Intensive X-ray source optimization
Possibility of optimization of an intensive source of the electron radiation in crystals based on the Compton scattering of X-radiation is considered.
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irk-123456789-812292015-05-14T03:02:10Z Intensive X-ray source optimization Bochek, G.L. Kulibaba, V.I. Maslov, N.I. Ovchinnik, V.D. Экспериментальные методы и обработка даных Possibility of optimization of an intensive source of the electron radiation in crystals based on the Compton scattering of X-radiation is considered. Розглядається можливість оптимізації джерел інтенсивного рентгенівського випромінювання прискорених електронів з використанням методики на основі комптонівського розсіяння. Рассматривается возможность оптимизации источников интенсивного рентгеновского излучения ускоренных электронов с использованием методики на основе комптоновского рассеяния. 2005 Article Intensive X-ray source optimization / G.L. Bochek, V.I. Kulibaba, N.I. Maslov, V.D. Ovchinnik // Вопросы атомной науки и техники. — 2005. — № 6. — С. 59-62. — Бібліогр.: 21 назв. — англ. 1562-6016 PACS: 07.85.+n; 13.60.Fz http://dspace.nbuv.gov.ua/handle/123456789/81229 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Экспериментальные методы и обработка даных Экспериментальные методы и обработка даных |
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Экспериментальные методы и обработка даных Экспериментальные методы и обработка даных Bochek, G.L. Kulibaba, V.I. Maslov, N.I. Ovchinnik, V.D. Intensive X-ray source optimization Вопросы атомной науки и техники |
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Possibility of optimization of an intensive source of the electron radiation in crystals based on the Compton
scattering of X-radiation is considered. |
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Article |
| author |
Bochek, G.L. Kulibaba, V.I. Maslov, N.I. Ovchinnik, V.D. |
| author_facet |
Bochek, G.L. Kulibaba, V.I. Maslov, N.I. Ovchinnik, V.D. |
| author_sort |
Bochek, G.L. |
| title |
Intensive X-ray source optimization |
| title_short |
Intensive X-ray source optimization |
| title_full |
Intensive X-ray source optimization |
| title_fullStr |
Intensive X-ray source optimization |
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Intensive X-ray source optimization |
| title_sort |
intensive x-ray source optimization |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2005 |
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Экспериментальные методы и обработка даных |
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http://dspace.nbuv.gov.ua/handle/123456789/81229 |
| citation_txt |
Intensive X-ray source optimization / G.L. Bochek, V.I. Kulibaba, N.I. Maslov, V.D. Ovchinnik // Вопросы атомной науки и техники. — 2005. — № 6. — С. 59-62. — Бібліогр.: 21 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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AT bochekgl intensivexraysourceoptimization AT kulibabavi intensivexraysourceoptimization AT maslovni intensivexraysourceoptimization AT ovchinnikvd intensivexraysourceoptimization |
| first_indexed |
2025-07-06T05:41:53Z |
| last_indexed |
2025-07-06T05:41:53Z |
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1836875008482213888 |
| fulltext |
INTENSIVE X-RAY SOURCE OPTIMIZATION
G.L. Bochek, V.I. Kulibaba, N.I. Maslov, V.D. Ovchinnik
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
e-mail: maslov@kipt.kharkov.ua
Possibility of optimization of an intensive source of the electron radiation in crystals based on the Compton
scattering of X-radiation is considered.
PACS: 07.85.+n; 13.60.Fz
1. INTRODUCTION
The radiation, arising as relativistic electrons pass
through the crystal, is investigated very intensively [1-8]
because can be used to create quasimonochromatic,
polarized and spectrally intense X-ray and gamma
source. But all known experimental results have been
obtained only for very low electron current regimes,
when the radiation is created by single electron passing
through the crystal. As a result of this, the predictions of
high current situation have discrepancies up to 5 orders
[9] for X-radiation. The prospect and requirement of
creation of intensive coherent x-ray sources causes the
necessity of experimental techniques development for
creation and measurement of the basic characteristics of
such radiation: intensity of radiation; spectral and
angular distributions, etc. The difficulties on
optimisation of an intensive gamma-quanta source are
connected with application necessity of the high current
of the accelerated electrons and thick crystal converters.
In this work the method of optimization of intensive
X-ray sources is proposed. The method is based on the
results received by authors at investigations of gamma
radiation of electrons in thick single crystals [10-12]. In
the measurements are used the method of the nonlinear
conversion of initial gamma radiation by a Compton
scattering on the target - scatterer [10].
2. MEASUREMENTS OF INTENSIVE
GAMMA-RADIATION SOURCE
Fig. 1 shows the experimental layout [10]. Gamma-
radiation of electrons from the target 1 after cleaning
magnets 3, 5 hit the scatterer 6. The Compton scattered
photons after measuring-channel collimators 9,11,12 are
registered by gamma-spectrometer 14. The transference
of the scatterer along A-C allows the measuring of the
spectral-angular distribution of the gamma-radiation.
This technique was tested on Kharkov linear electron
accelerator at electron energy 1 GeV [10, 11].
The method allows:
–to measure the "true" spectral - angular distribu-
tions of radiation without this radiation distortion in
experimental conditions of a multiple production of
gamma quanta by one electron;
– to measure the "true" spectral-angular distributions
of radiation in experimental conditions of intensive
pulse beam (impulse combination from gamma quanta
in spectrometer).
Fig. 1. Scheme of the experimental setup: 1- target;
2- goniometer; 3- deflecting electromagnet; 4- photon
beam collimator; 5, 10- cleaning electromagnets; 6-
scatterer; 7- ionization chamber; 8- lead block; 9, 11,
12- measuring-channel collimators; 13- cleaning
magnet; 14- gamma spectrometer; 15- lead shielding of
the spectrometer; 16- concrete wall
Figs. 2,3 show, for example, the experimental
gamma-quanta spectra measured by technique [10]. The
radiation spectra of 1.2 GeV electrons in 70 μm and
63 mm thick silicon single crystals are shown in Fig. 2.
The spectra have a prominent peak at ω=15 MeV, whose
width is about 50 MeV. It is seen from Fig. 2 that the
spectrum shape and the energy value at the intensity
maximum are practically independent of the crystal
thickness. The radiation spectrum from the tungsten
crystals of various thickness averaged over experimental
points, are presented in Fig. 3. It is seen from Fig. 3, that
the spectrum curve for the tungsten crystals of 1.18 mm
and 3.2 mm thickness have practically coinciding
maximum at the gamma-quanta energy ω=22 MeV. But
these spectra considerably differ from each other in
intensity in the whole interval of gamma-quanta energy.
The most visible decrease in intensity is observed in the
hard part of spectrum, beginning from ω>20 MeV. This
is likely to be caused by decrease in a number of
gamma-quanta because of pair creation.
3. INTENSIVE X-RAY SOURCE
OPTIMIZATION
Measuring X-rays spectrums with energy of some
tens keV, it is necessary to take into account the
Doppler broadening of scattered quanta spectrum
caused by the non-zero initial momentum distribution of
the atomic electrons.
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2005, № 6.
Series: Nuclear Physics Investigations (45), p. 59-62. 59
Fig. 2. Spectra of gamma-radiation by 1,2 GeV
electrons passing through the Si crystals along the
<111> axis. The collimation angle ϑc = 0.213 mrad
Dashed line – spectra levels for random crystals
Fig. 3. (a) –spectra of gamma-radiation by 1.2 GeV
electrons passing through W crystals..
1– W (100), 1.18 mm ; 2– W (111), 3.2 mm thickness;
3 – W, random, 3.2 mm thickness
(b) – the same spectra, fitted at the energy ω=22 MeV
At photon scattering on free rest electron the energy
of scattered photon is associated with initial photon
energy and scattering angle by known Compton
formula:
( )θω
ωω
cos11 1
1
2
−+
=
m
, (1)
where ω1 and ω2 is the energy of initial and scattered
photon, consequently, θ is scattering angle, m is electron
rest mass.
Fig. 4 shows the dependence of scattered photons
energy from the initial photon energy for two scattering
angles 30° and 110°.
The cross-section of the photon scattering on angle
ϑ in this case is (formula Klein-Nishina):
Ω
−+
= drd θ
ω
ω
ω
ω
ω
ωσ 2
2
1
2
2
2
1
22
0 sin
2
1
. (2)
Compton equation (1) and formula (2) were obtained
in assumption that the photon scattering occur on free
rest electron. However, for energy electron less 100 keV
this assumption is invalid at the photon scattering on
atomic electrons, which have bond energy and impulse
distribution.
Fig. 4. The dependence of scattered photon energy
vs the initial photon energy for two scattering angles 30
° and 110°
If initial photon energy is small on the comparison
with rest electron energy the Compton cross-section
may be written in form:
)(
212
1
2
qJ
kk
m
d
d
dd
d
Th
−
=
Ω ω
ω
ω
σ
ω
σ
, (3)
where
Thd
d
ω
σ
-nonrelativistic Tomson cross-section,
odpppnqJ ∫
∞
=
0 00 )(2)( π – Compton profile,
21021 /)( kkpkkq
−⋅−= , and ∫
∞
∞−
= 1)( dqqJ for
one electron. Here n(p0) is the probability that an
electron in the ground state of the system will have
momentum p0.
The authors of work [13] on the visualization
systems simulation are used the relativistic equation for
double differential cross section for scattering at angle
ϑ per differential solid angle dΩ, per differential energy
dω' from work [14]:
60
θωωωω
ω
σ cos'2'
2
1
' 1
22
1
2
0
2
−+=
Ω
mr
dd
d ×
)(sin
'
'' 21
11
qJ⋅
−+
θ
ω
ω
ω
ω
ω
ω , (4)
where ω' is the energy of scattered photon. Compton
profiles in this work was used from published
calculations with use of the precise Hartree-Fock wave
functions [15]. Equation associating energy of scattered
photon with q is
2/1
1
2
2
2
22
)cos''(
)'()cos1('
θωωωω
ωωθωω
−+
−−−
=
mq , (5)
where ω2 is energy of scattered photon predicted by
Compton equation (1).
The presence of a bound electron momentum results
in the energy distribution of scattered photons for a
fixed scattering angle and the violation of a single
valued bond between the scattering angle and the
photon energy (Compton spectra).
Fig. 5 and 6 show the Compton spectra for hydrogen
systems with different Z=1 and 3 for two values of
energy ω1 calculated in impulse approximation [16].
The widths of the distributions on the half-height are
about 1.5 % and 7 %, accordingly.
The spectrum of the scattered photons measured in
experiment is bound with the initial spectrum of
scattered photons by equation [17]:
NEXP (ω2)=Φ(ω2) +
+ ∫ ωωηωωω+ωω−ωω '''''''' d)()(C)(A)](M)(J)[(S)(N 222222222 (6)
∫ ωωηωωω+ωω−ωω '''''''' d)()(C)(A)](M)(J)[(S)(N 222222222 ,
where N(ω2) – the initial spectrum of scattered photons,
S(ω2) – detector system's response, J(ω2) – Compton
profile, M(ω2) – the multiple scattering function, A(ω2)
– probability of photoelectric absorption in scatterer, C(
ω2) – Compton scattering cross-section on free
electrons, η(ω2) – detector efficiency function, φ(ω2) –
background distribution.
With point of view of the experiment the appearance
of these Compton distributions (Figs. 5,6) leads to
aggravation of the energy resolution of the measuring
system, which perhaps removed, in principle, by
deconvolution procedure [18] for inverting the
equation (6).
In the case of coherent polarization radiation the
photons have the high degree of linear polarization
[19,20].
The photons polarized perpendiculars to scattering
plane are scattered stronger then the photons polarized
parallel to scattering plane [21]. This fact can to lead to
distortion of the measuring X-ray spectra and has to be
taken into account on measuring of the spectral
characteristics of the X-ray intensive source.
The estimations are showing that on the using of
scatterer from 1 mm beryllium and registration solid
angle 10-6 sr it is possible to measure the spectral
Fig. 5. Compton spectra for hydrogen systems with
different Z for No Kα1 radiation (ω1≈17,4 keV)
calculated in impulse approximation [16]
Fig. 6. Compton spectra for hydrogen systems with
Z=3 for W Kα1 radiation (ω1≈59,3 keV) calculated in
impulse approximation [16]
distributions of continuos X-ray radiation on the fluency
1012…1013 quanta per second.
4. CONCLUSIONS
The method of the measuring of spectral-angular
distributions of gamma-quanta on base of the Compton
scattering on the atomic electrons is allowed the spectral
characteristics measuring of the X-ray radiation with
energy more 10 keV, but with insufficiently high energy
resolution about 5…7 % caused by Doppler broadening.
On measuring with use of the Ge(Li) detector the
energy resolution is determined, in the main, by the
Doppler broadening, as the modern semiconductor
detectors have high-energy resolution.
The method allows to measure the "true" spectral -
angular distributions of X-radiation in experimental
conditions of intensive pulse beam without this radiation
distortion in conditions of a multiple production of
gamma quanta in thick crystals by one electron .
The resolution corrected X-ray spectra of scattered
quanta may be obtained by using of the deconvolution
procedure with using of the experimental Compton
profile and resolution function of detector.
61
To obtain the initial “true” spectrum of X-radiation,
it is necessary to restore the spectrum of the measured
scattered radiation through the use of the inverse
Compton transforms.
On the using of scatterer from 1 mm beryllium and
registration solid angle 10-6 sr it is possible to measure
the spectral distributions of continuos X-ray radiation
on the fluency 1012…1013 quanta per second.
ACKNOWLEDGMENT
Authors are very thankful to many colleagues for the
valuable discussions and constructive remarks.
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ОПТИМИЗАЦИЯ ИСТОЧНИКОВ ИНТЕНСИВНОГО РЕНТГЕНОВСКОГО ИЗЛУЧЕНИЯ
Г.Л. Бочек, В.И. Кулибаба, Н.И. Маслов, В.Д. Овчинник
Рассматривается возможность оптимизации источников интенсивного рентгеновского излучения
ускоренных электронов с использованием методики на основе комптоновского рассеяния.
ОПТИМІЗАЦІЯ ДЖЕРЕЛ ІНТЕНСИВНОГО РЕНТГЕНІВСЬКОГО ВИПРОМІНЮВАННЯ
Г.Л. Бочек, В.І. Кулібаба, М.І. Маслов, В.Д. Овчинник
62
Розглядається можливість оптимізації джерел інтенсивного рентгенівського випромінювання
прискорених електронів з використанням методики на основі комптонівського розсіяння.
63
1. INTRODUCTION
|