Ultra relativistic electron beam spatial size estimation from angular distribution of their radiation in thin crystals
The use of ultra relativistic electron (positron) emission in thin crystals to estimate particle beam spatial sizes for projected electron-positron colliders is proposed. The existing position-sensitive X-ray range detectors and the average path of secondary electrons in a detector restrict the mini...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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| Цитувати: | Ultra relativistic electron beam spatial size estimation from angular distribution of their radiation in thin crystals / Yu.A. Goponov, M.A. Sidnin, K. Sumitani, Y. Takabayashi, I.E. Vnukov // Вопросы атомной науки и техники. — 2015. — № 6. — С. 108-113. — Бібліогр.: 31 назв. — англ. |
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irk-123456789-1123832017-01-21T03:01:57Z Ultra relativistic electron beam spatial size estimation from angular distribution of their radiation in thin crystals Goponov, Yu.A. Sidnin, M.A. Sumitani, K. Takabayashi, Y. Vnukov, I.E. Взаимодействие релятивистских частиц с кристаллами и веществом The use of ultra relativistic electron (positron) emission in thin crystals to estimate particle beam spatial sizes for projected electron-positron colliders is proposed. The existing position-sensitive X-ray range detectors and the average path of secondary electrons in a detector restrict the minimum value of the measured beam size to a level of approximately 10 μm, which is far greater than the planned sizes of collider beams. We propose to estimate the electron (positron) beam divergence over the diffracted transition radiation from angular distribution measurements. The spatial size can be obtained from the calculated beam emittance or the experimental emittance, which is measured during the earlier stage of acceleration using optical methods. The problem of crystal destruction under the influence of a high intensity electron beam is discussed. The use of surface parametric X-ray radiation, where the problem of crystal destruction is almost absent, to measure the electron beam parameters is discussed. Пропонується використовувати випромінювання ультрарелятивістських електронів (позитронів) у тонких кристалах для оцінки розмірів пучків електрон-позитронних колайдерів, що проектуються. Існуючі позиційно-чутливі детектори рентгенівського діапазону і середній пробіг вторинних електронів у детекторі обмежують мінімальне значення вимірюваного розміру пучка величиною близько 10 мкм, що набагато більше планованих розмірів пучків колайдера. Пропонується оцінювати розбіжність пучка за кутовим розподілам дифрагованого перехідного випромінювання. Поперечні розміри можуть бути отримані з розрахованого або виміряного значень емітанса пучка, який визначається на ранніх стадіях прискорення з використанням оптичних методів. Обговорюється проблема руйнування кристала під дією електронного пучка. Пропонується для вимірювання параметрів електронних пучків використовувати поверхневе параметричне рентгенівське випромінювання, де проблема руйнування кристала повністю відсутня. Предлагается использовать излучение ультрарелятивистских электронов (позитронов) в тонких кристаллах для оценки размеров пучков проектируемых электрон-позитронных коллайдеров. Существующие позиционно-чувствительные детекторы рентгеновского диапазона и средний пробег вторичных электронов в детекторе ограничивают минимальное значение измеряемого размера пучка величиной порядка 10 мкм, что гораздо больше планируемых размеров пучков коллайдера. Предлагается оценивать расходимость пучка по угловым распределениям дифрагированного переходного излучения. Поперечные размеры могут быть получены из рассчитанного или измеренного значений эмиттанса пучка, определяемого на ранних стадиях ускорения с использованием оптических методов. Обсуждается проблема разрушения кристалла под действием электронного пучка. Предлагается для измерения параметров электронных пучков использовать поверхностное параметрическое рентгеновское излучение, где проблема разрушения кристалла полностью отсутствует. 2015 Article Ultra relativistic electron beam spatial size estimation from angular distribution of their radiation in thin crystals / Yu.A. Goponov, M.A. Sidnin, K. Sumitani, Y. Takabayashi, I.E. Vnukov // Вопросы атомной науки и техники. — 2015. — № 6. — С. 108-113. — Бібліогр.: 31 назв. — англ. 1562-6016 PACS: 29.20.db, 29.27.Fh http://dspace.nbuv.gov.ua/handle/123456789/112383 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| topic |
Взаимодействие релятивистских частиц с кристаллами и веществом Взаимодействие релятивистских частиц с кристаллами и веществом |
| spellingShingle |
Взаимодействие релятивистских частиц с кристаллами и веществом Взаимодействие релятивистских частиц с кристаллами и веществом Goponov, Yu.A. Sidnin, M.A. Sumitani, K. Takabayashi, Y. Vnukov, I.E. Ultra relativistic electron beam spatial size estimation from angular distribution of their radiation in thin crystals Вопросы атомной науки и техники |
| description |
The use of ultra relativistic electron (positron) emission in thin crystals to estimate particle beam spatial sizes for projected electron-positron colliders is proposed. The existing position-sensitive X-ray range detectors and the average path of secondary electrons in a detector restrict the minimum value of the measured beam size to a level of approximately 10 μm, which is far greater than the planned sizes of collider beams. We propose to estimate the electron (positron) beam divergence over the diffracted transition radiation from angular distribution measurements. The spatial size can be obtained from the calculated beam emittance or the experimental emittance, which is measured during the earlier stage of acceleration using optical methods. The problem of crystal destruction under the influence of a high intensity electron beam is discussed. The use of surface parametric X-ray radiation, where the problem of crystal destruction is almost absent, to measure the electron beam parameters is discussed. |
| format |
Article |
| author |
Goponov, Yu.A. Sidnin, M.A. Sumitani, K. Takabayashi, Y. Vnukov, I.E. |
| author_facet |
Goponov, Yu.A. Sidnin, M.A. Sumitani, K. Takabayashi, Y. Vnukov, I.E. |
| author_sort |
Goponov, Yu.A. |
| title |
Ultra relativistic electron beam spatial size estimation from angular distribution of their radiation in thin crystals |
| title_short |
Ultra relativistic electron beam spatial size estimation from angular distribution of their radiation in thin crystals |
| title_full |
Ultra relativistic electron beam spatial size estimation from angular distribution of their radiation in thin crystals |
| title_fullStr |
Ultra relativistic electron beam spatial size estimation from angular distribution of their radiation in thin crystals |
| title_full_unstemmed |
Ultra relativistic electron beam spatial size estimation from angular distribution of their radiation in thin crystals |
| title_sort |
ultra relativistic electron beam spatial size estimation from angular distribution of their radiation in thin crystals |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2015 |
| topic_facet |
Взаимодействие релятивистских частиц с кристаллами и веществом |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/112383 |
| citation_txt |
Ultra relativistic electron beam spatial size estimation from angular distribution of their radiation in thin crystals / Yu.A. Goponov, M.A. Sidnin, K. Sumitani, Y. Takabayashi, I.E. Vnukov // Вопросы атомной науки и техники. — 2015. — № 6. — С. 108-113. — Бібліогр.: 31 назв. — англ. |
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Вопросы атомной науки и техники |
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ISSN 1562-6016. ВАНТ. 2015. №6(100) 108
ВЗАИМОДЕЙСТВИЕ РЕЛЯТИВИСТСКИХ ЧАСТИЦ
С КРИСТАЛЛАМИ И ВЕЩЕСТВОМ
ULTRA RELATIVISTIC ELECTRON BEAM SPATIAL SIZE
ESTIMATION FROM ANGULAR DISTRIBUTION OF THEIR
RADIATION IN THIN CRYSTALS
Yu.A. Goponov1, M.A. Sidnin1, K. Sumitani2, Y. Takabayashi2, I.E. Vnukov1
1Belgorod National Research University, Belgorod, Russia;
2SAGA Light Source, 8-7 Yayoigaoka, Tosu, Saga 841-0005, Japan
E-mail: vnukov@bsu.edu.ru
The use of ultra relativistic electron (positron) emission in thin crystals to estimate particle beam spatial sizes for
projected electron-positron colliders is proposed. The existing position-sensitive X-ray range detectors and the aver-
age path of secondary electrons in a detector restrict the minimum value of the measured beam size to a level of ap-
proximately 10 μm, which is far greater than the planned sizes of collider beams. We propose to estimate the elec-
tron (positron) beam divergence over the diffracted transition radiation from angular distribution measurements. The
spatial size can be obtained from the calculated beam emittance or the experimental emittance, which is measured
during the earlier stage of acceleration using optical methods. The problem of crystal destruction under the influence
of a high intensity electron beam is discussed. The use of surface parametric X-ray radiation, where the problem of
crystal destruction is almost absent, to measure the electron beam parameters is discussed.
PACS: 29.20.db, 29.27.Fh
INTRODUCTION
One of the most important parameters that determine
the efficiency of projected electron-positron linear col-
liders [1, 2] is the luminosity:
2
4
b rep
D
x y
n N f
L H
πσ σ
= , (1)
where nb is the number of bunches, N is the bunch pop-
ulation, frep is the repetition rate, HD is the luminosity
enhancement factor, and σx and σy are the characteristic
beam sizes in the horizontal and vertical directions, re-
spectively. The estimated luminosity L of the Internation-
al Linear Collider (ILC) is approximately 1034 cm-2⋅s-1
and higher, due to the small size of the beam at the in-
teraction point of 100×5 nm2 (σx×σy) [1]. Invasive [3]
and non-invasive [4, 5] methods developed to determine
the transverse beam size based on the registration of
optical radiation from metal foils set in the accelerator
cannot ensure measurement of the beam parameters
with such small sizes, due to coherent effects in the ra-
diation [6].
One method that can provide non-invasive meas-
urement of the spatial dimensions of an ultra-fast elec-
tron beam is to use the Shintake monitor, based on the
interaction of electrons with a target of laser interfer-
ence fringes, and record the scattered Compton photons
emitted in the direction of the electron beam [7]. Re-
cently, this method has been used to measure the dimen-
sions of the KEK-ATF beam in the range of 20 nm to
several microns with an accuracy of no more than 10%
[8]. To use this method, the electron beam must be bent
by a magnet after interaction; therefore, its use under the
conditions of the ILC would require significant addi-
tional expenditure. For the same reason it cannot be
used in a collider regime where there are two simulta-
neous particle beams or for intermediate diagnostics and
control of the beams inside the accelerator during the
acceleration process.
Another way to address this issue could be a de-
crease of the detected radiation wavelength by switch-
ing to the X-ray frequency range and employing the
mechanism of parametric X-ray radiation (PXR) pro-
posed in Refs. [9] and [10]. In the first approximation,
PXR may be considered as coherent scattering of the
electromagnetic field of a particle on the electron shells
of periodically arranged target atoms [11, 12]. PXR has
also been referred to as the result of self-field diffraction
of a fast charged particle moving through a crystal [13].
By analogy with X-ray diffraction in crystals, there
are two approaches to the description of PXR. The kin-
ematic approximation suggests that the multiple reflec-
tions of PXR photons at crystal planes are negligibly
small. If this condition is not satisfied, then it is neces-
sary to use dynamical theory. PXR can also be de-
scribed as a coherent polarization bremsstrahlung of
relativistic charged particles in a crystal [14] (see also
[15]). As part of this approach, it has been shown [16]
that for perfect crystals the contribution of dynamic ef-
fects is not more than 10%; therefore, the kinematic
approximation should be sufficient to describe the ex-
perimental data.
For fast electrons, PXR is always accompanied by
radiation diffracted in the crystal, which is generated
directly inside the target or on its surface [17, 18]. In the
first case, diffracted bremsstrahlung (DB) is considered,
while in the second case, diffracted transition radiation
(DTR) is considered. The former is dominant under the
condition ω>>γωp, where ω is the photon energy, γ is
the Lorentz factor, and ωp is the plasma frequency of
the medium, whereas the latter is dominant under the
opposite condition. If the condition ω~γωp is true, then
the contributions of both radiation mechanisms are ob-
served.
The choice of radiation mechanism corresponds with
the large angles of PXR emission in the direction of the
electron motion and it can be detected relatively easily
ISSN 1562-6016. ВАНТ. 2015. №6(100) 109
with conventional X-ray detectors. Numerous experi-
mental works (see, for example, [19] and references
therein) have demonstrated that the kinematic PXR the-
ory describes the results of measurements for electron
energies from a few mega electron-volt to several gig
electron-volt with accuracy better than 10…15%.
A study on the influence of the electron beam size
on the PXR spatial distribution from 855 MeV electrons
in a 50 μm thick silicon crystal using a high-resolution
X-ray camera (HR) [20] based on a thin scintillator
coupled waveguides with a CCD matrix [21] has con-
firmed that estimation of the electron beam size is pos-
sible with such measurements. Electron beam size
measurements for energy of 255 MeV using the PXR
spatial distribution in a 20 μm thick silicon crystal made
with a coordinate detector based on an imaging plate
(IP) [22] coincided with that using optical transition
radiation (OTR) [23].
Unlike the Shintake monitor, a device that can real-
ize this method of electron beam size measurement can
be used at any stage of acceleration, requires signifi-
cantly less expenditure, and can be relatively easily in-
tegrated into the accelerator control system by replacing
the existing beam monitors based on OTR [3], optical
diffraction radiation (ODR) [4], and Smith-Purcell radi-
ation [5]. The change in the ratio of PXR and diffracted
real photons of TR and bremsstrahlung with an increase
of electron energy up to 100…500 GeV [26] and a de-
crease in the size of the beam have yet to be clarified.
Thus, the unresolved problems, yet obvious ad-
vantages, of using the X-ray emission of electrons in
thin crystals to diagnose the parameters of ultra-high
energy electron beams suggests that research in this area
is important and relevant.
RESULTS AND DISCUSSION
1. GENERAL CONSIDERATIONS
In the experiment, all the radiation mechanisms gen-
erated at the Bragg angles are implemented simultane-
ously. The basic formulae and approaches for each
mechanism that was used for calculations are presented
in Refs. [18] and [24]. The kinematic PXR theory de-
scribes the results of measurements quite well; there-
fore, the PXR yield was calculated by using a PXR
spectral-angular distribution formula obtained in the
kinematic approximation in Ref. [27]. To determine the
yield of the diffracted radiation, it is necessary to deter-
mine the reflectivity of the crystal. Here we used the
method described in Ref. [24], which is based on the
approach proposed in Ref. [18] and allows multiple
Bragg re-scattering, absorption, and scattering photons
due to processes that are not associated with diffraction
to be taken into account.
Using X-rays to measure the size of a fast electron
beam by the PXR mechanism [10, 21, 23] is restricted
to the minimum size that can be measured with coordi-
nate detectors of X-ray range. The spatial resolution of
the devices used in the experiments [10, 21, 23] was
evaluated to be approximately 50 μm for photon ener-
gies up to 100 keV [20, 22]. For a fixed photon energy
as an estimation of the spatial resolution of these devic-
es, the root-mean-squared path of the secondary elec-
trons in the detector (photoelectrons and Auger elec-
trons) may be taken in account, providing the oxidation
of Eu2+ to Eu3+ in the case of an IP and the scintillation
yield in the case of an X-ray camera. The path value is
dependent on the energy of the detected radiation, de-
termined according to the crystal used and the observa-
tion angle, and the working medium of the detector. The
thickness of an IP and the scintillator of an X-ray cam-
era is less than 100 μm; therefore, the contribution of
characteristic X-ray radiation photons to the formation
of the detected spatial distribution in a first approxima-
tion may be ignored.
Here, we consider the use of devices such as the X-
ray camera, because in the case of the IP, the angular
distribution cannot be measured in real-time [11]. Con-
sequently, such a device cannot be used for fast collec-
tion of the electron beam parameters. In contrast, the
efficiency of an X-ray camera is relatively high. In the
experiment [21], the spatial radiation distribution meas-
urement for one crystal orientation took 4 seconds at an
average current of 0.5 μA, which was sufficient for con-
fident registration of the angular distribution with ~1013
electrons. This value is close to the number of electrons
for a single ILC spill (≈2.6·1013 electrons/cycle) [1].
Taking into account the significantly higher DTR angu-
lar density compared with that for PXR with high-
energy electrons [26], the number of electrons required
for reliable registration of the spatial distribution of the
radiation would be several orders of magnitude smaller.
For the experimental conditions [21] (absorption of
the first order reflection photons energy of 16 keV oc-
curs on the L-shell of gadolinium), the energy of sec-
ondary electrons is approximately 8 keV, which corre-
sponds to an approximately 1 μm path of the secondary
electrons [27]. For other observation angles and higher
reflection orders, this value may be increased to
10…30 μm. The typical size of a CCD pixel is approx-
imately 10 μm. In particular, the pixel dimensions of the
X-ray camera are 11.6×11.2 μm [20]. The dimension of
the projected collider beam is approximately 5…100 nm
[1, 2], which is significantly less than ten microns;
therefore, direct measurement of the spatial sizes of the
electron beam by transition to the X-ray range and the
PXR mechanism is not feasible due to the characteris-
tics of the existing detectors.
Therefore, we propose to measure the beam angular
divergence instead of the beam size. As described in
Refs. [1, 2], the beam divergence is not so small (a few
tens of μrad > γ-1), although the beam size is extremely
small. It is known that the main parameter that charac-
terizes the dynamics of the particle motion in an accel-
erator is the beam emittance εx,y= σx,yθx,y, where σx,y and
θx,y are the respective size and divergence of the beam
in the horizontal and vertical directions. Therefore,
measurement of the electron beam angular distribution
and divergence in one plane provides information re-
garding the beam size in this plane from the emittance
for this direction. The required value for emittance can
be obtained from measurements conducted in the early
stages of acceleration using conventional methods or
calculation results (see, for example, Ref. [1, 2]).
Conventional methods based on OTR and ODR can-
not provide the required accuracy for measurement of
ISSN 1562-6016. ВАНТ. 2015. №6(100) 110
the angular distribution of a particle accelerated to the
final energy due to coherent effects. The characteristic
angular size of a PXR photon beam is weakly dependent
on the electron energy and can be written in the form
[28]:
2 2 2 2/ph p msγ ω ω σ−Θ = + + , (2)
where σ2
ms is the root-mean-squared angle of multiple
scattering of particles in a crystal. For observation an-
gles of ΘD < 45º, Θph ≈ 2…5 mrad, depending on the
photon energy and the crystal used, exceed the diver-
gence of the electron beam at the interaction point
θ ≈ 40 and 15 μrad in the horizontal and vertical planes,
respectively, for the ILC [1], and exceed the divergence
of 7 to 10 μrad for the Compact Linear Collider (CLIC)
[2]. Therefore, measurements of the angular distribution
of PXR photons cannot help in the estimation of the
electron beam divergence incident on the crystal.
PXR is always accompanied by diffracted real pho-
tons of bremsstrahlung and TR emitted in a strictly
Bragg direction. The ratio between the yields of PXR
photons and diffracted real photons is determined by the
crystal thickness and the experimental conditions. Re-
cently, in Ref. [26], it was reported that the ratio be-
tween the angular density of PXR intensity and DTR
one is significantly changed with an increase in the elec-
tron energy up to tens GeV and higher. The angular
density of the DTR intensity becomes far higher than
that for PXR.
2. CALCULATION RESULTS
Fig. 1 shows the calculation results for the vertical
angular distribution of radiation with the experimental
geometry [21] and the first order reflections. The de-
tailed calculation method is described in Refs. [24] and
[25]. The electron beam is incident on a 50 µm thick
silicon crystal and the (220) reflection is investigated.
The detection system is located at a distance of 1 m
from the crystal at an angle ΘD=2ΘB=22.5º. Size of the
square detector is 0.05 0.05× mm, moved down through
the reflex center with 0.05 mm steps. Curves 1 and 2 are
the calculation results for the angular distributions of
PXR and DTR for electrons energy of 1 GeV.
Fig. 1. Vertical distribution of the X-ray yield for the
experimental geometry [21], and the first order reflec-
tion: 1 – PXR for E=1 GeV; 2 – DTR for E=1 GeV;
3 – PXR for E=10 GeV; 4 – DTR for E=10 GeV
Curves 3 and 4 are the same results for electrons en-
ergy of 10 GeV. The diffracted bremsstrahlung contri-
bution is negligibly small and is not represented for
conditions of ω = 16.55 keV<<γωp≈60 and 600 keV for
electron energies of 1 and 10 GeV, respectively.
Fig. 1 shows that the increase of the electron energy
did not change the PXR angular distribution significant-
ly. The small difference between the distributions for
different energies is due to the lower multiple scattering
for higher energy electrons. This difference is very large
for DTR angular distributions because the TR intensity
is proportional to the electron energy and the character-
istic size of the TR angular cone is approximately γ-2;
therefore, the DTR angular distribution for higher ener-
gy electrons is much narrower.
For larger electron energy and smaller electron beam
divergence compared with Θph, the central part of the
radiation reflex will be a low pedestal associated with
the registration of PXR photons. The narrow bright peak
width for γ-1 that corresponds to the contribution of
DTR is located in the center of the PXR angular distri-
bution. For ILC conditions, the electron (positron) beam
divergence at the interaction point θe is approximately
15…20 μrad over a wide range of particle energies [1],
which is significantly higher than the characteristic ra-
diation angle γ-1 ~ 1…3 μrad for particle energies above
200 GeV. Therefore, the shape of the radiation angular
distribution is not dependent on the particle energy, but
is defined only by the divergence of the electron (posi-
tron) beam.
Fig. 2. Vertical distribution of the X-ray yield for an
electron energy of 200 GeV and the first order reflec-
tion: 1 – PXR; 2 – DTR for θe < γ-1; 3 – DTR for
θe=20 μrad; 4 – DTR for θe=100 μrad
To illustrate this, Fig. 2 shows the calculation results
for the vertical angular distribution of the radiation for a
beam of electrons with an energy of 200 GeV incident
on a 50 μm thick silicon crystal, where the (220) reflec-
tion is used. The detection system is located at a dis-
tance of 2 m from the crystal at an angle
ΘD=2ΘB=22.5º. A square detector with a size of
10×10 μm is moved through the reflex center with 10
μm steps, which corresponds to the angular distribution
measurement using an X-ray camera with the same pix-
el size. Curves 1 and 2 show the calculation results of
the PXR and DTR angular distribution for a point-like
unidirectional beam of particles (θe<<γ-1). Curves 3 and
4 show that of the DTR for beam divergence of θe = 20
and 100 μrad, respectively. It is assumed that the angu-
lar distribution of the beam can be described by a two-
dimensional Gaussian distribution, and a standard de-
viation corresponds to the typical divergence angle of
the beam. The contribution of the diffracted bremsstrah-
lung and the spatial dimensions of the particle beam on
ISSN 1562-6016. ВАНТ. 2015. №6(100) 111
a crystal are not included. For simplicity, it is assumed
that the values of the beam divergence in both planes
are the same. With Θph>>θe, the PXR angular distribu-
tion for the remaining θe is virtually identical and is
therefore not presented.
Fig. 2 shows that the PXR contribution is concen-
trated in the observation angles θy > 0.5 mrad and the
maximum yield does not exceed 5·10-13 pho-
tons/electron. At lesser angles, the PXR yield is less
than 10-14 photon/electron. The DTR contribution is
concentrated in the reflex center and amounts to more
than the maximum PXR at 5 orders. Even for a beam
divergence of 100 μrad, the DTR yield is 3 orders great-
er than the PXR yield. The intensity of higher PXR or-
ders concentrated closer to the reflex center is substan-
tially lower than the first order. In addition, the detec-
tion efficiencies of X-ray detectors are significantly
decreased with increasing photon energy. The PXR con-
tribution in the reflex center is thus negligibly small
from analysis of the electron beam divergence and may
be ignored. For selected conditions where the character-
istic radiation angle γ-1 ~ 2.5 μrad is less than the detec-
tor angular capture υс = 5 μrad, the dip in the center of
the DTR angular distribution is absent, and its width
(see curve 2 in Fig. 2) is not more than 3-4 steps of the
detector. For this reason, the difference between the
angular distributions for θe<<γ-1 and θe = 20 μrad is not
very noticeable. The dependence obtained by processing
the calculated standard deviations of the distributions
σcalc for the beam divergence θe is shown in the Fig. 3.
Fig. 3. Dependence of σcalc on the beam divergence θe
Fig. 4. Vertical distribution of the X-ray yield for an
electron energy of 200 GeV and the first order reflec-
tion: 1 – DTR for θe<<γ-1; 2 – DTR for θe =1 μrad;
3 – DTR for θe =5 μrad; 4 – DTR for θe =10 μrad;
5 – DTR for θe =20 μrad
For small values of beam divergence (θe<10 μrad),
σcalc is almost two times more than θe, and the values
then begin to converge. σcalc and θe practically coincide
only when the condition θe>>γ-1 is satisfied.
To explain the dependence of σcalc on the value of
θe, calculations of the DTR angular distributions for a
crystal to detector distance of 20 m, which corresponds
to the angle of collimation cϑ ≈ 0.5 μrad (<γ-1) ≈
2.5 μrad were performed. The results of the calculations
for electron beam divergence θe = 0.2 (<<γ-1), 1, 5, 10,
and 20 μrad are shown in Fig. 4, respectively, where the
PXR contribution was not taken into account.
Under these conditions, the DTR angular distribu-
tion appears as expected. There is a dip in the emission
intensity for the strictly Bragg direction. A proportional
broadening of the angular distribution for the detected
radiation is observed as θe increases. The broadening is
determined by a convolution of the angular distribution
of the TR and that of the electron beam incident on the
crystal, and since the angular distribution of the TR has
a relatively long ''tail'', the angular distribution of the
detected radiation begins to coincide with the form of
that for the electron beam only when the condition
θe>>γ-1 is satisfied.
The divergence of the beam and the transverse di-
mensions of the ILC in the horizontal and vertical
planes are substantially different. Typical values for the
divergence are θx~50 μrad and θy~20 μrad in the hori-
zontal and vertical planes, respectively [1]. Accounting
for this difference will lead to some reduction in the
maximum intensity of the DTR angular distribution.
However, if the condition θe>>γ-1 is satisfied, as with
identical divergences in both planes, then the angular
distribution of the detected radiation almost completely
reproduces that of the particle beam incident on the
crystal. If this condition is not satisfied, the desired val-
ue of θe can be obtained from the dispersion of the
measured angular distribution and dependence shown in
Fig. 3, or its analogue for the two-dimensional Gaussian
distribution. Thus, by measuring the DTR angular dis-
tribution, information on the electron beam divergence
in both planes can be obtained, and based on the meas-
ured or calculated emittance value, the beam size at the
point of the measurement can be estimated.
The main barrier to the use of DTR in thin crystals
to estimate electron beam divergence and spatial sizes is
the destruction of the crystal structure under the influ-
ence of the intense electron beam during the measure-
ment process. For example, in Ref. [29] (and references
therein), the degradation of coherent effects for a
0.5 mm thick diamond crystal was observed at an elec-
tron energy of 16 GeV and a beam density of approxi-
mately 1019 electrons per cm2. For the ILC with a spatial
beam size of 100×5 nm, the beam density for one spill
(Ne≈ 2.6·1013 electrons per spill) will be greater than the
critical density for a 0.5 mm thick diamond crystal by
several orders.
A possible solution to the crystal destruction prob-
lem may be the use of surface PXR (see Ref. [30] and
references therein). This effect is related with the excita-
tion of electrons in crystal atoms by the electromagnetic
field of a charged particle moving near the crystal sur-
face and its subsequent irradiation. To realize this phe-
nomenon, it is necessary that the distance between the
particle and the crystal edge is approximately γλ or less,
where λ is the wavelength of the emission measured.
The intensity of the radiation is close to the PXR inten-
ISSN 1562-6016. ВАНТ. 2015. №6(100) 112
sity with a correction factor of approximately exp(-r/γλ),
where r is the distance between the particle trajectory
and the crystal edge.
Surface PXR is similar to the Smith-Purcell effect
[31], which is already used for electron beam parameter
diagnostics in accelerator physics [5]. In both cases, the
interference of electron radiation from atoms under the
field influence of a charged moving particle is meas-
ured. However, the X-ray radiation wavelength for the
experimental observation of this emission mechanism is
small and has thus not been discussed yet. For the ILC
and CLIC conditions, γλ becomes sub-millimeter; there-
fore, this type of radiation can be experimentally ob-
served and used for electron beam parameter diagnostics.
However, here we have the same problem as with
conventional PXR in crystals. The characteristic angular
size of the PXR photon beam is far larger than the beam
divergence measured. Because of practically whole
analogy between surface and usual PXR we may wait
existence of surface diffracted transition radiation with
parameters closed to ordinary DTR. If this type of emis-
sion really exists then we may hope on its usage for
measurement of high energy electrons beam parameters.
SUMMARY AND CONCLUSIONS
The results of the study may be briefly stated as fol-
lows:
1) The space resolution of any devices for X-ray
beam spatial distribution measurements is limited by the
size of the CCD pixel or the root-mean-squared path of
the secondary electrons in the detector. The sizes of the
planned electron-positron linear collider beams in both
directions are far less than the typical size of a CCD
pixel or other devices used for X-ray spatial distribution
measurements. Therefore, PXR spatial distribution
measurements cannot provide information regarding the
sizes of such beams.
2) These data may be obtained from information on
electron beam emittance in both planes and divergence,
which may be obtained from measurements of an elec-
tron beam angular distribution. The beam emittance
may be obtained from calculations or measurements at
the earlier stages of acceleration using traditional meth-
ods with optical devices.
3) A typical value for the PXR characteristic angle is
far greater than the ILC and CLIC beam divergences.
Therefore, the influence of beam divergence on the
PXR angular distribution is negligibly small. This type
of fast electron emission in a crystal cannot facilitate
beam divergence measurements.
4) For a particles energy approximately some hun-
dreds of GeV, the DTR intensity in a narrow cone is far
larger than the PXR intensity. The DTR angular distri-
bution is compared with the electron beam angular dis-
tribution and may be used for measurement of the elec-
tron beam divergence.
5) In contrast to the Shintake monitor, the devices
used in the proposed method are less expensive and may
be installed in any part of the accelerator to control the
electron beam parameters in the acceleration process.
6) The main barrier that can prevent the use of DTR
in thin crystals for the estimation of electron beam di-
vergence and spatial sizes is destruction of the crystal
structure under the influence of a high intensity beam.
For the ILC and CLIC conditions, crystal structure deg-
radation can be expected after one spill of the accelera-
tor. However, the proposed method may prove useful
when the beam current is low, such as at the commis-
sioning stage of the accelerator.
7) A possible solution to the crystal destruction
problem may be the use of surface PXR. However, the
same problem as with ordinary PXR in crystals can be
expected. The characteristic angular size of the PXR
photon beam is far larger than the measured beam di-
vergence.
This work was supported by a grant from the Rus-
sian Science Foundation (Project N 15-12-10019).
REFERENCES
1. ILC Technical Design Report, 2013.
2. A Multi-TeV Linear Collider Based on CLIC Tech-
nology: CLIC Conceptual Design Report, 2012.
3. R.B. Fiorito. Recent Advances in Beam Diagnostic
Techniques // Proc. of PAC09. 2009, p. 741.
4. J. Urakawa et al. Feasibility of optical diffraction
radiation for a non-invasive low-emittance beam di-
agnostics // NIM. 2001, v. A472, p. 309.
5. G. Kube, H. Backe, W. Lauth, H. Schope. Smith-
Purcell radiation in View of Particle Beam Diagnos-
tics // Proc. of DIPAC2003. 2003, p. 40.
6. H. Loos et al. Observation of Coherent Optical
Transition Radiation in the LCLS Linac // Proc. of
FEL08. 2008, p. 485.
7. T. Shintake. Proposal of a nanometer beam size
monitor for e+e− linear colliders // NIM. 1992,
v. A311, p. 453.
8. J. Yan et al. Measurement of nanometer electron
beam sizes with laser interference using Shintake
Monitor // NIM. 2014, v. A740, p. 131.
9. A. Gogolev, A. Potylitsyn, G. Kube. A possibility
of transverse beam size diagnostics using parametric
X-ray radiation // J. Phys. Conf. Ser. 2012, v. 357,
012018.
10. Y. Takabayashi. Parametric X-ray radiation as a
beam size monitor // Phys. Lett. A. 2012, v. 376,
p. 2408.
11. G.M. Garibyan, C. Yang. Quantum Microscopic
Theory of Radiation by a Charged Particle Moving
Uniformly in a Crystal // Sov. Phys. JETP. 1972,
v. 34, p. 495.
12. V.G. Baryshevsky, I.D. Feranchuk. Transition radia-
tion of γ-rays in a crystal // Sov. Phys. JETP. 1972,
v. 34, p. 502.
13. E.A. Bogomazova et al. Diffraction of real and vir-
tual photons in a pyrolytic graphite crystal as source
of intensive quasimonochromatic X-ray beam //
NIM. 2003, v. B201, p. 276.
14. V.P. Lapko, N.N. Nanosov. On the parametric X-
rays by a relativistic charged particle travelling
through a crystal // Sov. Phys. Tech. Phys. 1990,
v. 35(5), p. 633.
15. N.N. Nasonov. Collective effects in the polarization
bremsstrahlung of relativistic electrons in condensed
media // NIM. 1998, v. B145, p. 19.
16. H. Nitta. Theoretical notes on parametric X-ray radi-
ation // NIM. 1996, v. B115, p. 401.
ISSN 1562-6016. ВАНТ. 2015. №6(100) 113
17. K.H. Brenzinger et al. Investigation of the produc-
tion mechanism of parametric X-ray radiation // Z.
Phys. 1997, v. A358, p. 107.
18. A.N. Baldin, I.E. Vnukov, E.A. Karataeva,
B.N. Kalinin. O vklade difrakcii realnyx fotonov v
nablyudaemye spektry parametricheskogo rent-
genovskogo izlucheniya elektronov v sovershennyx
kristallax // Poverxnost. 2006, № 4, s. 72-85 (in
Russian).
19. K.H. Brenzinger et al. How narrow is the line width
of parametric X-ray radiation // Phys. Rev. Lett.
1997, v. 79, p. 2462.
20. High-Resolution X-Ray Camera:
http://www.proxivision.de/datasheets/X-Ray-
Camera-HR25-x-ray-PR-0055E-03.pdf.
21. G. Kube, C. Behrens, A.S. Gogolev, Yu.P. Popov,
A.P. Potylitsyn, W. Lauth, S. Weisse. Investigation
of the applicability of parametric x-ray radiation for
transverse beam profile diagnostics // Proc. of
IPAC2013, 2013, p. 491.
22. A.L. Meadowcroft, C.D. Bentley, E.N. Stott. Evalu-
ation of the sensitivity and fading characteristics of
an image plate system for x-ray diagnostics // Rev.
Sci. Instrum. 2008, v. 79, p. 113102.
23. Y. Takabayashi, K. Sumitani. New method for
measuring beam profiles using a parametric X-ray
pinhole camera // Phys. Lett. A. 2013, v. 377,
p. 2577.
24. S.A. Laktionova, O.O. Pligina, M.A. Sidnin,
I.E. Vnukov. Influence of real photons diffraction
contribution on parametric X-ray observed charac-
teristics // J. Phys. Conf. Ser. 2014, v. 517, 012020.
25. Yu.A. Goponov, S.A. Laktionova, O.O. Pligina,
M.A. Sidnin, I.E. Vnukov. Influence of real photon
diffraction on parametric X-ray radiation angular
distribution in thin perfect crystals // NIM. 2015,
v. B355, p. 150.
26. H. Nitta. Kinematical theory of parametric X-ray
radiation // Phys. Lett. A. 1991, v. 158, p. 270.
27. В.И. Беспалов. Взаимодействие ионизирующих
излучений с веществом. Томск, ТПУ. 2008, 396 с.
V.I. Bespalov. Vzaimodejstvie ioniziruyushhix izlu-
chenij s veshhestvom. Tomsk: TPU, 2008, 396 s.
28. I.D. Feranchuk, A.V. Ivashin. Parametric X-Ray:
From the theoretical prediction to the first observa-
tion and applications // J. Phys. (Paris). 1985, v. 46,
p. 1981.
29. R. Schwitters. The SLAC Coherent Bremsstrahlung
Facility: SLAC-TN-70-32, 1970.
30. A.I. Benediktovitch, I.D. Feranchuk. Laser induced
x-ray radiation under the grazing incidence geome-
try // J. Phys. Conf. Ser. 2010, v. 236, 012015.
31. S.J. Smith, E.M. Purcell. Visible Light from Local-
ized Surface Charges Moving across a Grating //
Phys. Rev. 1953, v. 92, p. 1069.
Article received 28.09.2015
ОЦЕНКА ПОПЕРЕЧНЫХ РАЗМЕРОВ ПУЧКА УЛЬТРАРЕЛЯТИВИСТСКИХ ЭЛЕКТРОНОВ
ПО ИХ ИЗЛУЧЕНИЮ В ТОНКИХ КРИСТАЛЛАХ
Ю.А. Гопонов, М.А. Сиднин, K. Sumitani, Y. Takabayashi, И.Е. Внуков
Предлагается использовать излучение ультрарелятивистских электронов (позитронов) в тонких кристал-
лах для оценки размеров пучков проектируемых электрон-позитронных коллайдеров. Существующие пози-
ционно-чувствительные детекторы рентгеновского диапазона и средний пробег вторичных электронов в
детекторе ограничивают минимальное значение измеряемого размера пучка величиной порядка 10 мкм, что
гораздо больше планируемых размеров пучков коллайдера. Предлагается оценивать расходимость пучка по
угловым распределениям дифрагированного переходного излучения. Поперечные размеры могут быть по-
лучены из рассчитанного или измеренного значений эмиттанса пучка, определяемого на ранних стадиях
ускорения с использованием оптических методов. Обсуждается проблема разрушения кристалла под дей-
ствием электронного пучка. Предлагается для измерения параметров электронных пучков использовать по-
верхностное параметрическое рентгеновское излучение, где проблема разрушения кристалла полностью
отсутствует.
ОЦІНКА ПОПЕРЕЧНИХ РОЗМІРІВ ПУЧКА УЛЬТРАРЕЛЯТИВІСТСЬКИХ ЕЛЕКТРОНІВ
ЗА ЇХ ВИПРОМІНЮВАННЯМ У ТОНКИХ КРИСТАЛАХ
Ю.А. Гопонов, М.А. Сіднін, K. Sumitani, Y. Takabayashi, І.Є. Внуков
Пропонується використовувати випромінювання ультрарелятивістських електронів (позитронів) у тон-
ких кристалах для оцінки розмірів пучків електрон-позитронних колайдерів, що проектуються. Існуючі по-
зиційно-чутливі детектори рентгенівського діапазону і середній пробіг вторинних електронів у детекторі
обмежують мінімальне значення вимірюваного розміру пучка величиною близько 10 мкм, що набагато бі-
льше планованих розмірів пучків колайдера. Пропонується оцінювати розбіжність пучка за кутовим розпо-
ділам дифрагованого перехідного випромінювання. Поперечні розміри можуть бути отримані з розрахова-
ного або виміряного значень емітанса пучка, який визначається на ранніх стадіях прискорення з викорис-
танням оптичних методів. Обговорюється проблема руйнування кристала під дією електронного пучка.
Пропонується для вимірювання параметрів електронних пучків використовувати поверхневе параметричне
рентгенівське випромінювання, де проблема руйнування кристала повністю відсутня.
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