Direct Vlasov solvers

In these proceedings we will describe the theory and practical steps required to build Vlasov solvers such as those commonly used to compute coherent instabilities in synchrotrons. Thanks to a Hamiltonian formalism, we will derive a compact and general form of the linearized Vlasov equation, written using Poisson brackets. This in turn will be the basis of a procedure to build Vlasov solvers, applied to the specific example of transverse instabilities arising from beam coupling impedance.Comment: 25 pages, 2 figure

The LHC Transverse Coupled-Bunch Instability

In this thesis, the problem of the transverse coupled-bunch instabilities created by the Large Hadron Collider (LHC) beam-coupling impedance, that can possibly limit the machine operation, is addressed thanks to several new theories and tools. A rather complete vision of the problem is proposed here, going from the calculation of the impedances and wake functions of individual machine elements, to the beam dynamics study. Firstly, new results are obtained in the theory of the beam-coupling impedance for an axisymmetric two-dimensional structure, generalizing Zotter's theories, and a new general theory is derived for the impedance of an infinite flat two-dimensional structure. Then, a new approach has been found to compute the wake functions from such analytically obtained beam-coupling impedances, over-coming limitations that could be met with standard discrete Fourier transform procedures. Those results are then used to obtain an impedance and wake function model of the LHC, based on the (resistive-) wall impedances of various contributors (collimators, beam screens and vacuum pipe) and additional estimations of the geometrical impedance contributions. Finally, the existing code HEADTAIL, which is a macroparticle simulation code for beam dynamics studies with wake fields, is improved to make possible the simulation of multibunch trains, and a spectral analysis technique is found to facilitate the analysis of the output given by this code, giving the complex tune shifts of the unstable modes present in a simulation. All those theories and tools are used to obtain new results concerning the LHC transverse coupled-bunch instabilities, demonstrating the rather small impact on coupled-bunch instabilities of the number of bunches in a train when the bunch spacing is fixed, and the existence of coupled-bunch modes with intrabunch motion which are more critical than their single-bunch counterparts. A full verification of the complete procedure (impedance theories, impedance model and simulation code) is also performed by comparing the simulation results with actual measurements in the LHC, giving a very good agreement at injection energy and a correct order of magnitude at 3.5 TeV/c. In the end, several predictions concerning the beam stability at the future 7 TeV/c operation of the machine are performed in the case of 50 ns spacing (1404 bunches), revealing that the coupled-bunch transverse mode coupling instability threshold is far above the ultimate bunch intensity but about 20% smaller than its single-bunch counterpart. Stability studies with Landau octupoles at their maximum currents reveal that the beam remains stable at nominal intensity with Q' = 2 in both planes, provided the particle transverse distributions are Gaussian. At ultimate intensity with either Q' = 0 or Q' = 2, or at nominal intensity when the chromaticity is zero, the beam happens to be unstable, even with the octupoles at their maximum currents

GENERALIZED FORM FACTORS FOR THE BEAM COUPLING IMPEDANCES IN A FLAT CHAMBER

The exact formalism from B. Zotter to compute beam coupling impedances has been fully developed only in the case of an infinitely long circular beam pipe. For other two dimensional geometries, some form factors are known only in the ultrarelativistic case and under certain assumptions of conductivity and frequency of the pipe material. We present here a new and exact formalism to compute the beam coupling impedances in the case of a collimator-like geometry where the jaws are made of two infinite plates of any linear material. It is shown that the impedances can be computed theoretically without any assumptions on the beam speed, material conductivity or frequency range. The final formula involves coefficients in the form of integrals that can be calculated numerically. This way we obtain new generalized form factors between the circular and the flat chamber cases, which eventually reduce to the so-called Yokoya factors under certain conditions

THE SIX ELECTROMAGNETIC FIELD COMPONENTS AT LOW FREQUENCY IN AN AXISYMMETRIC INFINITELY THICK SINGLE-LAYER RESISTIVE BEAM PIPE

In this study B. Zotter’s formalism is applied to a circular infinitely long beam pipe made of a conductor of infinite thickness where an offset point-charge travels at any given speed. Simple formulae are found for the impedances and electromagnetic fields both at intermediate frequencies (recovering Chao’s results) and in the low frequency regime where the usual classic thick wall impedance formula does not apply anymore due to the large skin depth compared to the pipe radius

IMPEDANCES OF AN INFINITELY LONG AND AXISYMMETRIC MULTILAYER BEAM PIPE: MATRIX FORMALISM AND MULTIMODE ANALYSIS

Using B. Zotter’s formalism, we present here a novel, efficient and exact matrix method for the field matching determination of the electromagnetic field components created by an offset point charge travelling at any speed in an infinitely long circular multilayer beam pipe. This method improves by a factor of more than one hundred the computational time with three layers and allows the computation for more layers than three. We also generalize our analysis to any azimuthal mode and finally perform the summation on all such modes in the impedance formulae. In particular the exact multimode direct space-charge impedances (both longitudinal and transverse) are given, as well as the wall impedances to any order of precision

A posteriori metadata from automated provenance tracking: Integration of AiiDA and TCOD

In order to make results of computational scientific research findable, accessible, interoperable and re-usable, it is necessary to decorate them with standardised metadata. However, there are a number of technical and practical challenges that make this process difficult to achieve in practice. Here the implementation of a protocol is presented to tag crystal structures with their computed properties, without the need of human intervention to curate the data. This protocol leverages the capabilities of AiiDA, an open-source platform to manage and automate scientific computational workflows, and TCOD, an open-access database storing computed materials properties using a well-defined and exhaustive ontology. Based on these, the complete procedure to deposit computed data in the TCOD database is automated. All relevant metadata are extracted from the full provenance information that AiiDA tracks and stores automatically while managing the calculations. Such a protocol also enables reproducibility of scientific data in the field of computational materials science. As a proof of concept, the AiiDA-TCOD interface is used to deposit 170 theoretical structures together with their computed properties and their full provenance graphs, consisting in over 4600 AiiDA nodes

Structural, vibrational and thermodynamic properties of carbon allotropes from first-principles : diamond, graphite, and nanotubes

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2005.Includes bibliographical references (p. 95-104).The structural, dynamical, and thermodynamic properties of different carbon allotropes are computed using a combination of ab-initio methods: density-functional theory for total-energy calculations and density-functional perturbation theory for lattice dynamics. For diamond, graphite, graphene, and armchair or zigzag single-walled nanotubes we first calculate the ground-state properties: lattice parameters, elastic constants and phonon dispersions and density of states. Very good agreement with available experimental data is found for all these, with the exception of the c/a ratio in graphite and the associated elastic constants and phonon dispersions. Agreement with experiments is recovered once the experimental c/a is chosen for the calculations. Results for carbon nanotubes confirm and expand available, but scarce, experimental data. The vibrational free energy and the thermal expansion, the temperature dependence of the elastic moduli and the specific heat are calculated using the quasi-harmonic approximation. Graphite shows a distinctive in-plane negative thermal-expansion coefficient that reaches its lowest value around room temperature, in very good agreement with experiments. The predicted value for the thermal-contraction coefficient of narrow single-walled nanotubes is half that of graphite, while for graphene it is found to be three times as large.(cont.) In the case of graphene and graphite, the ZA bending acoustic modes are shown to be responsible for the contraction, in a direct manifestation of the membrane effect predicted by I. M. Lifshitz over fifty years ago. Stacking directly hinders the ZA modes, explaining the large numerical difference between the thermal-contraction coefficients in graphite and graphene, notwithstanding their common physical origin. For the narrow nanotubes studied, both the TA bending and the "pinch" modes play a dominant role. For larger single-walled nanotubes, it is postulated that the radial breathing mode will have the! most significant effect on the thermal contraction, ultimately reaching the graphene limit as the diameter is increased.by Nicolas Mounet.S.M

Electromagnetic field created by a macroparticle in an infinitel long and axisymmetric multilayer beam pipe

This paper aims at giving an as complete and detailed as possible derivation of the six electromagnetic field components created by an offset point charge travelling at any speed in an infinitely long circular multilayer beam pipe. Outcomes from this study are a novel and efficient matrix method for the field matching determination of all the constants involved in the field components, and the generalization to any azimuthal mode together with the final summation on all such modes in the impedance formulas. In particular the multimode direct space-charge impedances (both longitudinal and transverse) are given, as well as the wall impedance to any order of precision. New quadrupolar terms for the transverse wall impedance are found, which look negligible in the ultrarelativistic case but might be of significance for low-energy beams. In principle from this analysis the electromagnetic fields created by any particular source, with a finite transverse shape, can then be computed using convolutions

IMPEDANCES OF TWO DIMENSIONAL MULTILAYER CYLINDRICAL AND FLAT CHAMBERS IN THE NON-ULTRARELATIVISTIC CASE

Two dimensional electromagnetic models (i.e. assuming an infinite length) for the vacuum chamber elements in a synchrotron are often quite useful to give a first estimate of the total beam-coupling impedance. In these models, classical approximations can fail under certain conditions of frequency or material properties. We present here two formalisms for flat and cylindrical geometries, enabling the computation of fields and impedances in the multilayer case without any assumption on the frequency, beam velocity or material properties (except linearity, isotropy and homogeneity)

MULTI-BUNCH EFFECT OF RESISTIVEWALL IN THE CLIC BDS

Wake fields in the CLIC Beam Delivery System (BDS) can cause severe single or multi-bunch effects leading to luminosity loss. The main contributors in the BDS are geometric and resistive wall wake fields of the collimators and resistive wall wakes of the beam pipe. The present work focuses only on the multi-bunch effects from resistive wall. Using particle tracking with wake fields through the BDS, we have established the aperture radius, above which the effect of the wake fields becomes negligible. Our simulations were later extended to include a realistic aperture model along the BDS as well as the collimators. The two cases of 3 TeV and 500 GeV have been examined