STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA

the results of the fits.
The vertical profile for both the 56 MeV and 20 MeV energy recovered beam
are well represented by a single Gaussian over the complete (5 to 6 orders of mag-
nitude) dynamic range. The horizontal profile for the 56 MeV beams shows a small
additional contribution on the left side of the plot, most likely due to beam scrap-
ing, however there still exists a good Gaussian fit over 5 orders of magnitude. The
broader width of the horizontal profile at 20 MeV is explained by the fact that the
measurement was located in a region of dispersion (0.5 m) and the width is there-
fore scaled by a factor of ∆E/E. This may account for the observed increase in
horizontal scraping and beam loss when operating with a 20 MeV injection energy.
2.6 Measuring Energy Spread
The rms beam size squared is expressed as
σ 2 = βɛg + (ηδ) 2
54
(2.18)
where η is the dispersion and δ (= ∆E/E) is the fractional energy spread. Emit-
tance measurements were performed in regions of zero dispersion so that the only
contribution to the beam size is from the beta function and the emittance. In
the same manner, the energy spread can be measured in a dispersive region where
(ηδ) 2 >> βɛg and the dispersion is known.
The results of the energy spread measurements, which were performed only on
the accelerating pass beam, are displayed in Table 2.4 and Table 2.5.
On first inspection, the energy spread data does not follow the expected scaling
relation with energy. Rather than decreasing with increasing beam energy, the
measured relative energy spreads in arc 2 are greater than in arc 1. However, by
taking into account RF phasing errors the data becomes consistent [47].