Passage of positively and negatively charged particles through straight and bent nanotubes
Passage of high-energy charged particles through oriented crystals and nanotubes is investigated. It is shown that the particle passage through crystals and nanotubes may to be described in the same manner. The possibility of positively and negatively charged particle deflection by bent nanotube due...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2001 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2001
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| Цитувати: | Passage of positively and negatively charged particles through straight and bent nanotubes / A.A. Greenenko, N.F. Shul’ga // Вопросы атомной науки и техники. — 2001. — № 6. — С. 118-120. — Бібліогр.: 18 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860099823184642048 |
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| author | Greenenko, A.A. Shul’ga, N.F. |
| author_facet | Greenenko, A.A. Shul’ga, N.F. |
| citation_txt | Passage of positively and negatively charged particles through straight and bent nanotubes / A.A. Greenenko, N.F. Shul’ga // Вопросы атомной науки и техники. — 2001. — № 6. — С. 118-120. — Бібліогр.: 18 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | Passage of high-energy charged particles through oriented crystals and nanotubes is investigated. It is shown that the particle passage through crystals and nanotubes may to be described in the same manner. The possibility of positively and negatively charged particle deflection by bent nanotube due to axial channelling phenomenon is demonstrated. Computer simulation results for relativistic charged particle beam passage through straight and bent nanotubes are presented.
|
| first_indexed | 2025-12-07T17:27:59Z |
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| fulltext |
PASSAGE OF POSITIVELY AND NEGATIVELY CHARGED
PARTICLES THROUGH STRAIGHT AND BENT NANOTUBES
A.A. Greenenko a, N.F. Shul’ga a,b
a National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
b Belgorod State University, Belgorod, Russia
Passage of high-energy charged particles through oriented crystals and nanotubes is investigated. It is shown that
the particle passage through crystals and nanotubes may to be described in the same manner. The possibility of posit-
ively and negatively charged particle deflection by bent nanotube due to axial channelling phenomenon is demon-
strated. Computer simulation results for relativistic charged particle beam passage through straight and bent nan-
otubes are presented.
PACS: 05.45. -a; 07.05.Tp; 29.27.Ac; 61.82.Rx
1. INTRODUCTION
In 90th it were discovered new periodical structures –
carbon nanotubes (see [1,2] and refs. herein). Nanotubes
are long cored cylinders with about 1 nm diameter. The
nanotube surface is formed by periodically situated car-
bon atoms. In [3-9] it was paid attention to the fact, that
for particle passage through nanotubes there are possible
effects similar to effects under particle passage through
crystal near one of it axis. There are, in particular, chan-
nelling, rainbow scattering and orbiting of particles.
Special interest for the fast charged particle interac-
tion with a crystal has process of the particle passage
through a bent crystal, when the effective beam deflec-
tion effect is possible. It was paid attention ([10]) to the
possibility of such effect, while plane channelling of
positively charged particles in bent crystal was studied.
In [11,12] it was paid attention to another possibility
of the relativistic beam deflection deals with a charged
particle multiple scattering by atomic strings of a bent
crystal. The effect takes place both for positively and
negatively charged particles [12-14]. The computer sim-
ulation program for the beam passage through straight
and bent crystals was developed in [12-14]. This pro-
gram is based on crystal presentation as aggregate of
atomic strings.
In present paper passage of fast charged particles
through straight and bent nanotube is studied. The pos-
sibility of positively and negatively charged particle de-
flection by a bent nanotube due to axial channelling phe-
nomenon is shown. Computer simulation results for
particle passage through nanotube with account both co-
herent and incoherent effects in scattering are presented.
2. BEAM DEFLECTION AND SPLITTING
UNDER SCATTERING BY CRYSTAL
ATOMIC STRINGS
The motion of a fast charged particle near the crystal-
lographic axis (z-axis) is determined mainly by the con-
tinuous string potential, which is the crystal potential
averaged along the z-axis [15,16]. In such potential,
particles may perform finite (channelling) as well as in-
finite (over-barrier) motion in the plane orthogonal to
the z-axis. In a straight crystal the multiple scattering of
over-barrier particles by atomic strings results in so-
called donut scattering effect, when the particle scatter-
ing over azimuthal direction sufficiently exceed the
scattering in radial direction (see for instance [16]).
In [13] it was shown that in a bent crystal the beam
deflection as whole is possible. It is due to both chan-
nelling and donut scattering mechanisms [14]. Together
with the effect of beam deflection, for particle motion
near the crystal axis the beam splitting effect is possible
[11,14]. In [14] it was shown, that the splitting effect is
a result of donut scattering too. For detailed investiga-
tion of particle passage in a straight and bent crystal the
computer simulation program was developed [12-14].
In this program the particle interaction with a crystal is
based on the particle interaction with atomic strings,
which compound the crystal. Computer simulation results
confirm the possibility of the beam deflection and splitting
under it passage through a bent crystal near crystallograph-
ic axis [8,12-14].
3. PARTICLE CHANNELING AND
DECHANNELING IN NANOTUBE
Nanotubes can be represented (see for instance [1,7])
as an aggregate of carbon atom strings, which situated in
parallel to nanotube axis. Such geometry lead to forma-
tion of deep two-dimensional potential hole with minim-
um in centre of nanotube. The value of the potential bar-
rier for protons is about 100 eV in this case (see Fig. 1,2
of [7]). Thus, similarly to the channelling phenomenon
in crystals, the channelling phenomenon is possible too
for the particle motion along nanotube axis. Because of
potential hole shape, positively charged particles per-
form channelling inside nanotube along it axis, while
negatively charged particles perform channelling near
nanotube surface. Like to the crystal case, incoherent
scattering of particles by thermal vibrations of atoms
and by an electron subsystem of nanotube lead to the
particle dechannelling. The investigation of these effects
can to be realised on base of the computer simulation
method, which was developed for investigation of the
particle passage through crystals [14]. Fig. 1 presents
results of computer simulation for channelling and
118 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2001, № 6, p. 118-120.
dechannelling processes of charged particles in nan-
otubes.
Fig. 1. Channelling fraction with nanotube length
for the beam passage through straight and bent nan-
otubes along nanotube axis. Particle energy is
ε = 10 GeV. (a) protons: (1,2)−nanotube (10,1), (3,4)−
nanotube (10,0); (b) −π pions: (1,3) − straight nan-
otube, (2,4) − bent nanotube with bending radius
R = 10 cm. Simulation statistics is 1000 particles
The Fig. 1 shows that the dechannelling lengths of
positively charged particles in nanotubes exceed suffi-
ciently that for negatively charged particles. It deals with
the fact that the positive particle channelling is inside
nanotube far from it surface, while the channelling of
negative particle is directly in the region of thermal vi-
brations of nanotube atoms and in the region of high
electron density. From Fig. 1 it is seen, that the particle
fraction in channel depends of nanotube curvature and it
geometry (definition of nanotube indexes see for in-
stance in [2]).
4. BEAM DEFLECTION UNDER AXIAL
CHANNELING IN A BENT NANOTUBE
In a bent nanotube those particles, which perform the
axial channelling, will follow axial channel bend simil-
arly to the particle plane and axial channelling in a bent
crystal. Deflection condition based on the fact, that axial
channel is not destroyed by crystal bend (same as for
bent crystal planar channel case [10,17])
2
a⋅=>
H
c U
RR ε
, (1)
where cR is the radius of the critical bend, ε is the
particle energy, a is the width of the potential well,
HU is its depth and R is the bending radius of nan-
otube.
For particle motion near crystal axis the value of
HU is of the order of several eV, that limits the possib-
ilities of such deflection mechanism. In nanotubes HU
~100 eV and according to (1), the critical radius of nan-
otube bending for proton beam with 10 GeV energy is
cR ~ 4 cm (such bending is not a problem for nan-
otubes).
Figs. 2, 3 present horizontal profiles for positively
and negatively charged particles after passage through
bent nanotube.
Fig. 2. The horizontal profile of the proton beam
with energy 10 GeV after passage through the bent nan-
otube with thickness L = 1 cm and curvature radius
R = 10 cm. (a) nanotube (10,0); (b) nanotube (10,1).
Numbers above right peaks correspond to fraction of
particles, which were deflected to whole angle of nan-
otube bend (in % of beam particles, which were initially
captured by the nanotube channel). The simulation stat-
istics is 1000 particles
Particle deflection is due to channelling mechanism.
Thus channelling fractions of Fig. 1 determine fractions
of deflected particles. In this case the deflection angle
Rθ for particle bending by nanotube is
R
L
R =θ , (2)
where L is the nanotube thickness.
119
Fig. 3. Same as on Fig. 2., but for beam of −π pions
and nanotube thickness L = 200 mµ
Presented simulation results confirm the possibility
of large deflection angles of relativistic beams by short
nanotubes [8]. As one can see from Figs. 2,3 possible
deflection angles for positively charged particles exceed
sufficiently that for negatively charged particles. It is
due to above noted differences in dechannelling of pos-
itively and negatively charged particles. Nevertheless,
the efficiency of negatively charged particle deflection
by a bent nanotube (Fig. 3) exceeds the efficiency of
negatively charged particle deflection by a bent crystal
[8,11,14,18].
Thus, nanotube is of sufficient interest as possible in-
strument for deflection of high-energy beams of posit-
ively as well negatively charged particles.
ACKNOWLEDGMENTS
The work is partly supported by the INTAS project
(grant №97-30392) and by the grant №00-02-16337
from RFBR.
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ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2000, №2.
Серия: Ядерно-физические исследования (36), с. 3-6.
120
A.A. Greenenko a, N.F. Shul’ga a,b
a National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
PACS: 05.45. -a; 07.05.Tp; 29.27.Ac; 61.82.Rx
1. INTRODUCTION
2. BEAM DEFLECTION AND SPLITTING UNDER SCATTERING BY CRYSTAL ATOMIC STRINGS
3. PARTICLE CHANNELING AND DECHANNELING IN NANOTUBE
4. BEAM DEFLECTION UNDER AXIAL CHANNELING IN A BENT NANOTUBE
ACKNOWLEDGMENTS
REFERENCES
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| id | nasplib_isofts_kiev_ua-123456789-79438 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T17:27:59Z |
| publishDate | 2001 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Greenenko, A.A. Shul’ga, N.F. 2015-04-01T19:55:22Z 2015-04-01T19:55:22Z 2001 Passage of positively and negatively charged particles through straight and bent nanotubes / A.A. Greenenko, N.F. Shul’ga // Вопросы атомной науки и техники. — 2001. — № 6. — С. 118-120. — Бібліогр.: 18 назв. — англ. 1562-6016 PACS: 05.45. -a; 07.05.Tp; 29.27.Ac; 61.82.Rx https://nasplib.isofts.kiev.ua/handle/123456789/79438 Passage of high-energy charged particles through oriented crystals and nanotubes is investigated. It is shown that the particle passage through crystals and nanotubes may to be described in the same manner. The possibility of positively and negatively charged particle deflection by bent nanotube due to axial channelling phenomenon is demonstrated. Computer simulation results for relativistic charged particle beam passage through straight and bent nanotubes are presented. The work is partly supported by the INTAS project (grant №97-30392) and by the grant №00-02-16337 from RFBR. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Electrodynamics of high energies in matter and strong fields Passage of positively and negatively charged particles through straight and bent nanotubes Прохождение положительно и отрицательно заряженных частиц через прямые и изогнутые нанотрубки Article published earlier |
| spellingShingle | Passage of positively and negatively charged particles through straight and bent nanotubes Greenenko, A.A. Shul’ga, N.F. Electrodynamics of high energies in matter and strong fields |
| title | Passage of positively and negatively charged particles through straight and bent nanotubes |
| title_alt | Прохождение положительно и отрицательно заряженных частиц через прямые и изогнутые нанотрубки |
| title_full | Passage of positively and negatively charged particles through straight and bent nanotubes |
| title_fullStr | Passage of positively and negatively charged particles through straight and bent nanotubes |
| title_full_unstemmed | Passage of positively and negatively charged particles through straight and bent nanotubes |
| title_short | Passage of positively and negatively charged particles through straight and bent nanotubes |
| title_sort | passage of positively and negatively charged particles through straight and bent nanotubes |
| 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/123456789/79438 |
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