The potential in the Radio Frequency Quadrupole (RFQ) can be expressed as a sum of a transverse multipolar expansion: $\sum_{m=1}^\infty{A_{0m}}\left(\frac{r}{r_0}\right)^{2m}\cos(2m\theta)$, and a longitudinal term expressed as sum of Bessel functions: $\sum_{m=0}^\infty\sum_{n=1}^\infty A_{nm}I_{2m}(nkr)\cos(2m\theta)\cos(nkz)$. Since the paper of Kapchinskii and Teplyakov \cite{osti_4032849} this potential is used considering only the first term in transversal and longitudinal components, unfortunately such approximation does not reproduce properly a realistic RFQ as the one installed at the European Spallation Source (ESS). In this paper we evaluate the potential when more terms are considered and we compare it with the field map obtained from a numerical Poisson solver used at ESS.

Modern SRF applications require precise control of a wide range of material properties, from microscopic material parameters to macroscopic surface structures. Historically, Nb has been the primary superconducting material in SRF cavities. The past decade has seen increasing amounts of research into the development of cavities using next generation materials, such as Nb3Sn. These materials have great promise for improving SRF performance, but their small coherence lengths require even greater control of surface and material defects. Mesoscopic simulation of superconductors has proven itself to be a powerful tool in SRF development, connecting the results of ab initio/quantum calculations to the mesoscopic structures of the material, allowing for investigation of many phenomena which are difficult to probe experimentally. One particular phenomenon of concern is the field enhancement effect, which causes increased magnetic field near rough surface features, potentially leading to vortex nucleation or other dissipative processes. We outline a two-domain finite element framework of the Time-Dependent Ginzburg-Landau equations which allows for the simulation of magnetic field enhancement due to supercurrent screening near rough surface features. We apply this framework to several different candidate surface structures which may occur in Nb3Sn, and determine their impact on dissipation and vortex nucleation. We discuss the implications of these results for SRF cavity design.

An algorithm for determining the eigenvalues of the eigenfunctions of a multilayer cylindrical waveguide is constructed. A relationship is found between dispersion relations and impedances. A method for determining the resonant frequencies of the wake field in the linear and helical motion of a particle is described. The damping coefficients of eigenmodes at resonant frequencies are determined.

A promising approach for compact linear accelerators in the THz frequency range is based on dielectric-loaded waveguides (DLWs). Higher breakdown fields expected at THz frequencies should enable higher acceleration gradients. However, the accelerating mode of a cylindrical DLW (TM₀₁) is not the fundamental and only mode inside the waveguide at operating frequency. Therefore, a method is required to ensure excitation of the proper mode only. Here we present a coupler design to convert the guided electromagnetic TE₁₀ mode in a rectangular waveguide to the TM₀₁ mode of a cylindrical DLW. The symmetry of the structure and its feeding waveguides allow us to suppress all undesired modes and consequently increase the coupling efficiency to the desired mode. Moreover, this configuration shows an extremely wide bandwidth and low quality factor suggesting the coupler is also suitable for short THz pulses.

One of the interesting topics among accelerator physicists in the last decades has been the resistive wall impedance of vacuum chambers with general cross sections. The resistive wall impedance of a round pipe was calculated more than half a century ago, followed by parallel plates, rectangular pipes, and, in more recent years, oval shapes. Analytical solutions usually require some approximations to simplify them. It is possible to solve Maxwell's equations in the vacuum chamber with simulation codes in order to obtain an exact solution for Resistive wall impedance. Although some of them show promising results, the need for a versatile code that can calculate resistive wall impedance and wakefield in a general cross-section vacuum chamber is still necessary. VACI-suite is a finite element solver that tries to solve this problem. Compared to well-known theories and simulation codes for well-known geometries, the code's results show remarkable agreement.

Corrugated structures have been used widely in X-ray free-electron laser facilities for chirp control, fresh-slice applications, and diagnostics. In this paper, we present a general method for calculating the short-bunch wakefield of corrugated structures with arbitrary shapes. At zeroth order, we give analytical solutions via the method of conformal mapping. At first order, we give steady-state wake calculation by solving a set of integral equations.

Magnetic Field Tools is an open source library being developed by the Insertion Devices and Magnets group at the ESRF. It is dedicated to the analysis of static magnetic field values obtained from simulations and measurements. Magnetic field models such as 2D and 3D multipoles in various geometries, as well as boundary element models, can be built from sets of field samples. The library was designed in order to be easily extendable to other types of field models. It is implemented in C++ and a Python binding is available. Application to undulator magnets, 3D multipole fringe fields and solenoids will be presented.

Electromagnetic processes of charged particles interaction with oriented crystals provide a wide variety of innovative applications such as beam steering, crystal-based extraction/collimation of leptons and hadrons in an accelerator, a fixed-target experiment on magnetic and electric dipole moment measurement, a positron source for lepton and muon colliders, X-ray and gamma radiation source for radiotherapy and nuclear physics as well as plasma acceleration in the crystal media. One of the main challenges is to develop an up-to-date, universal and fast simulation tool to simulate these applications. We present a new simulation model capable to simulate both steering and radiation electromagnetic processes in oriented crystals implemented into the Geant4 simulation toolkit*. We validate the model with the experimental data and benchmark it with other simulations**. We discuss the advantages and perspectives of this model for the applications of oriented crystals mentioned above.

SLAC has been developing the parallel finite element electromagnetics simulation suite ACE3P (Advanced Computational Electromagnetics 3D Parallel) for accelerator modeling using high performance computing (HPC) platforms. ACE3P employs the parallel high-order finite-element method with conformal (tetrahedral) mesh for high-fidelity representation of geometry, and further accuracy can be obtained using quadratic surface and high-order elements resulting in reduced computational cost. Currently, the treatment of material properties applies to linear dielectrics and metals, wherein the electric displacement field is directly proportional to the electric field. There is a rapid need for new interaction regimes of high fields that would drive nonlinear response in materials which are in turn essential for novel accelerator applications. Moreover, efficient conversion between photons of different energies is needed for harmonic and THz generation, as well as quantum sensors which inherently require materials with second- or third-order optical nonlinearity. In this work we present the current status of the development of the nonlinear EM solver, in ACE3P which includes nonlinear response of the dielectric material. This utilizes parallel and scalable architecture to perform simulations and virtual prototyping on multiscale optical and quantum systems.

Space charge forces represent main induced effects in an RF-injector that degrade the beam quality. In this scenario the laser distribution sent on the photocathode acquires an important role in the emittance compensation process, as the slice analysis shows. A novel model of space charge forces is proposed for bunch with arbitrary charge distribution to derive expressions of self-induced forces. As the performance of the fields near the cathode is under present analysis, we can investigate use of this model in low charge regime. Further, the model has been benchmarked with the behavior of the distributions present in the literature and studied for new ones. It has also been applied for the study of the optimization of a C-band hybrid photoinjector now being commissioned, thus explaining the factor two reduction of the emittance observed at the exit of the gun by changing the initial distribution at the cathode.

Gradient-free algorithms are commonly used because of the lack of knowledge about the derivative of the beam properties with respect to the accelerator parameters while running accelerator optimization simulations. However, similar to the automatic differentiation algorithms widely used in the AI/ML community, recent efforts have been made in the accelerator community to develop differentiable simulation models. In particular, differentiable space charge simulations benefit because computation time is usually critical in beam dynamics simulations. Recently, automatic differentiation of space charge simulations using truncated power series algebra (TPSA) has been proposed and shows its potential. In this study, we developed a differentiable self-consistent spatial charge model based on Green's function solver using the Hockney-Eastwood and Vico-Greengard-Ferrando algorithms.