Paper  Title  Page 

MOAAI3 
SelfConsistent Transfer Maps for High Intensity Beams  


Funding: This work was supported by the Department of Energy under Contract No. DEFG0208ER41532 with Northern Illinois University. Transfer maps methods and and associated analysis tools, such as the normal form method, are wellknown in the single particle beam dynamics realm. When space charge effects are not negligible, it becomes more difficult to include them in a selfconsistent map picture. In this talk, we present a basisfunction method that relies on particle distribution moments and differential algebraic integration techniques that allow, for the first time, the extraction of selfconsistent high order Taylor maps of space charge dominated beam dynamics with almost the same ease as in the single particle case. 

Slides MOAAI3 [5.945 MB]  
MOABC2 
Molecular Dynamics Simulations for LaserCooled Sources  


Electron and ion sources based on lasercooling and trapping techniques are a relatively new reality in the field of charge particle accelerators. The dynamics of these sources is governed by stochastic effects, and not by the usually dominant spacecharge forces. This is the direct consequence of higher phasespace density. The transition from a spacecharge regime to a stochastic regime requires a radical shift in simulation techniques: We need to replace the ParticleInCell workhorse with molecular dynamics simulations, i.e. track each and every particle including all pairwise interactions. The two main candidates for such molecular dynamics simulations are the Fast Multipole Method (FMM) and the Barnes&Hut scheme (B&H). Tradeoffs are given, and simulation results for the B&H method implemented in the General Particle Tracer (GPT) code are presented for realistic testcases.  
Slides MOABC2 [54.203 MB]  
MOABC3  Simulating the LHC Collimation System with the Accelerator Physics Library MERLIN, and Loss Map Results  12 


Funding: FP7 EUCARD Cockcroft Institute We present large scale simulations of the LHC collimation system using the MERLIN code for calculations of loss maps, currently using up to 1.5·10^{9} halo particles. In the dispersion suppressors following the collimation regions, protons that have undergone diffractive interactions can be lost into the cold magnets. This causes radiation damage and could possibly cause a magnet quench in the future with higher stored beam energies. In order to correctly simulate the loss rates in these regions, a high statistics physics simulation must be created that includes both accurate beam physics, and an accurate description of the scattering of a 7 TeV proton in bulk materials. The current version includes the ability to simulate new possible materials for upgraded collimators, and advances to beamcollimator interactions, including protonnucleus interactions using the DonnachieLandshoff ReggePomeron scattering model. Magnet alignment and field errors are included, in addition to collimator jaw alignment errors, and their effects on the beam losses are systematically estimated. Collimator wakefield simulations are now fully parallel via MPI, and many other speed enhancements have been made. 

Slides MOABC3 [8.057 MB]  
MOACC1 
Beam Simulations for FLUTE, a Linac Based Compact THz Source  


FLUTE is a compact acceleratorbased THz source in the final design phase at the Karlsruhe Institute of Technology (KIT). The design is based on a 7 MeV photoinjector gun, Sband linac with a maximum energy of 50 MeV and a bunch compressor in order to study the production of coherent radiation in the Terahertz frequency range. In this paper comparative simulations of the beam dynamics in FLUTE with different simulation codes are presented. In addition, we show the results of error studies taking into account alignment errors, field errors, rferrors in amplitude and phase as well as timing errors of the gun laser in order to define tolerable limits in terms of bunch length and longitudinal bunch profile after the bunch compressor.  
Slides MOACC1 [1.478 MB]  
MOACC3  Tracking of a PETRA III Positron Bunch with a PreComputed Wake Matrix due to Electron Clouds  31 


Funding: Work supported by DFG under contract number RI 814/202. At the synchrotron radiation facility at DESY transversal tune spectra have been observed which are characteristic for an interaction of the positron beam with possible electron clouds in the ring. The filling patterns at which this incoherent tune shifts happen are favourable to the growth of the electron density, i.e. long bunch trains with short intrabunch distances or filling with short trains but also short distances between the trains. Eventually the vertical emittance growth with the originally designed equidistant filling (with 8 or 16 ns bunch spacing) has been avoided by fillings with shorter trains and longer gaps between the trains by still achieving the designed beam current of 100 mA. In this paper we examine the positron bunch stability of PETRA III for certain ecloud densities and bunch parameters. A PIC simulation of the interaction of the bunch with an ecloud yields the wake kick on the tail particles for an offset in the transverse centroid position of the head parts. With such a precomputed wake matrix, we investigate the stability of a single bunch by tracking it through the linear optics of the ring while at each turn applying the kick from the ecloud. 

Slides MOACC3 [5.237 MB]  
TUADI1  Storage Ring EDM Simulation: Methods and Results  99 


The idea of Electric Dipole Moment search using the electrostatic storage ring with polarized beam is based on accumulation of additional tiny spin rotation, about onebillionth of radians per second, occurred only in the presence of EDM. This method can be realized under condition of the longtime spin coherency ~1000 seconds. During this time each particle performs about 109 turns in ring moving on different trajectories. At such conditions the spinrotation aberrations associated with various types of space and time dependent nonlinearities start playing a crucial role. To design such a ring the computer simulation is necessary taking into account all factors affecting the spin. We used COSYInfinity and integrating program with symplectic RungeKutta methods in composition with analytic methods. We developed a new lattice based on the alternating spin rotating. As a result, we can achieve the SCT of ~5000 seconds. The difficulties of these studies are still in the fact that the aberrations growth is observed in the scale of 109 turns and few million particles. For this simulation we use a supercomputer with parallel computing process.  
Slides TUADI1 [0.951 MB]  
TUADC2 
Spin Dynamics in PTC: Normal Forms, Invariant Spin Fields, and Resonance Strengths  


Funding: This work supported in part by the US DOE Office No. DESC0004432. Over the past several years, Forest has added spin motion and related capabilities to PTC [1]. The capabilities include, via FPP [2], the computation of a spin normal form. This normal form, and the associated normalising maps for orbit and spin, provide us with immediate access to important quantities, including the invariant spin field and resonance strengths. The algorithms in PTC/FPP thus represent an alternative approach to computing significant quantities for the analysis of spin dynamics in particle accelerators. We describe the PTC algorithm, note similarities with the case of the orbital normal form, and give illustrative examples. In particular, we apply PTC to the wellunderstood COSY lattice, and we compare the results computed by PTC with those computed by the welltested code EpsSLICK [3]. [1] E. Forest, F. Schmidt, and E. McIntosh, KEK Report 20023. [2] E. Forest, Y. Nogiwa, and F. Schmidt, ICAP2006, p. 191193. [3] D. Barber, DESY Report, DESY200915. 

Slides TUADC2 [1.595 MB]  
TUADC3  Implementing New Beam Line Elements into a Moment Method Beam Dynamics Code  104 


Funding: This research is funded by grant "KUL 3E100118" "Electromagnetic Field Simulation for Future Particle Accelerators". Developing beam dynamics simulation tools using the moment method has advantages in terms of precision and efficiency when interests lie in average or rms dimensions of the beam, projected emittances or total energy. The moment method implemented in the VCode solves the Vlasov equation by time integration, from an initial particle distribution represented by a discrete set of characteristic moments, accounting for all acting internal and external forces along the particle's path. The moment method delivers highly accurate beam dynamics results within a very small CPU time. This article proposes, illustrates and validates a new beam line element for a radiofrequency quadrupole (RFQ) for insertion in the VCode. The focus will be on the RFQ cell structure, the electric field distribution and the insertion of the field distribution in the moment code. 

Slides TUADC3 [4.387 MB]  
WESAI3  Simulating the Wire Compensation of LHC Longrange Beambeam Effects  135 


The performance of the Large Hadron Collider (LHC) and its minimum crossing angle are limited by longrange beambeam collisions. Wire compensators can mitigate part of the longrange effects. We perform simulations to explore the efficiency of the compensation at possible wire locations by examining the tune footprint and the dynamic aperture. Starting from the weakstrong simulation code BBTrack we developed a new Lyapunov calculation tool, which seems to better diagnose regular or chaotic particle behavior. We also developed faster ways to execute the simulation and the postprocessing. These modifications have allowed us to study different wire positions (longitudinal and transverse), varying wire currents, several wire shapes, and a range of beambeam crossing angles, in view of a prototype wire installation in the LHC foreseen for 2014/15. Our simulations demonstrate that the wire can provide a good compensation,also for reduced crossing angle. Benefits of an LHC wire compensator include a better overlap of colliding bunches,as well as the possibility of smaller β^{*} or higher beam current  
Slides WESAI3 [17.486 MB]  
WESAI4  Electron Cloud Simulations with PyECLOUD  138 


PyECLOUD is a newly developed code for the simulation of the electron cloud (EC) buildup in particle accelerators. Almost entirely written in Python, it is mostly based on the physical models already used in the ECLOUD code but, thanks to the implementation of new optimized algorithms, it exhibits a significantly improved performance in accuracy, speed, reliability and flexibility. PyECLOUD simulations have been already broadly employed for benchmarking the EC observations in the Large Hadron Collider (LHC). Thanks to the new feature of running EC simulations with bunchbybunch length and intensity data from machine measurements, the “scrubbing” process of the LHC beam pipes could be reconstructed from heat load measurements in the cryogenic dipoles. In addition, PyECLOUD simulations also provide the estimation of the bunchbybunch energy loss, which can be compared with the measurements of the stable phase shift. They can also provide the correct EC distribution data for beam dynamics simulations with the HEADTAIL code.  
Slides WESAI4 [3.466 MB]  
WEP01  Simulations for Ion Clearing in an ERL  143 


Funding: supported by BMBF under contract no. 05K10HRC Energy Recovery Linacs (ERLs) being the most promising candidates for nextgeneration light sources put very high demands on preservation of beam brightness and reduction of beam losses. Thus, it is mandatory to avoid the impact of ionized residual gas considered as a source for instabilities in accelerators. Recently, we have presented simulations for the clearing of ionized residual gas with electrodes performed with an upgraded version of software package MOEVE PIC Tracking [1] which is being currently further developed to model the interaction of the ions with the electron beam in presence of external electromagnetic potentials such as the field of clearing electrodes. The tracking code allows for studies on clearing times for electrodes with different voltage as well as detailed studies of the behavior of the ions in the environment of the electrodes. In this paper we take further steps to study possible designs of clearing electrodes. Especially, we will consider the influence of different gas mixtures on clearing times and possible configurations for the clearing electrodes. We use parameters planned for BERLinPro as an example for our studies. [1] G. Pöplau, A. Meseck, U. van Rienen, Simulation of the Behavior of Ionized Residual Gas in the Field of Electrodes, IPAC 2012, New Orleans. 

WEP02  Numerical Studies on the Influence of Fill Patterns on Ion Clouds  146 


Funding: supported by BMBF under contract no. 05K10HRC Energy Recovery Linacs (ERLs) are the most promising candidates for nextgeneration light sources now under active development. An optimal performance of these machines requires the preservation of the high beam brightness generated in the injector. For this, the impact of the ionized residual gas on the beam has to be avoided as it causes instabilities and emittance growth. Obviously, the vacuum chamber has to be cleared out of ions but as the potential of the electron beam attracts the ions, it is not enough to install vacuum pumps. One measure for ion clearing are gaps in the bunch train long enough that the ions have time to escape the force of the bunch potential. In this paper, we present numerical studies of the behavior of an ion cloud that interacts with a bunch train. Especially, we consider different distributions for the particles in the bunch, different fill patterns and several mixtures of ions in the residual gas. The simulations are performed with the package MOEVE PIC Tracking. The presented numerical investigations take into account the parameters of the ERL BERLinPro with the objective to deduce appropriate measures for the design and operation of BERLinPro. 

WEP03 
Tune Analysis by Particle Tracking in KIRAMS430 Superconducting Cyclotron  


This paper shows the results of the tune analysis by fitting the particle's trajectory around equilibrium orbits of KIRAMS430 superconducting cyclotron. In the analysis, the beam trajectory fits well with sine waves of 3 frequencies of ν_{r}, NSectorν_{r}, NSector+ν_{r} in radial motion and ν_{z}, NSectorν_{z}, NSectorν_{z} at axial motion. The homemade SIMCODE tracking package with Mathematica program has been used for this analysis to get equilibrium orbits and simulate beam trajectories, and analysis the tune of thos trajectories with 3 sine waves.  
WEP04 
Comparison of Beam Tracking Codes for KIRAMS430 High Energy Beam Transport  


An accurate beam transverse size control at the isocenter is one of the most crucial clinical requirements for particle therapy. The RMS beam transverse sizes at the isocenter are in 3 mm to 10 mm range with beam energy from 430 MeV/u to 145 MeV/u. Beam tracking study with realistic magnetic field distribution is mandatory to predict accurate beam transverse size. In order to estimate beam size accurately, the effects of chromaticity and multipole field components were evaluated with various beam tracking codes. With the comparisons, further analysis direction is established.  
WEP06  Particle Tracking in Electrostatic Fields with Energy Conservation  149 


The key idea of the research is to consider spin dynamics in electrostatic fields. Due to the fact, that spin rotation frequency explicitly depends on velocity of the particle and its kinetic energy is changed in electrostatic fields it is important to use some technique that provides both conservation energy and symplicticity condition. An appropriate mathematical model is described and the results of numerical calculation are shown. In conclusion, fringe fields influence is examined and compared with case of ideal fields.  
WEACC2  Space Charge Effects and Focusing Methods for Laser Accelerated Ion Beams  184 


Funding: GSI Helmholtzzentrum für Schwerionenforschung Planckstr. 1 D64291 Darmstadt We employ the 3D PIC simulation code VORPAL to study the transport of laser accelerated proton beams in the framework of the LIGHT project at GSI. Initially the beam is assumed to be neutralized by comoving electrons. For different initial beam distribution models we study the effect of space charge after the electrons have been removed. The results of the simulations are compared to an envelope model. We derive conditions in terms of the beam parameters and the distance from the production target for a safe removal of the electrons. As an option for the controlled deneutralization of the beam a thin metallic foil is studied. Besides space charge, we also account for the effect of secondary electrons generated from the foil. 

Slides WEACC2 [0.993 MB]  
WEACC3  Matrix Formalism for Longterm Evolution of Charged Particle and Spin Dynamics in Electrostatic Fields  187 


The matrix formalism as a numerical approach for solving of ODE equations is considered. It is a map method and has several advantages over classical stepbystep integration methods. This approach allows to present the solution as set of numerical matrices. A complete derivation of the equations this method is based on will be shown. Problems of symplectification and computing performance are discussed. We have developed an application that provides a tool for differential equations solving. The developed program allows to generate the final programming codes on C++, Fortran, MATLAB, C#, Java languages. The given approach is applied to longterm evolution of charged particle and spin dynamics in electrostatic fields.  
Slides WEACC3 [1.441 MB]  
THAAI3  MADX Progress and Future Plans  211 


The design efforts for the High Luminosity upgrade of the Large Hadron Collider (HLLHC) will require significant extensions of the MADX code widely used for designing and simulating particle accelerators. These changes are framed into a global redesign of the MADX architecture meant to consolidate its structure, increase its robustness and flexibility, and improve its performance. Some examples of recent extensions to MADX like the RFmultipole element will be presented. Improvement for models and algorithms selection providing better consistency of the results and a wider range of use will be discussed. The computation efficiency will also be addressed to better profit of recent technologies. In this paper, we will describe the last improvements and the future plans of the project.  
Slides THAAI3 [6.830 MB]  
THP02  Beam Dynamics Simulations Using GPUs  227 


PATRIC is a particle tracking code used at GSI to study collective effects in the FAIR synchrotrons. Due to the need for calculationintense simulations, parallel programming methods are being explored to optimize calculation performance. Presently the tracking part of the code is parallelized using MPI, where each node represents one slice of the particles that travel through the accelerator. In this contribution different strategies will be presented to additionally employ GPUs in PATRIC and exploit their support for data parallelism without major code modifications to the original tracking code. Some consequences of using only singleprecision in beam dynamics simulations will be discussed.  
THP03 
GPUAccelerated Spin Dynamics and Analysis for RHIC  


Funding: This work supported in part by the US DOE Office No. DESC0004432. Graphics processing units (GPUs) have now become powerful tools for scientific computation. Here we present our work on using GPUs to speed the tracking of both orbital and spin degrees of freedom in particle accelerators. This work includes the development of new spin integrators that are both fast and accurate. We have also developed an integrated set of tools for analysing the results. To demonstrate the utility of these new tools, we use them to study the spin dynamics of protons in the Relativistic Heavy Ion Collider at Brookhaven National Lab. 

THSCI1 
Rigorous Fixed Point Enclosures and their Application to HighOrder Transfer Maps  


Funding: This work was supported in part by the US Department of Energy and the Studienstiftung des Deutschen Volkes. A common task in the design and analysis of an accelerator is the study of the transfer map of the system. Of particular interest is the estimation of the region of stability of a given system. Typically, this is done using symplectic particle tracking and visual analysis of the resulting Poincare maps for signatures of chaoticity and island structures near highperiod fixed points. We describe a method to compute rigorous enclosures of all periodic points of a given order in a given map based on Taylor Model methods. We then apply this algorithm to a real world transfer map of the Tevatron accelerator to rigorously identify islands and resonances in its transfer map. This mathematically rigorous method to locate resonances in the transfer map automatically yields all regions where resonances up to a certain order appear. The island structure exhibited by the map in those regions is then studied further by computing the invariant manifolds associated with the hyperbolic periodic points of the map. This manifold structure can provide further insight into the dynamics of the map, including the emergence of chaotic motion at the appearance of crossings of the manifolds. 

Slides THSCI1 [3.230 MB]  
THADI1 
Multilevel Optimization of FELs  


The operation of freeelectron lasers with high performance depends on the design of the facility and on the choice of working points. Both are based on numerical simulations of beam dynamics. Such tracking calculations of charged particles in electromagnetic fields require the simultaneous solution of the equation of motion and of Maxwell’s equations. The effort for high level models, that consider physical effects from first principles, is limited by the capabilities of modern computer clusters. The resolution and precision is chosen so that a result is achieved in hours, days or weeks. On the other hand, many fine details and effects can be omitted at the beginning or taken into account analytically. Such simple models allow fast scans to be carried out that deliver the desired results in minutes. Of course, the results of the simple models should later be checked and modified with the full one.  
Slides THADI1 [4.567 MB]  
THADC2 
Precision Nonlinear Dynamics in Electrostatic Rings for EDM Studies  


Funding: US Department of Energy Recent interest electric dipole moments of hadrons and light nuclei necessitates the design of storage ring designs relying on electrostatic elements for deflection and focusing. Since the effects of interest are exceedingly small and difficult to extract from the dynamics, unusually high precision in the understanding of the linear and nonlinear optics is required. This leads to the need of precise treatment of a various effects that are often of subdued importance, including the detailed shape of fringe fields and their influence on steering, spin flip devices, and rf cavities out of synch with the frequency of the ring. In all studies, it is important to perform symplectic tracking for the full spinorbit dynamics. At the same time it is necessary to preserve the particle’s energy during transversal of electric potentials, errors in which are similarly detrimental as errors in symplecticity. Unfortunately it is known that schemes to preserve symplecticity do not simultaneously preserve energy and vice versa. We present some hybrid approaches based on highorder maps that minimize the violations of either invariant while minimally impacting spinorbit motion. 

THADC3 
Nonlinear, Nonscaling CW FFAG Design and Modeling Using Map Methods  


Funding: US Department of Energy, FNAL, Particle Accelerator Corporation FFAGs are being considered for various new classes of accelerators, including proton drivers for muon colliders and neutrino factories, for accelerator driven subcritical reactors, and for medical applications. Their key advantages are compactness, CW operation and large acceptance. However, due to the complicated field arrangements, beam dynamics simulations are challenging for conventional simulation codes. Among various levels of sophistication of dealing with beam elements, one of the most advanced modes of the code COSY INFINITY computes the 3D field distributions along the trajectory of the particles, not only at the point of interest but also in the neighborhood with functional dependencies, using DA PDE solvers based on Differential Algebraic techniques. The scheme allows the code developer and user to describe rather complicated field arrangements with rather limited effort. Of particular advantage is the seamless integration with mapbased symplectic tracking schemes. The methods are illustrated in design studies of FFAGs for various different machine types, including both conventional strong focusing and continuously varying combined function setups. 

Slides THADC3 [3.843 MB]  