548
M. Lamont et al.
Fig. 9.9 Batch compression (top to bottom) or expansion (bottom to top)
difference harmonic |h 1 − h 2 |,
V = V 1 sin h 1 ω R t + V 2 sin h 2 ω R t
= 2V 0 cos
h 1 + h 2
2
ω R t
· sin
h 1 − h 2
2
ω R t
at V 0 = V 1 = V 2 . (9.58)
In case h 1 and h 2 have common dividers, the process repeats gcd(h 1 , h 2 ) (gated
common divider) times around the circumference, which allows to compress or
expand multiple batches of bunches simultaneously.
The amount of compression achievable in a single step is limited by the
acceptance of the buckets holding the edge bunches. A consequence is that multiple
batch compression steps are necessary to reach large compression factors, and
complicated manipulations of RF parameters are involved.
Non-linear voltage programs can be applied to improve the adiabaticity of the
process [73].
9.7 Collimation
R. W. Assmann
9.7.1 Introduction
The concept of a collimator and its design are introduced in [74]. The design process
for a collimation system and several important issues are discussed in [75]. In this