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The Julia programming language was created 10 years ago and is now a mature and stable language with a large ecosystem including more than 8,000 third-party packages. It was designed for scientific programming to be a high-level and dynamic language as Python is, while achieving runtime performances comparable to C/C++ or even faster. With this, we ask ourselves if the Julia language and its ecosystem is ready now for its adoption by the High Energy Physics community. We will report on a number of investigations and studies of the Julia language that have been done for various representative HEP applications, ranging from computing intensive initial data processing of experimental data and simulation, to final interactive data analysis and plotting. Aspects of collaborative code development of large software within a HEP experiment has also been investigated: scalability with large development teams, continuous integration and code test, code reuse, language interoperability to enable an adiabatic migration of packages and tools, software installation and distribution, training of the community, benefit from development from industry and academia from other fields.

We present a novel approach for an event generator inherently using exact QED descriptions to predict the results of high-energy electron-photon scattering experiments that can be performed at modern X-ray free-electron laser facilities. Future experiments taking place at HIBEF, LCLS, and other facilities targeting this regime, will encounter processes in x-ray scattering from (laser-driven) relativistic plasmas, where the effects of the energy spectrum of the laser field as well as multi-photon interactions can not be neglected anymore. In contrast to the application window of existing QED-PIC codes, our event generator makes use of the fact, that the classical nonlinearity parameter barely approaches unity in high-frequency regimes, which allows taking the finite bandwidth of the x-ray laser into account in the description of the QED-like multi-photon interaction. Consequently, we exploit these effects in Compton scattering, Breit-Wheeler pair-production and trident pair-production in x-ray laser fields as one of the driving forces of electromagnetic cascades and plasma formation.

We present a novel approach for an event generator inherently using exact QED descriptions to predict the results of high-energy electron-photon scattering experiments that can be performed at modern x-ray laser facilities. With the advent of advanced laser systems producing high-frequency x-ray beams, e.g. the EuropeanXFEL as a prominent example, a regime of laser-plasma interaction is reached, where all-optical methods are no longer applicable. Instead, the interaction of hot electrons and the x-ray laser pulse needs to be modeled with a QED-driven approach. Future experiments taking place at HED-HIBEF, LCLS, and other facilities targeting this regime, will encounter processes in x-ray scattering from (laser-driven) relativistic electrons, where the effects of the energy spectrum of the laser field as well as multi-photon interactions can not be neglected anymore. In contrast to the application window of existing QED-PIC codes, our event generator makes use of the fact, that the classical nonlinearity parameter barely approaches unity in high-frequency regimes. Therefore, based on a momentum-space Furry-picture formulation of strong-field QED, this allows taking the finite bandwidth of the x-ray laser into account in the description of the QED-like multi-photon interaction. Consequently, we exploit these effects in Compton scattering, Breit-Wheeler pair production, and trident pair production in x-ray laser fields.

Efficient Monte Carlo integreation is crucial for modeling processes at the European XFEL. However, traditional approaches to importance sampling like VEGAS do not perform well when integrands display multiple features or non-coordinate aligned features. In this work, we present an implementation of neural importance sampling (NIS) in the Julia programming language to address this challenge. We demonstrate the effectiveness of NIS by applying it to processes in strong-field QED at high energies, showing superior adaption of the integrand and thus enabling efficient event generation.

Monte Carlo event generation is essential for analysis in high energy physics and fast implementations are required to keep up with the large amounts of data measured by experiments. Therefore, these methods need to reflect the theoretical predictions accurately to enable efficient data generation, e.g. by rejection sampling. However, traditional importance sampling algorithms, such as the commonly used VEGAS algorithm, often struggle with adapting targets with multiple or non-coordinate aligned features, as is common in high energy physics. Especially in strong-field QED, processes dynamically depend on field parameters, which means the use of established codes for these problems needs to be questioned. An importance sampling approach using neural networks applied to strong-field processes is presented within the framework QED.jl. The quality of the generated proposals, e.g. the unweighting efficiency, is compared to VEGAS, providing insights beneficial to applications beyond strong-field QED.

We present a novel approach for an event generator inherently using exact QED descriptions to predict the results of high-energy electron-photon scattering experiments that can be performed at modern X-ray laser facilities. With the advent of advanced laser systems producing high-frequency x-ray beams, e.g. the EuropeanXFEL as a prominent example, a regime of laser-plasma interaction is reached, where all-optical methods are increasingly questionable (see Fig. 1). Instead, the interaction of hot electrons and the X-ray laser pulse must be modeled with a QED-driven approach. Future experiments taking place at HED-HIBEF, LCLS, and other facilities targeting this regime, will encounter processes in x-ray scattering from (laser-driven) relativistic electrons, where the effects of the energy spectrum of the laser field as well as multi-photon interactions can not be neglected anymore. In contrast to the application window of existing QED-PIC codes, our event generator makes use of the fact that the classical nonlinearity parameter barely approaches unity in high-frequency regimes. Therefore, based on a momentum-space Furry-picture formulation of strong-field QED, this allows taking the finite bandwidth of the x-ray laser into account in the description of the QED-like multi-photon interaction.

Usually, quantum electrodynamics acts as the prime example, when it comes to a well-understood and outstandingly precise description of elementary particle processes. However, modern laser facilities provide highly intense light with a non-trivial temporal structure, where an arbitrary number of ‘photons’ from the light source may interact with the colliding particles. In this case, the standard perturbative treatment known from quantum electrodynamics becomes cumbersome and impractical. Accordingly, there are, among others, wide theoretical investigations w.r.t. scattering processes of particles impinging these extreme light sources. This has been done by applying the strong-field quantum electrodynamics, a theory of electromagnetic interactions within coherent highly intense light treated as a classical background field. Here, the distinction between a classical background field and a quantized photon field revealed a vast amount of novel non-linear structures and non-perturbative phenomena. In this seminar, we introduce the basic concepts of strong-field QED and derive the Feynman rules for the theory in momentum space. Then, we explore their general structure and implications from fundamental principles, namely gauge invariance.

The impact of a strong electromagnetic background field on otherwise perturbative QED processes is studied in the momentum-space formulation. The univariate background field is assumed to have finite support in time, thus being suitable to provide a model for a strong laser pulse in plane-wave approximation. The usually employed Furry picture in position space must be equipped with some non-obvious terms to ensure the Ward identity. In contrast, the momentum space formulation allows for an easy and systematic account of these terms, both globally and order-by-order in the weak-field expansion. In the limit of an infinitely long-acting (monochromatic) background field, these terms become gradually suppressed, and the standard perturbative QED Feynman diagrams are recovered in the leading-order weak-field limit. A few examples of three- and four-point amplitudes are considered to demonstrate the application of our Feynman rules which employ free Dirac spinors, the free photon propagator, and the free Fermion propagator, while the external field impact is solely encoded in the Fermion-Fermion-photon vertex function. The appearance of on-/off-shell contributions, singular structures, and Oleinik resonances is pointed out.

We present a computational scheme that derives a global polynomial level set parametrisation for smooth closed surfaces from a regular surface-point set and prove its uniqueness. This enables us to approximate a broad class of smooth surfaces by affine algebraic varieties. From such a global polynomial level set parametrisation, differential-geometric quantities like mean and Gauss curvature can be efficiently and accurately computed. Even 4th-order terms such as the Laplacian of mean curvature are approximates with high precision. The accuracy performance results in a gain of computational efficiency, significantly reducing the number of surface points required compared to classic alternatives that rely on surface meshes or embedding grids. We mathematically derive and empirically demonstrate the strengths and the limitations of the present approach, suggesting it to be applicable to a large number of computational tasks in numerical differential geometry.

Some studies of applying a 50 keV XFEL for strong-field physics, modelled by the interaction with an electron beam, were presented. The process of electron-positron pair production in strong fields deviates from the well-known perturbative result in weak field backgrounds. In a strong field background, an electron can directly emit a photon, generating a pair via the trident process. Using 50 keV photons, only about 5 MeV kinetic electron energy is required to reach the trident threshold, which is available by electron guns or laser acceleration (in solids, or wakefield). The trident process can also be used to test models for dark matter candidates. Using the proposed massive “dark photon”, the assumed mass and coupling to ordinary could be determined more precisely than with hadron experiments. Certain exclusion regions can be scanned, but the trident experiment could also be used to detect dark matter (instead of excluding certain mass/coupling ranges) because there is full control over the QED background. A second scheme is the interaction of hard x-rays with electrons in the presence of an intense, infrared few-cycle laser light field. It allows to study of laser-assisted Compton scattering, Breit Wheeler pair production and trident, where during the peaks of the few-cycle IR laser field, spectral features are introduced. A (quasi-) continuous X-ray beam (as in a synchrotron) is not sufficient for strong-field studies as high intensity is required. A user community, similar to established synchrotron or XFEL users, may not exist yet. Many colleagues work on theoretical models, but more experimentalists will emerge with upcoming experimental capabilities at XFELs. The LUXE experiment at DESY, and the detection of QED vacuum birefringence at HED/HIBEF, EuXFEL, are examples of such developments.

Usually, quantum electrodynamics is the prime example, when it comes to a well-understood and outstandingly precise description of elementary particle processes. However, modern laser facilities provide highly intense light with a non-trivial temporal structure, where an arbitrary number of ‘photons’ from the light source may interact with the colliding particles. In this case, the standard perturbative treatment, e.g. known from quantum electrodynamics, becomes very cumbersome and impractical. Accordingly, there are, among others, wide theoretical investigations w.r.t. scattering processes of particles impinging these extreme light sources. This has been done by applying strong-field quantum electrodynamics, which is a theory of electromagnetic interactions within coherent highly intense light treated as a classical background field. Here, the distinction between a classical background field and a quantised photon field revealed a vast amount of novel non-linear structures and non-perturbative phenomena. In this seminar, we introduce the basic concepts of strong-field QED and derive the Feynman rules for the theory. Then we apply those rules to the Breit-Wheeler process, i.e. the electron-positron pair production in the collision of a laser field and a highly energetic photon

The inventors of the Julia programming language proclaim, that one can use high-level syntax to solve demanding numerical tasks. In order to evaluate this claim, we present possible applications of Julia by using it for the implementation of our Monte-Carlo event generator for laser-matter interaction. Especially the possible deployment of modern GPUs for demanding computing tasks during several stages of the event generation is discussed. In order to elaborate on these GPU capabilities, we show benchmarks of Julia's main programming interface for NVIDIA CUDA GPUs, namely `CUDA.jl`, and compare them with native CUDA-C++ implementations. Finally, Julia's capabilities for high-level abstraction for computations on heterogenous architectures are discussed and compared to low-level solutions like the `alpaka` library for C++.

The description of scattering processes in high-energy physics is usually done with Feynman Diagrams. The number of Feynman Diagrams that can be generated for a given process explodes factorially with the number of particles. We discuss a possible approach enabling the calculation of higher-multiplicity scattering processes. We propose representing the calculation for a process as a directed acyclic graph (DAG) of small computation tasks. Using Julia, we can optimize this graph using subgraph replacement strategies together with an optimization algorithm. Finally, efficient code targeting arbitrary heterogeneous HPC systems can be generated from the optimized DAG.

minterpy is an open-source Python package for a multivariate generalization of the classical Newton and Lagrange interpolation schemes as well as related tasks. It is based on an optimized re-implementation of the multivariate interpolation prototype algorithm (MIP) by Hecht et al.1 and thereby provides software solutions that lift the curse of dimensionality from interpolation tasks. While interpolation occurs as the bottleneck of most computational challenges, minterpy aims to free empirical sciences from their computational limitations.

We present a novel approach for an event generator inherently using exact QED descriptions to predict the results of high-energy electron-photon scattering experiments that can be performed at modern X-ray free-electron laser facilities. Our event generator makes use of the fact, that the classical nonlinearity parameter barely approaches unity in high-frequency regimes accessible at these facilities, while this parameter range is outside of the application window of existing QED-PIC codes. This constraint on the parameter range allows for an approximation which is capable of taking the finite bandwidth of the X-ray laser into account in the description of the interaction. We investigate the application of the new first-principle method to the generation of events in energy-driven electromagnetic cascades, which complements the studies on intensity-driven cascades at optical laser experiments.

Many solutions to the computational challenges arising in the fields of computational science and engineering rely on solving interpolation tasks of highly-varying sparse and scattered data. The tasks include surrogate modeling, sparse data regression, global black-box optimization, model inference, as well as solutions for partial differential equations (PDE) on complex geometries. Interpolation tasks in multi-dimensional space typically suffer from the curse of dimensionality in which the computational cost of interpolation scales exponentially with the number of dimensions. The open-source Python package minterpy developed and maintained by the Hecht-Lab, CASUS, aims to lift the curse of dimensionality from a brand field of interpolation tasks arising across scientific disciplines.

The accurate modelling of laser-matter interaction is a very challenging task. Especially, the generation of scattering events to mimic statistical particle distributions seen in experiments have demanding requirements on the computational methods and implementations. With this talk, we introduce the complicated structure of strong-field QED and formulate the fundamental building blocks for Monte-Carlo event generation using this theory, where a key feature is the dynamical coupling of the laser field to the scattering processes. This type of coupling can not be addressed with state-of-the-art event generators used to model processes from the standard model of particle physics. Therefore, we introduce a new implementation of e Monte-Carlo event generator, written in the Julia programming language. Furthermore, we introduce some key language features of Julia, which may come in handy for implementations of future event generators in general, where especially the capabilities of distributed computing will be highlighted.

While the high frequency of modern x-ray free-electron lasers has the benefit of requiring less energy of a seed electron for triggering the development of a QED cascade, the non-linearity parameter obeys a_0 < 1, in contrast to high-intensity optical lasers. Accordingly, we analyse the phenomenon of multi-photon effects in trident pair production in pulsed x-ray laser fields at such values of a_0. The impact of the energy spectrum and its temporal structure and the coherence of the laser field on the emergent particle distribution at the onset of further cascading is discussed. Besides the evolution of mean multiplicities in the course of an energy-powered cascade, we seek characteristic fluctuation patterns.

We estimate the energy distribution of positrons produced in the interaction of ultra-relativistic electrons with a high-intensity laser beam. The underlying trident process is factorized on the probabilistic level. That is, we deploy a two-step mechanism for the formation of electron-positron pairs. In the first step, a high-energy photon is produced as a result of nonlinear Compton scattering. In the second step, an electron-positron pair is created by the nonlinear (multi-photon) Breit-Wheeler process.

We present a new system for high repetition rate and real-time pulse analysis imple- mented at the Monoenergetic Positron Source (MePS) at the superconducting electron LINAC ELBE at Helmholtz-Zentrum Dresden-Rossendorf. Dedicated digital signal processing and op- timized algorithms are employed allowing for high bandwidth throughput, online pulse analysis and filtering. Positrons generated from radioisotopes and from bremsstrahlung pair production by means of highly intense accelerator-based positron beams serve as a microstructure probe allowing material characterizations with respect to chemical, mechanical, electrical, and magnetic properties. Positron annihilation lifetime events with up to 13 MHz repetition rate are being processed online without losses while performing signal selections for pile-up reduction, online energy calibration, and - for radioisotope-based measurements - identification of start and stop events.

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The probabilities of various elementary laser/photon/electron/positron interactions display in selected phase space and parameter regions typical nonperturbative dependencies such as proportional to P exp{/aE(crit)/E}, where P is a preexponential factor, E-crit denotes the critical Sauter/Schwinger field strength, and E characterizes the (laser) field strength. While the Schwinger process with a = a(S) pi and the nonlinear Breit/Wheeler process in the tunneling regime with a = a(nlBW) 4m/3 omega' (with omega' the probe photon energy and m the electron/positron mass) are famous results, we point out here that also the nonlinear Compton scattering exhibits a similar behavior when focusing on high harmonics. Using a suitable cutoff c > 0, the factor a becomes a = a(nlC) 2/3 cm/(p(0) + root p(0)(2) / m(2)). This opens the avenue toward a new signature of the boiling point of the vacuum even for field strengths E below E-crit by employing a high electron beam/energy p(0) to counter balance the large ratio E-crit/E by a small factor a to achieve E/a -> E-crit. In the weak/field regime, the cutoff facilitates a threshold leading to multiphoton signatures showing up in the total cross section at subthreshold energies.

Laser pulses facilitate multiphoton contributions to the trident pair production e_L^- \to e_L^- + e_L^+ + e_L^-, where the label L indicates a laser field dressed electron (e^-) or positron (e^+ ). We isolate the impact of the pulse envelope in the trident S matrix element, formulated within the Furry picture, in leading order of a series expansion in the classical non-linearity parameter a_0. Generally, the Fourier transform of the envelope carries the information on the pulse length, which becomes an easily tractable function in the case of a cos^2 pulse envelope. The transition to a monochromatic laser wave can be handled in a transparent manner, as also the onset of multiphoton effects for short pulses can be factorized out and studied separately.