Microsoft Word - Diffraction-Arxiv
Crystal channeling of LHC forward protons
with preserved distribution in phase space
V.M. Biryukov♦
Institute for High Energy Physics, Protvino, 142281, Russia
Abstract
We show that crystal can trap a broad (x, x', y, y', E) distribution of particles and
channel it preserved with a high precision. This sampled-and-hold distribution can be
steered by a bent crystal for analysis downstream. In simulations for the 7 TeV Large
Hadron Collider, a crystal adapted to the accelerator lattice traps 90% of diffractively
scattered protons emerging from the interaction point with a divergence 100 times the
critical angle. We set the criterion for crystal adaptation improving efficiency ~100-fold.
Proton angles are preserved in crystal transmission with accuracy down to 0.1 µrad. This
makes feasible a crystal application for measuring very forward protons at the LHC.
1. Introduction
A particle entering the crystal lattice parallel to a major crystallographic direction can be
captured and channeled by the lattice along a crystal axis or plane [1]. For instance, a positive
particle can be channeled between adjacent atomic planes. In a bent crystal, the channeled
particles can follow the bend [2]. This led to elegant technique of beam steering by bent
channeling crystals [3] now experimentally explored over six decades in energy from low MeV
[4] to 1 TeV [5]. The technique is used on permanent basis in IHEP Protvino where crystal
systems extract protons from 70 GeV main ring with efficiency of 85% at intensity up to 4×1012
protons using Si crystals just 2 mm along the beam [6]. Bent crystals channel in good agreement
with predictions up to the highest energies [6-9].
Crystal applications at the 7-TeV Large Hadron Collider are considered for beam collimation
and extraction [10] and in situ calibration of CMS and ATLAS calorimeters [11]. In another
proposal, crystal could capture the particles emerging from the interaction point (IP) with small
angles and channel them out of the beam [12]. This could help to improve on measurement of
small angle elastic and “quasi-elastic” scattering in CMS and ATLAS where lower momentum
transfers might become available for pp elastics scattering and lower proton momentum losses
for diffractive physics [12]. Groups in both CMS (with TOTEM) and ATLAS would like to add
very forward proton detectors, 420 m downstream on both sides, a project FP420 [13]. By
detecting protons that have lost less than 1% of their longitudinal momentum, a rich QCD,
electroweak, Higgs and BSM program becomes accessible, with the potential to make
measurements which are unique at LHC, and difficult even at a future linear collider [13].
The measurement of the displacement x and angle x’ (in the horizontal plane) of the outgoing
protons relative to the beam allows the momentum loss ξ=∆p/p and transverse momentum of the
scattered protons to be reconstructed. Protons emerging from diffractive scattering at LHC have
very small emission angles (10-150 µrad) and fractional momentum loss (ξ = 10-8 – 0.1). Hence
they are very close to the beam and can only be detected in the Roman Pots downstream if their
displacement at the detector location is large enough to escape the beam halo [13].
2. Crystal efficiency
As practice shows, crystal can go into a very limited space and get particles from there [6].
Most efficient crystal applications are based on so called “multipass” mode where particles can
encounter a crystal many times in the ring [6,14]. There are also successful experimental
demonstrations of highly efficient channeling in a single pass, with efficiency up to 60% at
CERN SPS [15]. Throughout this paper we consider only a single-pass channeling.
We show with simulations that at the LHC a crystal can efficiently channel forward protons.
For channeling simulations we apply a Monte Carlo code CATCH [16] successfully used for
prediction of experiments at CERN SPS [9], IHEP U-70 [6], Tevatron [7], RHIC [8] and KEK
[17] and crystal applications at the LHC [10,11].
Crystal capture is very selective in angle. The critical angle θC within which the capture is
possible is as small as about ±5 µrad / E1/2(TeV) at a high energy E in Silicon (110) planes.
Proton divergence of 150 µrad is almost 100 times θC at 7 TeV. Therefore it is not possible to
capture all these protons by a plain crystal. However, we can suggest an efficient solution
benefiting from the fact that all diffractively scattered protons originate from a small region at
the IP.
For standard LHC optics with beta function value at the IP β*=0.55 m, the beam size at the IP
is σbeam≈16 µm rms. The spread in the transverse position of the vertex point where outgoing
protons originate from is determined by the rms spread of the beam and equals σbeam/√2 [13]. As
protons emerge from diffractive scattering at LHC with emission angles up to ≈150 µrad and
interaction width σbeam/√2, the emittance of the beam to be trapped by a crystal is ≤ 2π µrad-mm
only. This corresponds to the acceptance of a Si crystal of ~1 mm transverse size. The match of
the diffractive-protons emittance to the crystal acceptance means that the particles could be
                                                                                                                                                            
♦ http://mail.ihep.ru/~biryukov/
trapped and channeled efficiently. To realize this, one has to match the crystal design and
location to the application. For the LHC scenario with high luminosity, we find the most efficient
design to be a crystal with a point-to-parallel focusing entry face. Focusing crystal proposed by
A.I Smirnov in 1985 has a face shaped so that the tangents to the crystal planes cross at a focus
line at some distance LF from the crystal [3]. This kind of crystal was successfully tested at IHEP
where it efficiently trapped a beam of ±2 mrad divergence (or ~100 times θC) [18]. The crystal
traps protons emerging from the focus line uniformly from all the angular range if the entry face
has a proper shape [18].
We find that for most efficient channeling in the LHC the focus distance LF of this crystal
should be equal to the effective distance Leff between the crystal location and the IP. In a drift
space, Leff is geometrical distance. In accelerator lattice, Leff =(β*βC)1/2sin∆ψ, where βC is β value
at the crystal and ∆ψ is the phase advance from the IP to the crystal. A plain crystal with a flat
entry face has LF = ∞.
In simulations with the low β* optics settings, a focusing crystal shows best efficiency if
installed at a location with effective distance Leff ≥ 15 m from the IP. It can be a Si (110) or (111)
crystal of ≈(0.15 mrad)×Leff ≥ 2.5 mm transverse size in order to capture efficiently all diffractive
protons. Simulation predicts that a focusing Si(110) crystal with LF=Leff traps 90% of 7 TeV
protons emerging from the IP in the angular range of 150 µrad width into channeling mode. The
efficiency figure is almost independent of the crystal location provided Leff ≥ 15 m.
The reason for high efficiency at high Leff is that, at a distance Leff from the IP, any point at
the crystal entry face sees the beam source of σ size (at the IP) at an angle of σ/Leff. Channeling
efficiency reduces by a factor of about (1-(σ/LeffθC)2)1/2 [3]. The reduction in efficiency by a
factor of ≈1-σ2/2L2effθC2 becomes negligible for L2eff >> σ2/2θC2 =β*ε/4θC2 where ε is beam
emittance. With β*=0.55 m and Si(110) crystal, channeling efficiency saturates for L2eff >> (4
One more idea for efficient channeling of forward protons in the LHC is that a crystal can be
installed with planes parallel to either x’ or y’ plane. For application, it is not critical whether
crystal bends protons in horizontal or vertical plane to produce an offset at the detector. But the
distance Leff in accelerator lattice from the IP to the crystal can be very different in x and y
planes. Then channeling efficiency is very different, whether crystal traps protons in x’ or y’
plane. We suggest in this case to install crystal for channeling in the plane with larger Leff.
For instance, on the location 200 m downstream of the IP5 (CMS) and some 20 m ahead of
the Roman Pot station at 220 m where crystal could be installed, Leff ≈6 m in x’ and ≈20 m in y’
plane. According to the analysis above, channeling efficiency in y’ plane should be great while in
x’ plane moderate. Indeed, our simulations for this location show channeling efficiency of ≈87%
in y’ and only ≈60% in x’ plane, for β*=0.55 m and optimal crystals of Si(110). A plain Si crystal
has channeling efficiency in x’ plane of just 3.5% or 17 times lower than a Si focusing crystal
adapted to the LHC lattice.
For the run-in phase of the LHC with β*=2 m we find that channeling efficiency of ≥ 85% can
be achieved if crystal is located at Leff ≥ 30 m downstream of the IP. The nominal, high
luminosity optics of the LHC is not optimized for forward proton detection. Therefore a
possibility to use a channeling crystal can be very helpful as it offers opportunities for diffractive
physics studies otherwise inaccessible in the nominal LHC settings.
The LHC options with a high β* (1540 and 90 m) are devised for the studies of diffractive
physics. With β*=1540 m, the emittance of diffractively scattered protons increases to ≈50π
µrad-mm. This corresponds to the acceptance of a Si crystal of ≥ 30 mm transverse size. Such a
crystal is not out of question, however the problem is where to fit it in the LHC. In terms of Leff,
good channeling efficiency requires a location with L2eff >> (130 m)2 in this optics.
We simulated channeling on the location 200 m from the IP5. In β*=1540 m optics, a 10-cm
Si(110) crystal trapped and bent protons 0.5 mrad in x’ plane with efficiency of 41%. A Ge(110)
crystal shows there 48% efficiency, i.e. comparable to Si. All figures assumed a perfect match
LF=Leff in crystal. A plain Si crystal gives efficiency of <<1%, or 300 times lower than a Si
focusing crystal adapted to the LHC lattice on this location.
In β*=90 m option on the same location, the choice of plane is important because Leff ≈10 m in
x’ and ≈170 m in y’ plane. Preferred location should have L2eff >> (60 m)2 so we expect very
different efficiencies in x’ and y’ planes. Our simulations give crystal efficiency of 72% in y’ and
only 7% in x’ plane for β*=90 m. Here, crystal application is feasible only with bending in
vertical plane.
Low efficiency may exclude a crystal use for double-pomeron-exchange events (pp→pXp)
with double-arm reconstruction, because the probability to have channeling in both arms in
coincidence becomes small, e.g. (41%)2≈17%. For reconstruction of single-diffraction events
(pp→pX) more detailed studies are required before the benefits (or their absence) from a crystal
use with high β* options can be understood.
In this paper we suggest the use of a single crystal for proton extraction from halo and
delivery to the detector. The use of a 2-stage crystal system [12], first crystal for extracting a
proton and second one for bending it a big angle, would reduce the overall efficiency by a factor
of ~0.6 (ideally) or less. The 2nd crystal traps only part of the protons channeled in the 1st one.
Finally, we notice that one can filter diffraction events with a crystal. Instead of trapping all
forward protons, crystal acceptance can be made smaller and sample e.g. only the most forward
protons emerging from the IP with the angles of a few µrad.
3. Precise transmission in a single (x, x’) plane
Whereas protons are physically delivered from the IP to detector with good efficiency, the
essential question is whether the information on phase space (x, x', y, y', E) distribution of
particles is lost or corrupted while the particles are captured and transmitted in crystal. The
success of experiments on measuring forward high momentum protons at the LHC depends on
the angular precision of proton track reconstruction. A plain crystal would destroy the phase
space information first by selecting particles from just a single direction and then disturbing the
exit angle of particle by coherent and incoherent scattering in crystal. Plain crystal acceptance is
±θC and crystal accuracy in angle transmission is again ±θC. That means, a plain crystal traps and
delivers about zero bit information on angle distribution. In this paper we design a crystal with
the acceptance of ~100 θC and angle transmission accuracy of ~0.1 θC, although it sounds against
the nature of crystal channeling.
Suppose particles are coming with a distribution over (x, x', y, y', E). Ideally, we would like
the crystal to trap all coming particles and preserve their distribution over (x, x', y, y', E), and
then shift an angle of θ each particle towards a physical setup where this distribution can be
analyzed in detail.
One should solve two problems. One problem was to trap and bend a beam with a divergence
much greater than the critical angle. A focusing crystal adapted to the LHC optics solves this
problem. In simulations, a focusing crystal traps with 90% efficiency all protons emerging from
the IP with the angular distribution ~100 times θC. Notice that the trapped particles fully preserve
also their distribution over the angle in the plane orthogonal to the plane of channeling. In such a
crystal, particles are trapped uniformly from a very broad distribution over x’ and y’.
A bent crystal would transform (x, x', y, y') at the entrance into (x, x'+θ, y, y') at the exit. To
do so, each trapped particle has to be channeled over the same distance in crystal. Therefore, the
shape of the crystal exit face must match the entry face. Then in a bent crystal each channeled
particle receives the same bending angle.
Although the crystal described above can solve the idea of sampling a broad distribution of
particles and delivering it to a required destination, second problem is how to preserve the
sampled distribution (x, x', y, y') “frozen” on transmission through the crystal lattice as precise as
possible. The coordinates (x, y) of particles are obviously preserved in crystal, so one should take
care of the accuracy in transmission of angles x’, y’ only.
The protons channeled between atomic planes in crystal are disturbed by (1) oscillations in
the channeling plane with an amplitude up to θC and by (2) scattering on a rarefied electronic gas
(mostly valence electrons) in both planes, x’ and y’. Notice that nuclear scattering will not
disturb the sample of transmitted channeled particles as this process is strongly suppressed for
channeled positive particles. Simply saying, any particle nuclear scattered would be dechanneled
and thus not present in the sample of bent particles.
That gives us the first idea that partially solves the problem of transmission accuracy. The
idea is that the information on crystal-captured particles is very well preserved in one plane, e.g.
(x, x'), while the particles are trapped and bent in another plane, e.g. (y, y’). Notice that particle
distribution in the plane orthogonal to channeling is favored twice. Firstly, they are easily
trapped with a broad angular distribution; secondly they are transmitted with a very little
scattering. Information in this plane will be best preserved. The opportunity to have perfect data
on just one plane is interesting for applications. The reconstruction of the Higgs boson mass in
reaction pp→p+H+p requires (x, x’) data in horizontal plane only [13].
Figure 1 The difference in proton angles, x’ and y’, before and after a Si(110) crystal.
Oscillations in the channeling plane on the atomic coherent potential are a greater problem.
Fig. 1 shows a distribution of the difference in proton angle in x’ and y’ planes before and after a
channeling in crystal, (x’OUT – x’IN) and (y’OUT – y’IN – 0.1 mrad), as obtained in simulations for a
Si(110) bent crystal channeling in y’ plane. The accuracy in x’ transmission in crystal is very
good indeed, ~0.1 µrad rms. The width of (y’OUT – y’IN – 0.1 mrad) distribution is much greater
due to oscillations in the potential of Si (110) planes.
4. Precise transmission in both planes
To solve the problem of accuracy in the other plane, i.e. the plane of channeling, one solution
is to use a channel with a lower critical angle, for instance Si(100) instead of (110) or (111). A
more universal solution is to use a strongly bent crystal. The critical angle θC is gradually
reduced to zero when the crystal curvature approaches a critical value. The strong focusing of a
strongly bent crystal suppresses channeling oscillations to any low level needed in the
application.
Fig. 2 shows the difference in proton angle in x’ and y’ planes before and after channeling in a
crystal, (x’OUT – x’IN– 0.1 mrad) and (y’OUT – y’IN), as obtained in simulations for a 2 mm Si(100)
crystal bent 0.1 mrad. The protons were channeled in x’ plane. The rms value of angle smearing
found in simulations is 0.2 µrad both for x’ and y’.
Figure 2 The same as in Fig. 1 but for a strongly bent Si (100) crystal.
This accuracy should be compared to the angular resolution of the detectors downstream of
the crystal. Measuring proton coordinates with ~10 µm resolution [13] over a base of ~8 m as
allowed by a drift space would give an angular accuracy of ~1.4×10µm/8m=1.8 µrad. Addition
(quadratic) of crystal transmission accuracies doesn’t change this resolution. That would be
perfect for crystal. With a much better resolution on the detector side, down to 0.5 µrad, the
overall resolution becomes ~0.55 µrad, i.e. just slightly disturbed. Crystal transmission in both
planes, x’ and y’, is still almost perfect.
Because of scattering on electronic gas, the protons loose energy in crystal. In simulations, the
energy loss and its fluctuations in crystal are ∆E/E ≈10-7–10-6, i.e. much smaller than even the
nominal energy spread in the LHC beam, 1.1×10-4. Energy losses in bent crystals were studied in
experiments at CERN SPS with protons of 450 GeV and Pb ions of 33 TeV where CATCH
predictions were also validated [9]. The diffractively scattered protons would have energy spread
on the order of 100 GeV, or ∆E/E ≈1.5%, at the crystal entrance. In simulations with β*=0.55-2
m optics, channeling efficiency was completely independent of energy even for ∆E/E≈10%. In
high β* options, crystal efficiency was uniform within ≈0.7% for ∆E/E ≈1.5%. One can say that a
phase space distribution (x, y, x', y', E) can be perfectly preserved in crystal and no information is
lost on transmission in crystal.
Figure 3 An example of beam space (x’, y’) at the entrance to the crystal (a) and at the exit (b).
Fig. 3 shows an example of a (x’, y’) plot at the entrance to the crystal (a) and at the exit of it
(b) where we tried to show how accurately a crystal can transmit a signature in angular space
(semicircle chosen as a probe). The resolution of the image transmitted by a crystal is ~0.2 µrad
in both planes. In terms of the critical channeling angle θC, the obtained resolution is an order of
magnitude finer than θC while the size of the trapped and channeled area can be some orders of
magnitude greater than θC.
In the applications there is no point to have a crystal transmission too perfect. It should match
the other sources of inaccuracy like a multiple scattering in the detectors and vacuum chambers,
etc. By tuning crystal parameters, in principle, one could very much improve in precision of the
beam image downstream of the crystal but loose in brightness of the image, i.e. in statistics rate,
as the efficiency of crystal transmission could be affected.
Finally, we suggest another idea for the channeling plane (a “microscope idea”) that improves
not only the crystal accuracy but even the detector resolution in that plane. Crystal can magnify
beam image in one plane, e.g. transform the entrance values (x, x', y, y') into exit values (x, Nx'
+θ, y, y'). The magnification factor N can be as big as 2 or 10 or even 100, and serve the purpose
to increase strongly the overall angular resolution in x’. In the above examples, the overall
resolution was ~1 µrad defined by detector resolution. With magnification optics, the overall
inaccuracy in x’ would be effectively reduced by factor N, bringing it below 0.1 µrad rms.
Magnification is realized by making the shape of the crystal exit face different from the entry
face. With a magnification factor of 10, e.g., the entry angular opening of 50 µrad would
correspond to the exit opening of 500 µrad.
5. Conclusion
We have shown in simulations that crystal lattice can trap with 90% efficiency a beam with a
(x', y') distribution much broader than a critical angle θC. To achieve that, one has to match the
crystal focus length to the effective length between the particle source and the crystal in the
accelerator lattice. Crystal adaptation to accelerator lattice improved channeling efficiency up to
300-fold. Crystal can transmit the trapped particles in channeled states with the phase space (x,
x', y, y', E) distribution preserved with accuracy an order of magnitude finer than θC. Several
solutions were proposed and supported by simulations for achieving a fine resolution in crystal
transmission.
This may give a beam instrument for collision products in colliders. Usually, accelerator beam
instruments prepare particles for collision: by cooling them, bending, focusing, etc. Detectors
sort out the results of collision. We change this a bit by introducing crystal optics between the
collision point and detectors.
A crystal adapted to the LHC lattice can trap with 90% efficiency all protons emerging from
the IP with divergence of 150 µrad or ~100θC. The trapped protons can be channeled to detectors
with precision down to 0.1 µrad rms. This makes feasible a crystal application for the
measurement of diffractive scattering in CMS and ATLAS at the LHC. While we showed the
physical capabilities of crystal channeling, its actual application in the LHC environment has to
take into account many technical considerations to fit into existing infrastructure of accelerator
and detectors.
Crystal channeling of LHC forward protons can improve proton acceptance in momentum
loss ξ and four-momentum transfer t both in TOTEM and FP420 and allow to reach the smallest
possible value of the scattering angle [9]. Now the sensitive detector area starts at ~12-15σ from
the LHC beam [10]. Crystal can be placed at ~6σ from the LHC beam as it is very small, ~cm Si,
and does not provoke beam instability. Such a crystal can trap and deliver a very useful
information on most forward high momentum “quasi-elastic” and elastic protons at LHC,
unavailable otherwise.
There are practical benefits as well. Crystal would relax tough requirements on β* needed for
TOTEM. Crystal may allow TOTEM to run at the early start of the LHC, possibly running in
parallel to other experiments. Thanks to crystal, FP420 detectors could possibly reside out of the
cold region. The detectors don’t need to be edgeless. Crystal works best with low β*, where
FP420 is interested most. If detectors can be more distanced from the beam, background
conditions may improve. For injection, the active areas of the detectors must be kept away from
the beams and then moved back; instead, one can move a crystal. Crystal can be introduced to
experiment on a later stage in an attempt to expand the horizons of the physics program.
References
[1] D.S. Gemmel, Rev. Mod. Phys. 46, 1 (1974)
[2] E.N. Tsyganov, FNAL TM-682 (1976). A.S. Vodopianov et al., JETP Lett. 30, 474 (1979)
[3] V.M. Biryukov, Yu.A. Chesnokov and V.I. Kotov, Crystal Channeling and its Application at High
Energy Accelerators. Berlin: Springer (1997)
[4] M.B.H. Breese, Nucl. Instr. and Meth. B 132, 540 (1997)
[5] R.A. Carrigan et al., Phys. Rev. ST AB 5, 043501 (2002)
[6] A.G. Afonin et al., Nucl. Instr. and Meth. B 234, 14 (2005); Phys. Lett. B 435, 240 (1998); JETP
Lett. 67, 781 (1998)
[7] R.A. Carrigan et al., Phys. Rev. ST AB 1, 022801 (1998); V. Biryukov. Phys. Rev. E 52, 6818
(1995)
[8] R.P. Fliller et al. Phys. Rev. ST AB 9, 013501 (2006); Nucl. Instr. Meth. B 234, 47 (2005); AIP
Conf. Proc. 693, 192 (2004)
[9] S.P. Moller et al. Phys. Rev. A 64, 032902 (2001); S.P. Moller et al., Nucl. Instr. and Meth. B 84,
434 (1994); V. Biryukov, Nucl. Instr. and Meth. B 117, 357 (1996).
[10] E. Uggerhoj and U.I. Uggerhoj, Nucl. Instr. and Meth. B 234, 31 (2005); V.M. Biryukov et al.,
Nucl. Instr. and Meth. B 234, 23 (2005); arXiv:physics/0307027
[11] V.M. Biryukov and S. Bellucci, Nucl. Instr. and Meth. B 252, 7 (2006); arXiv:hep-ex/0504021
[12] K. Eggert and P. Grafstrom. Presented at CARE-HHH-APD Mini-Workshop on Crystal
Collimation (CC-2005), Geneva, 2005. M. Albrow. Talk given at CERN (2006).
[13] M. Albrow et al., CERN/LHCC 2006-039/G-124.
[14] V. Biryukov, Nucl. Instrum. and Meth. B 53, 202 (1991); A. Taratin et al., Nucl. Instrum. and
Meth. B 58, 103 (1991); V.M. Biryukov, Nucl. Instr. and Meth. B 117, 463 (1996)
[15] A. Baurichter et al. Nucl. Instr. and Meth. B 164-165, 27 (2000)
[16] V. Biryukov. Phys. Rev. E 51, 3522 (1995); CERN SL/Note 93-74 AP (1993).
[17] S. Strokov et al., submitted to J. Phys. Soc. Jap.
[18] V.I. Baranov et al., Nucl. Instr. and Meth. B 95, 449 (1995).

  We show that crystal can trap a broad (x, x', y, y', E) distribution of
particles and channel it preserved with a high precision. This sampled-and-hold
distribution can be steered by a bent crystal for analysis downstream. In
simulations for the 7 TeV Large Hadron Collider, a crystal adapted to the
accelerator lattice traps 90% of diffractively scattered protons emerging from
the interaction point with a divergence 100 times the critical angle. We set
the criterion for crystal adaptation improving efficiency ~100-fold. Proton
angles are preserved in crystal transmission with accuracy down to 0.1
microrad. This makes feasible a crystal application for measuring very forward
protons at the LHC.

Introduction
A particle entering the crystal lattice parallel to a major crystallographic direction can be
captured and channeled by the lattice along a crystal axis or plane [1]. For instance, a positive
particle can be channeled between adjacent atomic planes. In a bent crystal, the channeled
particles can follow the bend [2]. This led to elegant technique of beam steering by bent
channeling crystals [3] now experimentally explored over six decades in energy from low MeV
[4] to 1 TeV [5]. The technique is used on permanent basis in IHEP Protvino where crystal
systems extract protons from 70 GeV main ring with efficiency of 85% at intensity up to 4×1012
protons using Si crystals just 2 mm along the beam [6]. Bent crystals channel in good agreement
with predictions up to the highest energies [6-9].
Crystal applications at the 7-TeV Large Hadron Collider are considered for beam collimation
and extraction [10] and in situ calibration of CMS and ATLAS calorimeters [11]. In another
proposal, crystal could capture the particles emerging from the interaction point (IP) with small
angles and channel them out of the beam [12]. This could help to improve on measurement of
small angle elastic and “quasi-elastic” scattering in CMS and ATLAS where lower momentum
transfers might become available for pp elastics scattering and lower proton momentum losses
for diffractive physics [12]. Groups in both CMS (with TOTEM) and ATLAS would like to add
very forward proton detectors, 420 m downstream on both sides, a project FP420 [13]. By
detecting protons that have lost less than 1% of their longitudinal momentum, a rich QCD,
electroweak, Higgs and BSM program becomes accessible, with the potential to make
measurements which are unique at LHC, and difficult even at a future linear collider [13].
The measurement of the displacement x and angle x’ (in the horizontal plane) of the outgoing
protons relative to the beam allows the momentum loss ξ=∆p/p and transverse momentum of the
scattered protons to be reconstructed. Protons emerging from diffractive scattering at LHC have
very small emission angles (10-150 µrad) and fractional momentum loss (ξ = 10-8 – 0.1). Hence
they are very close to the beam and can only be detected in the Roman Pots downstream if their
displacement at the detector location is large enough to escape the beam halo [13].
2. Crystal efficiency
As practice shows, crystal can go into a very limited space and get particles from there [6].
Most efficient crystal applications are based on so called “multipass” mode where particles can
encounter a crystal many times in the ring [6,14]. There are also successful experimental
demonstrations of highly efficient channeling in a single pass, with efficiency up to 60% at
CERN SPS [15]. Throughout this paper we consider only a single-pass channeling.
We show with simulations that at the LHC a crystal can efficiently channel forward protons.
For channeling simulations we apply a Monte Carlo code CATCH [16] successfully used for
prediction of experiments at CERN SPS [9], IHEP U-70 [6], Tevatron [7], RHIC [8] and KEK
[17] and crystal applications at the LHC [10,11].
Crystal capture is very selective in angle. The critical angle θC within which the capture is
possible is as small as about ±5 µrad / E1/2(TeV) at a high energy E in Silicon (110) planes.
Proton divergence of 150 µrad is almost 100 times θC at 7 TeV. Therefore it is not possible to
capture all these protons by a plain crystal. However, we can suggest an efficient solution
benefiting from the fact that all diffractively scattered protons originate from a small region at
the IP.
For standard LHC optics with beta function value at the IP β*=0.55 m, the beam size at the IP
is σbeam≈16 µm rms. The spread in the transverse position of the vertex point where outgoing
protons originate from is determined by the rms spread of the beam and equals σbeam/√2 [13]. As
protons emerge from diffractive scattering at LHC with emission angles up to ≈150 µrad and
interaction width σbeam/√2, the emittance of the beam to be trapped by a crystal is ≤ 2π µrad-mm
only. This corresponds to the acceptance of a Si crystal of ~1 mm transverse size. The match of
the diffractive-protons emittance to the crystal acceptance means that the particles could be
                                                                                                                                                            
♦ http://mail.ihep.ru/~biryukov/
trapped and channeled efficiently. To realize this, one has to match the crystal design and
location to the application. For the LHC scenario with high luminosity, we find the most efficient
design to be a crystal with a point-to-parallel focusing entry face. Focusing crystal proposed by
A.I Smirnov in 1985 has a face shaped so that the tangents to the crystal planes cross at a focus
line at some distance LF from the crystal [3]. This kind of crystal was successfully tested at IHEP
where it efficiently trapped a beam of ±2 mrad divergence (or ~100 times θC) [18]. The crystal
traps protons emerging from the focus line uniformly from all the angular range if the entry face
has a proper shape [18].
We find that for most efficient channeling in the LHC the focus distance LF of this crystal
should be equal to the effective distance Leff between the crystal location and the IP. In a drift
space, Leff is geometrical distance. In accelerator lattice, Leff =(β*βC)1/2sin∆ψ, where βC is β value
at the crystal and ∆ψ is the phase advance from the IP to the crystal. A plain crystal with a flat
entry face has LF = ∞.
In simulations with the low β* optics settings, a focusing crystal shows best efficiency if
installed at a location with effective distance Leff ≥ 15 m from the IP. It can be a Si (110) or (111)
crystal of ≈(0.15 mrad)×Leff ≥ 2.5 mm transverse size in order to capture efficiently all diffractive
protons. Simulation predicts that a focusing Si(110) crystal with LF=Leff traps 90% of 7 TeV
protons emerging from the IP in the angular range of 150 µrad width into channeling mode. The
efficiency figure is almost independent of the crystal location provided Leff ≥ 15 m.
The reason for high efficiency at high Leff is that, at a distance Leff from the IP, any point at
the crystal entry face sees the beam source of σ size (at the IP) at an angle of σ/Leff. Channeling
efficiency reduces by a factor of about (1-(σ/LeffθC)2)1/2 [3]. The reduction in efficiency by a
factor of ≈1-σ2/2L2effθC2 becomes negligible for L2eff >> σ2/2θC2 =β*ε/4θC2 where ε is beam
emittance. With β*=0.55 m and Si(110) crystal, channeling efficiency saturates for L2eff >> (4
One more idea for efficient channeling of forward protons in the LHC is that a crystal can be
installed with planes parallel to either x’ or y’ plane. For application, it is not critical whether
crystal bends protons in horizontal or vertical plane to produce an offset at the detector. But the
distance Leff in accelerator lattice from the IP to the crystal can be very different in x and y
planes. Then channeling efficiency is very different, whether crystal traps protons in x’ or y’
plane. We suggest in this case to install crystal for channeling in the plane with larger Leff.
For instance, on the location 200 m downstream of the IP5 (CMS) and some 20 m ahead of
the Roman Pot station at 220 m where crystal could be installed, Leff ≈6 m in x’ and ≈20 m in y’
plane. According to the analysis above, channeling efficiency in y’ plane should be great while in
x’ plane moderate. Indeed, our simulations for this location show channeling efficiency of ≈87%
in y’ and only ≈60% in x’ plane, for β*=0.55 m and optimal crystals of Si(110). A plain Si crystal
has channeling efficiency in x’ plane of just 3.5% or 17 times lower than a Si focusing crystal
adapted to the LHC lattice.
For the run-in phase of the LHC with β*=2 m we find that channeling efficiency of ≥ 85% can
be achieved if crystal is located at Leff ≥ 30 m downstream of the IP. The nominal, high
luminosity optics of the LHC is not optimized for forward proton detection. Therefore a
possibility to use a channeling crystal can be very helpful as it offers opportunities for diffractive
physics studies otherwise inaccessible in the nominal LHC settings.
The LHC options with a high β* (1540 and 90 m) are devised for the studies of diffractive
physics. With β*=1540 m, the emittance of diffractively scattered protons increases to ≈50π
µrad-mm. This corresponds to the acceptance of a Si crystal of ≥ 30 mm transverse size. Such a
crystal is not out of question, however the problem is where to fit it in the LHC. In terms of Leff,
good channeling efficiency requires a location with L2eff >> (130 m)2 in this optics.
We simulated channeling on the location 200 m from the IP5. In β*=1540 m optics, a 10-cm
Si(110) crystal trapped and bent protons 0.5 mrad in x’ plane with efficiency of 41%. A Ge(110)
crystal shows there 48% efficiency, i.e. comparable to Si. All figures assumed a perfect match
LF=Leff in crystal. A plain Si crystal gives efficiency of <<1%, or 300 times lower than a Si
focusing crystal adapted to the LHC lattice on this location.
In β*=90 m option on the same location, the choice of plane is important because Leff ≈10 m in
x’ and ≈170 m in y’ plane. Preferred location should have L2eff >> (60 m)2 so we expect very
different efficiencies in x’ and y’ planes. Our simulations give crystal efficiency of 72% in y’ and
only 7% in x’ plane for β*=90 m. Here, crystal application is feasible only with bending in
vertical plane.
Low efficiency may exclude a crystal use for double-pomeron-exchange events (pp→pXp)
with double-arm reconstruction, because the probability to have channeling in both arms in
coincidence becomes small, e.g. (41%)2≈17%. For reconstruction of single-diffraction events
(pp→pX) more detailed studies are required before the benefits (or their absence) from a crystal
use with high β* options can be understood.
In this paper we suggest the use of a single crystal for proton extraction from halo and
delivery to the detector. The use of a 2-stage crystal system [12], first crystal for extracting a
proton and second one for bending it a big angle, would reduce the overall efficiency by a factor
of ~0.6 (ideally) or less. The 2nd crystal traps only part of the protons channeled in the 1st one.
Finally, we notice that one can filter diffraction events with a crystal. Instead of trapping all
forward protons, crystal acceptance can be made smaller and sample e.g. only the most forward
protons emerging from the IP with the angles of a few µrad.
3. Precise transmission in a single (x, x’) plane
Whereas protons are physically delivered from the IP to detector with good efficiency, the
essential question is whether the information on phase space (x, x', y, y', E) distribution of
particles is lost or corrupted while the particles are captured and transmitted in crystal. The
success of experiments on measuring forward high momentum protons at the LHC depends on
the angular precision of proton track reconstruction. A plain crystal would destroy the phase
space information first by selecting particles from just a single direction and then disturbing the
exit angle of particle by coherent and incoherent scattering in crystal. Plain crystal acceptance is
±θC and crystal accuracy in angle transmission is again ±θC. That means, a plain crystal traps and
delivers about zero bit information on angle distribution. In this paper we design a crystal with
the acceptance of ~100 θC and angle transmission accuracy of ~0.1 θC, although it sounds against
the nature of crystal channeling.
Suppose particles are coming with a distribution over (x, x', y, y', E). Ideally, we would like
the crystal to trap all coming particles and preserve their distribution over (x, x', y, y', E), and
then shift an angle of θ each particle towards a physical setup where this distribution can be
analyzed in detail.
One should solve two problems. One problem was to trap and bend a beam with a divergence
much greater than the critical angle. A focusing crystal adapted to the LHC optics solves this
problem. In simulations, a focusing crystal traps with 90% efficiency all protons emerging from
the IP with the angular distribution ~100 times θC. Notice that the trapped particles fully preserve
also their distribution over the angle in the plane orthogonal to the plane of channeling. In such a
crystal, particles are trapped uniformly from a very broad distribution over x’ and y’.
A bent crystal would transform (x, x', y, y') at the entrance into (x, x'+θ, y, y') at the exit. To
do so, each trapped particle has to be channeled over the same distance in crystal. Therefore, the
shape of the crystal exit face must match the entry face. Then in a bent crystal each channeled
particle receives the same bending angle.
Although the crystal described above can solve the idea of sampling a broad distribution of
particles and delivering it to a required destination, second problem is how to preserve the
sampled distribution (x, x', y, y') “frozen” on transmission through the crystal lattice as precise as
possible. The coordinates (x, y) of particles are obviously preserved in crystal, so one should take
care of the accuracy in transmission of angles x’, y’ only.
The protons channeled between atomic planes in crystal are disturbed by (1) oscillations in
the channeling plane with an amplitude up to θC and by (2) scattering on a rarefied electronic gas
(mostly valence electrons) in both planes, x’ and y’. Notice that nuclear scattering will not
disturb the sample of transmitted channeled particles as this process is strongly suppressed for
channeled positive particles. Simply saying, any particle nuclear scattered would be dechanneled
and thus not present in the sample of bent particles.
That gives us the first idea that partially solves the problem of transmission accuracy. The
idea is that the information on crystal-captured particles is very well preserved in one plane, e.g.
(x, x'), while the particles are trapped and bent in another plane, e.g. (y, y’). Notice that particle
distribution in the plane orthogonal to channeling is favored twice. Firstly, they are easily
trapped with a broad angular distribution; secondly they are transmitted with a very little
scattering. Information in this plane will be best preserved. The opportunity to have perfect data
on just one plane is interesting for applications. The reconstruction of the Higgs boson mass in
reaction pp→p+H+p requires (x, x’) data in horizontal plane only [13].
Figure 1 The difference in proton angles, x’ and y’, before and after a Si(110) crystal.
Oscillations in the channeling plane on the atomic coherent potential are a greater problem.
Fig. 1 shows a distribution of the difference in proton angle in x’ and y’ planes before and after a
channeling in crystal, (x’OUT – x’IN) and (y’OUT – y’IN – 0.1 mrad), as obtained in simulations for a
Si(110) bent crystal channeling in y’ plane. The accuracy in x’ transmission in crystal is very
good indeed, ~0.1 µrad rms. The width of (y’OUT – y’IN – 0.1 mrad) distribution is much greater
due to oscillations in the potential of Si (110) planes.
4. Precise transmission in both planes
To solve the problem of accuracy in the other plane, i.e. the plane of channeling, one solution
is to use a channel with a lower critical angle, for instance Si(100) instead of (110) or (111). A
more universal solution is to use a strongly bent crystal. The critical angle θC is gradually
reduced to zero when the crystal curvature approaches a critical value. The strong focusing of a
strongly bent crystal suppresses channeling oscillations to any low level needed in the
application.
Fig. 2 shows the difference in proton angle in x’ and y’ planes before and after channeling in a
crystal, (x’OUT – x’IN– 0.1 mrad) and (y’OUT – y’IN), as obtained in simulations for a 2 mm Si(100)
crystal bent 0.1 mrad. The protons were channeled in x’ plane. The rms value of angle smearing
found in simulations is 0.2 µrad both for x’ and y’.
Figure 2 The same as in Fig. 1 but for a strongly bent Si (100) crystal.
This accuracy should be compared to the angular resolution of the detectors downstream of
the crystal. Measuring proton coordinates with ~10 µm resolution [13] over a base of ~8 m as
allowed by a drift space would give an angular accuracy of ~1.4×10µm/8m=1.8 µrad. Addition
(quadratic) of crystal transmission accuracies doesn’t change this resolution. That would be
perfect for crystal. With a much better resolution on the detector side, down to 0.5 µrad, the
overall resolution becomes ~0.55 µrad, i.e. just slightly disturbed. Crystal transmission in both
planes, x’ and y’, is still almost perfect.
Because of scattering on electronic gas, the protons loose energy in crystal. In simulations, the
energy loss and its fluctuations in crystal are ∆E/E ≈10-7–10-6, i.e. much smaller than even the
nominal energy spread in the LHC beam, 1.1×10-4. Energy losses in bent crystals were studied in
experiments at CERN SPS with protons of 450 GeV and Pb ions of 33 TeV where CATCH
predictions were also validated [9]. The diffractively scattered protons would have energy spread
on the order of 100 GeV, or ∆E/E ≈1.5%, at the crystal entrance. In simulations with β*=0.55-2
m optics, channeling efficiency was completely independent of energy even for ∆E/E≈10%. In
high β* options, crystal efficiency was uniform within ≈0.7% for ∆E/E ≈1.5%. One can say that a
phase space distribution (x, y, x', y', E) can be perfectly preserved in crystal and no information is
lost on transmission in crystal.
Figure 3 An example of beam space (x’, y’) at the entrance to the crystal (a) and at the exit (b).
Fig. 3 shows an example of a (x’, y’) plot at the entrance to the crystal (a) and at the exit of it
(b) where we tried to show how accurately a crystal can transmit a signature in angular space
(semicircle chosen as a probe). The resolution of the image transmitted by a crystal is ~0.2 µrad
in both planes. In terms of the critical channeling angle θC, the obtained resolution is an order of
magnitude finer than θC while the size of the trapped and channeled area can be some orders of
magnitude greater than θC.
In the applications there is no point to have a crystal transmission too perfect. It should match
the other sources of inaccuracy like a multiple scattering in the detectors and vacuum chambers,
etc. By tuning crystal parameters, in principle, one could very much improve in precision of the
beam image downstream of the crystal but loose in brightness of the image, i.e. in statistics rate,
as the efficiency of crystal transmission could be affected.
Finally, we suggest another idea for the channeling plane (a “microscope idea”) that improves
not only the crystal accuracy but even the detector resolution in that plane. Crystal can magnify
beam image in one plane, e.g. transform the entrance values (x, x', y, y') into exit values (x, Nx'
+θ, y, y'). The magnification factor N can be as big as 2 or 10 or even 100, and serve the purpose
to increase strongly the overall angular resolution in x’. In the above examples, the overall
resolution was ~1 µrad defined by detector resolution. With magnification optics, the overall
inaccuracy in x’ would be effectively reduced by factor N, bringing it below 0.1 µrad rms.
Magnification is realized by making the shape of the crystal exit face different from the entry
face. With a magnification factor of 10, e.g., the entry angular opening of 50 µrad would
correspond to the exit opening of 500 µrad.
5. Conclusion
We have shown in simulations that crystal lattice can trap with 90% efficiency a beam with a
(x', y') distribution much broader than a critical angle θC. To achieve that, one has to match the
crystal focus length to the effective length between the particle source and the crystal in the
accelerator lattice. Crystal adaptation to accelerator lattice improved channeling efficiency up to
300-fold. Crystal can transmit the trapped particles in channeled states with the phase space (x,
x', y, y', E) distribution preserved with accuracy an order of magnitude finer than θC. Several
solutions were proposed and supported by simulations for achieving a fine resolution in crystal
transmission.
This may give a beam instrument for collision products in colliders. Usually, accelerator beam
instruments prepare particles for collision: by cooling them, bending, focusing, etc. Detectors
sort out the results of collision. We change this a bit by introducing crystal optics between the
collision point and detectors.
A crystal adapted to the LHC lattice can trap with 90% efficiency all protons emerging from
the IP with divergence of 150 µrad or ~100θC. The trapped protons can be channeled to detectors
with precision down to 0.1 µrad rms. This makes feasible a crystal application for the
measurement of diffractive scattering in CMS and ATLAS at the LHC. While we showed the
physical capabilities of crystal channeling, its actual application in the LHC environment has to
take into account many technical considerations to fit into existing infrastructure of accelerator
and detectors.
Crystal channeling of LHC forward protons can improve proton acceptance in momentum
loss ξ and four-momentum transfer t both in TOTEM and FP420 and allow to reach the smallest
possible value of the scattering angle [9]. Now the sensitive detector area starts at ~12-15σ from
the LHC beam [10]. Crystal can be placed at ~6σ from the LHC beam as it is very small, ~cm Si,
and does not provoke beam instability. Such a crystal can trap and deliver a very useful
information on most forward high momentum “quasi-elastic” and elastic protons at LHC,
unavailable otherwise.
There are practical benefits as well. Crystal would relax tough requirements on β* needed for
TOTEM. Crystal may allow TOTEM to run at the early start of the LHC, possibly running in
parallel to other experiments. Thanks to crystal, FP420 detectors could possibly reside out of the
cold region. The detectors don’t need to be edgeless. Crystal works best with low β*, where
FP420 is interested most. If detectors can be more distanced from the beam, background
conditions may improve. For injection, the active areas of the detectors must be kept away from
the beams and then moved back; instead, one can move a crystal. Crystal can be introduced to
experiment on a later stage in an attempt to expand the horizons of the physics program.
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