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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6.2.3 Discussion<br />
The method of point-to-point focusing proved to be a straightforward and effec-<br />
tive method to suppress BBU much of the time. This is due to the fact that there is<br />
only a single dangerous mode that prohibits operation with 10 mA of beam current<br />
(see Table 4.2). One of the attractive features of this method is that the beam optics<br />
remain decoupled transversely and that the beam envelopes are minimally effected.<br />
There are, however, some limitations to this method. For an extended linac<br />
containing many dangerous modes, it may not be advantageous to modify the phase<br />
advance. While one mode may be stabilized, in all likelihood the resulting change in<br />
phase advance will have harmful effects on other modes which were previously not a<br />
threat for BBU. Although this was never investigated in earnest, there is evidence to<br />
suggest that this situation occurred in the FEL when the threshold current became<br />
as low as 400 µA. Adequate suppression was generated for the HOMs in cavity 7,<br />
but the resulting change in phase advance caused an order of magnitude increase in<br />
the M34 element of the recirculation matrix from cavity 1 back to itself, from which<br />
BBU was facilitated at an even lower threshold current. Therefore care should be<br />
taken when applying this method to large-scale ERLs with extended linacs.<br />
6.3 Local Reflection<br />
The idea behind implementing a local reflector is to map a BBU-induced vertical<br />
kick into the horizontal plane, and likewise to map a BBU-induced horizontal kick<br />
into the vertical plane. The transport matrix describing a reflection about a plane<br />
at 45 ◦ to the horizontal or vertical axis takes the following form, where each element<br />
represents a 2 × 2 matrix<br />
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