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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measured HOMs in zone 3, a BTF measurement was performed to determine if the<br />
mode posed a threat for causing BBU. The results of the measurement show that<br />
the mode is stabilized. The reason why 2106 MHz is unstable and 2116 MHz is<br />
pseudo-stable can be readily explained from Eq. (4.21). Since the machine optics<br />
are decoupled, M32 = M14 = 0. From the measurements discussed in Section 4.6.2,<br />
both modes are vertically polarized, α = 90 ◦ , and M ∗ reduces to M34. From the<br />
88 MeV machine lattice, the sign of M34 from cavity 7 back to itself is negative (for<br />
this discussion the magnitude is not important). It follows that for the recirculation<br />
time of the FEL Driver, 433.199 ns, that M34 sin(ω2106Tr) < 0 and 2106.007 MHz<br />
is unstable, whereas M34 sin(ω2116Tr) > 0 and 2116.585 MHz is in the pseudo-stable<br />
regime.<br />
As a historical aside, note that a technique similar to the BTF measurement<br />
was used to determine the threshold current at the Stanford SCA during the earliest<br />
experimental work on BBU [10, 80]. An external source was used to excite the HOM<br />
and the response measured from a different port. Measuring the power radiated<br />
without beam and in the presence of beam in the cavity, the threshold current could<br />
be calculated [81].<br />
5.4.4 Growth Rate Measurements<br />
With the flexibility in the beam bunching structures allowed by the Driver’s<br />
injector, it is possible, in addition to observing BBU in cw mode operation, to<br />
observe and measure BBU developing within a sufficiently long macropulse in pulsed<br />
mode operation. The evolution of the HOM voltage at currents above or below the<br />
threshold current is described by Eq. (5.7). This voltage behavior is illustrated in<br />
Fig. 5.15 where the cavity voltage as measured through a Schottky diode is plotted<br />
130<br />
against time for two 9 ms long macropulses of differing currents. The exponential