quadrupoles, higher-energy particles tend to be to the outside of the ideal orbit,
while lower-energy particles tend to be inside that orbit. Sextupoles can reverse
chromatic aberrations due to the quadrupoles by providing more focusing power on
the outside of the orbit and less on the inside. (Going beyond sextupoles, one of the
world’s most recent storage rings, Max-IV, uses a lattice that even includes octupole
magnets [14–16].)
2.3.4 Storage Ring Lattices
The array of magnets that guides a charged particle beam along the desired trajectory
in the storage ring is called the lattice. To simplify the design of storage rings,
lattices are divided into sectors that contain a particular sequence of magnets. These
superperiods are repeated a number of times to form most of the complete ring.
There are often smaller groups of magnets, called cells, which also repeat within a
superperiod. One superperiod of the APS lattice is shown in Fig. 2.7. The
superperiod structure determines the fundamental properties of the storage ring,
such as the size and divergence of the beam as well as its stability.
The complexity of magnet lattices continues to increase as machine physicists
seek to reduce the emittance (see below) of their storage rings. A state-of-the-art
storage ring has nearly 1000 magnets in the lattice! For example, NSLS-II uses
60 dipoles, 240 quadrupoles, 260 sextupoles, and ~270 “large aperture” and “corrector magnets” [17]. The MAX-IV storage ring has 20-fold symmetry, and each
superperiod employs 7 dipole, 16 quadrupole, and 18 sextupole magnets [14–
16]. Not to be outdone, the new lattice for the upgraded ALS, “ALS-U,” will have
nine dipole magnets in each superperiod.
2.3.5 Beam Perturbations and Loss Mechanisms
In practice, none of the electrons in a storage ring follow the ideal orbit for long. In
part, this is because electrons lose energy by synchrotron radiation as they travel
around the ring. The electrons are restored to the correct orbit by the focusing effect
of the quadrupole magnets and by differential acceleration in the rf cavity. Thanks to
these restoring forces, the particles oscillate around the ideal orbit. The longitudinal
motions around the ideal position are called synchrotron oscillations, while the
transverse motions are called betatron oscillations. The number of horizontal or
vertical betatron oscillations that occur during one revolution around the ring is
called the tune.
Machine physicists work hard to avoid integer values for the tune. Why? Suppose
there is some perturbation in the ring that causes an unwanted motion of the particle
beam. If the tune is an integer, then this perturbation will add in-phase during each
particle orbit, ultimately leading to loss of the beam. This is circumvented by using
tune values that avoid integers, as well as integer ratios of x and y tunes, as illustrated
in the “tune diagram” of Fig. 2.8.
2.3 The Storage Ring: Inside the Shield Walls
19
while lower-energy particles tend to be inside that orbit. Sextupoles can reverse
chromatic aberrations due to the quadrupoles by providing more focusing power on
the outside of the orbit and less on the inside. (Going beyond sextupoles, one of the
world’s most recent storage rings, Max-IV, uses a lattice that even includes octupole
magnets [14–16].)
2.3.4 Storage Ring Lattices
The array of magnets that guides a charged particle beam along the desired trajectory
in the storage ring is called the lattice. To simplify the design of storage rings,
lattices are divided into sectors that contain a particular sequence of magnets. These
superperiods are repeated a number of times to form most of the complete ring.
There are often smaller groups of magnets, called cells, which also repeat within a
superperiod. One superperiod of the APS lattice is shown in Fig. 2.7. The
superperiod structure determines the fundamental properties of the storage ring,
such as the size and divergence of the beam as well as its stability.
The complexity of magnet lattices continues to increase as machine physicists
seek to reduce the emittance (see below) of their storage rings. A state-of-the-art
storage ring has nearly 1000 magnets in the lattice! For example, NSLS-II uses
60 dipoles, 240 quadrupoles, 260 sextupoles, and ~270 “large aperture” and “corrector magnets” [17]. The MAX-IV storage ring has 20-fold symmetry, and each
superperiod employs 7 dipole, 16 quadrupole, and 18 sextupole magnets [14–
16]. Not to be outdone, the new lattice for the upgraded ALS, “ALS-U,” will have
nine dipole magnets in each superperiod.
2.3.5 Beam Perturbations and Loss Mechanisms
In practice, none of the electrons in a storage ring follow the ideal orbit for long. In
part, this is because electrons lose energy by synchrotron radiation as they travel
around the ring. The electrons are restored to the correct orbit by the focusing effect
of the quadrupole magnets and by differential acceleration in the rf cavity. Thanks to
these restoring forces, the particles oscillate around the ideal orbit. The longitudinal
motions around the ideal position are called synchrotron oscillations, while the
transverse motions are called betatron oscillations. The number of horizontal or
vertical betatron oscillations that occur during one revolution around the ring is
called the tune.
Machine physicists work hard to avoid integer values for the tune. Why? Suppose
there is some perturbation in the ring that causes an unwanted motion of the particle
beam. If the tune is an integer, then this perturbation will add in-phase during each
particle orbit, ultimately leading to loss of the beam. This is circumvented by using
tune values that avoid integers, as well as integer ratios of x and y tunes, as illustrated
in the “tune diagram” of Fig. 2.8.
2.3 The Storage Ring: Inside the Shield Walls
19