In the channeling of relativistic particles, the commonly used expression for the "transverse kintic energy!! is / 1 / Jt is the instantaneous angle between $ and the channeling direction. Expression
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.
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General considerationsWe consider the case of planar channeling. Under planar channeling regime a continuum potential determines the motion of a particle [l]. The expression for the continuum planar potential is [l, 21 where e is the distance of the point we consider from the crystal plane, R is the distance on the plane from the projection of the point, V ( r ) is an atomic screened Coulomb potential, a is the screening length, and n is the areal density of atoms.Two of the most commonly used and most accurate screening functions are those of Moliere [2 to 41 and the "Universal" one [5]. Both The potentialinside a crystal Expression (1) gives the potential for a particle, on a plane from which the particle's distance is e. But inside a crystal the potential is a result of the interaction with all the planes of the crystal lattice. In practice for the potential at a specific point two or at most a few planes were taken into account, by summing their contributions to the total potential. These calculations do not result in simple analytic expressions, easy to handle for further use.We proceed instead along the following way: suppose that a point P is at a distance e from one plane, say plane A, as shown in Fig. 1. We put d = dJ2. For a particle with l ) Panepistimiopolis, Ilissia, GR-15771 Athens, Greece.39 physica (b) 18012
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