6 Design and Principles of Synchrotrons and Circular Colliders
271
beams of extremely high brightness have come into operation. To enhance the
cooling, wiggler magnets are used, producing a succession of left and right bends.
This increases the radiation and thereby the damping rates. The heating can be kept
small by placing the wiggler at locations where the focusing functions of the ring
are appropriate to make the particle motion insensitive to kicks. More details for
cooling by synchrotron radiation are given in Sect. 6.5.
Radiation cooling and lattice properties of the storage ring are thus intimately
linked and by smart design, orders of magnitude in the equilibrium emittances have
been gained. This may serve as example for other cooling techniques for which the
art of ‘low emittance lattices’ is only now emerging.
6.10.2.2 Microwave Stochastic Cooling
For (anti-)protons and heavier ions, radiation damping is almost negligible at
the energies currently accessible in accelerators except for the LHC. One of the
‘artificial’ cooling methods devised for these heavy particles is stochastic cooling
by a broadband feedback system (Fig. 6.36). The name “stochastic damping” was
coined by Simon van der Meer who invented this method in 1968 (first published
in 1972) [102] to underline the statistical basis of the method. First successful
tests and observations were done at the CERN ISR (Intersecting Storage Rings)
[102] followed by a dedicated “Initial Cooling Experiment” ICE [103]. In 1984
Simon van der Meer shared the Nobel Prize [104] in physics with Carlo Rubbia
for his contribution to the observation of the intermediate vector boson. Microwave
stochastic cooling was considered a key ingredient for reaching sufficient phase
space density of the precious and rare antiprotons to produce a small number
of W- and Z-Bosons in the CERN Super Proton-Antiproton Synchrotron (SppS)
experiment in 1982. At the core of stochastic cooling is the observation, that the
phase-space density can be increased by a system that acts to reduce the deviation
of small sections, called samples, of the beam. By measuring and correcting the
statistical fluctuations (‘Schottky noise’) of the sample averages, the spreads in the
corresponding beam properties are gradually reduced. Stochastic cooling may thus
be viewed as a ‘sampling procedure’ where samples are continuously taken from the
beam and the average of each sample is corrected. The basic principle of (transverse)
stochastic cooling is sketched in Fig. 6.36.
A somewhat different picture is based on the behavior of a test particle. At each
passage it receives its own ’coherent’ kick plus the ‘incoherent’ random kicks due
to all other sample members. The sample length T s (response-time) is given by the
bandwidth W of the system through T s ≈ 1/2W and the number N s of particles per
sample is proportional to T s . Hence a large bandwidth is important to work with
small samples. Present day cooling rings have a revolution time between a fraction
of a μs (e.g. CERN AD) up to about 20 μs (Relativistic Heavy Ion Collider (RHIC),
Fermilab bunched beam cooling systems). The sample length T s amounts usually to
less than 1 ns which corresponds to a cooling system bandwidth of 500 MHz in
this case assuming the generalized Nyquist criterion for band-limited signals under
271
beams of extremely high brightness have come into operation. To enhance the
cooling, wiggler magnets are used, producing a succession of left and right bends.
This increases the radiation and thereby the damping rates. The heating can be kept
small by placing the wiggler at locations where the focusing functions of the ring
are appropriate to make the particle motion insensitive to kicks. More details for
cooling by synchrotron radiation are given in Sect. 6.5.
Radiation cooling and lattice properties of the storage ring are thus intimately
linked and by smart design, orders of magnitude in the equilibrium emittances have
been gained. This may serve as example for other cooling techniques for which the
art of ‘low emittance lattices’ is only now emerging.
6.10.2.2 Microwave Stochastic Cooling
For (anti-)protons and heavier ions, radiation damping is almost negligible at
the energies currently accessible in accelerators except for the LHC. One of the
‘artificial’ cooling methods devised for these heavy particles is stochastic cooling
by a broadband feedback system (Fig. 6.36). The name “stochastic damping” was
coined by Simon van der Meer who invented this method in 1968 (first published
in 1972) [102] to underline the statistical basis of the method. First successful
tests and observations were done at the CERN ISR (Intersecting Storage Rings)
[102] followed by a dedicated “Initial Cooling Experiment” ICE [103]. In 1984
Simon van der Meer shared the Nobel Prize [104] in physics with Carlo Rubbia
for his contribution to the observation of the intermediate vector boson. Microwave
stochastic cooling was considered a key ingredient for reaching sufficient phase
space density of the precious and rare antiprotons to produce a small number
of W- and Z-Bosons in the CERN Super Proton-Antiproton Synchrotron (SppS)
experiment in 1982. At the core of stochastic cooling is the observation, that the
phase-space density can be increased by a system that acts to reduce the deviation
of small sections, called samples, of the beam. By measuring and correcting the
statistical fluctuations (‘Schottky noise’) of the sample averages, the spreads in the
corresponding beam properties are gradually reduced. Stochastic cooling may thus
be viewed as a ‘sampling procedure’ where samples are continuously taken from the
beam and the average of each sample is corrected. The basic principle of (transverse)
stochastic cooling is sketched in Fig. 6.36.
A somewhat different picture is based on the behavior of a test particle. At each
passage it receives its own ’coherent’ kick plus the ‘incoherent’ random kicks due
to all other sample members. The sample length T s (response-time) is given by the
bandwidth W of the system through T s ≈ 1/2W and the number N s of particles per
sample is proportional to T s . Hence a large bandwidth is important to work with
small samples. Present day cooling rings have a revolution time between a fraction
of a μs (e.g. CERN AD) up to about 20 μs (Relativistic Heavy Ion Collider (RHIC),
Fermilab bunched beam cooling systems). The sample length T s amounts usually to
less than 1 ns which corresponds to a cooling system bandwidth of 500 MHz in
this case assuming the generalized Nyquist criterion for band-limited signals under