Features of angular distributions of 1 GeV electrons scattered by thin silicon monocrystal
The result of theoretical and experimental investigations of angular distribution structure of 1 GeV electrons scattered by silicon crystal of 10 mm thickness are presented. The electron beam was falling on the crystal under different angles (from zero to the critical channeling angle) in respect to...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2001
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| Cite this: | Features of angular distributions of 1 GeV electrons scattered by thin silicon monocrystal / S.P. Fomin, S.F. Shcherbak, V.I. Kasilov, N.I. Lapin, N.F. Shul'ga // Вопросы атомной науки и техники. — 2001. — № 6. — С. 138-143. — Бібліогр.: 8 назв. — англ. |
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| author | Fomin, S.P. Shcherbak, S.F. Kasilov, V.I. Lapin, N.I. Shul'ga, N.F. |
| author_facet | Fomin, S.P. Shcherbak, S.F. Kasilov, V.I. Lapin, N.I. Shul'ga, N.F. |
| citation_txt | Features of angular distributions of 1 GeV electrons scattered by thin silicon monocrystal / S.P. Fomin, S.F. Shcherbak, V.I. Kasilov, N.I. Lapin, N.F. Shul'ga // Вопросы атомной науки и техники. — 2001. — № 6. — С. 138-143. — Бібліогр.: 8 назв. — англ. |
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| container_title | Вопросы атомной науки и техники |
| description | The result of theoretical and experimental investigations of angular distribution structure of 1 GeV electrons scattered by silicon crystal of 10 mm thickness are presented. The electron beam was falling on the crystal under different angles (from zero to the critical channeling angle) in respect to the crystal axis <111>. The analysis of the experimental data was carried out with the help of computer simulation of electron beam passage through the crystal on the basis of binary collision model. It is shown, that the existence of several maxima in the angular distributions of scattered electrons is stipulated by contributions of different fractions of electron beam in crystal, namely: the channeled and the above-barrier. The combined technique (simulation-experiment) of investigation of elastic scattering makes it possible to obtain important quantitative information about relativistic electron beam dynamics in aligned crystals.
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FEATURES OF ANGULAR DISTRIBUTIONS OF 1 GEV ELECTRONS
SCATTERED BY THIN SILICON MONOCRYSTAL
S.P. Fomin, S.F. Shcherbak, V.I. Kasilov, N.I. Lapin, N.F. Shul'ga
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
e-mail: sfomin@kipt.kharkov.ua
The result of theoretical and experimental investigations of angular distribution structure of 1 GeV electrons scat-
tered by silicon crystal of 10 µm thickness are presented. The electron beam was falling on the crystal under different
angles (from zero to the critical channeling angle) in respect to the crystal axis <111>. The analysis of the experi-
mental data was carried out with the help of computer simulation of electron beam passage through the crystal on the
basis of binary collision model. It is shown, that the existence of several maxima in the angular distributions of scat-
tered electrons is stipulated by contributions of different fractions of electron beam in crystal, namely: the channeled
and the above-barrier. The combined technique (simulation-experiment) of investigation of elastic scattering makes
it possible to obtain important quantitative information about relativistic electron beam dynamics in aligned crystals.
PACS: 61.85; 41.75.H; 34.80.P
1. INTRODUCTION
When a beam of relativistic electrons passes through
a crystal at a small angle to one of crystallographic axes
there takes place a significant orientation effect in elec-
tron scattering exhibited as characteristic annular angu-
lar distributions of the particles outgoing from the crys-
tal (“doughnut scattering”) [1,2]. In this case the magni-
tude of a root-mean-square scattering angle of electrons
can exceed essentially (in several times) the correspond-
ing parameter at electron scattering in an amorphous tar-
get of the same thickness [2], and the less is the target
thickness, the more is this difference. This shows the ex-
istence of strong correlation in electron scattering, when
it sequentially collides with lattice atoms located along
the given crystallographic axis.
Another important manifestation of these correla-
tions is the coherent effect in Bremsstrahlung of rela-
tivistic electrons, when radiation intensity in crystal in a
low-energy part of spectrum can ten times exceed radia-
tion intensity in an amorphous target (see [3] and ref.
there). As it is in the case of elastic scattering, at Brems-
strahlung in crystal the strong dependence of radiation
intensity on the angle ψ0 of electron arrival to a crystal-
lographic axis is observed. The radiation intensity grows
fast while the angle ψ0 is decreasing. The radiation in-
tensity reaches maximum value at ψ0 < ψc , where ψc is
the critical angle of an axial channeling [4].
The last circumstance, apparently, was the reason
why during a long period of time high intensity of radia-
tion of relativistic electrons, incident along a crystallo-
graphic axis, was associated with a radiation of chan-
neled electrons, i.e. electrons involved in a finite motion
in a field of atomic strings located along the given axis
(see, for example, [5]). However, the analysis of the sta-
bility of 1 GeV electron motion in an axial channeling
regime has shown, that the incoherent scattering on ther-
mal oscillations of lattice atoms and on electronic sub-
system of crystal results in a fast dechanneling of elec-
trons, i.e. transition to a regime of above-barrier (infi-
nite) motion.
The radiation of an above-barrier electron (ψ0 > ψc)
has also a coherent character, high intensity (though
smaller, than for channeled electron) and maximum in a
low-energy part of a spectrum [3]. While solving many
problems, in particular, the problem of optimization of a
gamma-radiation source, it is necessary to know the con-
tribution of each of the indicated mechanisms. It is
worth to point out, that the position of a maximum in ra-
diation spectrum of above-barrier electrons coincides
with the position of a maximum of channeled electrons
radiation [3]. For this reason it is impossible to establish
the relative contribution of these two mechanisms to ra-
diation of an electron beam, passing through a crystal,
immediately from the analysis of a radiation spectrum.
Theoretical calculations of a share of channeled parti-
cles, as a function of depth of an electron beam penetra-
tion into a crystal, that were based on the use of the ki-
netic equation method (see., for example, [5]), gave
overstated results contradicting the value of radiation in-
tensity observed at the experiments.
To define a relative share of channeled electrons
from a relativistic electron beam passing through
aligned crystal the special experimental techniques that
use the effect of redistribution of a channeled electron
stream to the impact parameters to an atomic string have
been developed in NSC KIPT [6,7]. The matter is that
on average a channeled electron goes in a crystal close
to atomic strings during a longer period of time, than
above-barrier does. Thus, it has a higher probability of
138 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2001, № 6, p. 138-143.
processes stipulated by small impact parameters. Δ-elec-
tron emission [6], electronuclear reactions [7] etc. be-
long to such processes. Each of these techniques has its
advantages and drawbacks. The technique [6] is the
most simple for realization, however, it shows only an
integral effect on a crystal thickness. The technique [7],
that uses layer-by-layer etching of the crystal, irradiated
by an electron beam, and then the measurement of in-
duced activity of etched layers, enables to trace the de-
pendence of an output of electronuclear reactions (thus,
probability of close impacts) with the depth of electron
beam penetration into a crystal. The technological diffi-
culties connected with layer-by-layer etching and the
measurement of layer activity, however, have an effect
for the measurement accuracy. Furthermore both these
techniques use secondary electrodynamic processes for
revealing a share of channeled electrons. This also adds
errors to measurements.
The purpose of the present work is to research the
features of elastic scattering of relativistic electrons on
crystal atomic strings, and to study a possibility to deter-
mine a share of particles of an electron beam moving in
crystal in an axial channeling regime, by means of ana-
lyzing angular distributions of particles scattered by a
crystal.
The advantage of the given method is that the elastic
scattering of electrons, instead of secondary electrody-
namic processes is analyzed. The experiment is compli-
cated, because to observe a thin structure of angular dis-
tributions it is necessary to have an electron beam with
an initial divergence that is considerably smaller than
the critical angle of channeling, and a rather thin
monocrystal, so that the channeled electrons would
make a noticeable part of a beam on withdrawal from
crystal.
2. EXPERIMENT
These conditions were realized on the Kharkov lin-
ear accelerator of electrons (LAE-2 GeV). The collimat-
ed electron beam 0.3 x 0.3 mm sizes with energy
ε = 1 GeV and divergence 0.01 mrad fell on silicon
monocrystal of thickness T = 10 μm, located in go-
niometer at the distance 11.5 m from the collimator. The
orientation of monocrystal by the axis <111> in relation
to the axis of an electron beam was carried out by sec-
ondary electron emission effect [6].
Electrons scattered by crystal were registered by a
glass plate, which was located at the distance of 14.9 m
from monocrystal, and the doze of glass irradiation by
electrons was selected so that the darkening of glass was
in linear dependence on a doze. Then the irradiated
glass plates were scanned photometrically by a mi-
crophotometer IFO-451. The photometric measurement
was conducted through the center of angular distribution
of electrons on glass, with the breadth of the window of
the microphotometer Δx = 2 mm. The finite breadth of
the window of photometer, naturally, results in an inte-
gration of data in a strip of capture Δx and this deter-
mines the angular resolution of the given installation at
measurement of angular distributions of scattered elec-
trons.
The characteristic “print” of the angular distribution
of electrons scattered by monocrystal obtained on a
glass plate located across the beam (plane (x, y)) is indi-
cated on Fig. 1a. The electron beam fell on crystal at the
angle ψ0 = ψc to crystallographic axis <111> (axis z).
Under the conditions of the given experiment the value
of the critical angle of axial channeling makes
ψc= 0.41 mrad. As the figure shows the angular distribu-
tion of electrons has a complex structure: the azimuthal
inhomogeneous annular distribution round the direction
of the crystallographic axis with the apex angle ψ = ψ0
and with additional azimuthally homogeneous “spot” in
the center.
0
Θy/ψc
Θx/ψc
ΔΘx
1
1 -1
-1
-1 1 0
b)
a)
0
Θy/ψc
Fig. 1
On Fig. 1b the angular distribution of electrons (sol-
id curve), obtained as a result of a photometric measure-
ment of glass darkening along the axis Oy through the
center of a ring is demonstrated. In our case the capture
breadth of photometer in angular units made Δθx =
0.13 mrad (see Fig. 1a). This angular distribution con-
tains two clearly expressed maxima at Δθy = ψ0, which
are stipulated by scattering of above-barrier electrons.
Besides, for θy = 0 the local maximum is observed. This
maximum cannot be explained by scattering of above-
barrier particles, and consequently, it is connected with
scattering of channeled electrons.
At ψ0 = ψc practically all particles of the beam, when
entering the crystal, are in a regime of above-barrier mo-
tion. Channeled electrons can appear when a beam is
passing through a crystal as a result of above-barrier
139
electrons scattering on thermal fluctuations of lattice
atoms, on an electronic subsystem of crystal, and on var-
ious kinds of crystalline structure defects.
When a crystal misalignment angle diminishes from
ψc to zero, there grows the number of electrons, captured
into a channeling regime, when entering the crystal.
Therefore in the conducted experiment the angular dis-
tributions of scattered electrons with various values of
misalignment angles were investigated ψ0 = 0; 0.05;
0.21; 0.31; 0.41 mrad or in terms of ψc accordingly ψ0 =
0; 0.125; 0.5; 0.75; 1.0 ψc. However, it is necessary, to
bear in mind that when an angle diminishes, the charac-
teristic ring of angular distribution of above-barrier elec-
trons narrows and all three maxima merge to one, and
this does not allow to divide visually the contributions
of channeled and above-barrier fractions of a beam to
the formation of angular distribution of particles scat-
tered by crystal.
3. COMPUTER SIMULATION
Generally the dynamics of relativistic particle beam
in aligned crystal is rather complicated, as the various
fractions of a beam are involved in various regimes of
motion: finite and infinite, regular and chaotic with tran-
sitions between them. The analytical description of
beam dynamics can be conducted only in some limit
cases. Thus, for example, the theory of multiple scatter-
ing of relativistic charged particles on atomic strings of
crystal, based on the employment of a continuous string
approximation, describes the coherent azimuth scatter-
ing of above-barrier electrons (“doughnut scattering ef-
fect”) [2, 3]. However, this theory does not describe
transitions of particles between various fractions of an
electron beam in crystal, since the continuous string ap-
proximation does not take into account the contribution
of incoherent scattering. It is possible to take incoherent
scattering into account by analytical methods only in
case of rather large incident angles ψ0 >> ψc [8]. At the
same time, as it was already mentioned, orientation ef-
fects in scattering and radiation of a relativistic electron
beam, passing through a crystal, are most brightly exhib-
ited in the range of angles ψ0 < ψc. Therefore for the
quantitative description of these effects computer simu-
lation of passing of an electron beam through aligned
crystal appears to be the most adequate.
With the purpose of theoretical analysis of angular
distributions, obtained in the experiment, a computer
simulation on the basis of Monte-Carlo method with uti-
lization of a model of binary collisions of a relativistic
electron with atoms of a crystalline lattice was conduct-
ed. Such approach allows taking into account both co-
herent (correlated) scattering of fast electrons on atomic
strings of crystal located along a crystallographic axis,
and incoherent scattering of electrons on thermal fluctu-
ations of atom positions of atoms in a lattice and elec-
tronic subsystem of crystal. A rather small thickness of a
crystal (T = 10 μm) allows gathering a sufficient statistic
of events (N = 10000) during the acceptable period of
time.
Belonging of a particle of a beam to a fraction of
channeled or above-barrier electrons was controlled
along all the trajectory of a particle in crystal according
to the sign of transverse motion energy
)(2/2 ρεε Uv += ⊥⊥
, (1)
where ε is the energy of an electron, ⊥v
is the compo-
nent of particle velocity in the plane (x, y) in terms of
light velocity, U(ρ) is the field of atomic string of crys-
tal, averaged along the axis z. For the channeled electron
0≤⊥ε , for the above-barrier 0>⊥ε . Thus, there was
carried out a monitoring of a number of channeled elec-
trons, as a function of penetration depth of electrons into
crystal.
Fig. 2
In a continuous string approximation the transverse
motion energy of an electron ⊥ε is an integral of motion
[3]. The scattering of electrons in this case is possible
only at an azimuth angle φ (see Fig. 2), the polar angle
ψ, defining the transverse motion energy of a particle
before and after scattering on a string 2/2ψεε =⊥
does not vary. However, thermal oscillations of atoms in
lattice knots, other imperfections of a crystalline struc-
ture result in changing of ⊥ε and in the possibility of
transition of particles from one fraction into another.
Thus, the coherent scattering on an atomic string ensures
"fast" azimuth scattering of electrons on φ, and the inco-
herent scattering on imperfections of a crystalline lattice
is responsible for a rather "slow" scattering on the angle
ψ.
The angle of electron departure from crystal in rela-
tion to crystallographic axis ψs is determined by the en-
ergy value ⊥ε in the point of departure, and also by the
distance to the nearest atomic string ρs:
ερεψ /))((2 SS U−= ⊥ . (2)
The channeled electron ( ⊥ε < 0) makes a finite mo-
tion in a plane, orthogonal to the axis of the crystal. It is
obvious, that the angular distribution of this fraction of
beam particles should be concentrated within the limits
of a cone apex angle εψ /2 mc U= (where Um is the
depth of a potential hole U(ρ)) and with the maximum
along the crystallographic axis.
The above-barrier electron ( 0>⊥ε ) makes infinite
motion in the plane (x, y), being scattered sequentially
on various atomic strings of a crystal. The distribution
of above-barrier electrons in the angle ψ should have a
minimum in the direction of the crystallographic axis.
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2000, №2.
Серия: Ядерно-физические исследования (36), с. 3-6.
140
-2 -1 0 1 2
0,05
0,10
0,15
0,20
-2
-1
0
1
2
T = 1 µ mNe
θ x
θ y
-2 -1 0 1 2
0,05
0,10
0,15
0,20
-2
-1
0
1
2
5 µ m
Ne
θ x
θ y
-2 -1 0 1 2
0,05
0,10
0,15
0,20
-2
-1
0
1
2
10 µ m
Ne
θ x
θ y
Fig. 3
In Fig. 3 the results of computer simulation of a
1 GeV electron beam passing through a silicon crystal
when ψ0 = ψc are presented. This figure visually demon-
strates the evolution of angular distribution of scattered
electrons when the thickness of crystal is growing from
1 μm to 10 μm. It is necessary to mark, that practically
all the electrons, entering the crystal, with ψ0 = ψc initial-
ly are above-barrier. Fig. 3 shows that the coherent az-
imuth scattering of above-barrier electrons on crystal
atomic strings is much stronger than the incoherent, so
that a ring of azimuth scattering “has time” to get al-
ready "closed" at a thickness of about 10 μm, having a
little blurring under the influence of isotropic incoherent
scattering.
With the growth of thickness it is possible to notice
the emerging of a small local maximum in the angular
distribution of electrons in the crystallographic axis di-
rection, i.e. when θx = θy = 0. The analysis of the motion
parameters of the electron departing along the crystallo-
graphic axis and forming this maximum shows that the
majority of them are channeled, i.e. have 0≤⊥ε .
4. ANALYSIS OF EXPERIMENTAL DATA
The results of measurements of angular distributions
of electrons with energy ε = 1 GeV, scattered by silicon
monocrystal of thickness T = 10 μm with various values
of an incident angle of an electron beam to the crystallo-
graphic axis <111> are represented in Fig. 4 by solid
curves. These curves are obtained by a photometric
measurement of a print of two-dimensional angular dis-
tribution of scattered electrons along the axis Oy
through the center of the ring with photometer capture
breadth Δθx = ± 0.32 ψc (see Fig. 1a). In Fig. 4 the re-
sults of computer simulation of the process of elastic
electron scattering for the same conditions are represent-
ed as histograms. The black histogram corresponds to
the angular distribution of the channeled electrons, the
grey to the above-barrier electrons, and the white to
their sum, i.e. the angular distribution of the whole elec-
tron beam, that has past through the crystal.
The comparison of the experimental data on angular
distributions of scattered electrons of various values of
the crystal misalignment angle ψ0 with the results of the
computer simulation as a whole shows not only qualita-
tive, but also good quantitative agreement. The notice-
able divergence at ψ0 = 0.75 ψc , apparently, is connect-
ed to inaccuracy of azimuth orientation of a glass plate
at its photometric measurement, what is proved by the
obvious asymmetry of the measured angular distribution
in relation to the axis x. Unfortunately, the realization of
an updating measurement now is impossible because of
a stop of the accelerator LAE - 2 GeV.
When an electron beam is falling along the crystallo-
graphic axis (ψ0 = 0, see Fig. 4a) the significant widen-
ing of the angular distribution of electrons is observed
not only in comparison with an initial divergence of the
beam Δψ0 = 0.025 ψc , but also in comparison with elec-
tron scattering in an amorphous target of the same thick-
ness cam ψθ 34.02 = . This effect is explained by coher-
ent scattering of electrons by atoms of crystal atomic
string and it can be described as the influence of an av-
erage field of an atomic string U(ρ) on an electron beam
)(2/))((2/)(
)(2/
22
0
2
0
ss UtUt
U
ρψερψε
ρψεε
+=+=
=+=⊥ , (3)
where ρ0 is the distance to the nearest atomic string at the
electron entrance into the crystal. If the incident angle
141
-2 -1 0 1 2
0,0
0,1
0,2
0,3
a)
E = 1 GeV
Si <111>
ψ 0 = 0
Ne
θ y / ψ c
experiment
total beam
above-barrier
channeled
-2 -1 0 1 2
0,0
0,1
0,2
0,3
ψ o = 0.125 ψ c
b)
Ne
θ y / ψ c
--
-2 -1 0 1 2
0,0
0,1
0,2
0,3
ψ o = 0.5 ψ c
c)
Ne
θ y / ψ c
-2 -1 0 1 2
0,0
0,1
0,2
ψ o = 0.75 ψ c
d)
Ne
θ y / ψ c
-2 -1 0 1 2
0,0
0,1
ψ o = ψ c
e)
Ne
θ y / ψ c
Fig. 4
ψ0 = 0, then according to (3), the angle between the di-
rection of particle motion and the string axis changes
under the influence of the field U(ρ) as
ερρψ /))(()((2)( 0 tUUt −= , (4)
where ρ(t) is the trajectory of electron motion in the
plane (x, y). Depending on the point of departure from
crystal ρs the particle will have an angle
ερρψ /)()((2 0 ss UU −= . Averaging of values of parti-
cle departure angle on an electron beam results in the
angular distribution with a breadth Δθ ~ ψc even at zero
divergence of an incident electron beam. The thickness
of crystal in this case should exceed only a quarter of the
average value of the oscillation period of the channeled
electron that is about one micron for the conditions of
the discussed experiment.
The dependence of the mean-square scattering angle
of 1 GeV electron beam from a target thickness is repre-
sented in Fig. 5. The solid curve corresponds to the case
of ψ0 = 0; the dashed curve corresponds to the random
orientation of the crystal in relation to the electron beam
direction that is equivalent to the scattering in an amor-
phous target. Both these curves are obtained by comput-
er simulation of electron beam scattering with initial an-
gular divergence Δψ0 = 0.2 ψc .
Fig. 5 shows the sharp increase of electron multiple
scattering angle <θ> in aligned crystal in comparison
with a scattering in amorphous medium at the first mi-
crons from beam entering the target. This is the manifes-
tation of coherent mechanism of electron scattering on
crystal string atoms with the maximum value of scatter-
ing angle <θ> = ψc (see Eq. (2)). Further increase of
<θ> with target thickness T increasing is stipulated by
incoherent scattering and it occurs in the same manner
as in amorphous medium (see Fig. 5).
It should be noted that in the case 00 ≠ψ the ulti-
mate angle <θ> stipulated by coherent scattering mech-
anism is equal to 2ψ0, when the characteristic angular
distribution ring becomes closed. In this case the elec-
tron beam as a whole is turned by crystal to the angle ψ0
with the angular distribution width <θ> ≈ ψ0 .
Availability of particles with angles θy > ψc in angu-
lar distribution in Fig. 4a is stipulated by the contribu-
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2000, №2.
Серия: Ядерно-физические исследования (36), с. 3-6.
142
tion of the incoherent scattering, which, as it was
marked above, results in dechanneling of electrons, i.e.
transition to an above-barrier condition. The results of
the simulation show, that at ψ0 = 0 about 90 % of the
electrons are captured to an axial channeling regime at
the entrance into the crystal. However, after passing
10 μm through the crystal only 10 % of beam electrons
stay in the channel.
0 10 20 30 40
0,5
1,0
1,5
ψ 0 = 0
random
<θ >/ψ c
∆ ψ 0
Si <111> E=1GeV
T, µ m
Fig. 5
Of course, there is an opposite process, called
rechanneling, when above-barrier electron is captured to
the channeling regime of motion. At ψ0 = ψc all the elec-
trons are above-barrier at entering the crystal ( 0>⊥ε ).
However, as computer simulation shows, about 2% of
beam particles become channeled after passing 10 μm in
the crystal in this case.
It is impossible to make a conclusion about a quanti-
tative ratio between fractions of an electron beam from
the analysis of Fig. 4 immediately, since the area of a
photometric measurement covered not the whole angular
distribution of scattered particles (see Fig. 2). However,
the selected method of photometric measurement con-
tains the important information about the structure of an-
gular distributions of scattered electrons and allows to
observe the contribution of channeled electrons to this
angular distribution at ψ0 ≤ ψc .
When the gradual disalignment of the crystal as re-
lated to the electron beam takes place, the initial circular
distribution gradually passes to the annular with some
darkening in the centre of the ring. In Fig. 4 (a-e) this
transition corresponds to gradual division of one broad
maximum of angular distribution (see Fig. 4a) into three
separate maxima (see Fig. 4e). The computer simulation
of an electron beam passing through a crystal allows to
distinguish between the channeled and the above-barrier
electrons and to give the unambiguous interpretation of
a complex structure of the angular distributions, ob-
served in the experiment: two extreme maxima corre-
spond to the intersection of the photometric measure-
ment strip with the ring of angular distribution of above-
barrier electrons; the emerging of the central maximum
is stipulated by the angular distribution of channeled
particles.
5. CONCLUSION
The executed experiment demonstrates a possibility
of direct observation of the effect of relativistic electron
channeling in a thin monocrystal by means of angular
distributions of an electron beam that has past through a
crystal. Quantitative analysis of the angular distribu-
tions, based on the computer simulation of the process
of electron beam passing through a crystal, allows get-
ting important information about dynamics of an elec-
tron beam moving in a crystal along a crystallographic
axis.
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143
S.P. Fomin, S.F. Shcherbak, V.I. Kasilov, N.I. Lapin, N.F. Shul'ga
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
3. Computer Simulation
4. analysis of experimental data
5. Conclusion
REFERENCES
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| id | nasplib_isofts_kiev_ua-123456789-79420 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T18:24:13Z |
| publishDate | 2001 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Fomin, S.P. Shcherbak, S.F. Kasilov, V.I. Lapin, N.I. Shul'ga, N.F. 2015-04-01T19:19:03Z 2015-04-01T19:19:03Z 2001 Features of angular distributions of 1 GeV electrons scattered by thin silicon monocrystal / S.P. Fomin, S.F. Shcherbak, V.I. Kasilov, N.I. Lapin, N.F. Shul'ga // Вопросы атомной науки и техники. — 2001. — № 6. — С. 138-143. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS: 61.85; 41.75.H; 34.80.P https://nasplib.isofts.kiev.ua/handle/123456789/79420 The result of theoretical and experimental investigations of angular distribution structure of 1 GeV electrons scattered by silicon crystal of 10 mm thickness are presented. The electron beam was falling on the crystal under different angles (from zero to the critical channeling angle) in respect to the crystal axis <111>. The analysis of the experimental data was carried out with the help of computer simulation of electron beam passage through the crystal on the basis of binary collision model. It is shown, that the existence of several maxima in the angular distributions of scattered electrons is stipulated by contributions of different fractions of electron beam in crystal, namely: the channeled and the above-barrier. The combined technique (simulation-experiment) of investigation of elastic scattering makes it possible to obtain important quantitative information about relativistic electron beam dynamics in aligned crystals. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Electrodynamics of high energies in matter and strong fields Features of angular distributions of 1 GeV electrons scattered by thin silicon monocrystal Особенности угловых распределений электронов с энергией 1 ГэВ при рассеянии тонким монокристаллом кремния Article published earlier |
| spellingShingle | Features of angular distributions of 1 GeV electrons scattered by thin silicon monocrystal Fomin, S.P. Shcherbak, S.F. Kasilov, V.I. Lapin, N.I. Shul'ga, N.F. Electrodynamics of high energies in matter and strong fields |
| title | Features of angular distributions of 1 GeV electrons scattered by thin silicon monocrystal |
| title_alt | Особенности угловых распределений электронов с энергией 1 ГэВ при рассеянии тонким монокристаллом кремния |
| title_full | Features of angular distributions of 1 GeV electrons scattered by thin silicon monocrystal |
| title_fullStr | Features of angular distributions of 1 GeV electrons scattered by thin silicon monocrystal |
| title_full_unstemmed | Features of angular distributions of 1 GeV electrons scattered by thin silicon monocrystal |
| title_short | Features of angular distributions of 1 GeV electrons scattered by thin silicon monocrystal |
| title_sort | features of angular distributions of 1 gev electrons scattered by thin silicon monocrystal |
| topic | Electrodynamics of high energies in matter and strong fields |
| topic_facet | Electrodynamics of high energies in matter and strong fields |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/79420 |
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