Constants of motion network

The beauty of physics is that there is usually a conserved quantity in an always-changing system, known as the constant of motion. Finding the constant of motion is important in understanding the dynamics of the system, but typically requires mathematical proficiency and manual analytical work. In this paper, we present a neural network that can simultaneously learn the dynamics of the system and the constants of motion from data. By exploiting the discovered constants of motion, it can produce better predictions on dynamics and can work on a wider range of systems than Hamiltonian-based neural networks. In addition, the training progresses of our method can be used as an indication of the number of constants of motion in a system which could be useful in studying a novel physical system.Comment: Accepted to NeurIPS 202

STEP: extraction of underlying physics with robust machine learning

A prevalent class of challenges in modern physics are inverse problems, where physical quantities must be extracted from experimental measurements. End-to-end machine learning approaches to inverse problems typically require constructing sophisticated estimators to achieve the desired accuracy, largely because they need to learn the complex underlying physical model. Here, we discuss an alternative paradigm: by making the physical model auto-differentiable we can construct a neural surrogate to represent the unknown physical quantity sought, while avoiding having to relearn the known physics entirely. We dub this process surrogate training embedded in physics (STEP) and illustrate that it generalizes well and is robust against overfitting and significant noise in the data. We demonstrate how STEP can be applied to perform dynamic kernel deconvolution to analyse resonant inelastic X-ray scattering spectra and show that surprisingly simple estimator architectures suffice to extract the relevant physical information

Quantitative shadowgraphy and proton radiography for large intensity modulations

Shadowgraphy is a technique widely used to diagnose objects or systems in various fields in physics and engineering. In shadowgraphy, an optical beam is deflected by the object and then the intensity modulation is captured on a screen placed some distance away. However, retrieving quantitative information from the shadowgrams themselves is a challenging task because of the non-linear nature of the process. Here, a novel method to retrieve quantitative information from shadowgrams, based on computational geometry, is presented for the first time. This process can be applied to proton radiography for electric and magnetic field diagnosis in high-energy-density plasmas and has been benchmarked using a toroidal magnetic field as the object, among others. It is shown that the method can accurately retrieve quantitative parameters with error bars less than 10%, even when caustics are present. The method is also shown to be robust enough to process real experimental results with simple pre- and post-processing techniques. This adds a powerful new tool for research in various fields in engineering and physics for both techniques

Simulation of density measurements in plasma wakefields using photon acceleration

One obstacle in plasma accelerator development is the limitation of techniques to diagnose and measure plasma wakefield parameters. In this paper, we present a novel concept for the density measurement of a plasma wakefield using photon acceleration, supported by extensive particle in cell simulations of a laser pulse that copropagates with a wakefield. The technique can provide the perturbed electron density profile in the laser's reference frame, averaged over the propagation length, to be accurate within 10%. We discuss the limitations that affect the measurement: small frequency changes, photon trapping, laser displacement, stimulated Raman scattering, and laser beam divergence. By considering these processes, one can determine the optimal parameters of the laser pulse and its propagation length. This new technique allows a characterization of the density perturbation within a plasma wakefield accelerator

Quantitative single shot and spatially resolved plasma wakefield diagnostics

Diagnosing plasma conditions can give great advantages in optimizing plasma wakefield accelerator experiments. One possible method is that of photon acceleration. By propagating a laser probe pulse through a plasma wakefield and extracting the imposed frequency modulation, one can obtain an image of the density modulation of the wakefield. In order to diagnose the wakefield parameters at a chosen point in the plasma, the probe pulse crosses the plasma at oblique angles relative to the wakefield. In this paper, mathematical expressions relating the frequency modulation of the laser pulse and the wakefield density profile of the plasma for oblique crossing angles are derived. Multidimensional particle-in-cell simulation results presented in this paper confirm that the frequency modulation profiles and the density modulation profiles agree to within 10%. Limitations to the accuracy of the measurement are discussed in this paper. This technique opens new possibilities to quantitatively diagnose the plasma wakefield density at known positions within the plasma column

Quantitative single shot and spatially resolved plasma wakefield diagnostics

Diagnosing plasma conditions can give great advantages in optimizing plasma wakefield accelerator experiments. One possible method is that of photon acceleration. By propagating a laser probe pulse through a plasma wakefield and extracting the imposed frequency modulation, one can obtain an image of the density modulation of the wakefield. In order to diagnose the wakefield parameters at a chosen point in the plasma, the probe pulse crosses the plasma at oblique angles relative to the wakefield. In this paper, mathematical expressions relating the frequency modulation of the laser pulse and the wakefield density profile of the plasma for oblique crossing angles are derived. Multidimensional particle-in-cell simulation results presented in this paper confirm that the frequency modulation profiles and the density modulation profiles agree to within 10%. Limitations to the accuracy of the measurement are discussed in this paper. This technique opens new possibilities to quantitatively diagnose the plasma wakefield density at known positions within the plasma column

Simulation of density measurements in plasma wakefields using photon acceleration

The data was used in a paper with the same title. They were created in May 2014, from a simulation run in SCARF machine at Rutherford Appleton Laboratory