Dynamics of high-energy charged particles in straight and bent crystals

Abstract

The drop analyser, also termed the tensiograph, is an optical fibre-based instrument system for monitoring liquids. A comprehensive assessment of the drop analyser used as a UV-visible spectrophotometer has been undertaken employing both experimental and theoretical studies. A model of the tensiograph signal (tensiotrace) has been developed using a ray-tracing approach to accurately predict the form of the tensiotrace as an aid to drop spectroscopy. An analytical equation is derived for quantitative drop spectroscopy and the form of the equation has been experimentally tested. The equation applies to both the case of a growing drop and the situation in which the drop volume is held stationary. Measurements on both stationary and moving drops are of practical value. Modelling has been used to compute the average path length of the coupled light in the drop to give a result that compares favourably with values obtained from experimental measurements. An optimized method has been identified for quantitative drop spectroscopy measurements. Results from UV-visible studies on both pollutants in water and pharmaceuticals demonstrate the utility of this approach. Two key matters relating to the practicalities of drop spectroscopy are then discussed. Some experimental studies have been made to ascertain the practical limit in analyte concentration above which variations in transmitted light from the drop shape variations result. Here, tabulated information on a representative range of liquid types has been provided as a guide to optimized spectroscopic drop analysis. Secondly, the handling of micro-volume samples is discussed. The paper concludes with a brief evaluation of the usefulness of this drop spectroscopy approach, but specifically points to the importance of drop spectroscopy for nanoscience applications.

Channeling of high-energy particles in bent crystals – Experiments at the CERN SPS

“…However, axial de¯ection requires a beam which is well-de®ned in angles in both planes, whereas the angular acceptance along the planes for planar de¯ection is limited by the shape of the crystal only [42]. A discussion of axial de¯ection of protons and highly charged ions is given in [43,44] which present a comprehensive review of scattering by atomic strings.…”

<title>On the halo cleaning at the LHC by crystals</title>

“…8 However, it was soon demonstrated (and we will also demonstrate this) that an efficient beam deflection is only possible under the very large crystal bending radii, while under the smaller ones, which could provide deflection by the larger angles, most of particles do not follow the bent crystal axes. Most of the positively charged particles, however, are efficiently captured by crystal planes and experience considerable deflection, which could be useful for the purpose of halo cleaning at the LHC.…”

“…8 with the use of axis potential approximation making it possible to evaluate all the proton trajectory characteristics analytically. The essence of the approach 8 is the modification of the classical formulae 9 for the motion in a central field to the case of particle motion in the transverse xy-plain in the field of cylindrically symmetric "continuum" axial potential V (ρ), ρ = (x, y).…”

<title>Coherent scattering and radiation by relativistic electrons in crystals: proposals for SPARC</title>

“…The motion of above-barrier electrons in periodic field of crystal atomic strings can have regular and chaotic character. The electron collisions with different atomic strings can be considered as random at chaotic motion 4,5 . Such type of the motion is named as the dynamical chaos phenomenon.…”