274
B. J. Holzer et al.
example 1/τ ≤ 0.28W/N in the case of ˜
M = M instead of 1/τ ≤ W/N for perfect
mixing.
‘Optimum mixing lattices’ (also referred to as ‘split ring designs’) have been
proposed for the 10 GeV ‘SuperLEAR’ ring [108] (which was, however, never
built). The idea is to make the path P to K isochronous (η pk = 0) and the path
K to P strongly flight-time dispersive (η kp 0). These lattice properties have
to be reconciled with the many other requirements of the storage ring. The next
generation of stochastic cooling rings will use such split rings lattices. They were
discussed for RIKEN in Japan [109] and are under construction for GSI and FAIR
in Germany [110, 111]. It should be mentioned that the condition η pk = 0, η kp 0
can increase the cooling rate for transverse and for longitudinal ‘Palmer-Hereward’
cooling where the transverse displacement concurrent with the betatron amplitude
and the momentum error of the particles is used. For momentum cooling by the
filter (‘Thorndahl’) method, the split ring design brings less improvement since
here the time of flight over a full revolution is used as a measure of momentum. A
storage ring with η pk = 0 and η ≈ 1–2% is under construction for GSI and FAIR in
Germany, meeting best conditions for both transverse cooling and filter momentum
cooling of antiprotons [112].
Regarding the situation at GSI it should be mentioned that a first successful
experiment was performed at the ESR to measure the nuclear radius of the
radioactive nucleus 56Ni. To this purpose stochastic precooling and subsequent
electron cooling were used in order to accumulate enough intensity for a sufficient
S/N in a scattering experiment with an internal hydrogen target [113].
This is not the end of the mixing dilemma: during momentum cooling, as p/p
decreases, the M-factors increase (c.f. Eq. 6.75) and the mixing situation tends to
degrade. One can in principle stay close to the optimum by changing η (‘dynamic
transition tuning’) as cooling proceeds. Similar considerations hold for machines
with variable working energy where, through a change of η, good mixing can be
maintained. Again these improvements might be incorporated in the next generation
of cooling rings (e.g. at FAIR [112]).
As for the noise, from Eq. (6.74) it is clear that a balanced design aims at
U/Z 2 M. The noise to signal (power-)ratio depends on the technology of the preamplifier and other ‘low level components’ on the one hand and on the sensitivity
of the pick-up device on the other hand. There has been great progress in the
design of the pick-up and kicker structures and the other components of the cooling
loop. These components developed in different labs (e.g. BNL [114], CERN [107],
Fermilab [115], Forschungszentrum Jülich (FZJ) [116], GSI [112, 117]) are in fact
formidable ‘high-fidelity (HiFi) systems’ with an unprecedented combination of
high sensitivity, low noise, great bandwidth, large amplification, very linear phase
response, and excellent compatibility with the ultra-high vacuum of the storage ring.
A more detailed discussion of stochastic cooling hardware progress over the last
30 years can be found in [118]. Regarding pick-up and kicker structures we have
seen printed versions arriving in the late 1980s of the classical λ/4 strip-line couplers
which are referred to as printed loop or printed slotline couplers which are normally
B. J. Holzer et al.
example 1/τ ≤ 0.28W/N in the case of ˜
M = M instead of 1/τ ≤ W/N for perfect
mixing.
‘Optimum mixing lattices’ (also referred to as ‘split ring designs’) have been
proposed for the 10 GeV ‘SuperLEAR’ ring [108] (which was, however, never
built). The idea is to make the path P to K isochronous (η pk = 0) and the path
K to P strongly flight-time dispersive (η kp 0). These lattice properties have
to be reconciled with the many other requirements of the storage ring. The next
generation of stochastic cooling rings will use such split rings lattices. They were
discussed for RIKEN in Japan [109] and are under construction for GSI and FAIR
in Germany [110, 111]. It should be mentioned that the condition η pk = 0, η kp 0
can increase the cooling rate for transverse and for longitudinal ‘Palmer-Hereward’
cooling where the transverse displacement concurrent with the betatron amplitude
and the momentum error of the particles is used. For momentum cooling by the
filter (‘Thorndahl’) method, the split ring design brings less improvement since
here the time of flight over a full revolution is used as a measure of momentum. A
storage ring with η pk = 0 and η ≈ 1–2% is under construction for GSI and FAIR in
Germany, meeting best conditions for both transverse cooling and filter momentum
cooling of antiprotons [112].
Regarding the situation at GSI it should be mentioned that a first successful
experiment was performed at the ESR to measure the nuclear radius of the
radioactive nucleus 56Ni. To this purpose stochastic precooling and subsequent
electron cooling were used in order to accumulate enough intensity for a sufficient
S/N in a scattering experiment with an internal hydrogen target [113].
This is not the end of the mixing dilemma: during momentum cooling, as p/p
decreases, the M-factors increase (c.f. Eq. 6.75) and the mixing situation tends to
degrade. One can in principle stay close to the optimum by changing η (‘dynamic
transition tuning’) as cooling proceeds. Similar considerations hold for machines
with variable working energy where, through a change of η, good mixing can be
maintained. Again these improvements might be incorporated in the next generation
of cooling rings (e.g. at FAIR [112]).
As for the noise, from Eq. (6.74) it is clear that a balanced design aims at
U/Z 2 M. The noise to signal (power-)ratio depends on the technology of the preamplifier and other ‘low level components’ on the one hand and on the sensitivity
of the pick-up device on the other hand. There has been great progress in the
design of the pick-up and kicker structures and the other components of the cooling
loop. These components developed in different labs (e.g. BNL [114], CERN [107],
Fermilab [115], Forschungszentrum Jülich (FZJ) [116], GSI [112, 117]) are in fact
formidable ‘high-fidelity (HiFi) systems’ with an unprecedented combination of
high sensitivity, low noise, great bandwidth, large amplification, very linear phase
response, and excellent compatibility with the ultra-high vacuum of the storage ring.
A more detailed discussion of stochastic cooling hardware progress over the last
30 years can be found in [118]. Regarding pick-up and kicker structures we have
seen printed versions arriving in the late 1980s of the classical λ/4 strip-line couplers
which are referred to as printed loop or printed slotline couplers which are normally