The effect of radiation reaction is often negligible in inverse Compton scattering. However, in the nonlinear Compton regime, at high laser fields and high electron beam energies where electron recoil must be properly accounted for, there is experimental data which demonstrates the onset of radiation reaction * . We model the radiation reaction as a series of emissions from individual electrons with decreasing energy. This allows us to use the code we previously developed for simulating single-emission inverse Compton scattering events ** . We use the new code to simulate the experiment reported in Cole et al. 2018, and to compare it to other models of radiation reaction.

X-ray flash radiography is a powerful diagnostic used worldwide for investigating the structural response of matter under impulsive loading during hydrodynamic experiments. These experiments require a specific X-Ray source generated by a Linear Induction Accelerator (LIA). LIAs produce an intense electron pulsed beam, with a high-energy and providing a high dose at 1 m. Therefore, comprehension and prediction of the electron beam dynamic are essential to guarantee correct realization of the hydrodynamic experiments. At CEA DAM, X-Ray flash radiography experiments are performed on the UK/FR joint facility EPURE, a unique triple-axis radiographic facility with two LIAs and one Inductive Voltage Adder “MERLIN”. In this study, envelope and particle-in-cell codes simulate the electron beam transport from the production of the beam in the injector to its transport along the accelerator. Thanks to the developed models, parametric studies are made about the influence of beam parameters, as the initial emittance, on the transport. Moreover, the developed codes take into account some beam instabilities, as the beam breakup instability or corkscrew motion. Studies show that the initial beam centroid offset has a significant impact on the beam instabilities during the transport. In addition, simulation results are compared with experimental data acquired on the EPURE facility, notably comparisons about our method to center the beam for limiting beam instabilities.

Accurate and efficient particle tracking through Siberian Snakes is crucial to building comprehensive accelerator simulation model. At the Alternating Gradient Synchrotron (AGS) and Relativistic Heavy Ion Collider (RHIC), Siberian Snakes are traditionally modeled in MAD-X by Taylor map matrices generated at specific current and energy configurations. This method falls short during ramping due to the nonphysical jumps between matrices. Another common method is to use grid field maps for the Snakes, but field map files are usually very large and thus cumbersome to use. In this work, we apply a new method called the Generalized Gradient (GG) map formalism to model complex fields in Siberian Snakes. GG formalism provides an analytic function in x and y for which automatic differentiation, i.e. Differential Algebra or Truncated Power Series Algebra can find accurate high order maps. We present simulation results of the Siberian Snakes in both the AGS and RHIC using the Bmad toolkit for accelerator simulation, demonstrating that GG formalism provides accurate particle tracking results.

Optimization and design of particle accelerators is challenging due to the large number of free parameters and the corresponding lack of gradient information available to the optimizer. Thus, full optimization of large beamlines becomes infeasible due to the exponential growth of free parameter space the optimization algorithm must navigate. Providing exact or approximate gradient information to the optimizer can significantly improve convergence speed, enabling practical optimization of high-dimensional problems. To achieve this, we have leveraged state-of-the-art automatic differentiation techniques developed by the machine learning community to enable end-to-end differentiable particle tracking simulations. We demonstrate that even a simple tracking simulation with gradient information can be used to significantly improve beamline design optimization. Furthermore, we show the flexibility of our implementation with various applications that make use of different kinds of derivative information.

The existing code for particle scattering and tracking in collimation systems integrated in SixTrack, called K2, was migrated from the current software in FORTRAN, to a new Python/C interface integrated in the Xsuite tracking code that is being developed at CERN. This is an essential step towards a full integration of collimation studies using Xtrack, and will allow profiting from GPU computing advances and the BOINC volunteer computing network. Furthermore, several improvements to the functionality of the code were introduced, for example aperture interpolation for more precise longitudinal location of particle losses in a collimator. A thorough testing of the new implementation was performed, using as case studies various collimation layout configurations for the LHC Run 3 and HL-LHC. In this paper, the challenges are outlined and the first results are presented, including simulated loss maps which are compared to the reference results generated by SixTrack.

We present the latest updates to the PLACET3 tracking package which focus on the impact of both transverse and longitudinal wakefields on a beam travelling through accelerating and decelerating structures. The main focus of this update was the first implementation of 6D tracking through Power Extraction and Transfer Structures (PETS) for the Compact Linear Collider (CLIC) which is described through short and long-range longitudinal wakefields. Additionally, we present the impact of different numerical schemes on the computation of wakefields in accelerating structures.

Traditionally PIC solver compute electric field created by the beam as a mean field. The effect of particle collisions is normally neglected by the algorithm. In this proceeding we address how to include the collisions between the macro particles, and discuss the computational challenges and strategies to include the collisionallity in PIC solvers as particle-particle interaction. We present simulations that benchmark our understanding and analyse potential artifacts as energy conservation or other effects.

The description of coupling phenomena in electron storage rings is extended beyond the very common formula based on the coupled Hamiltonian [1] into the region where the small coupling is in competition with damping and diffusion from synchrotron radiation. In the derivation, the moment mapping approach is used in combination with the simplified simulation of radiation effects introduced by Hirata and Ruggiero [2]. The results of this theoretical approach are compared to the predictions of well-established theories dealing with coupling in electron storage rings: The envelope mapping approach from Ohmi, et al. [3], and Chao’s SLIM approach [4]. [1] G. Guignard, “Betatron coupling and related impact of radiation”, Phys. Rev. E 51, 6104, June 1995, or his contributions to CERN Accelerator Schools [2] K. Hirata, F. Ruggiero in “Treatment of Radiation for Multiparticle Tracking in Electron Storage Rings”, Part. Acc. Vol. 28, pp. 137-142 (1990) [3] K. Ohmi, et al., in “From the Beam-Envelope Matrix to Synchrotron-Radiation Integrals”, Phys. Rev. E, Vol. 49, p. 751 [4] A. Chao, in ”Evaluation of Beam Distribution Parameters in an Electron Storage Ring”, J. Appl. Phys. 50, 595 (1979) or SLAC-PUB-2143, June 1978

Linear coupling in storage rings mixes horizontal and vertical beam motion. This is similar to the mixing of states in an atomic two-level system by a resonant laser interaction or the mixing of the two states of any spin-½ particle in static and dynamic external magnetic fields like, for example, in nuclear magnetic resonance, NMR, measurements. These coupled two-level systems are usually described by the Bloch equation [1] which is a set of coupled, first-order differential equations connecting the population of the states with some other parameters which contain in addition to the strength of the coupling and the detuning, some sort of phase information of the involved states. In linearly coupled storage rings horizontal and vertical emittance can be viewed as the population of ground and excited level and it will be shown that the Bloch equations can also model the time-dependent evolution of the transverse emittances of an ensemble of circulating particles. This is especially useful in cases where the emittance is exchanged by crossing the coupling resonance or where the coupling strength itself is a function of time. [1] F. Bloch, “Nuclear induction,” Physical Review, vol. 70, no. 7-8, pp. 460–474, 1946.

Beam Delivery Simulation (BDSIM) is a program based on Geant4 that creates 3D radiation transport models of accelerators from a simple optical description in a vastly reduced time with great flexibility. It also uses ROOT and CLHEP to create a single simulation model that can accurately track all particles species in an accelerator to predict and understand beam losses, secondary radiation, dosimetric quantities and their origins. We present a broad overview of new features added to BDSIM in version 1.7. In particular, the ability to transform and reflect field maps as well as visualise the fields in Geant4 are presented. A new “CT” object is introduced to allow DICOM images to be used for simulations of Phantoms in proximity to a beamline. For experiments such as FASER, SHADOWS and NA62, a muon production biasing scheme has been added and is presented.

The self-consistent nonlinear dynamics of a relativistic charged particle beam interacting with its complete self-fields is a fundamental problem underpinning many of the accelerator design issues in high brightness beam applications, as well as the development of advanced accelerators. A novel self-consistent code is developed based on a Lagrangian method for the calculation of the particles’ radiation near-fields using wavefront/wavelet meshes via the Green’s function of the Maxwell equations. These fields are then interpolated onto a moving mesh for dynamic update of the beam. This method allows radiation co-propagation and self-consistent interaction with the beam in 2D/3D simulations at greatly reduced numerical errors. Multiple levels of parallelisms are inherent in this method and implemented in our code CoSyR [1] to enable at-scale simulations of nonlinear beam dynamics on modern computing platforms using MPI, multi-threading, and GPUs. Our simulations reveal the slice emittance growth in a bend and the interplay between the longitudinal and transverse dynamics that occurs in a complex manner not captured in the 1D longitudinal static-state coherent synchrotron radiation model. Finally, we show that surrogate models with symplectic neural networks can be trained from simulations with significant time-savings for the modeling of nonlinear beam dynamics effects.

The effect of radiation reaction is often negligible in inverse Compton scattering. However, in the nonlinear Compton regime, at high laser fields and high electron beam energies where electron recoil must be properly accounted for, there is experimental data which demonstrates the onset of radiation reaction * . We model the radiation reaction as a series of emissions from individual electrons with decreasing energy. This allows us to use the code we previously developed for simulating single-emission inverse Compton scattering events ** . We use the new code to simulate the experiment reported in Cole et al. 2018, and to compare it to other models of radiation reaction.

An accelerating charged particle emits electromagnetic radiation. The motion of the particle is further damped via self-interaction with its own radiation. For relativistic particles, the subsequent motion is described via a correction to the Lorentz force, known as the Lorentz-Abraham-Dirac force. The aim of this research is to use the Lorentz-Abraham-Dirac force to computationally simulate the radiation damping that occurs during nonlinear inverse Compton scattering. We build on our previous work and the code which simulates single-emission inverse Compton scattering to incorporate the effect of multiple emissions, thereby modeling the radiation reaction.

OPAL (Object Oriented Parallel Accelerator Library) is a C++ based massively parallel open-source program for tracking charged particles in large scale accelerator structures and beam lines, including 3D space charge, collisions, particle-matter-gas interaction, and 3D undulator radiation. The meticulous parallel architecture allows large and difficult problems, including one-to-one simulations with high resolution and no macro particles, to be tackled in a reasonable amount of time. The current code state as well as the most recent physics advancements and upgrades are discussed, including the unique feature of a sampler for creating massive, labeled data sets with tens of thousands of cores for machine learning. We also demonstrate scalability of our core algorithms up to 4600 GPUs and 32'000 CPUs, as part of our effort to make OPAL exascale ready.

The industrial, medical and homeland security markets for low-to-moderate energy electron linacs are growing rapidly, often requiring beam currents that strongly load the accelerating fields. The two-beam accelerator (TBA) is one concept for the structure wakefield acceleration approach to an electron-positron collider. Transient beam loading effects are a significant challenge for the drive beam in a TBA structure, where energy droop in high-charge bunch trains must be understood and compensated. The Hellweg code accurately models steady state beam loading for traveling wave RF structures with a fast reduced model. The Hellweg equations of motion have recently been generalized to include arbitrary charge-to-mass ratio and to use momentum as the dynamical variable. These and other recent developments are discussed, including a new browser-based GUI. Proposed future developments include support of standing wave RF structures and transient beam loading effects.

PyTao is a Python interface to the Bmad based Tao program for accelerator design and simulation. This enables advanced design and optimization beyond the normal capabilities of Tao as well as simplifying the use of Tao as an online model for an operating accelerator. Here we will describe this interface and some of its applications, including online models for the the LCLS and LCLS-II at SLAC National Accelerator Laboratory.

In the injector section of electron linacs, both internal space charge forces and wakefield effects influence the beam dynamics. To account for both effects, full electromagnetic PIC simulations are usually required. Unfortunately, PIC solvers require large computational resources. On the other hand, particle-tracking codes in the bunch reference frame describe the beam dynamics under space-charge fields. These codes, however, often fail to include the effect of geometric wakefields especially for low energy beams. As an alternative modeling approach, we propose to decouple the wakefield scattered by the geometry from the space-charge field. Then, we use for each of the contributions the simulation approach that is more appropriate for the respective interaction. We decompose the total electromagnetic field into an incident and a scattered part. The incident field is computed by a space-charge solver in the rest frame of the bunch assuming that particles are in free space. Since this field does not fulfill the boundary conditions at the chamber walls, it acts as an excitation for the scattered part. The latter can be efficiently computed using a particle-free wakefield code. In the full paper, we will present beam dynamics simulations for the injector section of the European XFEL. The aim of these simulations is the quantification of the uncorrelated energy spread induced by geometric wakefields at low energies, which so far is not considered in existing wakefield models.

The Generalized Gradient (GG) formalism of Venturini and Dragt for describing static magnetic or electric fields has been implemented in the Bmad toolkit for accelerator simulations. In conjunction with this, a new method for calculating GG derivatives from a field table has been developed which avoids some of the problems of the Venturini and Dragt method. Generalized gradients are also implemented in the PTC toolkit developed by Etienne Forest which is interfaced to Bmad. This allows for construction of spin/orbital Taylor maps useful for nonlinear analysis and rapid tracking.

The Accelerator Toolbox (AT) is a multipurpose tracking and lattice design code relying on a C tracking engine. Its MATLAB interface is widely used in the light source community for beam dynamics simulation and can be integrated in control systems through the MATLAB Middle Layer. In recent years major effort was made to develop a python interface to AT: pyAT. In this framework, several features were added to pyAT, in particular, the introductions of the 6D optics dynamic aperture and lifetime calculation, single and multi-bunch collective effects simulations and parallelized tracking capabilities. A python ring simulator was also developed based on pyAT for offline modeling of the accelerator control system. Following a presentation of the structure and main features of AT, an overview of these recent developments is provided.

Tracy, the code base used for designing synchrotron light sources with predictable performance, has been significantly refactored. Furthermore it now uses mad-ng gtpsa library. We describe the achieved progress, discuss its python interface. We show how to use it for achieving a robust design for a modern synchrhotron light source.

A common feature in the design of low-emittance lattices is the small momentum compaction, which implies a short nominal equilibrium bunch length. A short bunch length can lead to beam-induced heating of the storage ring vacuum components, and, combined with the small transverse emittances, can degrade the beam quality and pose severe limitations on the beam lifetime. To mitigate the aforementioned issues and improve the lifetime and quality of the beam, a common procedure is to use a higher-harmonic cavity (HHC) system, which leads to an increase of the equilibrium bunch length without an increase of the energy spread. An important issue in the design of an HHC system is the proper choice of the multi-bunch configuration and the HHC parameters, both in terms of HHC performance limitations and beam stability. In this contribution we discuss numerical simulations of HHC effects, with parameters of a 3HC system for the NSLS-II low-emittance upgrade, addressing both beam stability and the performance limitation due to a gap in the uniform multi-bunch configuration.

The tracking code RF-Track has been updated to include a large set of single-particle and collective effects: beam loading in standing and travelling wave structures, coherent and incoherent synchrotron radiation, intra-beam scattering, multiple Coulomb scattering in materials, and particle lifetime. This new set of effects was focused on the simulation of high-intensity machines such as linacs for medical applications. In these apparatuses, the beam propagation into air and water significantly impacts the beam propagation to and through the patient. Now, these effects can be included by design. Additionally, RF-Track can now simulate the cooling channel of a future muon collider.

Current analytical beam tomography methods require an accurate representation of the beam transport matrix between the reconstruction and measurement locations. In addition, these methods need the transport matrix to be linear as the technique depends on a simple mapping of the projections between the two areas, a rotation, and a scaling. This work will explore expanding beam tomography for transversely coupled beam and non-linear beam transports.