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

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

Simultaneous matching of dispersion function and Twiss parameters in a transfer line

Dispersion matching in a beam transfer line is an important issue in order to avoid blow-up and luminosity reduction. This is the case for the LHC beam, due to its small emittance and relatively large momentum spread. The dispersion matching can be performed with quadrupoles, but one has to impose the additional constraint of leaving the Twiss parameters unchanged, to preserve the betatron matching. A first order pertubative approach, using the MICADO solver, has been applied to the problem of simultaneous betatron and dispersion matching. A theoretical derivation of the correction matrix as well as simulated and experimental results are presented. (8 refs)

Hamiltonian theory of the crossing of the 2Qx−2Qy=0 nonlinear coupling resonance

In a recent paper, the adiabatic theory of Hamiltonian systems was successfully applied to study the crossing of the linear coupling resonance, $Q_x-Q_y=0$. A detailed explanation of the well-known phenomena that occur during the resonance-crossing process, such as emittance exchange and its dependence on the adiabaticity of the process was obtained. In this paper, we consider the crossing of the resonance of nonlinear coupling $2 Q_x -2 Q_y = 0$ using the same theoretical framework. We perform the analysis using a Hamiltonian model in which the nonlinear coupling resonance is excited and the corresponding dynamics is studied in detail, in particular looking at the phase-space topology and its evolution, in view of characterizing the emittance exchange phenomena. The theoretical results are then tested using a symplectic map. Thanks to this approach, scaling laws of general interest for applications are derived

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

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 $1.5 × 10^{13}$ protons per pulse, in preparation of the extraction commissioning. These fundamental steps for the new Multi-turn Extraction are presented and discussed in details

Analysis of adiabatic trapping phenomena for quasi-integrable area-preserving maps in the presence of time-dependent exciters

In this paper, new results concerning the phenomenon of adiabatic trapping into resonance for a class of quasi-integrable maps with a time-dependent exciter are presented and discussed in detail. The applicability of the results about trapping efficiency for Hamiltonian systems to the maps considered is proven by using perturbation theory. This allows determining explicit scaling laws for the trapping properties. These findings represent a generalization of previous results obtained for the case of quasi-integrable maps with parametric modulation as well as an extension of the work by Neishtadt \textit{et al.} on a restricted class of quasi-integrable systems with time-dependent exciters

Adiabaticity and Reversibility Studies for Beam Splitting using Stable Resonances

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

Probing the diffusive behaviour of beam-halo dynamics in circular accelerators

Circular particle accelerators at the energy frontier are based on superconducting magnets that are extremely sensitive to beam losses as these might induce quenches, i.e. transitions to the normal-conducting state. Furthermore, the energy stored in the circulating beam is so large that hardware integrity is put in serious danger, and machine protection becomes essential for reaching the nominal accelerator performance. In this challenging context, the beam halo becomes a potential source of performance limitations and its dynamics needs to be understood in detail to assess whether it could be an issue for the accelerator. In this paper, we discuss in detail a recent framework, based on a diffusive approach, to model beam-halo dynamics. The functional form of the optimal estimate of the perturbative series, as given by Nekhoroshev’s theorem, is used to provide the functional form of the action diffusion coefficient. The goal is to propose an effective model for the beam-halo dynamics and to devise an efficient experimental procedure to obtain an accurate measurement of the diffusion coefficient

Graphene edge method for three-dimensional probing of Raman microscopes focal volumes

In this work, a layer of graphene was used as a standard material for the measurement of the dimensions of Raman microscopes focal volumes of different confocal Raman spectrometers equipped with different objectives and excitation laser wavelengths. This method consists in probing the volume near the focal point of the system by using a flat graphene monolayer sheet with a straight edge. Graphene was selected because of its high Raman cross section and mechanically and chemically stability, allowing fast measurements and easy manipulation. In this paper, a method to employ graphene to accurately and precisely measure the three dimensions of the focal volume of a Raman microscope is presented; scanning along the axial and lateral directions, it is possible to reconstruct the three dimensions of the focal volume. Furthermore, these operations can be combined in a single procedure which allows the measurement of projections of the volume on planes parallel to the optical axis. Knowledge of these parameters enable absolute quantification of Raman-active molecules and support high-resolution Raman imaging

Non-invasive single-bunch matching and emittance monitor

On-line monitoring of beam quality for high brightness beams is only possible using non-invasive instruments. For matching measurements, very few such instruments are available. One candidate is a quadrupole pick-up. Therefore, a new type of quadrupole pick-up has been developed for the 26 GeV Proton Synchrotron (PS) at CERN, and a measurement system consisting of two such pick-ups is now installed in this accelerator. Using the information from these pick-ups, it is possible to determine both injection matching and emittance in the horizontal and vertical planes, for each bunch separately. This paper presents the measurement method and some of the results from the first year of use, as well as comparisons with other measurement methods.Comment: 10 pages, 10 figures; added figure, minor textual additions; To be resubmitted to Phys. Rev. ST-A