6 Design and Principles of Synchrotrons and Circular Colliders
281
An important technical problem is electron beam power consumption. To reduce
direct losses of the beam power the recuperation (recovering) method is used. It
assumes biasing of the collector to negative potential slightly above the cathode
potential. Then the power consumption is defined mainly by product of the beam
current by the difference of the collector and gun potentials.
In the two toroidal sections, adjacent to the overlap region, the solenoid to create
the longitudinal field is curved to guided the electron beam parallel to the ions at the
entrance and away from them at the exit. Also in the toroidal regions the solenoid
has a larger diameter to permit the penetration of the ion beam.
Many papers deal with the ‘exact and general theory’ [161] and computer
programs like BETACOOL [162] try to include all the subtle effects. Numerous
also are the experimental results from 11 (or so) present and past cooling rings. It
is not easy to compare the data from different experiments because the cooling in
each plane depends in a complicated way on the emittances in all three directions
both of the ion and the electron beam. Moreover different quantities are used to
measure/define ‘cooling strength’ (examples: cooling of a large injected beam,
response of a cold beam to a ‘kick’ or to a transverse or an energy displacement,
equilibrium with heating by noise).
In the context of the accumulation of lead ions for the future Large Hadron
Collider (LHC) [163], a program of experiments [164] was performed at the
LEAR ring to determine optimum lattice functions [165]. Results indicate rather
small optimum betatron functions (3–5 m instead of the expected 10 m) and
large dispersion (D = 2–3 m instead of the expected 0–1 m). The dependence on
dispersion is not fully reproduced by simple analytical formulae. There are other
old questions: e.g. the (dis)advantage of magnetic expansion, the dependence of
the cooling time on the charge of the ion, the (dis)advantage of neutralising the
electron beam, the enigma of the stability of the cooled beam [166], the puzzle of
the anomalously fast recombination of certain ions with cooling electrons [167], the
(dis)advantage of a hollow electron beam [168].
Considerations so far concern electron cooling at ‘low energies’ (T e = 2–
300 keV) where cooling rings have flourished since the 1980s. More recently
medium energy cooling (T e = 1–10 MeV) has re-gained a lot of interest [167–
169]. Clearly the higher energy requires new technology and extrapolation to a
new range of parameters. At Fermilab high energy e-cooling (with up to 5 MeV
electrons using electrostatic acceleration for cooling of 8 GeV bunched antiprotons
in the recycler) has been successfully developed and implemented. The generation
and recirculation of the 4.3 MeV and 0.5 Ampere electron beam and its adaptation
to the antiproton beam over a cooling length of 20 m are remarkable achievements.
Finally the idea of ‘very high energy electron cooling’ (T e ≥ 50 MeV) has been
revived as this might improve the luminosity of RHIC [168, 170]. At this energy the
electron beam could circulate in a small ‘low-emittance storage ring’ with strong
radiation damping. An attractive alternative is a scheme [170], in which the lowemittance beam after acceleration is re-decelerated after the passage through the
cooling section to recuperate its energy.
281
An important technical problem is electron beam power consumption. To reduce
direct losses of the beam power the recuperation (recovering) method is used. It
assumes biasing of the collector to negative potential slightly above the cathode
potential. Then the power consumption is defined mainly by product of the beam
current by the difference of the collector and gun potentials.
In the two toroidal sections, adjacent to the overlap region, the solenoid to create
the longitudinal field is curved to guided the electron beam parallel to the ions at the
entrance and away from them at the exit. Also in the toroidal regions the solenoid
has a larger diameter to permit the penetration of the ion beam.
Many papers deal with the ‘exact and general theory’ [161] and computer
programs like BETACOOL [162] try to include all the subtle effects. Numerous
also are the experimental results from 11 (or so) present and past cooling rings. It
is not easy to compare the data from different experiments because the cooling in
each plane depends in a complicated way on the emittances in all three directions
both of the ion and the electron beam. Moreover different quantities are used to
measure/define ‘cooling strength’ (examples: cooling of a large injected beam,
response of a cold beam to a ‘kick’ or to a transverse or an energy displacement,
equilibrium with heating by noise).
In the context of the accumulation of lead ions for the future Large Hadron
Collider (LHC) [163], a program of experiments [164] was performed at the
LEAR ring to determine optimum lattice functions [165]. Results indicate rather
small optimum betatron functions (3–5 m instead of the expected 10 m) and
large dispersion (D = 2–3 m instead of the expected 0–1 m). The dependence on
dispersion is not fully reproduced by simple analytical formulae. There are other
old questions: e.g. the (dis)advantage of magnetic expansion, the dependence of
the cooling time on the charge of the ion, the (dis)advantage of neutralising the
electron beam, the enigma of the stability of the cooled beam [166], the puzzle of
the anomalously fast recombination of certain ions with cooling electrons [167], the
(dis)advantage of a hollow electron beam [168].
Considerations so far concern electron cooling at ‘low energies’ (T e = 2–
300 keV) where cooling rings have flourished since the 1980s. More recently
medium energy cooling (T e = 1–10 MeV) has re-gained a lot of interest [167–
169]. Clearly the higher energy requires new technology and extrapolation to a
new range of parameters. At Fermilab high energy e-cooling (with up to 5 MeV
electrons using electrostatic acceleration for cooling of 8 GeV bunched antiprotons
in the recycler) has been successfully developed and implemented. The generation
and recirculation of the 4.3 MeV and 0.5 Ampere electron beam and its adaptation
to the antiproton beam over a cooling length of 20 m are remarkable achievements.
Finally the idea of ‘very high energy electron cooling’ (T e ≥ 50 MeV) has been
revived as this might improve the luminosity of RHIC [168, 170]. At this energy the
electron beam could circulate in a small ‘low-emittance storage ring’ with strong
radiation damping. An attractive alternative is a scheme [170], in which the lowemittance beam after acceleration is re-decelerated after the passage through the
cooling section to recuperate its energy.