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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linac and θNL is the RF phase. The energy of the beam in arc 2 is<br />
EA2 = Einj + ENL cos θNL + ESL cos θSL<br />
34<br />
(2.3)<br />
where ESL and θSL are the energy gain and RF phase in the south linac, respectively.<br />
The energy of the second pass beam through arc 1 is<br />
E (2)<br />
A1 = Einj + ENL cos θNL + ESL cos θSL + ENL cos(θNL + δ) (2.4)<br />
where δ is the change in RF phase due to the effect of passing through the phase<br />
delay chicane. For perfect energy recovery, the energy gained on the first pass<br />
exactly cancels the energy lost by the second pass beam through the north linac.<br />
The energy in arc 1 is then<br />
E (2)<br />
A1 = Einj + ESL cos θSL<br />
(2.5)<br />
Equation (2.5) says that for perfect energy recovery, δ = π, the energy of the second<br />
pass beam in arc 1 is independent of θNL. Through an iterative process of adjusting<br />
the field strength of the phase delay chicane dipole string (to vary the path length)<br />
and then varying the RF phase in the north linac, the condition of Eq. (2.5) could<br />
be satisfied.<br />
The strategy for threading the beam through the machine was to use minimal<br />
steering on the first pass. In that way local corrections could be used to alleviate<br />
any harmful RF effects incurred on the second pass. At low energy, and particularly<br />
on the second pass, transverse coupling was present. The source of this coupling<br />
is the presence of the skew quadrupole fields in the waveguide HOM coupler. This<br />
coupling was observed, for example, by inserting a beam viewer and watching the<br />
beam spot move diagonally across the screen when steering with a horizontal (or