Diffraction on a polycrystal for investigations and diagnostics of X-ray radiation of relativistic particles in a forward direction
It is shown that the diffraction on a polycrystal can be used for investigation and diagnostics of X-ray radiation emitted in a forward direction by relativistic charged particles moving in crystalline or other targets or fields. Methods for measuring radiation spectral density, divergence, and lin...
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| Published in: | Вопросы атомной науки и техники |
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| Date: | 2004 |
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| Language: | English |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2004
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| Cite this: | Diffraction on a polycrystal for investigations and diagnostics of X-ray radiation of relativistic particles in a forward direction / A.V. Shchagin // Вопросы атомной науки и техники. — 2004. — № 4. — С. 76-79. — Бібліогр.: 8 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859915674539786240 |
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| author | Shchagin, A.V. |
| author_facet | Shchagin, A.V. |
| citation_txt | Diffraction on a polycrystal for investigations and diagnostics of X-ray radiation of relativistic particles in a forward direction / A.V. Shchagin // Вопросы атомной науки и техники. — 2004. — № 4. — С. 76-79. — Бібліогр.: 8 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | It is shown that the diffraction on a polycrystal can be used for investigation and diagnostics of X-ray radiation
emitted in a forward direction by relativistic charged particles moving in crystalline or other targets or fields. Methods for measuring radiation spectral density, divergence, and linear polarization at any requisite energy from a few
units to tens of keV are proposed. The explanation for the origination of experimentally observed and earlier unidentified spectral peaks as a result of Bragg diffraction on a polycrystal is proposed. The experiment for verification of
the explanation is suggested.
У роботі показано, що дифракція на полікристалі може бути використана для дослідження і діагностики
рентгенівського випромінювання, що випускають у напрямку вперед релятивістські заряджені частки, що
рухаються в кристалічних або інших мішенях і полях. Запропоновано методи для виміру спектральної
густини, розбіжності і лінійної поляризації випромінювання при будь-якій бажаній енергії від декількох
одиниць до десятків кілоелектронвольт. Запропоновано пояснення походження спектральних піків, що
спостерігалися у експерименті і раніше не ідентифікованих, як результату дифракції Брегга на полікристалі.
Пропонується експеримент для перевірки цього пояснення.
В работе показано, что дифракция на поликристалле может быть использована для исследования и диагностики рентгеновского излучения, которое испускают в направлении вперед релятивистские заряженные
частицы, движущиеся в кристаллических или других мишенях и полях. Предложены методы для измерения
спектральной плотности, расходимости и линейной поляризации излучения при любой желаемой энергии от
нескольких единиц до десятков килоэлектронвольт. Предложено объяснение происхождения наблюдавшихся в эксперименте и ранее не идентифицированных спектральных пиков как результата дифракции Брэгга на
поликристалле. Предлагается эксперимент для проверки этого объяснения.
|
| first_indexed | 2025-12-07T16:05:13Z |
| format | Article |
| fulltext |
DIFFRACTION ON A POLYCRYSTAL FOR INVESTIGATIONS AND
DIAGNOSTICS OF X-RAY RADIATION OF RELATIVISTIC PARTICLES
IN A FORWARD DIRECTION
A.V. Shchagin
Kharkov Institute of Physics and Technology, Kharkov 61108, Ukraine;
E-mail: shchagin@kipt.kharkov.ua
It is shown that the diffraction on a polycrystal can be used for investigation and diagnostics of X-ray radiation
emitted in a forward direction by relativistic charged particles moving in crystalline or other targets or fields. Meth-
ods for measuring radiation spectral density, divergence, and linear polarization at any requisite energy from a few
units to tens of keV are proposed. The explanation for the origination of experimentally observed and earlier uniden-
tified spectral peaks as a result of Bragg diffraction on a polycrystal is proposed. The experiment for verification of
the explanation is suggested.
PACS: 41.50.+h; 41.60.-m; 07.85
1. INTRODUCTION
There exist several kinds of X-ray radiation of re-
lativistic charged particles moving through a radiator,
i.e., amorphous or crystalline targets or fields. These are
ordinary bremsstrahlung, transition radiation (TR), res-
onance transition radiation, coherent bremsstrahlung,
channelling radiation, parametric X-ray radiation
(PXR), undulator radiation, Thomson or Compton scat-
tering, etc. Most of them are going from the radiator in a
forward direction mainly within the angle of about 1−γ
relative to the incident particle velocity vector V
,
where γ is the relativistic factor of incident particles.
Several of the above-mentioned kinds of radiation can
be generated in the radiator (e.g., in a crystal) simultan-
eously, and the total radiation in a forward direction
(RFD) is going along the vector V
. To investigate the
composition of the total radiation and the role of its
components, experimental measurements of the RFD
spectral properties are needed. However, it is generally
difficult to measure the spectral properties of the RFD
from relativistic particle beams on account of its high
intensity, wide spectrum and a restricted counting rate
of spectrometers. In the gamma-ray band, it is the
Compton scattering that is successfully used for invest-
igations of the RFD. In the X-ray band, the use of Bragg
diffraction seems to be more natural. In this paper we
suggest that the Bragg diffraction in a polycrystal placed
behind the radiator should be used for measurements of
the RFD spectral density, divergence and linear polariz-
ation at any wanted X-ray energy. Besides, we shall dis-
cuss the experiment, where, in our opinion, the Bragg
diffraction of X-ray RFD by the polycrystal was ob-
served.
2. HOW TO MEASURE X-RAY RADIATION
IN A FORWARD DIRECTION WITH THE
USE OF A POLYCRYSTAL
The scheme of the setup for measurements of the
X-ray RFD properties is shown in Fig. The beam of in-
cident relativistic particles from the accelerator passes
through the radiator R and generates RFD going along
the particle beam within the angle of about 1−γ . Then
the RFD crosses the polycrystalline foil P. The particle
beam can be either deflected by the bending magnet or
can pass through the foil, too, if its radiation in the foil
does not prevent the observation of radiation under
study. The spectrometric X-ray detector D is installed at
an observation angle θ .
V
g Ω
R
RFD
P D
The relativistic particle beam passes through the radi-
ator R and generates radiation in a forward direction
(RFD). The RFD is going along the particle velocity vec-
tor V
and passes through the polycrystalline foil P. One
of randomly aligned grains of the polycrystal with the
crystallographic planes and corresponding reciprocal
vector g is shown in the foil. The spectrometric X-ray
detector D is installed at observation angle θ relative
to particle velocity vector. The observation direction is
shown by the unit vector Ω
. The detector can register
RFD diffracted by polycrystal at Bragg energies
The polycrystalline foil consists of a number of ran-
domly aligned crystalline grains. Some of them can ap-
pear oriented relative to the vector V
and the observa-
tion direction Ω
to satisfy the Bragg condition. One of
these grains with the crystallographic planes denoted by
the reciprocal lattice vector g is shown in the foil in
Fig. The X-ray RFD of Bragg energy BE will be reflec-
ted by these planes into the detector. Thus, the spectro-
metric detector will be able to register several spectral
peaks of energies BE corresponding to several main
crystallographic planes of the polycrystal. These ener-
gies can be found by the formula from Ref. [1]
|g|
gcEB Ω⋅
=
2
2
, (1)
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ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2004. № 4.
Серия: Плазменная электроника и новые методы ускорения (4), с. 76-79.76
where Ω
is the unit vector in the observation direction
at the observation angle θ relative to the particle velo-
city vector V
and the RFD axis,
22
θθπ singcos|g||g| =−=Ω⋅
,
a
nml|g|g
2222 ++== π , α is the lattice constant;
n,m,l are the Miller indices for the crystallographic
planes with a nonzero structure factor. The scheme in
Fig. is similar to the one used in the well-known Debye-
Scherrer method for investigations of polycrystalline
samples by a monochromatic X-ray beam. Here, we
propose that this scheme with the known polycrystal
should be used for investigation and diagnostics of in-
tense RFD X-ray beams that may have wide and com-
plicated spectra.
2.1. MEASUREMENT OF THE RFD SPECTRAL
DENSITY
The number of counts registered by the detector in
the spectral peak of energy BE is proportional to the
RFD spectral density at this energy. For absolute meas-
urements of RFD spectral density, one should calibrate
the foil+detector system using the radiator with the
known spectral density of X-ray radiation and provide a
reliable monitoring of the number of incident electrons.
For measurement of RFD spectral density in arbitrary
units, one can change radiators or their properties at a
fixed geometry of both the foil and the detector and re-
gister number of counts in the spectral peaks at energy
BE generated by constant number of incident particles.
For example, in this way one can measure the spectral
density of channelling radiation as a function of crystal-
radiator alignment. Note that only a small part of RFD
can be diffracted by a thin polycrystalline foil into the
detector. This is favourable for preventing the spectro-
meter from overloading at measurements of intense X-
ray RFD beams. The wanted energy BE can be
provided by a proper choice of the polycrystal and the
observation angle in accordance with the formula (1).
2.2. MEASUREMENT OF THE RFD DIVER-
GENCE
The width E∆ of the measured spectral peak at en-
ergy BE is a function of the experimental polar angular
resolution θ∆ and the incident X-ray RFD beam diver-
gence α in the observation plane, and also the energy
resolution of the detector dE∆ . The experimental angu-
lar resolution is determined by the angular size of both
the detector and the RFD beam spot on the foil in the
observation plane. Using the Eq.(1), one can find
)(
tan
EEE B
d
2222
2
2
αθθ +∆
+∆=∆ . (2)
In practice, the divergence can be measured
provided that the spectral peak broadening due to the
RFD divergence exceeds or is comparable to the broad-
ening due to the experimental angular resolution and en-
ergy resolution of the detector. In this case, the diver-
gence α in the observation plane can be found from Eq.
(2).
2.3. MEASUREMENT OF THE RFD LINEAR PO-
LARIZATION
The Bragg diffraction intensity has its maximum for
X-rays polarized in the plane perpendicular to the dif-
fraction plane, and its minimum for the X-rays polarized
in the plane of diffraction. These maximum and minim-
um are particularly pronounced at θ close to 2/π .
Due to these well-known peculiarities of Bragg diffrac-
tion, the setup shown in Fig. should possess the polariz-
ation analyzing power. The setup can be used for meas-
urements of the RFD linear polarization at energy BE .
To this end, one should perform measurements of poly-
crystal-diffracted radiation at a fixed observation angle
θ as a function of the azimuthal angle of the detector
rotation around the vector V
.
3. DISCUSSION OF SOME EXPERIMENTAL
RESULTS FROM REF. [2]
In our opinion, the diffraction of RFD by the poly-
crystal could be observed in Ref. [2]. The experimental
setup in Ref. [2] was partially similar to the one shown
in Fig. The authors of Ref. [2] studied the PXR and the
diffracted TR in the Bragg direction, the radiations be-
ing generated by the 150 MeV electron beam in silicon
single-crystal radiators of various configurations. Dif-
fraction of TR realized in the same single-crystal radiat-
ors. Behind the radiator, a 10 mµ thick molybdenum
foil was installed. The characteristic X-ray radiation, ex-
cited in the foil, was used for monitoring the number of
beam electrons that have passed through the radiators.
Those authors have measured a series of nice spectra
having a low spectral background by a Si(Li) detector at
825.=θ . In the spectra they observed clearly marked
spectral peaks of PXR and diffracted TR from the radi-
ator, and also the peaks of characteristic X-ray radiation
from the molybdenum foil at reference energies αKE
=17.45 keV and βKE =19.6 keV. Besides, they ob-
served spectral peaks with energies ≈ 12.5 keV and ≈
25.0 keV, the origin of which was not identified in Ref.
[2]. Here, we shall discuss the data concerned with these
unidentified spectral peaks (USPs).
In Ref. [2] the authors have noted that the molyb-
denum foil was amorphous. To understand the origin of
the USPs, let us suppose that the molybdenum foil is
polycrystalline. This polycrystal can diffract the radi-
ation of Bragg energies from the RFD, generated in the
radiator, into the cone and, in particular, in the detector
direction. The Bragg energies calculated by formula (1)
for the crystallographic planes with nonzero structure
factors (110), (220), (200) of molybdenum lattice [3] at
the reference lattice constant 153.a = A and o.825=θ
are )(
BE 110 =12.5 keV, )(
BE 220 =25.0 keV, )(
BE 200
_______________________________________________________________
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2004. № 4.
Серия: Плазменная электроника и новые методы ускорения (4), с. 76-79.77
=17.6 keV, respectively. The calculated energies
)(
BE 110 and )(
BE 220 are practically coincident with the
ones of both USPs observed in Ref. [2]. The energy
)(
BE 200 is close to αKE of the characteristic peak, and
these peaks are not seen resolved in the experimental
spectra in Ref. [2].
Consider some other experimental data concerned
with USPs described in Ref. [2]:
i. The USPs disappear if the radiator is removed.
This is because the RFD from the radiator disappears.
Therefore, only characteristic peaks excited by the elec-
tron beam in the foil are seen in Fig.11,b of Ref. [2].
Note that the spectral peaks of PXR with the energies
practically equal to the energies of USPs can be gener-
ated by the beam electrons in molybdenum grains. Their
absence in Fig. 11,b of Ref. [2] means that the PXR
from the polycrystal is weak and is no obstacle for cor-
rect measurements of RFD (see item 3 in next section).
ii. The USPs disappear if the molybdenum foil is re-
moved. This is because the Bragg diffraction without
the polycrystal is absent.
iii. The energies of USPs do not vary with signific-
ant variations of the crystal-radiator alignments. This is
because the RFD is going along the fixed vector V
in-
dependently of the crystal-radiator alignment.
iv. The energies of USPs are the same at arbitrary
alignment of the molybdenum foil. This is because the
RFD is diffracted by the molybdenum grains which ap-
pears at appropriate for Bragg diffraction alignment in-
dependently of the alignment of the whole foil.
v. The 12.5 keV USP seems to vanish with the align-
ment of the Si crystal-radiator <100> axis close to the
incident particle beam axis (see Fig.12,c in Ref. [2]).
This may be due to a significant broadening of the USP
as a result of an appreciably increased RFD divergence.
The increased RFD divergence may be a result of in-
creased electron beam scattering in the crystal-radiator
at this alignment because of the crystal-radiator config-
uration [2]. Besides, the increasing of the electron beam
scattering is possible at motion of electrons along the
<100> strings of the crystal.
Thus, the above-considered experimental data from
Ref. [2] seems are in agreement with our explanation of
the USPs origin as a result of the RFD Bragg diffraction
by the molybdenum polycrystal.
4. RESULTS AND DISCUSSION
1. In this paper we have suggested the methods for
diagnostics and measurements of intense X-ray RFD.
They permit measurements of spectral density, diver-
gence and linear polarization of the RFD with the use of
Bragg diffraction on a polycrystal. The methods seem
relatively simple and inexpensive, as only a single poly-
crystalline foil with an arbitrary alignment should be in-
stalled, and ordinary spectrometric detector(s) can be
used for measurements at any energy chosen in the
range from several keV to tens of keV.
2. Here, we have suggested the explanation of spec-
tral peak origination at energies of about 12.5 and
25.0 keV, observed and unidentified in Ref. [2]. The
peaks are due to the Bragg diffraction of RFD from the
radiator by a polycrystalline molybdenum foil installed
behind the radiator. This explanation can be additionally
verified with the experimental setup described in Ref.
[2]. For this purpose, one can vary the registration angle
of the detector θ and observe variations of the spectral
peak energies. For the molybdenum polycrystal, they
should obey the following formulae obtained from (1):
2
29691110
θsin
.E )(
B
⋅= keV (3)
for the spectral peak from the (110) plane of molyb-
denum ( ≈ 12.5 keV in Ref. [2] at o.825=θ ) and
2
89691220
θsin
.E )(
B
⋅= keV, (4)
for the spectral peak from the (220) plane of molyb-
denum ( ≈ 25.0 keV in Ref. [2] at o.825=θ ). Besides, a
new peak at energy
2
29691200
θsin
.E )(
B
⋅=
keV, (5)
from the (200) plane of molybdenum may appear. In the
experimental conditions [2] at o.825=θ , the energy of
this spectral peak )(
BE 200 =17.64 keV is close to the one
for the characteristic αK peak at αKE =17.45 keV.
These peaks could not be resolved by the detector with
an energy resolution of 450 eV used in [2].
Besides, our explanation can be verified by using an-
other kind of polycrystal at the same observation angle.
For example, the copper polycrystal can diffract the
RFD with energies 13.3, 15.4, 21.8 keV from crystallo-
graphic planes (111), (200), (220) respectively at
o.825=θ .
3. As we mentioned above, the electron beam can
generate the PXR in the randomly aligned crystal grains
of a polycrystal. However, only a small part of these
grains has a proper alignment and produces the PXR re-
flection in the observation direction. One can estimate
relative number of such grains. As the angular size of
PXR reflection is about 1−
effγ [6], only grains with recip-
rocal lattice vectors g within the solid angle ~ 2
effγ − can
take part in generation of the reflection in fixed observa-
tion direction. The relative number of such grains is
π
γ
2
2−
eff . The effective thickness effT for generation of
PXR reflection in fixed observation direction of the
polycrystal with thickness T may be estimated as
T~T eff
eff π
γ
2
2−
, (6)
where 2
1
0
2 −− += |)|(eff χγγ is the effective relativistic
factor [6], γ is the relativistic factor of incident
particles, 0χ is the dielectric susceptibility. Thus, the
78
PXR from ordinary polycrystal should be weak and
therefore is not seen in Fig. 11,b of Ref. [2].
4. To investigate radiation in a forward direction in
the wanted X-ray energy range, one can use a polycrys-
tal and position-sensitive X-ray detector(s) installed at
corresponding observation angles.
The diffraction on a polycrystal provides good pos-
sibility for studying the PXR and/or other kinds of radi-
ation diffracted in a crystal-radiator with simultaneous
measurements of radiation in a forward direction. For
example, the search for PXR in a forward direction may
be continued and/or channelling or transition radiation
may be studied with the use of a polycrystal.
5. FINAL NOTES AND ACKNOWLEDG-
MENTS
The author is thankful to V.M. Sanin for discussions
at preparation of preliminary publication of present
work as electronic preprint [4] (May, 2001). Then the
paper [4] was discussed in Ref. [5]. Note that RFD dif-
fraction and generation of PXR on common polycrystals
are considered in Refs. [4,5] and the present paper.
The author is thankful to N.N. Nasonov for discus-
sion of the misprint in Eq. (6) [4]. Value effγ [6] is
used in Eq. (6) of the present paper to eliminate this
misprint. Note, that PXR from common polycrystal was
studied theoretically in Ref [7] and experimentally in
Ref. [8].
The author is especially thankful to N.A. Khizhnyak
for his attention for preliminary preprint [4] and related
discussions for last months of his life in 2001.
Further development of research in this field was or-
ganized by I. Endo at Hiroshima University for 2002-
2004.
The paper became possible partially due to Project
STCU # 1030 from Science and Technology Center in
Ukraine.
REFERENCES
1. A.V. Shchagin, V.I. Pristupa, N.A. Khizhnyak //
Phys. Lett. 1990, A148, p.485.
2. K. Chouffani, M.Yu. Andreyashkin, I. Endo,
J. Masuda, T. Takahashi, Y. Takashima // Nucl. In-
strum. and Meth. 2001, B 173, p.241.
3. C. Kittel. Introduction to Solid State Physics.
Fourth Edition, John Wiley and Sons, Inc.
4. A.V. Shchagin. E-preprint, 2001.
http://arXiv.org/abs/physics/0105071
5. A.V. Shchagin // Scientific Bulletin, Belgorod State
University. 2001, v.14, p.6 [in Russian].
6. A.V. Shchagin // Investigations and properties of
PXR, in: Electron-Photon interactions in dense me-
dia, ed. by H. Wiedemann, NATO Science Series, II
Mathematics, Physics and Chemistry. 2002, v.49,
p.133-151.
7. N.N. Nasonov // Nucl. Instr. and Meth. 1998, B
145, p.19.
8. S. Blazhevich, A. Chepurnov, V. Grishin et al. //
Phys. Lett. 1999, A 254, p.30.
ИСПОЛЬЗОВАНИЕ ДИФРАКЦИИ НА ПОЛИКРИСТАЛЛЕ ДЛЯ ИССЛЕДОВАНИЙ И ДИАГНО-
СТИКИ РЕНТГЕНОВСКОГО ИЗЛУЧЕНИЯ РЕЛЯТИВИСТСКИХ ЧАСТИЦ В НАПРАВЛЕНИИ
ВПЕРЕД
А.В. Щагин
В работе показано, что дифракция на поликристалле может быть использована для исследования и диа-
гностики рентгеновского излучения, которое испускают в направлении вперед релятивистские заряженные
частицы, движущиеся в кристаллических или других мишенях и полях. Предложены методы для измерения
спектральной плотности, расходимости и линейной поляризации излучения при любой желаемой энергии от
нескольких единиц до десятков килоэлектронвольт. Предложено объяснение происхождения наблюдавших-
ся в эксперименте и ранее не идентифицированных спектральных пиков как результата дифракции Брэгга на
поликристалле. Предлагается эксперимент для проверки этого объяснения.
ВИКОРИСТАННЯ ДИФРАКЦІЇ НА ПОЛІКРИСТАЛІ ДЛЯ ДОСЛІДЖЕНЬ І ДІАГНОСТИКИ
РЕНТГЕНІВСЬКОГО ВИПРОМІНЮВАННЯ РЕЛЯТИВІСТСЬКИХ ЧАСТОК У НАПРЯМКУ
ВПЕРЕД
O.В. Щагін
У роботі показано, що дифракція на полікристалі може бути використана для дослідження і діагностики
рентгенівського випромінювання, що випускають у напрямку вперед релятивістські заряджені частки, що
рухаються в кристалічних або інших мішенях і полях. Запропоновано методи для виміру спектральної
густини, розбіжності і лінійної поляризації випромінювання при будь-якій бажаній енергії від декількох
одиниць до десятків кілоелектронвольт. Запропоновано пояснення походження спектральних піків, що
спостерігалися у експерименті і раніше не ідентифікованих, як результату дифракції Брегга на полікристалі.
Пропонується експеримент для перевірки цього пояснення.
_______________________________________________________________
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2004. № 4.
Серия: Плазменная электроника и новые методы ускорения (4), с. 76-79.79
А.В. Щагин
|
| id | nasplib_isofts_kiev_ua-123456789-80444 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T16:05:13Z |
| publishDate | 2004 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Shchagin, A.V. 2015-04-18T04:35:52Z 2015-04-18T04:35:52Z 2004 Diffraction on a polycrystal for investigations and diagnostics of X-ray radiation of relativistic particles in a forward direction / A.V. Shchagin // Вопросы атомной науки и техники. — 2004. — № 4. — С. 76-79. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS: 41.50.+h; 41.60.-m; 07.85 https://nasplib.isofts.kiev.ua/handle/123456789/80444 It is shown that the diffraction on a polycrystal can be used for investigation and diagnostics of X-ray radiation emitted in a forward direction by relativistic charged particles moving in crystalline or other targets or fields. Methods for measuring radiation spectral density, divergence, and linear polarization at any requisite energy from a few units to tens of keV are proposed. The explanation for the origination of experimentally observed and earlier unidentified spectral peaks as a result of Bragg diffraction on a polycrystal is proposed. The experiment for verification of the explanation is suggested. У роботі показано, що дифракція на полікристалі може бути використана для дослідження і діагностики рентгенівського випромінювання, що випускають у напрямку вперед релятивістські заряджені частки, що рухаються в кристалічних або інших мішенях і полях. Запропоновано методи для виміру спектральної густини, розбіжності і лінійної поляризації випромінювання при будь-якій бажаній енергії від декількох одиниць до десятків кілоелектронвольт. Запропоновано пояснення походження спектральних піків, що спостерігалися у експерименті і раніше не ідентифікованих, як результату дифракції Брегга на полікристалі. Пропонується експеримент для перевірки цього пояснення. В работе показано, что дифракция на поликристалле может быть использована для исследования и диагностики рентгеновского излучения, которое испускают в направлении вперед релятивистские заряженные частицы, движущиеся в кристаллических или других мишенях и полях. Предложены методы для измерения спектральной плотности, расходимости и линейной поляризации излучения при любой желаемой энергии от нескольких единиц до десятков килоэлектронвольт. Предложено объяснение происхождения наблюдавшихся в эксперименте и ранее не идентифицированных спектральных пиков как результата дифракции Брэгга на поликристалле. Предлагается эксперимент для проверки этого объяснения. The author is thankful to V.M. Sanin for discussions at preparation of preliminary publication of present work as electronic preprint [4] (May, 2001). Then the paper [4] was discussed in Ref. [5]. Note that RFD diffraction and generation of PXR on common polycrystals are considered in Refs. [4,5] and the present paper. The author is thankful to N.N. Nasonov for discussion of the misprint in Eq. (6) [4]. Value eff γ [6] is used in Eq. (6) of the present paper to eliminate this misprint. Note, that PXR from common polycrystal was studied theoretically in Ref [7] and experimentally in Ref. [8]. The author is especially thankful to N.A. Khizhnyak for his attention for preliminary preprint [4] and related discussions for last months of his life in 2001. Further development of research in this field was organized by I. Endo at Hiroshima University for 2002-2004. The paper became possible partially due to Project STCU # 1030 from Science and Technology Center in Ukraine. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Параметрическое излучение Diffraction on a polycrystal for investigations and diagnostics of X-ray radiation of relativistic particles in a forward direction Використання дифракції на полікристалі для досліджень і діагностики рентгенівського випромінювання релятивістських часток у напрямку вперед Использование дифракции на поликристалле для исследований и диагно- стики рентгеновского излучения релятивистских частиц в направлении вперед Article published earlier |
| spellingShingle | Diffraction on a polycrystal for investigations and diagnostics of X-ray radiation of relativistic particles in a forward direction Shchagin, A.V. Параметрическое излучение |
| title | Diffraction on a polycrystal for investigations and diagnostics of X-ray radiation of relativistic particles in a forward direction |
| title_alt | Використання дифракції на полікристалі для досліджень і діагностики рентгенівського випромінювання релятивістських часток у напрямку вперед Использование дифракции на поликристалле для исследований и диагно- стики рентгеновского излучения релятивистских частиц в направлении вперед |
| title_full | Diffraction on a polycrystal for investigations and diagnostics of X-ray radiation of relativistic particles in a forward direction |
| title_fullStr | Diffraction on a polycrystal for investigations and diagnostics of X-ray radiation of relativistic particles in a forward direction |
| title_full_unstemmed | Diffraction on a polycrystal for investigations and diagnostics of X-ray radiation of relativistic particles in a forward direction |
| title_short | Diffraction on a polycrystal for investigations and diagnostics of X-ray radiation of relativistic particles in a forward direction |
| title_sort | diffraction on a polycrystal for investigations and diagnostics of x-ray radiation of relativistic particles in a forward direction |
| topic | Параметрическое излучение |
| topic_facet | Параметрическое излучение |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/80444 |
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