STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA

The solution to Eq. (1.3) is
U(t) = Uoe −t/τL (1.4)
where Uo is the stored energy at t = 0 and τL = QL/ω, is the decay time constant.
Because SRF cavities are characterized by their very high quality factors, they are
exceptionally good at storing energy. For example, an SRF cavity operating at
1500 MHz with a QL of 2×10 7 would have a time constant of 13 ms. On the other
hand, for a normal conducting cavity operating at the same frequency, the loaded
Q is typically 3 orders of magnitude lower and leads to a time constant of 13 µs.
While a high quality factor for the accelerating mode is desirable, care must be
taken to reduce, or damp, the quality factors of HOMs. If not sufficiently damped,
the energy deposited into these modes by the beam will remain on time scales long
enough such that multibunch instabilities, like beam breakup, develop.
The shunt impedance is a quantity used to characterize losses in a cavity and
is defined as
Ra =
V 2
acc
Pdiss
8
(1.5)
where Vacc is the accelerating voltage and Pdiss is the power dissipated on the cavity
walls. From Eq. (1.5) it is clear that the goal is to maximize the shunt impedance
for the accelerating mode in order to minimize the power dissipated. The reverse
is true for higher-order modes, where the aim is to decrease the shunt impedance.
Taking the ratio of Eq. (1.5) and Eq. (1.1) results in another useful figure of merit
Ra
Qo
= V 2
acc
ωU
(1.6)
which depends solely on the geometry of the cavity. The ratio (R/Q) of a mode is
used to indicate the extent to which the mode is excited by passing charges. In that