Tomographic measurements of longitudinal phase space density

Tomography - the reconstruction of a two-dimensional image from a series of its one-dimensional projections - is now a very broad topic with a wealth of algorithms for the reconstruction of both qualitative and quantitative i mages. One of the simplest algorithms has been modified to take into accoun t the nonlinearity of large-amplitude synchrotron motion in a particle acce lerator. This permits the accurate reconstruction of longitudinal phase spa ce density from one-dimensional bunch profile data. The algorithm was devel oped in Mathematica(TM) in order to exploit the extensive built-in function s and graphics. Subsequently, it has been recoded in Fortran 90 with the ai m of reducing the execution time by at least a factor of one hundred. The c hoice of Fortran 90 was governed by the desire ultimately to exploit parall el architectures, but sequential compilation and execution have already lar gely yielded the required gain in speed. The use of the method to produce l ongitudinal phase space plots, animated sequences of the evolution of phase space density and to estimate accelerator parameters is presented. More ge nerally, the new algorithm constitutes an extension of computerized tomogra phy which caters for nonrigid bodies whose projections cannot be measured s imultaneously. (C) 1999 Elsevier Science B.V.