Urs Rohrer and Werner Joho, SIN

Beam Tomography Tomography is a method for reconstructing a multidimensional source from a number of selected projections. Its initial and best known applications today are in medical radiology. The goal of two-dimensional beam tomography is the reconstruction of the probability distribution in two-dimensional phase space from a few (at least three, one near a waist) measured profiles. The method is non-destructive, i.e. the emittance may be monitored on line at 120 uA (beam power 70 kW at 590 MeV). The reconstruction is done using the computer programme MENT2A [1], which we received from Los Alamos. The algorithm for reconstructing the distributions is designed to converge to a solution with maximum entropy [2] or - in other words - yields an image with the lowest information content consistent with the measured profile data. The incomplete information concerning the beam (only a few projections) is thus supplemented by demanding that the probability distribution has the smoothest shape permitted by the profile data [3]. The initial code was changed so that both drift-lengths and quadrupole lenses may be placed between the profile monitors. This modification was necessary to increase the amount of available data for firmer values of the emittances. The phase space distribution of a beam may also be monitored by measuring profiles at the same location with different quadrupole excitations, but the transfer matrix elements of the lenses must be well known. At SIN, beam tomography has been tested successfully with three proton beam lines (IW1, PKM and PKB) and with two pion beam lines (piE1 and uE1). Figure 1 shows results from the 590 MeV proton beam line (PKM, horizontal plane). The method of data taking using a small dedicated computer (PDP 11/24) and that of fitting the data and producing graphical output of the results using a more powerful computer (VAX 11/782) has been described elsewhere. In order to avoid the formation of artifacts during the reconstruction of the phase space distribution, two digital filters were added to the code. With the help of a fast Fourier transform (FFT) noisy profile data may be smoothed. In addition the bandwidth of the functions needed for the reconstruction (H-factors) may also be limited. Computing the emittance from measured profile widths (4 sigma) with the programme TRANSPORT [5] and comparing it with the corresponding value extracted from the log(1-f) diagram (see Fig. 1 and Ref.[6]) shows no difference within the error (ex = 2 pi mm mrad, f = 1-e-² = 0.86, f = fraction of beam inside emittance ex). It was observed that beam tomography based on the MENT algorithm tends to overestimate the emittances, whereas TRANSPORT tends to underestimate them. For beam lines where the available profile data come from optically unfavorable locations, the values extracted from the two methods may differ by a factor of two.

Beam Tomography

Fig. 1 (caution: not exactly the same as in the annual report !! )

Urs Rohrer, Werner Joho Example of the horizontal emittance in the proton channel. The measured beam profiles (MHP5, MHP7, MHP9, MHP11, MHP13 and MHP15) are shown. The data points are marked with + symbols. The curves through these points are the projections of the reconstructed (x,x')-distribution, which is shown as a contour-diagram and as a three-dimensional plot at the z-coordinate of MHP11 (near waist). A quadrupole pair is placed between MHP7 and MHP9. Also plotted is the function log(1-f) versus ex. In this representation beams with gaussian profile shapes produce straight lines. Deviations from gaussian can therefore be seen very easily.


[1] Beam Tomography in two and four Dimensions, O.R. Sander, G.N. Minerbo, R.A. Jameson and D.D. Chamberlin, 1979 Linear Accelerator Conference, Report BNL-51134, Brookhaven Nat. Lab., Upton, NY (1980) p. 314 - 318
[2] MENT: A Maximum Entropy Algorithm for Reconstructing a Source from Projection Data, Gerald Minerbo, Computer Graphics and Image Processing 10 (1979) p. 48 - 68
[3] On the Rational of Maximum-Entropy Methods, Edwin T. Jaynes, Proceedings of the IEEE 7O (1982) p. 939 - 952
[4] SIN Annual Report 1980, p. 15, 32 and 33
[5] TRANSPORT: A Computer Program for Designing Charged Particle Beam Transport Systems, K.L. Brown, D.C. Carey, Ch. Iselin and F. Rothacker, CERN 80-04 (Geneva, 1980)
[6] Representation of Beam Ellipses for Transport Calculations, W. Joho, SIN-Report TM-11-14 (1980) p. 30

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Beam Tomography Beam Tomography Last updated by Urs Rohrer on 1-Mar-2006