STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA

TABLE 2.4: Fractional energy spread measured at various locations in the machine with
the injector set to 56 MeV.
Location ∆E/E (10 −3 ) Energy (MeV)
Injector 0.32 ± 0.01 56
Arc 1 0.0080 ± 0.0023 556
Arc 2 0.020 ± 0.0018 1056
TABLE 2.5: Fractional energy spread measured at various locations in the machine with
the injector set to 20 MeV.
Location ∆E/E (10 −3 ) Energy (MeV)
Injector 0.15 ± 0.01 20
Arc 1 0.0072 ± 0.0010 520
Arc 2 0.0100 ± 0.0014 1020
For example, with an injection energy of 20 MeV, the intrinsic fractional energy
spread is 0.15 × 10 −3 . With appropriate scaling, and for a perfectly phased linac,
the arc 1 energy spread is expected to be [48]
∆E
=
E 520
∆E
E
20
2 20
+
520
δφ4 2
55
(2.19)
where δφ is the rms bunch length in radians. Using the measured data, the con-
tribution to the energy spread from the bunch length can be calculated. Plugging
in values and solving for the bunch length yields 0.14 ◦ (rms). The expected energy
spread in arc 2 can be calculated using Eq. (2.19) by modifying the energy scaling
factor from (20/520) to (20/1020). The result is 0.0052 × 10 −3 and is 74% smaller
than the measured value. The effect of RF crest phasing errors can cause increases
in the observed fractional energy spread and can account for this discrepancy. The
effect is illustrated in Fig. 2.18 and described by
∆E = E cos(φo + δφ) − cos(φo − δφ)
(2.20)
where φo is the error in RF phase relative to on-crest acceleration. Equation (2.20)