By Dieter Möhl
This lecture word describes the most analytical ways to stochastic cooling. the 1st is the time area photo, during which the beam is quickly sampled and a statistical research is used to explain the cooling behaviour. the second one is the frequency area photograph, that's quite precious because the observations made at the beam are mostly during this area. This moment photograph is constructed intimately to evaluate key parts of contemporary cooling idea like blending and sign defensive and to demonstrate many of the diagnostic equipment. eventually using a distribution functionality and the Fokker-Plank equation, which provide the main entire description of the beam in the course of the cooling, are discussed.
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Additional resources for Stochastic Cooling of Particle Beams
Example text
It has the maximum at low frequency. A response function Fk≡≡ similar to Eq. 18) also holds for the second type of transverse kicker. 2. 2 Transfer impedances (per pickup or kicker unit) of different loop coupler arrangements when the impedance of the signal transfer system is Z0 /2. 1. The transfer impedances for the difference kickers which are only given for the range where g⊥ or g≡≡ vary linearly with distance y or x respectively, see Figs. 4 Matching to the Cooling Loop When the impedance of the signal transmission system is matched to the pickup output and the kicker input then the transfer is just determined by ZP and ZK as previously defined.
43) xp,P U = 0 In Eq. 43) x s = xp + xβ s is the total pickup signal of a sample containing both the betatron and the momentum contribution. We simplify, again assuming zero derivative of D(s) at the kicker, but we allow for different D at pickup and kicker. 13 Hereward Cooling 29 Fig. 13 Reduction of betatron oscillation by a momentum jump. At s0 the momentum is abruptly changed by p/p. The particle continues its betatron oscillation around the new orbit centre, which is displaced by D( p/p). 44) 2 2 2 Here noise (xn2 ) and mixing are included.
The central band, the harmonic n = 100 of the revolution frequency, is visible as the beam is not completely centred at the position pickup. 3. The difference between the base line of the trace and the bottom line (zero signal) is given by the noise of the pickup system. The span covers (approximately) an interval of frequency, frev . e. 21) where I (t) consists of the single-particle current [Eq. 1)] plus the Schottky noise current. To fix our ideas, we may think of Palmer cooling, where the pickup signal is given by the particle current and the displacement x = D · δp/p at the pickup D · δp/p).