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

Greenenko, A.A.

Shul’ga, N.F.

Наукова електронна бібліотека періодичних видань НАН України (Vernadsky National Library of Ukraine)

PASSAGE  OF  POSITIVELY  AND  NEGATIVELY  CHARGED PARTICLES  THROUGH  STRAIGHT  AND  BENT  NANOTUBESA.A. Greenenko a, N.F. Shul’ga a,ba National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraineb Belgorod State University, Belgorod, RussiaPassage 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.Rx1. INTRODUCTIONIn 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 STRINGSThe 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 NANOTUBENanotubes 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)  −pi  pions:  (1,3) − straight  nan-otube,  (2,4) − bent  nanotube  with  bending  radius  R = 10 cm. Simulation statistics is 1000 particlesThe 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 NANOTUBEIn 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])2a⋅=>Hc URR 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 particlesParticle 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 isRLR =θ  , (2)where L is the nanotube thickness.119Fig. 3. Same as on Fig. 2., but for beam of −pi  pions and nanotube thickness L = 200 mµPresented 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.ACKNOWLEDGMENTSThe work is partly supported by the INTAS project (grant  №97-30392)  and  by  the  grant  №00-02-16337 from RFBR.REFERENCES1. J.W. Mintmire,  B.I. Dunlap,  C.I. White.  Are fullerene tubules metallic? //  Phys. Rev. Lett. 1992, v. 68, p. 631-634.2. A.V. Eletskii.  Carbon  nanotubes  //  Uspekhi  Fiz.  Nauk. 1997, v. 167, №9, p. 945-972.3. V.V. Klimov, V.S. Letokov. Monochromatic  γ-radi-ation emitted by a relativistic electron moving in a carbon nanotube //  Physics Letters. 1997,  v. A226, p. 244-252.4. G.V. Dedkov. Fullerene nanotubes can be used when transporting gamma-quanta, neutrons, ion beams and radiation from relativistic particles //  Nucl. Instr. & Meth. 1998, v. B143. p. 584-590.5. L.A. Gevorgian,  K.A. Ispirian,  R.K. Ispirian.  High energy particle channeling in nanotubes //  Nucl. In-str. & Meth. 1998, v. B145. p. 155-159.6. N.K. Zhevago and V.I. Glebov.  Channeling of  fast charged and neutral particles in nanotubes // Physics  Letters. 1998, v. A250, p. 360-368.7. N.F. Shul’ga,  A.A. Greenenko,  V.I. Truten’, S.P. Fomin. Passage of fast charged particles through nanotubes  //  Yad.  Fiz. 2001,  v. 64,  №5,  p. 1061-1065.8. A.A. Greenenko,  N.F. Shul’ga.  Passage  of  fast charged particles through bent crystal and nanotubes // Nucl. Instr. & Meth. 2001, v. B (to be printed).9. V.I. Truten',  N.F. Shul'ga.  Rainbow,  orbiting  and Ramsauer-Townsend-type  effect  at  fast  charged particles scattering by crystal atomic string and nan-otube // Nucl. Instr. & Meth. 2001, v. B (to be prin-ted).10.E.N. Tsyganov. Some aspects of the mechanism of a  charged particle penetration through a monocrystal. Batavia, Fermilab TM-682, 1976.11.J.F. Bak et al. Detailed investigation of the channel-ling phenomena involved in bending of high-energy beams  by  means  of  crystal  //  Nucl.  Phys. 1984, v. B242, p. 1-30. 12.A.A. Greenenko and N.F. Shul'ga.  Turning a beam of high-energy charged particles by means of scatter-ing by atomic rows of a curved crystal // JETP Lett. 1991, v. 54, №9, p. 524-528.13.A.I. Akhiezer,  N.F. Shul'ga,  V.I. Truten', A.A. Greenenko,  V.V. Syshchenko.  Dynamics  of high-energy  charged  particles  in  straight  and  bent crystals // Phys. Uspekhi. 1995, v. 38, №10, p. 1119-1145.14.A.A. Greenenko,  N.F. Shul’ga.  About  the  mechan-isms of high energy charged particle deflection by a bent crystal  //  Nucl. Instr. & Meth. 2001, v. B173, p. 178-183.15.J. Lindhard. Influence of crystal lattice on motion of energetic  charged  particles  //  Dansk.  Vid.  Selsk.  Math. Phys. Medd. 1965, v. 34, №14.16.A.I. Akhiezer  and N.F. Shul'ga.  High-Energy  Elec-trodynamics  in  matter. Amsterdam:  “Gordon  and Breach Publisher”, 1996, 388 p.17.J.A. Ellison.  Bending  of  GeV  particle  beams  by channelling  in  bent  crystal  planes  //  Nucl.  Phys. 1982, v. B206, p. 205-220.18.A. Baurichter et al. New results from the CERN-SPS beam  deflection  experiments  with  bent  crystals  // Nucl. Instr. & Meth. 1996, v. B119, p. 172-180.ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2000, №2.Серия: Ядерно-физические исследования (36), с. 3-6.120

Passage of positively and negatively charged particles through straight and bent nanotubes

http://dspace.nbuv.gov.ua/bitstream/handle/123456789/79438/25-Greenenko.pdf?sequence=1

Passage of positively and negatively charged particles through straight and bent nanotubes

Abstract

Similar works

Full text

Available Versions

Наукова електронна бібліотека періодичних видань НАН України (Vernadsky National Library of Ukraine)