Analytical considerations for linear and nonlinear optimization of the TME cells. Application to the CLIC pre-damping rings

The theoretical minimum emittance cells are the optimal configurations for achieving the absolute minimum emittance, if specific optics constraints are satisfied at the middle of the cell's dipole. Linear lattice design options based on an analytical approach for the theoretical minimum emittance cells are presented in this paper. In particular the parametrization of the quadrupole strengths and optics functions with respect to the emittance and drift lengths is derived. A multi-parametric space can be then created with all the cell parameters, from which one can chose any of them to be optimized. An application of this approach are finally presented for the linear and non-linear optimization of the CLIC Pre-damping rings.Comment: Submitted for publication in Physical Review Special Topics - Accelerators and Beam

Efficient control of accelerator maps

Recently, the Hamiltonian Control Theory was used in [Boreux et al.] to increase the dynamic aperture of a ring particle accelerator having a localized thin sextupole magnet. In this letter, these results are extended by proving that a simplified version of the obtained general control term leads to significant improvements of the dynamic aperture of the uncontrolled model. In addition, the dynamics of flat beams based on the same accelerator model can be significantly improved by a reduced controlled term applied in only 1 degree of freedom

Luminosity Scans for Beam Diagnostics

A new type of fast luminosity separation scans ("Emittance Scans") was introduced at the CERN Large Hadron Collider (LHC) in 2015. The scans were performed systematically in every fill with full-intensity beams in physics production conditions at the Interaction Point (IP) of the Compact Muon Solenoid (CMS) experiment. They provide both emittance and closed orbit measurements at a bunch-by-bunch level. The precise measurement of beam-beam closed orbit differences allowed a direct, quantitative observation of long-range beam-beam PACMAN effects, which agrees well with numerical simulations from an improved version of the TRAIN code

Extracting chromatic properties of electron beams from spectral analysis of turn-by-turn beam position data

A method to estimate linear chromaticity, RMS energy spread, and chromatic beta-beating, directly from turn-by-turn beam position data in a circular electron accelerator, is presented. This technique is based on frequency analysis of a transversely excited beam, in the presence of finite chromaticity. Due to the turn-by-turn chromatic modulation of the beam's envelope, betatron sidebands appear around the main frequency of the Fourier spectra. By determining the amplitude of both sidebands, chromatic properties of the beam can be estimated. In this paper, analytical derivations justifying the proposed method are given, along with results from tracking simulations. To this end, results from practical applications of this technique at the KARA electron ring are demonstrated

Identification and characterization of high order incoherent space charge driven structure resonances in the CERN Proton Synchrotron

Space charge is typically one of the performance limitations for the operation of high intensity and high brightness beams in circular accelerators. In the Proton Synchrotron (PS) at CERN, losses are observed for vertical tunes above $Q_y=6.25$, especially for beams with large space charge tune shift. The work presented here shows that this behaviour is associated to structure resonances excited by space charge due to the highly symmetric accelerator lattice of the PS, typical for first generation alternating gradient synchrotrons. Experimental studies demonstrate the dependency of the losses on the beam brightness and the harmonic of the resonance, and simulation studies reveal the incoherent nature of the resonance. Furthermore, the calculation of the Resonance Driving Terms (RDT) generated by the space charge potential shows that the operational working point of the PS is surrounded by multiple space charge driven incoherent resonances. Finally, measurements and simulations on both lattice driven and space charge driven resonances illustrate the different behaviour of the beam loss depending on the source of the resonance excitation and on the beam brightness

Interplay of Space Charge and Intra-Beam Scattering in the LHC ion injector chain

The ion injectors of the CERN accelerator chain, in particular the Super Proton Synchrotron (SPS) and the Low Energy Ion Ring (LEIR), operate in a strong Space Charge (SC) and Intra-Beam Scattering (IBS) regime, which can degrade beam quality. Optimizing the ion beam performance requires thus to study the interplay of these two effects in tracking simulations by incorporating both SC and IBS effects interleaved with lattice non-linearities. In this respect, the kinetic theory approach of treating IBS effects has been deployed. A new, modified approach has been introduced using the formalism of the Bjorken and Mtingwa model and the complete integrals of the second kind for faster numerical evaluation. This IBS kick is implemented in PyORBIT and extensive benchmarking cases against analytical models are shown. Results of combined space charge and intra-beam scattering simulations for the SPS and LEIR are presented and compared with observations from beam measurements.Comment: 13 pages, 13 figures, to be submitted to Physical Review Accelerators and Beam

Detecting chaos in particle accelerators through the frequency map analysis method

The motion of beams in particle accelerators is dominated by a plethora of non-linear effects which can enhance chaotic motion and limit their performance. The application of advanced non-linear dynamics methods for detecting and correcting these effects and thereby increasing the region of beam stability plays an essential role during the accelerator design phase but also their operation. After describing the nature of non-linear effects and their impact on performance parameters of different particle accelerator categories, the theory of non-linear particle motion is outlined. The recent developments on the methods employed for the analysis of chaotic beam motion are detailed. In particular, the ability of the frequency map analysis method to detect chaotic motion and guide the correction of non-linear effects is demonstrated in particle tracking simulations but also experimental data.Comment: Submitted for publication in Chaos, Focus Issue: Chaos Detection Methods and Predictabilit

APPLICATION DE LA METHODE D'ANALYSE EN FREQUENCE EN DYNAMIQUE GALACTIQUE

We study the well-known logarithmic galactic potential through the frequency map analysis method of Laskar in order to deepen our knowledge regarding the dynamics of triaxial power-law galactic models. The principal dynamical features of the system are reviewed within the appropriate Hamiltonian frame of reference. The impact of this new approach in galactic dynamics is investigated by applying the method to the axisymmetric version of the logarithmic potential. The reliability of the method is demonstrated via perturbative techniques and numerical transformations in action-angle variables. Comparison with previous studies involving Fourier methods are also given. By means of frequency map analysis, we provide a global vision of the dynamics of the planar potential for various values of the perturbation parameter. The location and extent of the chaotic zones can be easily visualised. All the important resonances are detected with their actual strength, as well as the associated periodic orbits. The method is then applied to the complete threedimensional version of the logarithmic potential. The quasi-periodic approximations furnished by the method permit to clarify the dynamics of the principal types of orbits and their connection with perturbations of integrable cases of the general Hamiltonian. All the fine details of the dynamics associated with the addition of the third degree of freedom are displayed in the complete frequency map, a direct representation of the system's Arnol'd web. The extent of the chaotic zones and the influence of resonant lines are directly visualized in the physical space of the system. This approach reveals many unknown dynamical features of triaxial galactic potentials and gives strong indications that chaos should be an innate characteristic of triaxial configurations. The impact of these results in the construction of self-consistent galactic models are finally discussed.Dans le but de clarifier les aspects dynamiques des modèles galactiques triaxiaux, le potentiel logarithmique est étudié a travers la méthode d'analyse en fréquence. Les caractéristiques dynamiques principales du système sont présentées en utilisant le formalisme hamiltonien approprié. Afin de comparer cette nouvelle approche avec des études précédentes, la méthode est appliquée a la version axisymétrique du potentiel. La précision de la méthode est démontrée a travers des techniques de perturbation et des transformations numériques en variables action-angle. En outre, la construction des applications fréquence pour plusieurs valeurs du paramètre de perturbation permet de fournir une vision globale de la dynamique du potentiel plan. Les zones chaotiques, les résonances importantes ainsi que les orbites périodiques sont détectées. La méthode est appliquée ensuite a la version tridimensionnelle du potentiel logarithmique. Les approximations quasi-périodiques fournies par la méthode permettent de clarifier la dynamique des types d'orbites principales et leur connexion avec des perturbations du hamiltonien général. Tous les détails fins de la dynamique, qui sont associés a l'addition du troisième degré de liberté, sont représentés dans les applications fréquence complètes, des images instantanées du réseau d'Arnold (''Arnol'd web'') du système. Ainsi, nous pouvons visualiser l'étendu des zones chaotiques et l'influence des lignes résonantes dans l'espace physique du système. Cette approche révèle plusieurs caractéristiques dynamiques inconnues des potentiels galactiques triaxiaux et indique que le chaos doit être une caractéristique importante des configurations triaxiales. Nous discutons finalement l'influence de ces résultats sur la construction des modèles galactiques auto-consistants