Abstract

Tomographic methods have the potential for useful application in beam diagnostics. The tomographic reconstruction of transverse phase space density from turn-by-turn profile data has been studied with particular attention to the effects of dispersion and chromaticity. It is shown that the modified algebraic reconstruction technique (ART) that deals successfully with the problem of non-linear motion in the longitudinal plane cannot, in general, be extended to cover the transverse case. Instead, an approach is proposed in which the effect of dispersion is deconvoluted from the measured profiles before the phase space picture is reconstructed using either the modified ART algorithm or the inverse radon transform. This requires an accurate knowledge of the momentum distribution of the beam and the modified ART reconstruction of longitudinal phase space density yields just such information. The method has been tested extensively with simulated data.

Highlights

  • Tomographic methods have the potential for useful application in beam diagnostics

  • If higher order effects are neglected, transverse phase space density performs a rigid rotation in phase space for each turn in a circular machine

  • This is manifest in normalised phase space, where all particles follow circular trajectories, rotating at the betatron frequency

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Summary

The Algebraic Reconstruction Technique

Tomographic methods have the potential for useful application in beam diagnostics. The tomographic reconstruction of transverse phase space density from turn-by-turn profile data has been studied with particular attention to the effects of dispersion and chromaticity. An approach is proposed in which the effect of dispersion is deconvoluted from the measured profiles before the phase space picture is reconstructed using either the modified ART algorithm or the inverse Radon Transform. This requires an accurate knowledge of the momentum distribution of the beam and the modified ART reconstruction of longitudinal phase space density yields just such information.

The Inverse Radon Transform
The Problem of Dispersion
Modified ART with Dispersion
Deconvolution of Dispersive Effects
How to Measure the Dispersive Spread?
Simulation and Reconstruction Codes
Reconstructions
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