STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
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TABLE 4.1: Experimental measurements of HOM polarizations of dangerous dipole<br />
modes in zone 3.<br />
Cavity Mode Frequency QL Orientation<br />
(MHz) (10 6 ) (degrees)<br />
8<br />
7<br />
4<br />
3<br />
TM110 3π/7<br />
TM110 4π/7<br />
TM110 3π/7<br />
TM110 4π/7<br />
TM110 3π/7<br />
TM110 4π/7<br />
TM110 3π/7<br />
TM110 4π/7<br />
2102.591 2.61 84 ± 11<br />
2103.009 0.21 8 ± 13<br />
2113.346 3.10 80 ± 2<br />
2114.154 0.35 11 ± 2<br />
2105.999 6.11 88 ± 2<br />
2106.697 0.33 4 ± 1<br />
2116.583 6.66 86 ± 10<br />
2117.225 0.49 4 ± 1<br />
2102.537 0.27 25 ± 1<br />
2102.642 0.63 63 ± 1<br />
2113.991 0.37 33 ± 1<br />
2114.151 5.21 87 ± 6<br />
2104.201 2.49 38 ± 1<br />
2104.408 0.29 14 ± 1<br />
2115.386 2.88 75 ± 1<br />
2115.683 0.39 18 ± 2<br />
4.7 Validity of Single Mode Threshold Current<br />
Formula<br />
The analytical results of Sections 4.2 and 4.4 are very powerful provided they<br />
are applied properly. While Eq. (4.21) holds for coupled transverse optics, consider<br />
for the moment only decoupled optics (M14 = M32 = 0). The first criterion that<br />
must be satisfied is an assumption made in deriving the threshold current formula,<br />
namely, that the HOM voltage decay is negligible on the scale of the recirculation<br />
time. Furthermore, in any real world accelerator there will be more than one dipole<br />
HOM present in the linac, even if the linac consists of only a single cavity. So then,<br />
the second criterion for applying Eq. (4.21) to individual modes is that the modes<br />
106<br />
are separated in frequency by at least ω/2QL. Modes which are separated less than