Multiple scattering of channeled ions in crystals

The generalized local Boltzmann equation is derived for the distribution function of energetic particles interacting with the thermal vibrations of the lattice. On using the Boltzmann collision term the particle energy losses A(&,) and the diffusion function B(EJ.) are obtained. The functions A ( e l ) and B(E,) have singularities (fracture, peak) connected with the difference of the contributions of the particles moving in the regimes of channeling, quasichanneling, and random motion. L'Cquation locale gCnCra1isi.e de Boltzmann est obtenue pour la fonction de la distribution des particules BnergCtiques cooperant avec les vibrations thermique du rBseau. Les pertes BnergBtiques des particules A(&,) et la fonction de diffusion B ( E~) sont obtenus sur la base du terme de collision de Boltzmann. Les fonctions A ( E~) et B ( E~) ont les particularitCs (fracture, pic) likes avec la diffBrence entre les contributions des particules mouvant dans le rBgime canale, quasicanale et dans le mouvement chaotique.

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“…(12) are small. Therefore, the collision term ( l l b ) may be expanded in terms of powers of and 5.…”

Section: Energy Losses and Diffusion Function In First Born Approximamentioning

confidence: 96%

“…However, the coefficients which are derived on the basis of local kinetic equations [5, 12,17 to 201 have only a limited interest since all proofs of these equations contain rough approximations. In [23] the author developed a more consistent derivation on using the Schrodinger equation.…”

Section: Introductionmentioning

confidence: 99%

Diffusion model of dechanneling based on the Boltzmann equation: Three regimes of energetic particle motion in crystals

Kashlev

Sadykov

1996

Physica Status Solidi (b)

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“…The first term in brackets of the above expression can be written in a more convenient way, using (2) and (3), as follows Because of (13) the left-hand side of ( 5 ) (we use the symbol L for it) becomes…”

Section: At P Z Atmentioning

confidence: 99%

The Exact Fokker‐Planck Type Equation for Planar Channeling of Relativistic Positrons

Doumanis¹,

Trikalinos²

1993

Physica Status Solidi (b)

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The motion of relativistic positrons under the planar channeling regime is investigated. The corresponding Fokker-Planck type equation is established considering the longitudinal momentum as constant and then taking into account the exact expressions for the transverse and longitudinal energy. Thus we conclude on the exact form of the Fokker-Planck type equation. An approximate solution is given without taking into account multiple scattering. This solution, although approximate shows that we have the phenomenon of particles that spread out of the channel instead of damping. The exact solution of the equation requires computer calculation. Our result may be used for the explanation of stronger dechanneling of relativistic particles in planar channeling where the intensity of channeling radiation is less than the expected one.Le mouvement de positrons relativistes en canalisation plane est considere. L'equation correspondante de type Fokker-Planck est etablie, en considerant le moment longitudinal constant et ensuite en utilisant les expressions exactes pour I'energie transverse et longitudinale. On obtient ainsi la forme exacte de l'iquation de type Fokker-Planck. La solution approximative de cette equation est donnee dans le cas od on ne considere pas les collisions multiples. Cette solution malgre le fait qu'elle est approximative prouve que les particules sortent plus facilement du canal au lieu de ce concentrer au centre. Ce resultat peut itre utilise pour l'explanation de la decanalisation plus forte des particules relativistes en canalisation plane od l'intensite du rayonnement de canalisation est moins forte que celle qu'on attend.') Panepistimiopolis, Ilissia, 15 771 Athens, Greece. 5*

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Spatial distribution of channeled ions

Kumakhov¹,

Muralev²

1981

Phys. Stat. Sol. (a)

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An investigation is made of the dependence of distributions of implanted heavy ions, with the inclusion of the channeling effect, upon the initial ion energy, the thickness of the amorphous layer on the crystal surface, the direction of target irradiation, the target temperature, the angle of orientation of the ion beam with respect to the channel axis, the type of irradiating ions, and the radiation dose. Problems of capture of ions into channels are also considered. TeopeTHsecm H3ysaIOTCH npOCTpaHCTBeHHbIe paCnpeAeneHHH KaHaJlHpOBaHHbIX IlOHOB B 3aBHCIlMOCTH OT Ha%lJlbHOfi 3HeprEIH EIOHOB, OT TOJIlrlIlHbI aMOp@HOI' O CJIOH Ha no-BePXHOCTH KpHCTaJlJla, OT HaIIpaBJleHHH o 6 n y y e~~~ MHUIeHH, OT TeMIlepaTyphI MEIUleHIl, OT yrna MeKay ocbm KaHana H HanpaBnemeM nywa, OT copTa EIOHOB, OT ~0 3~ o6ny-YeHHH. 06CyKn~ieTCH TaKxie npo6ne~a 3 a x~a~a HOHOB B HaHan. 117234 Moscow, USSR.

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Multiple scattering of channeled ions in crystals

Cited by 53 publications

References 5 publications

Diffusion model of dechanneling based on the Boltzmann equation: Three regimes of energetic particle motion in crystals

Diffusion model of dechanneling based on the Boltzmann equation: Three regimes of energetic particle motion in crystals

The Exact Fokker‐Planck Type Equation for Planar Channeling of Relativistic Positrons

Spatial distribution of channeled ions

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