Transverse cooling and heating in ion channeling

Abstract

In contrast to predictions from the standard theory of ion channeling we have observed strong redistributions of initially isotropic ion beams after transmission of thin crystal foils. Depending on the experimental parameters, there can be strong enhancements, corresponding to ''transverse cooling,'' or strong reductions, ''transverse heating,'' of the ion flux along a crystal axis or plane. For most ions there is a transition from cooling to heating when the ion energy is decreased, which depends on the crystal direction and on the atomic numbers of the ion and of the crystal atoms. In this paper we present an overview of this newly discovered phenomenon. Redistribution of an initially isotropic flux violates basic symmetries in the theory of channeling. We have argued earlier that the observed transverse cooling or heating can be understood as a consequence of fluctuations in the charge state of the channeled ions, but a detailed explanation of the transition from cooling to heating has yet to be established. A theoretical description is the most difficult for ions with many electrons. A different type of simulation has been developed based on n-body classical trajectory Monte-Carlo procedures and the first results are discussed.

Classical many-body-approach to transverse cooling and heating in ion channeling

“…Under such circumstances it is hardly possible to measure any redistribution of the channeled vs. the non-channeled flux. But our group has found very strong angular flux redistributions when using ion beams that were initially nearly isotropic within the acceptance angle of the detector [1,5]. These experiments show strong violations in the sense that, depending on experimental conditions, an initially isotropic flux can be enhanced along crystal directions by up to a factor of 4 or be reduced by a factor of 5 ( Fig.…”

“…[5]. In addition, the average thermal amplitude q therm ¼ 0:08 Å of the atoms in a Si-lattice has been drawn as a horizontal line in Fig.…”

“…Assuming the experimental arrangement of Ref. [5] where a Si crystal is illuminated with ions of a charge state distribution corresponding to random incidence, he calculates how this distribution is changed after traversing the crystal along the h1 0 0i axis. It turns out that both in case of cooling and heating the distribution is shifted to larger charge states.…”

“…In a first attempt to explain the phenomena it was argued, that if the mean capture radius is smaller than the mean loss radius, a net irreversible loss of transverse momentum follows, hence transverse cooling, while the reversed condition would lead to transverse heating [1,8]. However, in face of the body of experimental data gathered in the meanwhile [5], a much more complex behavior was seen which prevents any explanation in such simple terms -especially the transition behavior, which was found to depend on ion type and energy.…”

Using channeling properties for studying the impact-parameter dependence of electron capture by 20-MeV/u uranium ions in a silicon crystal

“…This is due, on the one hand, to transverse energy changes related to charge exchange and, on the other hand, to multiple scattering. Let us first evaluate the influence of charge exchange, which has been studied in detail by Grüner et al [22]. The variation (where ψ c is the Lindhard critical angle) that is of the order of 1 eV for Q ∆ =1 in the <110> direction.…”