Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms
Monte Carlo modeling of crystal channeling at high energies
Introduction
Crystals are increasingly used in synchrotrons around the world for their channeling properties. At CERN, they are considered as an option for the collimation system upgrade of the LHC taking place in the next years. This creates the need for a tool being able to track beam particles and secondaries in the crystal environment, be it in amorphous or channeling mode. Planar channeling consists in the passage of well-oriented charged particles in-between lattice planes. In this paper, we treat planar channeling of positively charged particles. The model is foreseen to be adapted to negatively charged particles in the future.
At CERN, the Monte Carlo code FLUKA is used for beam-machine interaction studies [1], [2]. In view of the possible use of crystals as an important ingredient of the future collimation system, a comprehensive tool is needed to track particles through crystals in channeling orientation. This will enable energy deposition calculations in crystals as well as the tracking of secondaries downstream. The tools presently available do not allow such an investigation. On the one hand, standard tracking codes (like SIXTRACK [3] or ICOSIM [4]) have been interfaced to an empirical description of crystal effects tuned to particular conditions [5]. On the other hand, more sophisticated crystal models (for example [6]) are not yet integrated into the mentioned codes being regularly used to assist the design and the operation of big accelerators.
In Section 2, we describe the main features of this semi-classical, microscopic model developed from scratch. Channeling conditions are determined through comparison of the energy of the particle transverse motion with the continuous potential introduced by Lindhard [7]. Channeled particles follow crystal channels unless dechanneling occurs based on Coulomb scattering events and have an altered interaction rate based on the amplitude of their oscillatory path. Single scattering also leads to the capture of quasi-channeled particles. In addition, volume reflection is implemented according to Bondarenco’s geometrical model [8]. Section 3 is dedicated to the benchmarking of the model with experimental data from the UA9 collaboration, in particular from runs using a 400 GeV/c proton beam extracted from CERN SPS [9]. Section 4 is devoted to conclusions.
Section snippets
Geometry
Crystals, as modeled in the considered framework are defined through two orthogonal vectors, as shown in Fig. 1. The first one, denoted as A, indicates the channel orientation and the second, B, also belongs to the crystal planes that form the channels. For the sake of example, we assume here that A is along the z-axis and B is along the y-axis at the crystal entry face. Actually, our implementation is intended to treat a crystal region with any orientation, as included in a potentially much
Results and discussion
Crystal collimation could allow to achieve better collimation efficiency and reduce radiations levels in the concerned areas [15]. Over the last years, the UA9 collaboration has been assessing the quality of a number of crystals in CERN North Area on the H8 beamline extracted from SPS [9] before installing them in the second UA9 experiment situated in the SPS, where they operate in multi-turn regime.
Comparison of the model results with data from these experiments is presented hereafter. Typical
Conclusions
In this paper we described a model of coherent interactions of beam particles with crystals. Channeling is represented by reduced interaction rates and faculty for particles to follow the channel direction throughout their travel in the crystal. Particles get channeled if the transverse energy, calculated on the basis of the incoming angle and random sampling of the initial position in the channel, is smaller than the continuous potential barrier. Dechanneling is reproduced via microscopic
Acknowledgement
We acknowledge the support from UA9 collaboration colleagues and we especially thank W. Scandale for fruitful discussions about different aspects of the project.
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