The multibunch growth rates at the expected operating current of 0.536 A are given in Fig. 3.
Figure 3: Growth rates of multibunch modes for the LHC at injection.
The value of the growth rate is plotted versus the multibunch
mode number. The plot consists of several lines, one for each
type of internal-bunch motion. Each line is really M separate
points connected by a line, one point for each multibunch mode.
The computation is done for M symmetrically placed bunches,
with a total beam current of I M/kB=0.674 A. The large peak
on the left side of the figure is primarily caused by two of the
septum cavity higher order modes: the one at 516.7 MHz, and the
one at 1117.9 MHz (see Tab. 4 and
Fig. 4). The peak all the way to the
right of the figure is primarily caused by the resistive-wall
impedance.
Note that the computation is done for a symmetric filling pattern. As described in [10, 1], if one does not have a symmetric filling pattern, one can take the bunch that has the highest current, and use it's current as the current for every bunch; this will give an upper bound on the growth rate (this statement should be qualified slightly; see [1] for a discussion). Thus, for this and all remaining multibunch computations in this paper, I multiply the real total current by M/kB to get the current at which the computation is done. Thus, the plot in Fig. 3 is done at 0.674 A.
Figure 4 gives a way of determining which cavity modes generate individual peaks in Fig. 3 and subsequent figures.
Figure 4: Aid for determining the source of peaks in
Fig. 3 and subsequent figures.
Each vertical line represents one of the cavity higher order modes
given in Tabs. 4 and
7. Each line is labeled with the
frequency in megahertz of the associated cavity mode. The lower
set are from the accelerating cavities, the upper set are from
the septum cavities.