2,912 research outputs found

    Progress in the Beam preparation for the Multi-Turn Extraction at the CERN Proton Synchrotron

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    A new type of extraction based on beam trapping inside stable islands in the horizontal phase space will become operational during 2008 at the CERN Proton Synchrotron. A series of beam experiments was carried out to prove lossless capture with high intensity and multi-bunched beams, up to 1.5Ă—10131.5 Ă— 10^{13} protons per pulse, in preparation of the extraction commissioning. These fundamental steps for the new Multi-turn Extraction are presented and discussed in details

    Harnack inequality for fractional sub-Laplacians in Carnot groups

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    In this paper we prove an invariant Harnack inequality on Carnot-Carath\'eodory balls for fractional powers of sub-Laplacians in Carnot groups. The proof relies on an "abstract" formulation of a technique recently introduced by Caffarelli and Silvestre. In addition, we write explicitly the Poisson kernel for a class of degenerate subelliptic equations in product-type Carnot groups

    Experimental Evidence of Beam Trapping with one-third and one-fifth Resonance Crossing

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    Beam trapping in stable islands of the horizontal phase space generated by non-linear magnetic fields is realized by means of a given tune variation so to cross a resonance of order n. Whenever the resonance is stable, n + 1 beamlets are created whereas if the resonance is unstable, the beam is split in n parts. Experiments at the CERN Proton Synchrotron showed protons trapped in stable islands while crossing the one-third and one-fifth resonance with the creation of 3 and 6 stable beamlets, respectively. The results are presented and discussed

    Adiabaticity and Reversibility Studies for Beam Splitting using Stable Resonances

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    At the CERN Proton Synchrotron, a series of beam experiments proved beam splitting by crossing the one-fourth resonance. Depending on the speed at which the horizontal resonance is crossed, the splitting process is more or less adiabatic, and a different fraction of the initial beam is trapped in the islands. Experiments prove that when the trapping process is reversed and the islands merged together, the final distribution features thick tails. The beam population in such tails is correlated to the speed of the resonance crossing and to the fraction of the beam trapped in the stable islands. Experiments and possible theoretical explanations are discussed
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