The miscut angle influence on the future LHC crystal based collimation system
The paper concerns the future LHC crystal based collimation system. The dependence of collimation efficiency on the muscut angle characterizing nonparallelity of the channeling planes and crystal surface is mainly addressed. We demonstrate that even the preferable positive miscut can increase the nu...
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| Cite this: | The miscut angle influence on the future LHC crystal based collimation system / V.V. Tikhomirov, A.I. Sytov // Вопросы атомной науки и техники. — 2012. — № 1. — С. 88-92. — Бібліогр.: 7 назв. — англ. |
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| citation_txt | The miscut angle influence on the future LHC crystal based collimation system / V.V. Tikhomirov, A.I. Sytov // Вопросы атомной науки и техники. — 2012. — № 1. — С. 88-92. — Бібліогр.: 7 назв. — англ. |
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| description | The paper concerns the future LHC crystal based collimation system. The dependence of collimation efficiency on the muscut angle characterizing nonparallelity of the channeling planes and crystal surface is mainly addressed. We demonstrate that even the preferable positive miscut can increase the nuclear reaction rate in the perfectly aligned crystal collimator by a factor of 4.5 in the UA9 experiment. We also discuss the possible miscut influence on the future LHC crystal collimation system suggesting simple estimates for the beam diffusion step, average impact parameter of particle collisions with the collimator and angular divergence of the colliding particle beam portion.
Для будущей системы коллимации ускорителя LHC при помощи кристаллов обсуждается зависимость эффективности коллимации от миската угла, характеризующегося непараллельностью кристаллических плоскостей и поверхности кристалла. Показано, что даже предпочтительный положительный мискат может увеличить число ядерных реакций в идеально ориентированном кристаллическом коллиматоре в 4,5 раза в эксперименте UA9. Для исследования возможного влияния миската на будущую систему коллимации БАКа предложены простые оценки диффузионного шага пучка, среднего прицельного параметра падения частицы на коллиматор и угловой расходимости падающего пучка.
Для майбутньої системи колімації прискорювача LHC за допомогою кристалів обговорюється залежність ефективності колімації від міскату кута, що характеризується непаралельністю кристалічних площин і поверхні кристала. Показано, що навіть кращий позитивний міскат може збільшити число ядерних реакцій в ідеально орієнтованому кристалічному коліматорі в 4,5 рази в експерименті UA9. Для дослідження можливого впливу міскату на майбутню систему колімації LHC запропоновані прості оцінки дифузійного кроку пучка, середнього прицільного параметра падіння частинки на коліматор і кутової розбіжності падаючого пучка.
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THE MISCUT ANGLE INFLUENCE ON THE FUTURE LHC
CRYSTAL BASED COLLIMATION SYSTEM
V.V. Tikhomirov and A.I. Sytov ∗
Research Institute for Nuclear Problems, Belarus State University, 220030, Minsk, Belarus
(Received October 25, 2011)
The paper concerns the future LHC crystal based collimation system. The dependence of collimation efficiency on
the muscut angle characterizing nonparallelity of the channeling planes and crystal surface is mainly addressed. We
demonstrate that even the preferable positive miscut can increase the nuclear reaction rate in the perfectly aligned
crystal collimator by a factor of 4.5 in the UA9 experiment. We also discuss the possible miscut influence on the future
LHC crystal collimation system suggesting simple estimates for the beam diffusion step, average impact parameter
of particle collisions with the collimator and angular divergence of the colliding particle beam portion.
PACS: 29.20.c, 29.27.a, 61.14.Dc, 03.80.+r
1. INTRODUCTION
Crystal based collimation was proposed to facilitate
the beam halo cleaning at large accelerators long ago.
Its application to the LHC upgrade becomes more
and more topical [2–4]. The basic idea is to use a bent
crystal in channeling mode to deflect halo particles
by relatively large angles to high impact parameters
of particle collisions with an absorber [2–5].
Fig. 1. A crystal with positive miscut angle before
(left) and after (right) bending with angle ϕ. θc (pos-
itive), θm (positive) and θs = θc − θm (negative)
are, respectively, the crystal plane misalignment
angle, miscut angle and crystal surface misorienta-
tion angle, all measured in the direction of crystal
bending, at that the angles θc and θs – from the
z axis, parallel to the velocity of the particle just
touching the crystal, and the angle θm – from the
crystal surface direction. Particles, moving from the
left to the right with small impact parameters, enter
the crystal through the lateral (upper) crystal surface
If the first particle collision with the crystal colli-
mator occurs at sufficiently small particle incidence
angle w.r.t. the crystal planes (at pure alignment,
θc = 0), the probability of particle capture into the
channeling regime reaches its maximum. However
even a small nonparallelity of the lateral crystal sur-
face with atomic planes, characterized by the miscut
angle θm, is able to severely disturb the motion of
particles hitting the crystal with small impact para-
meters. In particular, if the miscut angle is negative,
the channeling motion can be interrupted before the
particle reaches the exit crystal face [5]. Since a con-
siderable number of such particles will not reach an
absorber fast, the negative miscut is recommended
to be avoided [5]. By this reason the positive one
(Fig. 1) was chosen for the recent UA9 experiments
[2] aimed to demonstrate the viability of crystal col-
limation. However the nuclear reaction rate in the
perfectly aligned crystal collimator about five time
exceeding the theoretically predicted [3] value was
observed. In this paper for the first time we investi-
gate the influence of positive miscut on collimation
efficiency and demonstrate that it gives rise to up to
4.5 time increase of the nuclear reaction rate in the
collimator. We also predict the low influence of the
positive miscut on the efficiency of the future LHC
crystal collimation system but first suggest simple
estimates for the beam diffusion step, impact para-
meter of particle collisions with the collimator and
angular divergence of the part of the beam particles
colliding with the latter for the first time.
2. PARTICLE DIFFUSION IN THE
ACCELERATOR RING
When positively charged particles strike a bent crys-
tal moving strictly parallel to its planes, they can be
captured into the regime of stable channeling motion
with a probability of 80-85%. However because of
beam angular divergence, the “channeling probabil-
ity” decreases by the value ΔPch ∝ 〈ϑ2〉 [1]. This
decrease remains negligible only if 〈ϑ2〉 ≤ 0.01ϑ2
ch.
Fortunately, the angular divergence of the beam por-
tion striking a primary collimator first time often sat-
isfies this condition. So, the 15... 20% of particles can
escape channeling at the crystal penetration through
its normal entrance face and can be considerably de-
flected. Particles entering a crystal with negative
miscut [5] at small enough impact parameters are
angularly dispersed even stronger. Because of this
and also since a miscut can not be avoided in prac-
tice, the positive miscut is commonly preferred [5]. In
∗Corresponding authors E-mail address: vvtikh@mail.ru, alex sytov@mail.ru
88 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2012, N 1.
Series: Nuclear Physics Investigations (57), p. 88-92.
this case, the particles with the small enough impact
parameters enter the crystal through its lateral face
frequently avoiding capture even in the case of pure
crystal alignment. The uncaptured particles are scat-
tered like in amorphous matter, acquiring the average
deflection angle squared proportional to the length
Δz of particle path through the crystal. Besides the
angles of miscut θm value depends on the particle
impact parameter Δ with the crystal collimator and
some other parameters (see [1] and Fig. 2).
Beam diffusion parameter
Accelerator ε τ σ(μm) ρc/σ δ
SPS UA9 120 GeV 10 h 1010 3.5 0.086 nm
SPS UA9 120 GeV 4 min 1010 3.5 13 nm
LHC 7 TeV 10 h 200 6 5.4 μm
LHC 7 TeV 10 h 420 6 11.4 μm
Having limited access to the parameters of parti-
cle motion in the accelerators and since a joint de-
scription of all processes leading to particle collisions
with crystal collimator [4] is hardly available, we will
proceed from a simple estimate based on the accel-
erator beam lifetime τ . Assuming that the beam is
axially symmetric and has normal distribution [4]
dN
dρ
=
Nρ
σ2
exp
(
− ρ2
2σ2
)
(1)
and taking into account that the particle loss rate at
the collimator position ρc can be written in two ways
dN
dt
=
N
τ
=
(
dN
dρ
)
ρc
δ
T
, (2)
one can obtain the estimate of diffusion step (see [1]):
δ =
σ2T
τρc
exp
(
ρ2
c
2σ2
)
. (3)
N is a total number of particles in the ring, T and σ
are particle revolution period and r.m.s. beam radius
correspondingly. The table illustrates Eq. (3) appli-
cation to the cases of both the UA9 experiment and
IR7 beta collimation region at the LHC [6]. Note a
really drastic δ difference in the cases of the UA9 ex-
periment with low intensity beam and ρc � 3.5σ and
the intensive LHC beam and ρc = 6σ.
3. PARTICLE IMPACT PARAMETER
AND DEFLECTION ANGLE
To simulate both the particle impact parameter and
angular deflection at the moment of the first collision
with the collimator we will proceed from the pseudo-
harmonic representation of the betatron oscillations:
x(ψ) = x0 cosψ. (4)
Here ψ and x0 =
√
εβ are, respectively, the oscil-
lation phase and amplitude, the latter of which is
determined by the beam emittance ε and accelerator
beta function β. The particle direction of incidence
on the crystal will be described by the angle
θ(ψ) = −x0
β
[
sinψ − 1
2
dβ
ds
cosψ
]
(5)
of the velocity deviation from the direction of parti-
cle motion touching the collimator having x0 = xc.
δ
0 ze l
Δz
x
xc
Δ
xs(0)
θ
xe
θs
Fig. 2. A particle entering the crystal through the
lateral surface. The crystals extends from z = 0
to z = l, xc is the collimator radial coordinate,
(xe = xs(ze), ze) is the particle enter point while
(xs(0), 0) is the left upper corner of the crystal, θ and
θs are the deflection particle angle and crystal sur-
face misalignment one, respectively, Δz is the length
of particle trajectory inside the crystal, δ and Δ are,
respectively, the particle diffusion step and impact
parameter
The process of increase of the betatron oscillation
amplitude was simulated using the formula
x0(n) = x0(n− 1) + 2δξ1, (6)
where n = 1, 2, .. is the number of particle revolution
in the ring after the moment when x0(0) = xc. ξ1
(like ξ2 and ξ3 below) are random numbers uniformly
distributed through the interval (0, 1). In absence of
phase correlations between betatron oscillations on
different revolution periods according to [1] we can
obtain single and cumulative collision probabilities:
pn � 1
π
√
2nδ
xc
, PN =
n=N∑
n=1
pn � 2
3π
√
2δ
xc
N3/2. (7)
Since the cumulative collision probability increases
faster and faster with the revolution number N , the
“collision condition” |ψ| ≤ ψ(x0(n)) inevitably be-
comes fulfilled at some revolution N with some ran-
dom values of x0(N) and ψ allowing to evaluate both
the collision coordinate (4) and angle (5) of particle
deflection at the moment of collision.
89
Fig. 3. Particle distribution in impact parameter for the UA9 (SPS) (a) and the same for the LHC (b)
and particle distribution in deflection angle for both the UA9 (SPS) and the LHC (c)
Particle distributions in the impact parameter
Δ ≡ x − xc and deflection angle θ, simulated for
the UA9 and LHC cases, are represented in Fig. 3. A
three order in value difference in the impact parame-
ter in the UA9 and LHC cases is directly related to
that in the diffusion step – see the table. Assuming
that the collisions occur at PN ∼ 1, Eq. (7) can be re-
versed to estimate the typical revolution number be-
fore the collision, the average impact parameter and
absolute value of the deflection angle respectively:
N � (3πPN )2/3
2
3
√
xc
δ
∼ 2 3
√
xc
δ
, (8)
〈Δ〉 = P−1
N
n=N∑
n=1
pn[x0(n) cos(ψ) − xc] � (9)
� 3(3πP ′
N )2/3
10
3
√
xcδ2 ∼ 1.3 3
√
xcδ2,
〈|θ|〉 = P−1
N
n=N∑
n=1
pnx0(n) sin(ψ)/β � (10)
� 3(3πP ′′
N)1/3
8
3
√
x2
cδ
β
∼ 0.8
3
√
x2
cδ
β
.
The right hand sides of Eqs. (8)-(10) contain numeri-
cal factors found from the simulations and determin-
ing effective collision probabilities PN , P
′
N , P ′′
N ∼ 1
which should be considered as the parameters com-
pensating a slight model inconsistency. Additionally,
Eqs. (8)-(10) allow to compare the conditions of the
UA9 experiment with the possible LHC crystal colli-
mation system as well as to estimate the perspectives
of crystal collimation development [7]. Fig. 4, a again
demonstrates that the radical difference in diffusion
steps results in the drastic difference in average im-
pact parameters in the UA9 and LHC cases.
4. COLLIMATION EFFICIENCY FOR
THE UA9 EXPERIMENT
A simulated value of the impact parameter Δ can be
directly used to evaluate both the entrance transverse
coordinate (4) and angle (5), the knowledge of both
of which is necessary to simulate the particle trajec-
tory inside the crystal in order to obtain the angle of
particle deflection by the latter. Recall that we mea-
sure the angles from the direction of motion of the
particle just touching the collimator at its maximum
displacement x(ψ = 0) = x0 = xc from the beam axis
(see Fig. 2). Note de bene esse that the chosen zero
direction forms the angle w.r.t. the beam axis:
dx(ψ = 0)
ds
=
1
2
√
ε
β
dβ
ds
= −xc
β
α. (11)
Here s is the beam longitudinal coordinate and α =
−dβ/ds/2 is the conventional Twiss parameter. In
the ideal case a crystal has no miscut and its planes
form zero angle w.r.t. the chosen direction. Particles
neither enter the crystal through its lateral surface
no leave the one through it if they are channeled.
The real situation is complicated by the inevitable
presence of both crystal miscut and crystal plane mis-
alignment at the entrance surface, characterized by
the angles θm and θc, respectively. The crystal mis-
alignment angle is assumed to be positive if the planes
are rotated in the direction of crystal bending. If
one determines the miscut angle as the one of crys-
tal plane rotation in the direction of crystal bending
w.r.t. the crystal lateral surface, the misorientation
angle of the latter, measured from the same zero an-
gle direction, will be equal to θs0 = θs(0) = θc − θm.
If the crystal is bent with radius R, the surface tan-
gential direction will vary like θs(z) = θs0 +z/R with
the longitudinal coordinate z � s− sc:
xs(z) = xs(0) +
∫ z
0
θs(z)dz = xs(0) + θs0z + z2/2R.
(12)
A behavior of the surface coordinate (12) also mea-
sured in the crystal bending direction, considerably
differs if θs0 > 0 and θs0 < 0 and, in the latter case, if
|θs0| > ϕ and |θs0| < ϕ, where ϕ = l/R is the bend-
ing angle of the crystal with length l. So, if θs0 < 0 a
particle can enter the crystal through the lateral sur-
face and, if −ϕ < θs0 < 0, also leave it through the
latter. On the opposite, if θs0 > 0 particles always en-
ter the crystal through the entrance face, while leave
it either through the lateral or exit ones. All the
cases are determined by the impact parameter Δ. To
get simple formulae for all possible situations we first
determined the minimal crystal surface coordinate
xmin ≡ xc. After the Monte Carlo sampling of the
impact parameter value Δ = x(ψ) − xc correspond-
ing transverse collision coordinate x(ψ) was used to
evaluate the longitudinal one ze from the equation
xs(ze) = x(ψ). Then both the particle entrance point
coordinates (x(ψ), ze) and initial deflection angle (5)
were used as the initial conditions for its trajectory
simulation inside the crystal.
90
Fig. 4. Average impact parameter vs average beam diffusion step for the SPS UA9 (upper curve) and the
LHC (lower one). Solid parts mark the actual parameter regions (a).
Measured in centimeters average length 〈Δz〉 of scattering of particles entering the crystal through the lateral
crystal surface vs both miscut angle and diffusion step at perfect crystal alignment (b).
Probability of nuclear reactions in the crystal collimator vs miscut angle at perfect crystal alignment (c)
A possibility to leave the crystal through the lat-
eral surface at some z < l was permanently moni-
tored using Eq. (12). The particle transverse coor-
dinate and deflection angle at the exit together with
the crystal position sc in the ring became the initial
conditions for the particle motion simulation in the
accelerator ring with the simplest model of betatron
motion. We used at first a simplified approach to
elaborate a general view on the influence of positive
miscut on the collimation efficiency. The idea origi-
nates from the mentioned proportionality of the de-
crease of the channeling efficiency at the second crys-
tal penetration to the squared angle of multiple scat-
tering of particles entering the crystal first through
the lateral surface. Since the latter, in turn, is pro-
portional to the scattering length Δz, one can con-
clude that simply ΔPch ∝ Δz and reduce the issue
to the analysis of the behavior of the averaged length
〈Δz〉 of the first pass through the crystal of the parti-
cles entering the latter exclusively crossing its lateral
surface. Fig. 4, b illustrates the simulated behavior
of 〈Δz〉 in the typical UA9 case of l = 2 mm and
ϕ = l/R = 150 μrad. Surprisingly, the simulations
unambiguously point to the region θm ∼ 100 μrad
and δ ∼ 1 Å of the UA9 experiment parameters as
to the one of the greatest possible miscut influence
on the collimation. Since the scattering length deter-
mines the decrease of the channeling probability and
since nonchanneled particles induce more nuclear re-
actions that the channeled ones, Fig. 4, b has to si-
multaneously reflect the behavior of the rate of the
nuclear reactions induced in the crystal collimator.
To illuminate the possible role of positive miscut in
the UA9 experiment we, according to Ref. [3] and
the table, had put δ = 1 Å and conducted detail
Monte Carlo simulations of the nuclear reactions in
the miscut angle interval −300 μrad≤ θm ≤ 300 μrad
taking now into detail consideration also the particle
motion in the crystal collimator. The dependence
obtained (Fig. 4, c) demonstrates an evident agree-
ment with that of 〈Δz〉 along the vertical (red) line
drawn at δ = 1 Å in Fig. 4, b, confirming thus the
strong influence of the positive miscut on the colli-
mation process. In principle, positive miscut causes
even slightly larger increase in nuclear reaction rate
(the right peak) than the negative one (the left one).
At this the increase of the reaction probability caused
by the positive miscut with θm � 125 μrad reaches
8.6/1.9 � 4.5. Thus, the miscut influence, for sure,
should be taken into consideration for the full inter-
pretation of the UA9 experiments [2].
5. MISCUT INFLUENCE AT THE LHC
For the future possible application at the LHC it
is important to clarify how the deteriorating miscut
influence can be avoided. A joint consideration of
the particle motion in both the ring and the crys-
tal results in the encouraging conclusion that the ob-
served undesirable increase in nuclear reaction rate
can be easily avoided in both UA9 and LHC cases.
In fact, some of the conditions of the UA9 experi-
ment prove to be practically optimal for the demon-
stration of the maximum miscut role. The point is
a perfect matching of the average impact parameter
(9) 〈Δ〉 � 0.039 μm with the width xs(0) − xc =
θ2mR/2 � 0.067 μm of the impact parameter region
allowing particle entrance through the lateral crystal
surface. This matching made possible both the lat-
eral entrance of the majority of particles and their
relatively continuous path inside the crystal, the av-
erage value of which 〈Δz〉 � 1.2 mm exceeds a half
of the crystal length l = 2 mm. It is namely the
nearly “amorphous” scattering at such a length which
gave the origin to the angular dispersion of particle
beam causing the decrease of the capture probability
to the channeling regime at their subsequent passages
through the crystal collimator.
At least two ways to decrease the miscut role
by fulfilling the condition Δ
xs(0) − xc < θml
can be readily suggested. The most evident, though,
probably, more difficult, is to lessen the miscut angle
down to about 10 μrad, as Figs. 4, b and 4, c suggest.
The second is to increase the collision parameter (9)
〈Δ〉 ∝ δ2/3 by means of beam diffusion acceleration.
While the diffusion step could be nearly freely cho-
sen in the collimation UA9 experiment, the actual
91
set of the LHC parameters solves this problem auto-
matically. Indeed, if R = 100 m and l = 4 mm, one
obtains xs(0)−xc � 0.32 μm, or more than a hundred
times less than 〈Δ〉 � 43 μm� 130(xs(0) − xc) with-
out special measures. Thus, only a negligible portion
of the LHC protons will enter the crystal collimator
through the lateral crystal surface even at the typical
miscut angles of θm ∼ 100 μrad.
It also should be noted that despite the relatively
large value of the diffusion step δ, the angular diver-
gence (10) of the colliding beam portion, as Fig. 3c
demonstrates, is low enough to provide the probabil-
ity of capture into the channeling regime comparable
to the maximum one. Nevertheless some decrease in
divergence remains desirable. The sharp dependence
(3) of the diffusion step on the collimator aperture
xc/σ allows to decrease δ by means of a slight de-
crease of the latter. At this, if the divergence of the
colliding beam portion is decreased by several times,
it will become possible to sharply rise the probability
of particle capture into the channeling regime up to
99% by the method of the crystal cut [7].
In conclusion, the positive miscut influence indeed
could increase the nuclear reaction probability in the
crystal collimator up to 4.5 times. Nevertheless if
the crystal collimator system based on the channeling
particle deflection is realized at the LHC, its function-
ing will not be considerably disturbed by the influ-
ence of crystal miscut. In addition, the performance
of the crystal collimator can be drastically improved
by the method [7] of the crystal cut.
Acknowledgements
One of the authors (V.T.) is obliged for an invita-
tion to the UA9 Workshop to Dr. W. Scandale and
Dr. G. Cavoto and also gratefully acknowledges use-
ful discussions with Prof. V. Guidi and Dr. A. Maz-
zolari.
References
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cut influence on the crystal collimation efficiency
// arXiv : 1109.5051v2 [physics.acc-ph], 2011.
2. W. Scandale et al. First results on the SPS beam
collimation with bent crystals // Phys. Lett.
2010, v. B692, p. 78-82.
3. W. Scandale, A. Taratin. Simulation of “CRYS-
TAL”, the bent crystal based collimation exper-
iment in the SPS // CERN report : CERN-AT-
2008-21, 2008.
4. V. Previtali. Performance evaluation of a crystal-
enhanced collimation system for the LHC //
These de Doctorat. Lausanne, 2010.
5. K. Elsener et al. Proton extraction from the
CERN SPS using bent silicon crystals // NIM.
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// PAC. Portland, Oregon, USA, 2003; CERN-
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JINST 2007, v. 2, P08006, 11 p.
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| id | nasplib_isofts_kiev_ua-123456789-107002 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T16:01:06Z |
| publishDate | 2012 |
| publisher | Research Institute for Nuclear Problems, Belarus State University |
| record_format | dspace |
| spelling | Tikhomirov, V.V. Sytov, A.I. 2016-10-10T20:13:15Z 2016-10-10T20:13:15Z 2012 The miscut angle influence on the future LHC crystal based collimation system / V.V. Tikhomirov, A.I. Sytov // Вопросы атомной науки и техники. — 2012. — № 1. — С. 88-92. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS: 29.20.c, 29.27.a, 61.14.Dc, 03.80.+r https://nasplib.isofts.kiev.ua/handle/123456789/107002 The paper concerns the future LHC crystal based collimation system. The dependence of collimation efficiency on the muscut angle characterizing nonparallelity of the channeling planes and crystal surface is mainly addressed. We demonstrate that even the preferable positive miscut can increase the nuclear reaction rate in the perfectly aligned crystal collimator by a factor of 4.5 in the UA9 experiment. We also discuss the possible miscut influence on the future LHC crystal collimation system suggesting simple estimates for the beam diffusion step, average impact parameter of particle collisions with the collimator and angular divergence of the colliding particle beam portion. Для будущей системы коллимации ускорителя LHC при помощи кристаллов обсуждается зависимость эффективности коллимации от миската угла, характеризующегося непараллельностью кристаллических плоскостей и поверхности кристалла. Показано, что даже предпочтительный положительный мискат может увеличить число ядерных реакций в идеально ориентированном кристаллическом коллиматоре в 4,5 раза в эксперименте UA9. Для исследования возможного влияния миската на будущую систему коллимации БАКа предложены простые оценки диффузионного шага пучка, среднего прицельного параметра падения частицы на коллиматор и угловой расходимости падающего пучка. Для майбутньої системи колімації прискорювача LHC за допомогою кристалів обговорюється залежність ефективності колімації від міскату кута, що характеризується непаралельністю кристалічних площин і поверхні кристала. Показано, що навіть кращий позитивний міскат може збільшити число ядерних реакцій в ідеально орієнтованому кристалічному коліматорі в 4,5 рази в експерименті UA9. Для дослідження можливого впливу міскату на майбутню систему колімації LHC запропоновані прості оцінки дифузійного кроку пучка, середнього прицільного параметра падіння частинки на коліматор і кутової розбіжності падаючого пучка. One of the authors (V.T.) is obliged for an invitation to the UA9 Workshop to Dr. W. Scandale and Dr. G. Cavoto and also gratefully acknowledges useful discussions with Prof. V. Guidi and Dr. A. Mazzolari. en Research Institute for Nuclear Problems, Belarus State University Вопросы атомной науки и техники Section B. QED Processes at High Energies The miscut angle influence on the future LHC crystal based collimation system Влияние угла миската на будущую систему коллимации LHC на основе кристаллов Вплив міскату кута на майбутню систему колімації LHC на основі кристалів Article published earlier |
| spellingShingle | The miscut angle influence on the future LHC crystal based collimation system Tikhomirov, V.V. Sytov, A.I. Section B. QED Processes at High Energies |
| title | The miscut angle influence on the future LHC crystal based collimation system |
| title_alt | Влияние угла миската на будущую систему коллимации LHC на основе кристаллов Вплив міскату кута на майбутню систему колімації LHC на основі кристалів |
| title_full | The miscut angle influence on the future LHC crystal based collimation system |
| title_fullStr | The miscut angle influence on the future LHC crystal based collimation system |
| title_full_unstemmed | The miscut angle influence on the future LHC crystal based collimation system |
| title_short | The miscut angle influence on the future LHC crystal based collimation system |
| title_sort | miscut angle influence on the future lhc crystal based collimation system |
| topic | Section B. QED Processes at High Energies |
| topic_facet | Section B. QED Processes at High Energies |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/107002 |
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