14th International Computational Accelerator Physics Conference

The beam longitudinal dynamics code BLonD is a framework developed in the RF group at CERN since 2014. It has emerged as a central tool for performing particle tracking simulations in the longitudinal plane in synchrotrons. This talk covers several applications for existing accelerator facilities (e.g., Proton Synchrotron Booster, Large Hadron Collider, etc.) and future projects. The main code features including, among others, beam generation, collective effects, and interactions with RF control loops, as well as recent optimizations that enabled complex simulations will be presented. Further development plans will also be briefly discussed.

High-order transfer maps offer many advantages in the study of both single-pass systems, where they represent optical aberrations, and multi-pass systems, where they allow the direct computation of relevant properties like high-order dispersions, chromaticities, and amplitude- and parameter dependent tune shifts. They also allow for symplectic tracking even for very complicated systems that cannot be described by inherently symplectic kicks and related methods. However, one remaining question is always how accurate a map of a given expansion order really is – while in many cases, the sizes of high order contributions decrease as a function of order, this does not always have to be the case, for example for the muon g-2 ring, strong nonlinearities newly arise at order 9 and beyond. In this talk, we present methods to determine mathematically rigorous bounds on all missing orders beyond the one explicitly considered. The computational effort to determine these bounds is small compared to the cost of the underlying high-order transfer map computation.

Slow beam losses have been consistently observed during operation of the Large Hadron Collider (LHC) with closely-spaced proton bunches. Observations after dedicated studies support that a significant part of the losses is driven by the non-linear forces of electron clouds in the Inner Triplet quadrupoles of the LHC. This contribution presents a method for efficient weak-strong simulations of the effect of electron clouds forming in the two-beam chamber of the Inner Triplets, where the closed orbit and the betatron functions of both beams vary considerably along the longitudinal coordinate. Finally, dynamic aperture simulations confirm the negative impact from these effects in the operational configuration of the LHC during Run 2 and Run 3.

The nonlinear space-charge effects play an important role in
high intensity high brightness particle accelerators.
In this talk, we will report on progress in modeling space-charge
effects in recent years.
We will discuss about simulating the space-charge effects using
a quantum Schrodinger approach and possible implementation on
quantum computers. We will also discuss differentiable space-charge
modeling for accelerator design.

CERN has recently launched the Efficient Particle Accelerators (EPA) project to enhance the reliability, efficiency, and beam performance of its injector complex. Over the next five years, both classical automation concepts and advanced machine learning (ML) techniques will be pivotal in achieving the project's goals. This talk will provide a brief overview of the EPA project scope and CERN’s control systems infrastructure, before delving into the application of ML techniques in various aspects of beam operations.

Key topics will include equipment automation, the mitigation of magnetic hysteresis effects, dynamic beam scheduling, and the implementation of on-demand optimization and continuous control. The discussion will feature specific (near-)operational examples, highlighting the challenges encountered and lessons learned from integrating ML into the control room. The presentation will conclude with an outlook on future plans and the timeline for the EPA project.

Fourth-generation synchrotron light sources enable orders-of-magnitude increases in beam brightness and corresponding X-ray source flux. Operating these machines at such high energy densities necessitates improvements in machine protection systems, as equipment failures may trigger beam aborts capable of depositing significant energy in collimators and beam dumps. We present a code coupling methodology capable of estimating the deposition and response of collimator materials under irradiation of high-intensity electron beams. Our approach integrates particle dynamics modeling via elegant, particle-matter interaction via FLUKA, and hydrodynamic evolution of collimator material via FLASH. Careful arrangement and iteration between these three codes enables self-consistent modeling of the beam and structure response during simulated beam aborts. We apply these tools to the study of the APS-U storage ring, leveraging recent experiments with the APS to inform collimator material state characterization and response. We discuss the role of material response and phase change in determining the loss-characteristics of the beam and present comparisons of these simulations under different machine operating conditions and material response models. We also discuss efforts to enhance modeling efficacy and next steps in expanding the physics capabilities of our models.

Accurate and efficient numerical modeling of beam propagation in RF accelerator cavities is inevitable for understanding and optimizing cavity characteristics in electron accelerators. Existing modeling tools are typically based on differential equation-based electromagnetic solvers, such as CST or ACE3P. These solvers require volumetric discretization of the computational domain and can suffer from numerical dispersion, both leading to high computational costs for high-fidelity wide-band modeling. This work investigates several boundary element method (i.e., Green's function)-based algorithms, which do not require volumetric mesh and are free from numerical dispersion. These methods can be further augmented by fast compression-based algorithms and high-order discretization. We demonstrate the efficacy of the proposed algorithm for both time-harmonic and transient modeling beam-cavity interaction. This is joint work with Tianhuan Luo, Ji Qiang, Yikai-Kan, Mustafa Rahman, and Sherry Li from Lawrence Berkeley National Lab.

Finite element non-overlapping Domain Decomposition Methods (DDMs) based on the Schwarz method are promising iterative techniques for addressing large-scale electromagnetic wave problems in the frequency domain. The convergence of these methods highly depends on the transmission conditions (TCs) employed between subdomains. Typically used TCs, which are based on free space open boundary conditions, face issues when applied to guided wave problems, such as those encountered in in-vacuum undulators (IVUs). Higher-order variants struggle with convergence around cutoff frequencies of modes at interfaces, while zeroth-order TCs fail completely for evanescent waves. Superior convergence is obtained by considering the physics of the waves travelling through the interfaces, which leads to the modal transmission condition (MTC).

In this contribution, we extend the MTC to include a particle beam through the domain interfaces, making the method applicable to problems encountered in particle accelerators. We apply this enhanced MTC to the electromagnetic simulation of an in-vacuum undulator at PETRA, DESY. The Schwarz domain decomposition method allows the problem to be divided into several subproblems, which can be distributed across nodes of an HPC cluster. The MTC enables particularly efficient use of HPC resources by significantly reducing the number of iterations required, while adding only minimal computational overhead compared to a zeroth-order free space TC.

In the field of accelerator physics, the determination of electromagnetic wakefields and their impact on accelerator performance remains a critical challenge. These wakefields, generated within the accelerator vacuum chamber by the interaction between the structure and a passing beam, significantly influence machine behavior. Characterizing these effects through beam-coupling impedance is essential for predicting power dissipation and maintaining beam stability. For simple structures, beam-coupling impedance can be computed using analytical formulas. However, realistic accelerator devices require full-wave 3D numerical soluctions of Maxwell's Equations. In the framework of CERN's open science mission, this paper presents "wakis", an open-source 3D electromagnetic time-domain solver designed to compute wake potential and impedance for both longitudinal and transverse planes in general 3D structures. Fully implemented in Python, the tool includes features such as the incorporation of material tensors (permittivity, permeability, conductivity) with support for anisotropy, and a CAD geometry importer (.stl format) for defining embedded boundaries and material regions. It supports various boundary conditions including PEC, PMC, periodic, ABC-FOEXTRAP, and multiple time-domain sources such as particle beams with custom profiles, plane waves, and wave packets. The fully exposed API allows dynamic modification of material tensors and fields during simulations, leveraging NumPy and SciPy sparse routines for efficient calculations. Additionally, "wakis" offers on-the-fly 1D, 2D, and 3D vtk-based plotting capabilities, optimized memory consumption, and GPU acceleration via CuPy/CuPyx. "wakis" is under continuous development on GitHub, aiming to provide an open-source platform for the community to collaboratively address future accelerator challenges and surpass current software limitations.

The calculation of wake impedances in a resonator is difficult. The wakelength that needs to be considered extends enormously due to the high quality factors of the different resonant modes.
This makes calculating wake impedances with a wake field solver computationally very expensive.
The eigenmode solver was designed to calculate the field distribution of electromagnetic fields in resonant structures. It solves for the desired field values in a quick and precise manner.
The wake impedances \begin{align}
Z_\parallel(\omega) &= - \frac{1}{\tilde{I}} \int_{-\infty}^{\infty}\text{d}z \tilde{E}z(z)\, e^{jkz}\
Z\perp(r_b, \omega) &= - \frac{j}{\tilde{I}\, r_b} \int_{-\infty}^{\infty}\text{d}z \left[ \tilde{E}(r_b, z) + v
\times \tilde{B}(r_b, z)\right]_\perp \, e^{jkz}
\end{align} can be directly calculated from electromagnetic field components.
It assumes the field to be excited by a beam with the Fourier transformed charge density $\tilde{I}$ travelling with the velocity $v$ in $z$-direction and a possible transverse offset $r_b$.
This work aims to find the method to calculate the transverse shunt impedance directly from the field solutions of the eigenmode solver. Thus, the approach will be developed on the basis of the fundamental understanding of wake fields. Finally, the impedances of an exemplary problem calculated using this method will be compared with the results of the common wakefield solver and the analytical solution.

Model and computation of photoionization of negative hydrogen ion by using strong laser is considered. The method of H- photoionization is interesting for laser assisted charge exchange injection project. In this paper we develop calculation of high efficiency photoionization through time dependent wave equation with application of powerful lasers that has nonlinear effects compared to conventional linear crossection method of calculation. Other mechanisms of photoionization like excitation of hydrogen ion resonances are also considered.

A simulation workflow has been developed to study dark current (DC) radiation effects using ACE3P and Geant4. The integrated workflow interfaces particle data transfer and geometry between the electromagnetic (EM) cavity simulation code ACE3P and the radiation code Geant4, targeting large-scale problems using high-performance computing. The process begins by calculating the operating mode in the vacuum region of an accelerator structure and tracking field-emitted electrons influenced by the EM fields of the mode calculated by ACE3P. It then transfers particle data at the vacuum-wall interface for subsequent radiation calculations within the wall enclosure materials through Geant4 calculation. The whole integrated simulation workflow will be demonstrated through large-scale dark current radiation calculations for the KEK 56-cell traveling-wave structure, and the efficiency of performing these simulations on the NERSC supercomputer Perlmutter will be presented.

Design parameters in accelerator projects are frequently subject to change, necessitating repeated optimisation and calculation of various figures of merit, along with updating plots and tables, which can be time-consuming. In the context of designing superconducting radiofrequency (SRF) cavity geometries, these tasks typically involve eigenmode and wakefield simulations and occasionally multipacting simulations. CAV-SIM-2D is a specialised tool developed for the rapid simulation, analysis, and comparison of 2D axisymmetric SRF cavity geometries. The software is designed to facilitate swift optimisation, calculation, and comparison of critical figures of merit in SRF cavity design, thereby streamlining the design process and significantly enhancing efficiency in the development of effective accelerator cavities.

Funded by CERN under ADDENDUM FCC-GOV-CC-00213 (KE4978/ ATS) to FCC-GOV-CC-0213/2431149/KE4978 VERSION 1.0.

The complexity of the GSI/FAIR accelerator facility demands a high level of automation to maximize the time for physics experiments. Accelerator laboratories across the globe are investigating numerous techniques to achieve this goal, including classical optimization, Bayesian optimization (BO), and reinforcement learning. This presentation will provide an overview of recent activities in these domains at GSI. Beginning with conventional optimization, the beam loss during the multi-turn injection into the SIS18 synchrotron was reduced from 40% to 15% in approximately 15 minutes, whereas manual adjustments may take up to 2 hours. The implementation of the Generic Optimization Framework & Frontend (GOFF) at GSI, supported by the EURO-Labs project, has significantly enhanced workflow, requiring only a few hours to adapt to new accelerators and optimization tasks. GOFF has also been effectively utilized at the GSI Fragment Separator (FRS) for beam steering and focusing. Additional experimental endeavors include closed-orbit correction for specific broken-symmetry high-transition-energy SIS18 optics using physically-informed BO, compared to traditional SVD-based correction. The data-driven model predictive control and physically-informed BO for automated injection optimization are currently under investigation via simulation.

For the stable operation of synchrotrons, a controlled closed orbit is essential. The closed orbit correction methods are designed to keep the particle beam on the desired orbit. Information regarding the position of the beam is only accessible via the beam position monitors (BPM). It is feasible to attain zero deviation at the BPM with the conventional correction methods (e.g. SVD-based correction). However, given the remaining multitude of residual closed orbits errors, the objective is to achieve a minimal discrepancy between the closed orbit and the target orbit throughout the entire ring. Therefore, a Bayesian Optimization (BO) based correction method, which introduces a probabilistic modeling perspective, should be combined with beam dynamics in order to infer pattern between the BPMs, where no information are available through direct measurement.
The Bayesian Optimization method is a global optimization technique for black-box functions, where a probability distribution (Gaussian Process, GP) acts as a surrogate model. A GP is fully defined by two key components: the mean function and the kernel, or covariance function.
The concept of physics-informed BO for closed orbit correction is to include beam dynamics in the GP model by estimating the kernel (and mean function) by evaluating simulated realizations. These simulations are performed with a MAD-X simulation software model of the synchrotron SIS18. Perturbations, erroneous input data, non-linearities, and noise are incorporated into the model. From these, the GP should be able to infer some information about the behavior in between the BPMs. The objective is to develop a machine model with uncertainty quantification and noise handling. This would allow for the implementation of a closed-orbit correction not only at the BPMs but also in between BPMs. Furthermore, the lattice functions could be extracted and utilized, for instance, for dispersion correction.

Slow extraction is an important mode of operation of the present GSI heavy ion synchrotron SIS18 for providing particle beams of desired intensity with longer time intervals to various experiments. One of the methods to reduce uncontrolled beam loss during slow extraction is the implementation of automated optimization of the accelerator settings.
In the present work, an algorithm based procedure is developed in order to minimize particle losses. The optimizers were run with direct access to the detectors used for measuring the circulating and extracted particles and to the magnets to be set via the control system of the synchrotron. Three different algorithms were applied. Tuning up 5 parameters allowed to reach the extraction efficiency up to 90 %. The measurement results were compared to the results of optimization runs based on particle tracking simulations and show agreement for all parameters. The research is still ongoing, and the model can be used to predict the extracted beam intensities for the FAIR project.

In recent decades, the development of high-power lasers has increased interest in the use and research of laser-accelerated ions. While offering excellent characteristics, such as high brightness, high energies, and very short pulse duration, laser-accelerated ions also pose significant challenges regarding their capture and transport due to high initial divergence and a wide energy spectrum. These challenges necessitate more accurate, high-fidelity simulations compared to reduced-physics models.

Leveraging the accuracy of high-fidelity simulations to train machine learning-based surrogate models offers the advantage of using gradient-based optimization methods, as neural networks are inherently backpropagable. This study demonstrates that such an optimization scheme provides accurate predictions for maximizing the transmission of a beam line handling laser-accelerated ion beams. Using transported particle distributions generated by a Runge-Kutta field tracking algorithm, a solenoid surrogate model was trained and incorporated into a toy model consisting of two solenoids and a radio frequency cavity. This toy model, a simulated counterpart of the LIGHT experiment at GSI Helmholtzzentrum für Schwerionenforschung, was subsequently optimized using the gradient-based optimizer Adam, which computed the optimal parameters such as solenoid currents and drift spaces to minimize the loss function. The resulting parameters were then implemented into the initial field tracking simulation to analyze the accuracy and robustness of the provided operating point with regard to transmission.

PyORBIT is a Partice-in-Cell simulation code widely used in the accelerator community. We have developed accelerator simulation software that includes EPICS and runs PyORBIT as its physics model. This PyORBIT virtual accelerator is currently in use as a digital twin for developing Control Room software, training and testing Machine Learning models, and training operators at the Spallation Neutron Source.

In this study, we introduce a novel application of data-driven Model Predictive Control (MPC) to enhance the multi-turn injection (MTI) process within the SIS18 synchrotron, diverging from traditional numerical optimization techniques our approach epitomizes a sample-efficient strategy that resides at the confluence of model-based reinforcement learning and advanced control theory. This synergy facilitates a reduction in optimization iterations while significantly improving the adherence to control performance criteria, crucially addressing delays and safety concerns such as septum protection.

Our methodology offers a unified framework that harnesses the predictive prowess of Gaussian processes within the MPC paradigm, achieving a state-based optimization process that transcends the capabilities of conventional reinforcement learning and Bayesian optimization. The proposed MPC framework not only ensures rapid convergence but also guarantees safety, paving the way for secure online training and real-time implementation in the SIS18 MTI scenario.

The findings demonstrate the efficacy of this data-driven MPC approach in optimizing complex non-linear control systems, setting a precedent for its application in similar high-stakes environments. This research thus establishes a foundational basis for the deployment of safe, efficient, and robust online control strategies in advanced accelerator physics control.

Ultrashort bunch length measurements are essential in modern accelerator experiments like high-gradient plasma-based accelerators and free electron lasers. These require quality electron bunches in the femtosecond-length scale and thus pose significant challenges for developing novel beam instrumentation and diagnostics. This contribution presents current results on the development of a shot-to-shot bunch-length monitor with femtosecond resolution using broadband imaging of coherent transition radiation (CTR) that will operate online and minimally invasively as a virtual diagnostic. The implemented method successfully reconstructed the longitudinal bunch profiles from simulated CTR images by using ensemble methods and deep learning models like convolutional neural networks (CNNs). The CTR images were simulated using Zemax OpticStudio for different bunch profile lengths and shapes below 200 fs. The ensemble learning models accurately reconstructed bunch profiles with resolution in the few femtosecond ranges. Uncertainty measures for the reconstructions were calculated to study the reliability and precision of the results. The results and observed resolution confirm the suitability of the proposed diagnostic for plasma accelerator applications and highlight the potential of machine learning for producing high-resolution virtual diagnostics for these and other short-pulse accelerator experiments. The next stage in the research will include testing the ensemble learning models with more realistic electron bunches and plasma accelerator-specific datasets combining both simulated and experimental data while further exploring relevant models to develop reliable virtual diagnostics.

The development of ultra-low emittance storage rings, such as the e+/e- Future Circular Collider (FCC-ee) with a circumference of about 90 km, aims to achieve unprecedented luminosity and beam size. One significant challenge is correcting the optics, which becomes increasingly difficult as we target lower emittances. The use of stronger quadrupoles and sextupoles makes these machines particularly sensitive to misalignments, which can severely impact performance. This study investigates optics correction methods to address these challenges. We examined the impact of arc region magnet alignment errors in the baseline optics for the FCC-ee @ Z energy. To establish realistic alignment tolerances, we developed a sequence of correction steps using the Python Accelerator Toolbox (PyAT) to correct the lattice optics, achieve nominal emittance, and large Dynamic Aperture (DA). We focused initially on the Linear Optics from Closed Orbit (LOCO) method, which fits the measured Orbit Response Matrix (ORM) to the lattice model to determine optimal parameters such as quadrupole strengths. We implemented a Python-based numerical code for LOCO correction and evaluated its effectiveness for the FCC-ee. Results indicated successful optics corrections. We also compared LOCO with phase advance + $\eta_x$ and coupling Resonance Driving Terms (RDTs) + $\eta_y$ optics correction, finding that the latter performed better in achieving design emittance values and a large DA area for realistic alignment tolerances.

The development of next-generation superconducting magnets requires advanced quench simulation tools and methods. To achieve practical simulation times and high accuracy, appropriate computational methods, such as finite elements or finite differences, are essential. Enhancements in computational efficiency can be further realized through strategic modelling assumptions, approximations, reduced-order methods, homogenization, or the use of lumped elements. By incorporating these techniques, simulation tools can offer versatile and comprehensive analyses of quench events and protection strategies.
Significant advancements are further possible through the synergistic integration of various simulation tools, enabling capabilities far exceeding that of individual tools used in isolation. This synergy, especially in complex simulation environments and with tools developed by different teams in various programming languages, has been successfully realized in the STEAM framework at CERN. The STEAM framework enables sequential, cooperative, or parametric simulations using tools such as FiQuS, LEDET, and the STEAM SDK package.
This presentation will provide an overview of the STEAM framework's capabilities, highlighting recent developments and modelling methodologies employed by individual tools.

Fast orbit feedback systems are essential parts of fourth-generation synchrotron radiation sources. Their purpose is to keep the beam position under tight control by correcting for disturbances up to the kilohertz range. Simulating the electromagnetic fields in the fast corrector magnets at elevated frequencies is a challenging task: the laminated structure of the yokes and the low eddy-current skin depths necessitate a very fine mesh and a small time step. The computational cost can be decreased by using special homogenization techniques, but this comes with the assumption of a linear magnetization curve. To lift this limitation, we set up a simulation procedure combining such homogenization techniques with the harmonic balance finite element method, allowing us to perform efficient nonlinear simulations of the magnets without resolving the laminations by the mesh and without time-stepping. In this contribution, we give an overview of our linear simulation results for the fast corrector magnets of the new synchrotron radiation source PETRA IV at DESY and discuss the capabilities and limitations of the combined method for the nonlinear simulations.

The efficient production and capture of muons as well as their immediate acceleration towards high particle energies are severe engineering challenges on the path towards the first 10TeV synchrotron-based muon-collider, envisioned by the European MuCol program. The required ramp rates of up to 4.5kT/s within the rapid-cycling-synchrotron can reliably be provided by normal-conducting magnets in combination with a periodically switched capacitor-based powering system.

The numerical analysis of this subsystem necessitates transient simulation schemes considering both circuit and magnet, whereby the latter is discretized as finite-element (FE) model. The calculations are especially demanding due to highly non-linear circuit elements such as switches and diodes as well as the non-linear and hysteretic behavior of the ferromagnetic laminated iron core.

This contribution presents a pragmatic modeling approach for the transient and nonlinear analysis of bending magnets powered by current pulses of few ms. An implementation within a conventional 2D/3D FE framework led to novel insights in magnet and power supply design.

Superconducting coils in accelerator magnets consist of several cables composed of multiple superconducting wires. This makes a finite element (FE) simulation discretizing all individual wires computationally very demanding. Reduced magnetic vector potential formulations avoid the explicit discretization of those wires at the cost of calculating a Biot-Savart integral in the computational domain. In the standard approach [1], the Biot-Savart integral has to be evaluated in the whole computational domain, which can still be quite computationally expensive, especially for a 3D field simulation. Moreover, screening currents in the superconducting wires induced by transient magnetic fields are usually modeled by adding artificial wires into the geometry, which further increase the computational cost of this approach.

We present an alternative reduced magnetic vector potential formulation [2], which requires the evaluation of the Biot-Savart integral only on an interface of the computational domain, leading to a huge improvement in computational efficiency compared to the standard approach. Furthermore, we introduce the magnetic dipole moment into the formulation in order to take screening currents into account without adding artificial wires into the geometry. The method is implemented in the open-source FE solver GetDP and employed for the magnetic field simulation of superconducting magnets in 2D and 3D.

[1] O. Bíró, K. Preis, W. Renhart, K. R. Richter, and G. Vrisk, "Performance of different vector potential formulations in solving multiply connected 3-D eddy current problems," in IEEE Transactions on Magnetics, vol. 26, no. 2, pp. 438–441, March 1990.
[2] L. A. M. D’Angelo et al., "Efficient Reduced Magnetic Vector Potential Formulation for the Magnetic Field Simulation of Accelerator Magnets," in IEEE Transactions on Magnetics, vol. 60, no. 3, pp. 1–8, March 2024.

The SNS Beam Test Facility is equipped with advanced phase space diagnostics that enable very detailed characterization of beam distributions at the beginning and end of a test beamline. I show the latest results in benchmarking with PyORBIT after a significant reconfiguration of the beamline. I will discuss on-going efforts to improve the simulation accuracy, with implications for modeling of beam halo relevant to prediction of scraping losses in an operational linac. I will also discuss model requirements for the benchmark simulation.

Laser-wake field accelerators (LWFAs) are potential candidates to produce intense relativistic electron beams to drive compact free electron lasers (FELs) in VUV and X-ray regions. The High-Field Physics and Ultrafast Technology Laboratory at National Central University (NCU) is actively developing a compact LWFA-based high gain harmonic generation (HGHG) FEL aimed at coherent extreme ultraviolet (EUV) radiation. However, the high divergence and excessive energy spread of the LWFA electron beam increase the difficulties in both beam transportation and radiation power growth. Here a start-to-end simulation is presented to study the electron quality threshold of a compact HGHG FEL based on the estimated experimental data of the NCU LWFA group with electron energy of 250MeV. Compare to a Slow-varying envelope approximation-based simulation, a PIC-based calculation is presented to consider the effects of an ultrashort electron bunch. Numerical results indicate that a 4th harmonic radiation at 66.5nm wavelength with megawatt level peak power can be obtained with energy spread up to 0.25%. Showing the feasibility of the proposed scheme and the capability of producing monochromatic coherent radiation.

The International Muon Collider Collaboration (IMCC) is engaged in a design study for a future facility intended for the collision of muons.Subsequent to the initial linear acceleration, the counter-rotating muons and anti-muons are accelerated in a chain of rapid cycling synchrotrons (RCS) up to the multi-TeV collision energy. To maximise the number of muons available in the collider, it is essential to exploit the time dilation of the muon lifetime by employing a large accelerating gradient.
The 1.3 GHz TESLA cavity serves as the baseline for the RCS chain. Considering the high bunch population and the small aperture of the cavity, the resulting beam-induced voltage per bunch passage is considerable, resulting in a substantial perturbation of the cavity voltage for the subsequent bunch passages. In this contribution, the effects of beam loading during the acceleration cycle for muons are calculated with the objective of determining the optimum parameters for minimising the cavity voltage transients. The interaction of the induced voltages by the counter-rotating beams is also considered. The results are subsequently used to estimate the impact of the transient beam loading on the muon acceleration and survival rate in the RCS chain. This work has been sponsored by the Wolfgang Gentner Programme of the German Federal Ministry of Education and Research (grant no. 13E18CHA).

Specialised tools are required to perform single-particle tracking simulations that include collimation systems. These tools describe the particle-matter interactions that occur when a particle impacts a collimator jaw, and provide means to pinpoint the longitudinal locations of losses. One such tool is Xcoll, a recent Python package fully integrated into the Xsuite environment - the latest tool for particle tracking simulations, currently under active development. Xcoll provides a built-in scattering engine called Everest, optimised for computation speed by assuming no particle type changes nor secondary particle production. This approximation suffices for simulating the scattering of high-energy protons in matter. For simulations where these assumptions are no longer valid, like for lepton or ion beams, Xcoll also provides couplings to established tools such as FLUKA or Geant4. This talk details the ongoing development of Xcoll and its various scattering engines. Extensive testing of the new implementation will also be discussed, using different collimation layout configurations for the LHC Run 3 and HL-LHC as case studies.

The presentation will provide an overview of the capabilities of the Methodical Accelerator Design Next Generation (MAD-NG) tool. MAD-NG is a standalone, all-in-one, multiplaform tool well suited for linear and nonlinear optics design and optimisation, and has already been used in large-scale studies such as HiLumi-LHC or FCC-ee. It embeds LuaJIT, an extremely fast tracing just-in-time compiler for the Lua programming language, delivering exceptional versatility and performance for the forefront computational physics. The core of MAD-NG relies on the fast Generalised Truncated Power Series Algebra (GTPSA) library, which has been specially developed to handle many parameters and high-order differential algebra, including Lie map operators. This echosystem offers powerful features for the analysis and optimisation of nonlinear optics, thanks to the fast parametric nonlinear normal forms and the polyvalent matching command. Some examples and results will be presented in conclusion.

SciBmad is a new, open source software project that will provide a modern, differentiable, and full-featured toolkit for all types of accelerator physics simulations and design tasks. A set of modular, extensible packages providing all the fundamental tools needed for accelerator physics simulations is currently being developed in the Julia programming language. Julia is a relatively new high-level, high performance computing language that adopts multiple dispatch with just-in-time (JIT) compilation as a central paradigm, and includes a powerful type system providing universal, ad-hoc, and subtype polymorphisms; such features drastically simplify the code, and enable automatic differentiation of type-agnostic code with zero extra effort. Furthermore, users instantly have access to the entirety of Julia's rich ecosystem of optimizers, integrators, machine learning toolkits, plotting packages, etc. SciBmad will include, in a fully-differentiable environment, all features currently in present Bmad (fully nonlinear tracking, normal form analysis including spin and radiation, and multipass lattices to name a few), and significantly more capabilities, including GPU-parallelized particle tracking and machine learning. In this work we detail the current status of SciBmad development and plans for the future.

SciBmad (formally called Bmad-Julia) is a new, open-source project to develop, in the Julia language, a set of modular packages providing the fundamental tools and methods commonly needed for accelerator simulations. This discussion is for those interested in collaboration to ask questions.

Storage rings based on the integrable optics concept, such as the Integrable Optics Test Accelerator (IOTA) at Fermilab, pose several challenges to effective numerical modeling due to the complex, nonperturbative structure of the nonlinear dynamics and (for operation with protons) the interplay with high-intensity space charge. A primary modeling goal is to ensure symplectic treatment of both single-particle and collective dynamics for high-fidelity modeling on long time scales. We describe numerical tools implemented to address these issues, challenges posed by validation against theory, and applications to understanding nonlinear integrable dynamics with space charge in IOTA.

Machine learning has emerged as a powerful solution to the modern challenges in accelerator physics. However, the limited availability of beam time and the high computational cost of simulation codes pose significant hurdles in generating the necessary data for training state-of-the-art machine learning models. Furthermore, optimisation methods can be used to tune accelerators and perform complex system identification tasks. However, they too require large numbers of samples of expensive-to-compute objective functions in order to achieve state-of-the-art performance. In this work, we introduce Cheetah, a PyTorch-based high-speed differentiable linear-beam dynamics code that enables fast collection of large datasets and sample-efficient gradient-based optimisation, while being easy to use, straightforward to extend and integrating seamlessly with widely adopted machine learning tools. Ultimately, we believe that Cheetah will simplify the development of machine learning-based methods for particle accelerators and fast-track their integration into everyday operations of accelerator facilities.

The Muon $g\textrm{-}2$ Experiment (E989) at Fermilab conducted high-precision measurements of the muon anomalous magnetic moment $a_\mu$ using a storage ring from 2018 to 2023, achieving a remarkable precision of $0.20\:\mathrm{ppm}$ over Runs 1-3, with analyses for Runs 4-6 ongoing. A comprehensive understanding of the storage ring's beam dynamics and its accurate simulations are crucial for achieving the experiment's ambitious goals. One of the requirements for this effort is a very detailed knowledge of the phase space distribution of the beam. To address this requirement, we performed high-statistics simulations of the Muon $g\textrm{-}2$ Target Station (AP0) and the Muon Campus beamlines: M2 and M3, followed by the Delivery Ring, and then M4 and M5. The resulting muon distribution at the end of the M5 beamline from our previous $3\times 10^{12}$ protons-on-target (PoT) simulation serves as an essential input for the storage ring simulations. In 2024, to facilitate the analyses of Runs 4-6, we have updated our Muon Campus models and re-optimised certain parameters to reflect the operational currents and wire chamber measurements of the beam. For these optimisations, we employed the heterogeneous island method, implemented in our evolutionary optimisation tool, $\mathtt{glyfada}$. This key update addresses the need to use the best possible beam for the storage ring simulations and thus supports the experiment's overall precision. The Muon $g\textrm{-}2$ Experiment at Fermilab has successfully achieved its $70\:\mathrm{ppb}$ systematic uncertainty goal and collected $21$ times more data than its predecessor at BNL. The updated and improved Muon Campus models and simulations not only facilitate the experiment's efforts to potentially resolve the current tension between experimental measurements and theoretical predictions of $a_\mu$, but also provide a basis for future simulations for the Mu2e Experiment (E-973), which utilises shared Muon Campus beamlines.

The projected SIS-100 synchrotron at FAIR will provide heavy ion beams
for many different user experiments. Most of these experiments will require
beams from slow extraction. Slow extraction is mainly characterized by the
amount of uncontrolled beam losses and temporal microscopic structures on the
extracted beam also referred to as spill. For both characteristics, predictions
are done based on particle tracking simulations. The requirements to both types
of simulations are different which results in differences in the computational
demands.Determining particle losses requires the application of the full lattices
with a comprehensive model of magnet errors and all apertures, whereas spill
structures can be characterized using a less precise lattice model.
On the other hand, spill structure simulations require realistic particle
numbers and time intervals, which can be reduced when only looking for
particle losses.

A unique particle beam dynamics simulation code, CoSyR [1], has been developed using MPI + Kokkos to exploit exascale computing and multi-GPU acceleration. This new simulation code tackles a fundamental problem of beam nonlinear dynamics from its radiation self-fields, which underpins many accelerator design issues in high brightness beam applications as well as those arising in the development of advanced accelerators. CoSyR, together with other state-of-the-art codes dedicated for coherent synchrotron radiation (CSR) study, such as LW3D and CSRtrack, are a unique suites of complementary simulation capability employing first-principle models but with a hierarchy of model complexities and assumptions, which are ideal for the understanding of the CSR effects in increasingly high-brightness beams. In this work, we will present the design and benchmark of CoSyR with other CSR simulation codes and the widely used static-state analytic models in applicable beam conditions. We will highlight the understanding of the interplay of the longitudinal and transverse CSR effects, which is generally not captured in 1D CSR models. Detailed study with experiment validation to elucidate CSR model differences and applicability to complex beams is being explored for future accelerator designs. We will also discuss plan to include the accelerator channel or magnetic dipole shielding effect by making use of the cavity Green's functions. Finally, we introduce a pilot work to develop and train a class of phase space structure-preserving neural networks — Henon Neural Networks (HenonNets) [2], as a fast surrogate of radiative collective effects for nonlinear beam dynamics problems.

Work supported by DOE HEP award DE-SC0024445 and the LDRD program at LANL.

[1] C.-K. Huang et al., "CoSyR: A novel beam dynamics code for the modeling of synchrotron radiation effects," Nucl. Instruments Methods Phys. Res. Sect. A Accel. Spectrometers, Detect. Assoc. Equip., vol. 1034, no. April, p. 166808, Jul. 2022, doi: 10.1016/j.nima.2022.166808; https://github.com/lanl/cosyr.

[2] C.-K. Huang et al., “Symplectic neural surrogate models for beam dynamics,” J. Phys. Conf. Ser., vol. 2687, no. 6, p. 062026, Jan. 2024, doi: 10.1088/1742-6596/2687/6/062026.

The baseline design of the ILC (International Linear Collider) positron source requires the production of an intense flux of gamma rays. In this paper we present an investigation of using the gamma ray beam of the ILC for additional applications, including nuclear physics. As a result of changing the collimator shape, as well as the parameters of the undulator magnets, we obtained spectra from numerical simulations using the HUSR/GSR software package. We present results from simulations and a discussion of possible future investigations in this paper.

The helical undulator-based positron source is taken into consideration for the International Linear Collider (ILC) baseline design. A multi-MeV circularly polarized photon beam is generated by passing a multi-GeV electron beam via a long superconducting helical undulator. We then direct the photon beam to a thin rotating target, which creates an electron-positron (e-e+) pair with longitudinal polarization. An Optical Matching device (OMD) captures the polarized positron beam before sending it to the Interaction Point (IP). The ILC will initially operate at 250 GeV Centre-of-mass energy (ILC-250) before upgrading to 350 GeV (ILC-350) and 500 GeV (ILC-500) GeV, as well as higher options. Each stage's goal is to probe fundamental questions in particle physics with unprecedented precision. The photon source, which generates a high-energy photon beam using helical undulators, is one of the essential parts of the ILC. Each undulator parameter affects the produced photon spectrum, which in turn affects the created positron beam. This study examines the potential benefits and drawbacks of using a shorter undulator period for the ILC-250 option. A shorter undulator period means a shorter total undulator length. As a result, synchrotron radiation deposited less power at the superconducting undulator wall. Furthermore, we anticipate that a shorter undulator period will boost photon energy and beam brightness, both of which are critical for positron production. However, this improvement comes with significant technical challenges, such as the need for stronger magnetic fields and the design and fabrication of magnets. Our research looks at whether it is possible to use a shorter undulator period for the non-ideal ILC-250 option, considering the fact that the ILC-250 needs a certain number of positrons. For the ILC-250 option, we conducted detailed simulations to assess the impact of a shorter period of non-ideal helical undulators on the photon beam spectrum.

Historically, development of accelerator physics simulation programs has, for the most part, been a haphazard affair with individual people or groups developing code independent of the wider community. This process is wasteful both in time and manpower and leads to suboptimal code that is generally not interoperable with code developed elsewhere. This meeting is intended for those interested in discussing how we, as a community, can collaborate more effectively to address these issues. The discussion will be open-ended with no set agenda. Potential topics include the current efforts at community collaboration, establishing a standard for exchanging lattice information, and developing standards for code interoperability.

The Muon $g\textrm{-}2$ Experiment (E989) at Fermilab aims to measure the muon anomalous magnetic moment $a_{\mu}$ with unprecedented precision, potentially uncovering physics beyond the Standard Model of particle physics. The result based on Runs 1-3, released in 2023, achieved a precision of $0.20\:\mathrm{ppm}$. The experiment circulates muons in a storage ring, measuring $a_{\mu}$ from decay positron time and energy measurements collected with calorimeters. To achieve the required accuracy, it is crucial to measure and control the magnetic field in the ring with high precision. Beam dynamics corrections are necessary for muons not orbiting exactly in the midplane, for their oscillations, and for electric field effects. Highly accurate beam dynamics simulations are instrumental for quantifying and validating the beam dynamics corrections, ultimately improving the precision of the $a_{\mu}$ measurement and facilitating the achievement of the ambitious $70\:\mathrm{ppb}$ systematic uncertainty goal. The measured field data was incorporated into models for simulations using three codes: $\mathtt{gm2ringsim}$ (an internal Geant4-based code), COSY INFINITY, and BMAD. The advantages of $\mathtt{gm2ringsim}$ include using CAD-based geometry and modelling the detector effects. COSY INFINITY is a highly accurate and efficient code that uses high-order differential-algebraic transfer maps, precise fringe field calculations, and advanced symplectification methods. Symplectification is important for maintaining the physical correctness of the muon beam behaviour with high precision over the storage time, ensuring conservation of phase space volume and preventing artificial damping or excitation of particle motion. The experiment completed its final Run 6 in July 2023, collecting $21$ times more data than the previous BNL experiment. Analyses of data from Runs 4-6 are ongoing, with results planned for release in 2025, potentially resolving the current tension between experiment and theory.

The system under investigation is an infinite plasma column surrounded by a perfect conducting cylindrical wall and space charge fields govern the motion of the particles. Additionally, the drift-kinetic approximation is valid which allows to track just the drift centers of the particles. Commonly, perturbations of the equilibrium space charge field are decomposed into modes. Driving those modes can be used for plasma diagnostics or even for compression of the plasma column. These are valuable techniques in experiments with trapped plasma in Penning-Malmberg traps like the the antiProton Unstable Matter Annihilation experiment (PUMA), where antiprotons will be transported in a trap from one facility to another which requires very long confinement times. In contrast to experiments, simulations allow full control of the plasma parameters and therefore may help to deepen the physical understanding of the response of the plasma column to external field perturbations.
To track the drift centers and investigate the response of the plasma to a drive, several conditions have to be fulfilled. In particular the compression is a weak effect, the relative change of the central density during one characteristic rotation of the plasma column is approximately $10^{-6}$. This requires very low numerical noise and long computation times. Moreover, reducing unwanted higher modes would be beneficial to stabilize the simulation. Two methods are tested. A Particle-In-Cell code with a Cartesian grid for the space charge calculation and a spectral solver in cylindrical coordinates. The first method takes advantage of the efficient field calculations on Cartesian grids but the numerical noise prohibits up to now the investigation of the compression effects. The second method is advantageous in terms of the present cylindrical symmetries and the naturally integrated low-pass-filter. Furthermore, it allows the direct read out of the important parameters. First results will be presented whether this approach can reduce the numerical noise.

At the King Abdulaziz City for Science and Technology KACST, a beam line injector is being constructed to provide the multi-purpose low-energy, ELectrostAtic Storage Ring (ELASR), with the required high-quality ion beams. The injector is being equipped with a 90 degree high resolution mass analyzing selector magnet system and a new ECR ion source. The magnet system was designed to provide a singly-charged ion beam of kinetic energy up to 50 keV and ion mass up to 1500 amu with the mass resolution of ∆ m/m = 1/1500. In this paper, the ion-optical calculations, the determination of the required momentum resolution and the actual analyzing magnet system parameters will be discussed. The simulation of the beam envelope along the injector and through the magnet will be presented.

Current research in magnet technology focuses on superconductors and technologies to achieve dipole fields in the 12-16 T range using $\mathrm{Nb_3Sn}$ wire. With their anisotropic and stress-dependent material properties, these materials require multiphysics simulations right from the start of the magnet-design process, particularly for stress management and magnet protection. Owing to the many empirical parameters to be specified in multiphysics simulations, an essential part of the design work is the validation of the model to obtain a match between simulations and measurements.

Magnet protection in case of a quench relies on quench heaters (QH), extraction resistors, and coupling-loss induced resistance (CLIQ) to speed up and homogenize the energy dissipation and thus avoid conductor degradation due to overheating. The efficiency of the measures is estimated using multi-physics simulations based on numerical solutions of ordinary and partial differential equations (network models, finite element, and boundary element methods, among others). Unfortunately, both simulations and measurements are affected by uncertainty and biased by ignorance. Mitigation measures exist for most sources of uncertainty, such as oversampling, signal compensation, calibration, convergence studies, and maxwellification by imposing the regularity conditions of magnetic fields. However, ignorance, in the sense of unrecognized systematic effects of the underlying physics, can only be addressed by merging simulations and measurements.

In this paper, we first study the sensitivity of the observable quantities (such as voltages and current decay curves) to the material parameters and loss mechanisms implemented in the CERN field computation program ROXIE. The test data from the 11T dipole program and MQXF quadrupoles for the LHC upgrade is analyzed, and statistical models are developed to compensate for the ignorance in the numerical model.

The updated models allow the extrapolation of performance parameters to the next generation of magnets.

Magnetic measurement data is collected at various points in an accelerator magnet's life cycle. It is used, for example, to calibrate model parameters in the prototyping phase, for quality assurance and fault detection in the production phase, and for state observation and prediction during magnet operation. In all cases, the numerical model of the accelerator magnet is at the center of the analysis.

Although magnetic measurement data is highly accurate, it is typically incomplete, i.e., the state space is not observable by a finite number of magnetic field sensors. On the other hand, numerical field simulations can predict the magnet state but are limited in accuracy and often fall short of the stringent requirements for magnet operation. For this reason, measurement data must be integrated with numerical field calculations to enable predictions with the required accuracy of one unit in 10$^4$ to 10$^5$.

We are developing application-specific hybrid models in all stages of the accelerator magnet lifecycle based on the principles of Model-based systems engineering, which focuses on models and simulations rather than documents for operation, performance evaluation, maintenance, and information exchange.

In this talk, we will focus on developing delta models, where boundary element methods (BEM) are used to model the discrepancy between measurements and observations using fictitious density functions at the iron air interface. Determining the discrepancy function from measurement data is an ill-posed inverse problem that requires a suitable regularization. For this purpose, deterministic methods (minimal energy solutions and truncated singular value decompositions) and stochastic methods such as Bayesian inference are compared.

Intense THz radiation has found critical applications in the study of quantum and semiconductor materials, as well as in the manipulation of electron beams. In response to this, a THz Free Electron Laser (FEL) facility has been developed at NSRRC, designed to deliver high peak power for user operations. This facility generates coherent radiation within the 0.6 to 1.4 THz frequency range. The radiation is produced by passing a sub-picosecond electron beam through a planar undulator with a 10-cm period length, where the undulator gap is adjustable. The short-bunch electron beam itself is produced by the NSRRC photoinjector, with a booster linac operating near the zero-crossing phase to achieve RF bunch compression. This method has successfully compressed the electron bunch to a minimum duration of 240 fs at a beam energy of 25 MeV. However, the bunch form factor's limited frequency range restricts the highest achievable superradiant THz frequency to around 1-2 THz.
To overcome this limitation, a double dogleg magnetic bunch compressor is being considered to further reduce the bunch duration, thereby extending the radiation to even higher frequencies. The output characteristics of the superradiant undulator emission are highly sensitive to the bunch form factor, which is closely tied to the longitudinal electron distribution. Since space charge effect in the photoinjector is significant, the 3D space-charge tracking code – IMPACT has been employed to simulate the RF bunch compression process and study beam dynamics in the double dogleg magnetic bunch compressor. These simulations have allowed for accurate determination of electron distributions at the entrance of undulator, which are then used in the broadband FEL code – PUFFIN to calculate the radiation output properties for the THz beamline design.
Additionally, the feasibility of developing a THz Self-Amplified Spontaneous Emission (SASE) FEL beyond the 3 THz frequency range is under consideration, driven by the same accelerator system. However, a beam dechirper may be required to reduce correlated energy spread after bunch compression. To study the effects of short-range wakefields produced by the dielectric-lined waveguide dechirper or other advanced designs on multi-particle dynamics within the accelerator, reliable wake functions have been deduced from CST-calculated wake potentials via deconvolution. This report will highlight the computational challenges involved in the development of THz FELs at NSRRC.

We will discuss the modeling and simulation of intrabeam scattering (IBS) in single pass electron injectors. This effect is well known and thoroughly investigated for circular machines and storage rings. Recently, however, concerns have been raised regarding the IBS induced growth of uncorrelated energy spread in electron linacs for coherent light sources. In particular, the IBS effect in the electron injector difficult to describe due to the complicated beam dynamics in this section. In the presentation, we will introduce the basic IBS theory, modeling techniques and describe beam dynamics simulations including the IBS effect for the injector sections of the European XFEL and that of the SwissFEL.

In this research, we present a detailed electromagnetic characterization and optimization study of nanostructured photocathodes for electron gun applications. The study concentrates on photocathodes operated at visible to infrared wavelengths, for which an accurate simulation model is constructed. For this, we apply a customized dispersion model for the cathode material, which can describe the measured permittivity data over a broad frequency range. Various geometries for nanopatterns are explored in order to understand how different geometric parameters affect cathode reflectivity. The results reveal an optimized model of nanostructured photocathodes, demonstrating improved absorptance at the target laser wavelength. Additionally, the impact of geometrical uncertainties on the reflectance spectra is examined.

In the injector section of electron linacs, both internal space charge forces and wake field effects influence the beam dynamics. Full electromagnetic PIC codes solving for the full set of particle motion and Maxwell’s equations require too high computational effort for practical applications.
On the other hand, conventional space charge solvers neglect transient EM waves, while wake field solvers can not account for internal particle dynamics. To fill this gap, we have developed a computational method to account for both effects self-consistently. It couples a space charge solver in the rest frame of the bunch with a wakefield solver by means of a scattered field formulation. The novelty of this approach is that it enables us to simulate the creation of wakefields throughout arbitrary emission and acceleration processes.
The method is used to simulate space charge and wake field effects in a traveling wave electron gun, providing detailed insights into the coupling of wake fields on bunches at low energies.
Specifically, uncorrelated energy spread and emittance are investigated which are of key interest for FEL operation.

Dielectric Laser Acceleration (DLA) is an advanced electron accelerator concept reaching gradients significantly larger than conventional RF cavities. DLAs contain dielectric nanostructures to modulate the electrical near-fields of ultrashort laser pulses. The experimental complexity of DLA experiments in the subrelativistic as well as in the relativistic regime increases with increasing structure length and the utilization of more complex laser pulse shapes, such as pulse front tilts. Consequently, the experiments involve many parameters demanding careful control and optimization. Previous studies have demonstrated the efficacy of machine learning in enhancing the performance of conventional accelerators. In this presentation, we introduce our BMBF research project, which aims to implement a machine learning-based control system. This system is designed to reconstruct, analyze and optimize the laser pulse shape used for DLA experiments at ARES, leveraging electron beam diagnostics after the DLA interaction. For reconstructing the experimental parameters from measurements a deep neural network is implemented using the framework PyTorch. Simulation data by the tracking code DLAtrack6D serves as training data and initially also for validation as long as the laser pulse shaping optics are being set up. We verified these simulations by comparing tracking results to experimental data. We optimized the hyperparameters to get the best accuracy in the reconstruction and studied possible experimental parameter sets, dedicated DLA structures and additional diagnostics to reduce potential issues due to the non-uniqueness of the numerical reconstructions. This is the basis to use the neural network as virtual diagnostics of laser pulse and electron beam in order to active control and optimize DLA experiments.

Dielectric laser accelerators (DLA) offer the possibility to miniaturize particle accelerators by switching from metal cavities driven by radiofrequency fields to dielectric structures driven by high repetition laser pulses in the optical wavelength regime. In the last years, acceleration in combination with alternating phase focusing was shown, resulting in substantial energy gains in up to 0.5 millimeter-long acceleration structures [1,2].

Due to the drastic decrease in wavelength, the periodicities of the dielectric structures now lie in the range of a few hundred nanometers, placing those structures in the regime of nanophotonics. When designing structures at this length scale, inverse design is a method that has successfully been used for many different applications [3], including the optimization of periodic dielectric laser accelerators to achieve high acceleration gradients [4,5].

We will show how this approach can be expanded to the case of sub-relativistic DLAs where it is necessary to taper the structure, i.e. to increase the width of the unit cells to maintain the phase matching condition as the electron accelerates. In this case it is not sufficient to only optimize a single periodic unit cell like shown in [4,5], but instead it is necessary to design the structure as a whole. We will discuss how a gradient descent-based inverse design approach can be used to precisely control the acceleration in each unit cell of the structure and show how the adjoint method can be used to efficiently obtain the gradient for an arbitrary number of parameters.

[1] Shiloh et al. Nature 597, 498–502 (2021).
[2] Chlouba et al. Nature 622, 476–480 (2023).
[3] Molesky et al. Nature Photon 12, 659-670 (2018)
[4] Hughes et al. Opt. Express 25, 15414-15427 (2017)
[5] Sapra et al. Science 367, 79-83 (2020)

QuickPIC is a parallel 3D PIC code that applies the quasi-static approximation. QuickPIC can efficiently simulate both beam driven and laser driven plasma wake field accelerators with a speed that is typically 1000 times faster than the conventional PIC code without losing accuracy. QPAD is a branch of QuickPIC that applies azimuthal decomposition in cylindrical coordinates. In this work, we will introduce the developments of explicit solvers in both QuickPIC and QPAD. The explicit solver does not need predictor-corrector loops when solving the quasi-static Maxwell's equations. We will also introduce the basic algorithm of a GPU + MPI version of QuickPIC. The comparison of computing time between GPU and CPU versions of QuickPIC will be presented.

We introduce a novel and efficient methodology for simulating fluid models within the framework of plasma wakefield acceleration (PWFA). Our approach is based on the Lattice Boltzmann Method (LBM), a widely used numerical scheme in computational fluid dynamics, which we couple with a finite difference time domain method to solve the electromagnetic field equations. We outline the key features of the LBM and demonstrate how it can be adapted for the simulation of the fluid equations in the PWFA. Additionally, we highlight the method's core capabilities, including its ability to model warm plasma dynamics using various closure schemes. We further discuss the emergence of closure-dependent thermal spread anisotropies in the plasma, emphasizing the implications for PWFA simulations.

The DA methods employed in COSY allow for the computation of arbitrary order transfer maps. The derivation and antiderivation operations of the differential algebraic structure allow the construction of map integrators based on either Picard iteration or directional derivates that are significantly more efficient than conventional integrators. The tools also allow the automatic computation of fully Maxwellian 3D fields if only midplane or on-axis field information is available, which for example allows recovering all nonlinear effects arising from increasing or decreasing fields in the fringes of particle optical elements. They also allow the computation of such fields from surface or volume field measurements, leading to a fully Maxwellian representation even in the presence of noise in the data. Differential Algebra-based normal form methods allow the computation of nonlinear dynamics aspects for orbit motion as well for the computation of invariant spin axes and spin normal forms. Utilizing metrics on symplectic spaces, it is possible to construct minimally invasive symplectification schemes for tracking based on maps. Various examples of the performance of the methods are given, with particular emphasis on the high accuracy requirements of the spin and orbit dynamics of the FNAL muon g-2 ring.