vertical beam size at the downstream momentum spoiler
According tracking simulations:
The beam area is increased by a factor of 6 wrt the linear beam at the
momentum spoiler position !
However, significant luminosity degradation !

17. CLIC nonlinear energy collimation system
Conceptual layout
Optical optimisation:
To cancel higher order aberrations a skew octupole and a normal sextupole
have been added downstream of the second skew sextupole.
For CLIC we have designed the following nonlinear energy collimation system. To cancel higher order aberrations two additional nonlinear magnets have been added: a skew octupole and a normal sextupole just downstream of the second skew sextupole.

18. CLIC nonlinear energy collimation system
Optical constraints to cancel geometric nonlinear terms between two skew sextupoles:
R12=0, R34=0, |R11|=|R33|, |R22|=|R44|
Phase advance:
μx(s1→s2)=nxπ, μy(s1→s2)=nyπ, where nx, ny are integers
Relation between the strength of the two skew sextupoles:
where Ks1 and Ks2 are the normalised strength of the 1st and 2nd sextupole respectively, and βx
and βx2 are the horizontal betatron function at the 1st and 2nd sextupole position respectively
We use –I transform in both x and y planes between the sextupoles, which is a special case of
the previous conditions: nx=1, ny=1, βx1 = βx2, βy1 = βy2, αx1= αx2, αy1= αy2. Therefore, Ks1=Ks2
In addition, to cancel chromatic and chromo-geometric aberrations between the skew sextupole
pair: Dx1= –Dx2
For the cancellation of geometric nonlinear terms (up to second order) between two skew sextupoles the following optical constraints have been established: ….
For simplicity we use a –I transform matrix in both x and y planes between the sextupoles, which is a special case of the previous conditions. The strength of the two skew sextupoles must be equal.
In addition, to cancel chromatic and chromo-geometric aberrations between the skew sextupole pair the horizontal first order dispersion must have opposite sign from each other.

19. CLIC nonlinear energy collimation system
Optical layout
BDS
Here you can see the optical layout of this nonlinear system. On the right, the complete CLIC BDS containing the nonlinear energy collimation section.

20. CLIC nonlinear energy collimation system Beamline performance
Multi-particle tracking simulations:
Using the code MAD
50000 macroparticles tracked through the CLIC BDS
Gaussian beam distributions for the transverse phase space
1% full energy spread (uniform distribution) IP s1 s2
BEAM
At 1st skew sextupole
At spoiler
At energy collimation
system exit
At IP
We have evaluated the performance of this lattice by means of multi-particle tracking simulations using the code MAD,
50000 macroparticles have been tracked through the CLIC BDS, considering
Initial gaussian beam distributions for the transverse phase space and
1% full energy spread (for a uniform distribution in energy)
Here you can see the transverse phase space distribution at different positions of the BDS:
-- at the 1st skew sextupole
-- at the spoiler
-- at the exit of the energy collimation section, where we compare the cases with and without nonlinear optimisation (including the additional nonlinear magnets as we mentioned previously) and
-- at the IP.
After optimisation the beam tails are significantly reduced at the IP, and the beam core is more compact and much less distorted.

21. CLIC nonlinear energy collimation system Beamline performance
Luminosity
Relative Luminosity vs skew sextupole strength
≈2% luminosity loss
Ks=8 m-2
≈35% luminosity loss
Concerning the luminosity performance we compare the relative luminosity as a function of the skew sextupole strength for the cases with and without nonlinear optimisation. Obviously, without optimisation the luminosity is degraded quickly as the skew sextupole strength increases.
With optimisation, the cancellation of high order aberrations, using the two additional nonlinear magnets, helps to significantly improve the luminosity. We allow a maximum 2 % luminosity loss, which corresponds to a skew sextupole strength of 8 m^-2 and the following values for the additional nonlinear magnets: (escritos en la transparencia).
K(skew octupole) = m-3
K(normal sextup.) = -0.4 m-2
With optimisation (additional nonlinear elements)

22. CLIC nonlinear energy collimation system Beamline performance
Luminosity
Energy bandwidth: Relative peak luminosity (within 1% of Ecm)
vs. beam energy offset δ0=ΔE/E0
If we check the energy bandwidth, we can see that both the linear and the nonlinear systems present a comparable bandwidth
Both linear and nonlinear systems present a comparable bandwidth !

23. CLIC nonlinear energy collimation system Beamline performance
Beam size at spoiler position
Transverse beam spot size vs. skew
sextupole strength for different beam
energy offsets
Transverse beam peak density vs.
skew sextupole strength for different
beam energy offsets
The other figure of merit we have to check is the beam spot size and beam peak density at the spoiler position.
For 1.5% mean energy offset, the nonlinear energy collimation system (using Ks=8 m-2)
increases 2 times the beam spot size (reduces 4 times the transverse peak density) at the
energy spoiler wrt the baseline linear collimation system
For 1.5% mean energy offset, the nonlinear energy collimation system (using Ks=8 m-2)
increases 2 times the beam spot size (reduces 4 times the transverse peak density) at the
energy spoiler wrt the baseline linear collimation system

24. Conclusions
The CLIC post-linac E-collimation system will play an essential role in protecting BDS against miss-steered beams
The E-collimation depth is determined by failure modes in the main linac
In order to improve the current baseline collimation system design, it is necessary to investigate and identify failure scenarios which could be critical in terms of collimator damage
Concretely we have studied failures which could generate a significant beam energy deviation, in such a way that the beam directly impacts on the energy spoiler
Tracking simulations LINAC + failure modes + BDS + thermo-mechanical analysis of the spoiler (FLUKA + ANSYS) for CLIC are in progress
Preliminary results show that it may be difficult to avoid fracture or permanent deformation of the spoiler with the current baseline design
Further studies have to be performed to evaluate the real magnitude of the fracture and the deformation. For example, a permanent deformation could translate into an increase of the roughness of the spoiler surface, hence increasing wakefield effects
We are currently investigating alternative spoiler designs and alternative optical layouts, such as a nonlinear collimation system, to reduce the risk of damage to the energy collimators
CONCLUSIONS
Practicamente leer lo que hay en transparencia.

25. Reservoir

26. MPS strategy for BDS ILC:
The MPS strategy is determined by the bunch train time structure
Parameter
ILC
CLIC
Number of bunches
2625
312
Bunch spacing [ns]
369
0.5
Pulse length [μs]
969
0.156
Pulse repetition rate [Hz] 5 50
Charge per bunch [nC]
3.2
0.6
ILC:
The relative long pulse and large bunch spacing allow that a fault can be detected and
the pulse aborted within the train itself.
An errant or miss-steered beam could be aborted at the beginning of the BDS by using a
fast kicker system (rise-times ~100 ns) to send the beam to an emergency dump
This fast abort system is intended to protect the BDS providing that the collimation
system can survive one bunch

27. MPS strategy for BDS CLIC:
In case of fast failures in the main linac (at microsecond time scales), the extremely short bunch spacing (0.5 ns) and small pulse length (156 ns) make the fault detection and abortion within the same train very difficult (not attainable with current kicker technology)
Then a first miss-steered train is detected and not extracted by the emergency kicker at the exit of the main linac, and the subsequent pulses could be extracted by the emergency abort system . After the detection of abnormal operation (in the pulse-to-pulse interval) an interlock system could stop operation
In this case, the protection of the BDS relies mainly on the collimation system
(passive protection). The E-collimation system is designed to withstands the impact of, at least, a bunch train.

28. Failure modes RF cavity fail: Transverse beam distribution at ESP
In terms of spoiler damage, the case of the total failure of a series of RF cavities at the start of the linac is less critical, since the energy spread increases and the beam suffers a rapid filamentation
Transverse beam distribution at ESP
300 RF structures OFF
400 RF structures OFF
~55% particles lost
along the linac and
the diagnostic
section of the BDS

29. Failure modes Beam charge error:
Beam centroid trajectory in the BDS for different beam charge errors
in the range [-50%, +50%]
In this case, the resulting energy deviation is relatively small for the beam
to be caught in the energy spoiler

30. Parameters for the CLIC nonlinear energy collimation
Spoiler parameters
Skew sextupole parameters
Spoiler Parameter
Value
Geometry
Rectangular
Hor. half gap ax [mm]
1.2
Vert. half gap ay [mm] 10
Tapered half radius b [mm]
Tapered part length LT [mm] 90
Taper angle θT [mrad]
97.5
Flat part length LF [X0]
0.05
Material Be
Optical parameter
Hor. beta function βxsp [m]
471.8
Ver. beta function βysp [m]
79.02
1st order hor. dispersion Dxsp [m]
0.093
2nd oder hor. dispersion T166 [m]
0.245
3rd order hor. dispersion U1666 [m]
-0.45
Parameter
Value
Sext. Strength K [m-2] 8
Product of pole-tip field and length BTls [T m] 2
Pole-tip radius as [mm] 10
Effective length ls [cm]
100
Optical Parameter
Hor. beta function βxs [m]
436.6
Vert. beta function βys [m]
110.2
Hor. Dispersion |Dxs| [m]
0.097