By Gert G. Schlessinger

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7) specifies the intensity of the nth spectral line of the mean-squared noise current for a group of N mono-energetic (equal ωrev ) particles with random initial phases. In reality we are faced with a distribution of revolution frequencies between ωrev ± ωrev /2. Clearly, then, the different components contribute current in the range n(ωrev ± ωrev /2) around each harmonic n. We thus have a band spectrum, the so-called ‘Schottky noise spectrum’ (or ‘Schottky band spectrum’) of a coasting beam. For a subgroup with a very narrow range dωrev of frequencies we can apply Eq.

Then there is a gain of a factor of 3 in the maximum momentum spread which the system can handle with the same cooling band. As in the filter method sum pickups with their high inherent sensitivity are used. However the electronic noise is—a priory—not reduced, in contrast to filter cooling. g. in the AA, LEAR and the AD at CERN). In the antiproton accumulators, it is used for pre-cooling the low intensity 34 2 Simplified Theory, Time-Domain Picture beam whereas Palmer cooling (with large bandwidth) is applied to control the stack.

It is clear from the analysis that they are due to the oscillatory nature of the particle motion. On average, the particle reveals only half the information on its amplitude when passing the pickup and the position has to transform to an angular error to be corrected at the kicker. The optimum phase-advance pickup to kicker is 28 2 Simplified Theory, Time-Domain Picture π/2 (modulo π ), as anticipated in Sect. 1. In analogy with Eq. 31) the cooling rate, Eq. 42), has a maximum which is proportional to [(1 − M˜ −2 ) sin( ψ)]2 .

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Inorganic Laboratory Preparations by Gert G. Schlessinger

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