Lattice Modules
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used. For example, the DBA lattice of the Shanghai Synchrotron Radiation
Facility (SSRF), Shanghai, China, contains two quadrupole doublets between
the bending magnets and two triplets outside. In fact, almost all synchrotron
light sources built in the past decade adopted DBA lattices.
9.3 Special Purpose Modules
9.3.1 The Low Beta Insertion
In both circular and linear colliders, the beam is focused as tightly as possible at the collision points to maximize the density of particles and hence
collision rate. The simplest low beta insertion consists of two quadrupole
doublets placed and excited symmetrically about the interaction point. The
upstream doublet is roughly a parallel–to–point system, in which an initially
nearly parallel beam is brought down to a small point and the downstream
doublet is a point–to–parallel system. In hadron colliders where the emittance
is relatively big, triplets are used to increase focusing power and reduce the
width of the beam in the quadrupoles. In addition, it provides more flexibility
for tuning.
Recall from eq. (6.13) that
β(s) = β
∗ +
s
2
β ∗ .
Since the distance between the interaction point and the last quadrupole is
on the order of 10 m and β
∗ is below 1 m, the β functions in the quadrupoles
range from hundreds m to over 1 km (see Fig. 9.11). Combined with high
gradient in the quadrupoles, the low beta insertion generates large chromatic
and geometric aberrations. In hadron colliders, due to the relatively large
emittance, the main effect of the aberrations is the additional chromaticities,
which are corrected by the sextupoles in the arcs. In addition, the large beam
size at the quadrupoles implies extra tight tolerances on multipole errors in
those quadrupoles, which, if too large, would excite undesirable resonances
causing emittance and/or beam loss. In electron-positron linear colliders,
the emittance is small and the aberrations generated by the low beta insertion would cause sizable increase in beam size at the interaction point. As a
result, the matching section between the low beta section and the linear accelerator (linac) is rather complicated. Telescopes are used to minimize certain
aberrations and sextupoles are used to correct chromatic aberrations.
235
used. For example, the DBA lattice of the Shanghai Synchrotron Radiation
Facility (SSRF), Shanghai, China, contains two quadrupole doublets between
the bending magnets and two triplets outside. In fact, almost all synchrotron
light sources built in the past decade adopted DBA lattices.
9.3 Special Purpose Modules
9.3.1 The Low Beta Insertion
In both circular and linear colliders, the beam is focused as tightly as possible at the collision points to maximize the density of particles and hence
collision rate. The simplest low beta insertion consists of two quadrupole
doublets placed and excited symmetrically about the interaction point. The
upstream doublet is roughly a parallel–to–point system, in which an initially
nearly parallel beam is brought down to a small point and the downstream
doublet is a point–to–parallel system. In hadron colliders where the emittance
is relatively big, triplets are used to increase focusing power and reduce the
width of the beam in the quadrupoles. In addition, it provides more flexibility
for tuning.
Recall from eq. (6.13) that
β(s) = β
∗ +
s
2
β ∗ .
Since the distance between the interaction point and the last quadrupole is
on the order of 10 m and β
∗ is below 1 m, the β functions in the quadrupoles
range from hundreds m to over 1 km (see Fig. 9.11). Combined with high
gradient in the quadrupoles, the low beta insertion generates large chromatic
and geometric aberrations. In hadron colliders, due to the relatively large
emittance, the main effect of the aberrations is the additional chromaticities,
which are corrected by the sextupoles in the arcs. In addition, the large beam
size at the quadrupoles implies extra tight tolerances on multipole errors in
those quadrupoles, which, if too large, would excite undesirable resonances
causing emittance and/or beam loss. In electron-positron linear colliders,
the emittance is small and the aberrations generated by the low beta insertion would cause sizable increase in beam size at the interaction point. As a
result, the matching section between the low beta section and the linear accelerator (linac) is rather complicated. Telescopes are used to minimize certain
aberrations and sextupoles are used to correct chromatic aberrations.