Tomography as a diagnostic tool for phase space mapping of intense particle beams

A technique is described for the tomographic mapping of transverse phase space in beams with space charge. Most prior studies where performed at high energy where space charge was negligible and therefore not considered in the analysis. The tomographic reconstruction process is compared with results of simulations using the particle-in-cell code WARP. The new tomographic technique is tested for beams with different intensities (both emittance and space-charge dominated), and with different initial distributions. Effects of various errors in the data collection process on the reconstructed phase space are discussed. It is shown that the crucial factor is not necessarily the number of projections but the range of angles over which the projections are taken. This study also includes a number of experimental results on tomographic phase space mapping performed on the University of Maryland Electron Ring.

Figure 1

Tomography experimental configuration: (a) simplified diagram; (b) actual experimental setup.

Figure 2

$X^{\prime }X$ tomographic recovery of the 0.6 mA (pencil beam) using a different number of projections. (a) 30 projections, (b) 70 projections, (c) 105 projections, (d) 210 projections.

Figure 3

$X^{\prime }X$ phase space for the 0.6 mA electron beam: (a) using tomography; (b) direct WARP.

Figure 4

$X^{\prime }X$ tomographic reconstruction of the pencil beam with different overall angular spans. (a) 170 degrees, (b) 175 degrees, (c) 178 degrees, (d) 180 degrees.

Figure 5

$X^{\prime }X$ phase space distribution of the pencil beam with different simulated systematic errors. (a) 1% error, (b) 2% error, (c) 4% error.

Figure 6

$X^{\prime }X$ phase space distribution of the 7 mA electron beam: (a) by tomography; (b) by direct WARP simulation.

Figure 7

Spatial distribution of the 7 mA electron beam starting with a Gaussian velocity distribution.

Figure 8

$X^{\prime }X$ phase space distribution of the 7 mA electron beam starting with a hollow velocity distribution: (a) by tomography; (b) by direct WARP simulation.

Figure 9

Spatial distribution of the 7 mA electron beam starting with a hollow velocity distribution.

Figure 10

Phase space from simulations of the 7 mA beam after propagating for different distances, clearly indicating the propagation of transverse density waves: tomography (top) vs direct WARP result (bottom) (cf. Ref. 19). Phase space after passing through (a) 3; (b) 5; (c) 7; (d) 9; and (e) 11 quadrupoles.

Figure 11

Phase space tomography results along the UMER injector line: (a) spatial distribution at the point where recovery is done; (b) $Y^{\prime }Y$ tomographic recovery of the electron beam; (c) $X^{\prime }X$ tomographic recovery of the electron beam.