On Landau damping of dipole modes by non-linear space charge and octupoles

The joint effect of space-charge non-linearities and octupole lenses is important for Landau damping of coherent instabilities. The octupole strength required for stabilisation can depend strongly on the sign of the excitation current of the lenses. This note tries to extend results, previously obtained for coasting beams and rigid bunches, to more general head--tail modes

The Status of Stochastic Cooling

Presented at a symposium to celebrate the 30th anniversary of electron cooling, this report is intended to give the status of the companion technique, stochastic cooling, some 28 years after its invention. An overview of past developments reveals the close relationship between the two cooling ideas. Then the report concentrates on the principal ingredients of stochastic cooling in order to discuss the limits encountered and some recent ideas for pushing back these limits

Beam Cooling: Past, Present and Future

To date, four main methods to increase the phase-space density of circulating beams in storage rings are operational: cooling of e+e- -beams by synchrotron radiation, cooling of protons and ions by electrons, stochastic cooling of (anti-)protons and ions, and cooling of special ions by laser light. A fifth method, ionisation cooling of muons, is under intense development. Each of these techniques will be covered in detail in specialised contributions at this workshop. The present paper is intended to introduce the different techniques and put them into perspective: specific features will be outlined, common characteristics will be sketched, and potential future applications will be mentioned

Production of Low-Energy Antiprotons

The production, collection and deceleration of antiprotons is reviewed with the aim of establishing guidelines for the design of a simple yet efficient source of stopped antiprotons. A high-energy (20-100 GeV) high-intensity (~ 1013 protons/pulse) proton accelerator is needed to produce antiprotons in copious numbers. A 'passive' conversion-target consisting of a thin iridium rod embedded in graphite, and a magnetic-horn type lens to collect the antiproton flux from the target represent a good compromise between yield and reliability. To transport the flux to low energy a large-acceptance cooling and deceleration ring working up to an energy equal to one-eighth to one-tenth of the primary proton energy is required. Stochastic cooling (at high energy) and electron cooling (at lower energy) are indispensable for providing low-energy beams of useful density

LEAR, history and early achievements

This report retraces the early history of the Low Energy Antiproton Ring (LEA) and recalls some of its unusual design features

Transverse Coherent Instabilities in the Presence of Linear Coupling

Strong coupling between the transverse planes of a particle beam leads to an "equipartition" of the oscillation energy, including the growth rates in the case of coherent instability. The aim of this paper is to give a general formula, which includes linear coupling and which extends to two dimensions the one-dimensional results of transverse coherent instabilities. From this equation, previous results are recovered as expected: (i) Sacherer's formula for the coherent modes of oscillation, (ii) Kohaupt's formula for the mode coupling instability, and (iii) the coupled Landau damping mechanism (transfer of frequency spread), which includes the sharing of the instability growth rates. Measurements have been performed in the CERN PS, which confirm the predicted beneficial effect of coupling by both frequency spread and chromaticity sharing

Control of Coherent Instabilities by Linear Coupling

One of the main challenges in the design of high-energy colliders is the very high luminosity necessary to provide significant event rates. This imposes strong constraints to achieve and preserve beams of high brightness, i.e. intensity to emittance ratio, all along the injector chain. Amongst the phenomena that can blow up and even destroy the beam are transverse coherent instabilities. Two methods are widely used to damp these instabilities. The first one is Landau damping by non-linearities. The second consists in using an electronic feedback system. However, non-linearities are harmful to single-particle motion due to resonance phenomena, and powerful wideband feedback systems are expensive. It is shown in this paper that linear coupling is a further method that can be used to damp transverse coherent instabilities. The theory of collective motion is outlined, including the coupling of instability rise and damping rates, chromaticity and Landau damping. Experimental results obtained at the CERN PS are reported, which are important for its role as LHC injector. Stabilisation by coupling explains (at least in part) why existing high intensity accelerators and colliders work best when adjusted relatively close to a coupling resonance. This method could be profitably used in the design of new machines

Stochastic cooling in hadron colliders

Stochastic cooling in big hadron colliders is hampered by the high particle density, the bunch structure and by an unexpectedly large "RF-activity" up to very high frequencies. The more modest goal of tail cleaning in the LHC is made difficult due to the high discrimination required for pick-ups which selectively observe the beam halo only. This paper reviews sources of these difficulties, which have so far frustrated attempts to apply stochastic cooling to bunched beams at high energy