Introduction
Numerical simulations are an essential tool for designing experiments, supporting the analysis of experimental results and exploring physical scenarios that are not directly accessible in the laboratory (e.g. astrophysical plasmas).
The PHI group is engaged in a number of numerical activities, ranging from the development of state-of-the-art simulation codes (e.g., WarpX, Gordon Bell Prize in 2022) to the realization of numerical simulations on the world’s most powerful supercomputers to simulate
advanced laser-plasma gas pedal schemes, or schemes to study quantum electrodynamics in a virtually unexplored regime using very intense lasers.
The PHI group is also interested in the study of radiative transfer, an essential process in inertial confinement physics and astrophysics; the study of XUV radiation absorption by plasmas falls within this context. Finally, our group is involved in interpreting results obtained at ENS on a quantum simulation platform.
Particle-In-Cell Codes and High-Performance Computing
In the PHI group, we are contributing to the development of the WarpX open-source particle-in-cell code, capable of running on the world’s most powerful supercomputers.
The most widely used technique for simulating laser-plasma interaction at very high intensities is the Particle-In-Cell (PIC) method, which simulates relativistic kinetic plasmas.
In a PIC code there are two main players: the electromagnetic field, which is simulated on a grid using a Maxwell solver, and “macro-particles”, each representing many particles in the plasma.
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At each time step, the particles move as a function of the electromagnetic field, generating an electric current which is used to evolve the electromagnetic field. Other physical processes can be added to this basic scheme with dedicated modules: QED, ionization, collisions, nuclear fusions… The main challenge with PIC simulations is often the enormous computing power required to produce reliable 3D simulations – computing power that may only be available with the most powerful supercomputers in the world.
The PHI group is heavily involved in the development of the WarpX open-source PIC code (https://github.com/ECP-WarpX/WarpX ), a code designed specifically to meet the challenge of “exascale” computing, i.e. using exaflopic machines capable of performing1018 operations per second. The WarpX code is being developed in collaboration with several public and private subjects, including LBNL (USA), CEA (FR), DESY (DE), SLAC (USA), Tae Technologies (USA)…
The numerous physics modules and advanced methods implemented in WarpX enable it to be used to simulate a wide variety of physics scenarios, of interest for laser-plasma interaction, plasma astrophysics and the design of machines for realizing nuclear fusion in the laboratory.
Thanks to the technical innovations implemented in WarpX and the performances achieved on the world’s most powerful machines, including Frontier (OLCF, USA), Fugaku (Riken, Japan) and Summit (OLCF, USA), in 2022 we won the Gordon Bell Prize, one of the most prestigious awards in the field of high-performance computing.
The PHI group regularly uses the WarpX code in production, thanks to allocations of computing hours on machines in the US (Frontier), Europe (LUMI, Finland) and France (Adastra).
Bibliography
- Publication “L.Fedeli et al. SC22 proceedings, IEEE, 2022 (2022)”
https://escholarship.org/content/qt5q63r9ph/qt5q63r9ph.pdf?t=rtbtm7 - Publication “L.Fedeli et al. New Journal of Physics 24.2, 025009 (2022)”
https://iopscience.iop.org/article/10.1088/1367-2630/ac4ef1 - Publication ” H.Vincenti et al. Computer Physics Communications, 228, 22-29 (2018) “
https://arxiv.org/pdf/1707.08500.pdf
Simulation of laser-plasma gas pedals
Laser-plasma gas pedals are used to accelerate high-energy electron packets over very short distances. We are studyingtechniques for maximizing load while maintaining quality.
The interaction of an ultra-intense laser with a gas jet can be used to accelerate very short electron packets to very high energies (from a few MeV to several GeV) over just a few centimetres.
The technique known as “Laser WakeField Acceleration” (LWFA) uses the laser to generate a density perturbation that propagates with itself.
These density perturbations are associated with an intense electrostatic field, which traps and accelerates some of the electrons.
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The small size of these devices and the brevity of the accelerated electron packets make them a promising technique for studying, for example, the FLASH effect in radiobiology/radiotherapy, which, for equivalent efficiency, reduces side effects on irradiated healthy tissue when dose rates are very high. However, the load delivered by this technique remains modest, which limits the scope of its applications.
Recently, within the PHI group, we have developed a new injection scheme that includes a solid target coupled to a gas jet to accelerate more charge, while preserving beam quality.
In 2022, we validated this concept with a campaign of large-scale simulations using the Particle-In-Cell WarpX code on 3 of the world’s 5 most powerful supercomputers, including Summit (OLCF, USA), Fugaku (Riken, Japan) and Frontier (OLCF, USA). These simulations also enabled us to guide the design of the first “proof-of-principle” experiments carried out at the Laboratoire d’Optique Appliquée (France).
The PHI group is also studying acceleration techniques based on the interaction of an ultra-intense laser with structured targets, notably gratings. If irradiated at their resonance angle, these targets excite a surface plasmon, whose electric field can accelerate high-charge electron packets along the target surface.
Bibliography
- Publication “L.Fedeli et al. SC22 proceedings, IEEE, 2022 (2022)”
https://escholarship.org/content/qt5q63r9ph/qt5q63r9ph.pdf?t=rtbtm7 - Publication “G.Cantono et al. Phys. Plasmas 25, 031907 (2018)”
https://arxiv.org/pdf/1802.05483.pdf - Publication “G.Cantono et al. Phys. Rev. Lett. 120, 264803 (2018)”
https://hal.science/hal-01846694/document
Simulations of high-field QED and Doppler-boosted lasers
By using “plasma mirrors”, we can boost the intensity of the world’s most powerful lasers to study quantum electrodynamics in extreme and virtually unexplored regimes.
Quantum Electrodynamics (QED), a fundamental pillar of modern physics, is one of the most thoroughly tested theories. Yet its so-called “strong field” regime, which characterizes the plasma around astrophysical objects such as black holes and pulsars, remains largely “terra incognita” from an experimental point of view.
Numerical simulation using the Particle-In-Cell WarpX code. A Doppler-boosted laser (field in blue/red) interacts with a solid target (electron density in grey) at intensities sufficient to “hollow out” a channel and generate gamma photons and electron/positron pairs (green and violet particles) via high-field QED processes
Indeed, investigating QED in strong fields requires gigantic electromagnetic fields, of the order of the “Schwinger field”: 1.32x1018V/m.
This value exceeds by more than three orders of magnitude the strongest fields available on Earth, those delivered by femtosecond lasers. Within the PHI group, we are studying a strategy to overcome this obstacle.
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When an ultra-intense laser interacts with a solid target, the latter forms a “plasma mirror” that oscillates at relativistic speeds, generating trains of attosecond pulses of Doppler harmonics of the initial beam.
The laser’s radiation pressure induces a curvature of the target, which can be controlled to optimize harmonic focusing. The intensity of the focused harmonics can exceed that of the initial laser by up to three orders of magnitude, thus narrowing the gap to the Schwinger field.
We are studying schemes where the harmonics are focused on a secondary target to “heat” its electrons to such high energies that the Schwinger field is exceeded in their reference frame. We are also studying schemes where the harmonics are focused on a packet of electrons from a gas pedal, in order to explore particularly extreme regimes of high-field QED.
Our simulations, performed with the open-source Particle-In-Cell code WarpX, show that it would be possible to explore high-field QED in regimes otherwise inaccessible with existing or soon-to-be-available PetaWatt lasers. Clear experimental signatures (such as the generation of relativistic positron beams) could be measurable for the first time.
To carry out these simulations, we need the computing power of the world’s most powerful supercomputers, including, for example, the world’s first exascale machine, Frontier (OLCF, USA).
Bibliography
- Publication “H.Vincenti. Physical Review Letters 123, 105001 (2019)”
https://arxiv.org/pdf/1812.05357.pdf - Publication “L.Fedeli et al. Physical Review Letters 127 (11), 114801 (2021)”
https://arxiv.org/pdf/2012.07696.pdf - Publication “N.Zaim et al. Physical Review Letters, accepted (2024)”
https://arxiv.org/abs/2303.17581
Measurement and theoretical interpretation of XUV absorption in plasma
Measurements of absorption in the extreme UV (XUV, photon energy around 100 eV) in hot, dense plasmas provide essential data for astrophysics and inertial confinement fusion. While numerous experiments have been carried out for decades in the X-ray range, XUV measurements are much rarer. What’s more, their theoretical interpretation is particularly complex. For example, in the copper studied here, this spectral domain involves transitions of principal quantum number n from 3 to 3, with a half-open 3d sublayer and possibly other open spectator sublayers, which means that a very large number of lines have to be taken into account.
We conducted a measurement campaign on the kJ-class LULI facility on a copper plasma with a temperature between 10 and 30 eV and a density of a few mg/cm3 in the 80-180 eV spectral region, using the indirect attack scheme [Poirier2019]. The device used enables moderate temperature and density gradients to be obtained, ensuring conditions close to local thermodynamic equilibrium. An interpretation of the measurements has been proposed, based on several atomic structure codes, including the SCO-RCG hybrid code [Porcherot2011]. Partial agreement has been obtained in this case, however the consideration of temperature gradients is certainly necessary.
Bibliography
- M. Poirier, S. Bastiani-Ceccotti, T. Blenski, M. Comet, C. Esnault, F. Gilleron, D. Gilles, J.-C. Pain, C. Reverdin, F. Thais, “Extreme-UV absorption processes in a laser-produced mid-Z plasma: Measurements and theoretical interpretation”, High Energy Density Phys. 33 100706 (2019).
https://cea.hal.science/cea-02293080v1 - Q. Porcherot, J.-C. Pain, F. Gilleron, T. Blenski, “A consistent approach for mixed detailed and statistical calculation of opacities in hot plasmas,” High Energy Density Phys. 7 234 (2011).
Measurement of the XUV transmission of a copper plasma on the LULI 2000 installation. Smoothing is applied to the raw data.
Theoretical interpretation using the SCO-RCG hybrid code. A simulation of the effect of gradients is carried out using transmissions at 10 eV and 20 eV.
Quantum simulation platform using doubly excited strontium atoms
This activity is part of a collaboration with S Gleyzes and M Brune of the Kastler-Brossel laboratory and the Collège de France. It is an extension of spectroscopic studies of large-kinetic-moment states carried out in our laboratory (SPAM) in the 80s and 90s.
Quantum simulation aims to resolve the difficulty inherent in studying quantum systems with a large number of particles by modeling them with another, better-controlled quantum system in which all local observables are experimentally accessible.
Among the various platforms of this type, Rydberg atoms with two active electrons, one of which is in a high angular momentum state, are a particularly attractive configuration. The team of S Gleyzes and M Brune has implemented an experimental device using a sequence of laser and radio-frequency excitation to create strontium atoms whose outer electron is in a circular state of high orbital momentum(n = 51, l = 50) [Muni2022].
The second electron can be carried in a weakly excited state (4d or 5p), and its presence enables the implementation of optical manipulation methods such as laser cooling.
We have been able to show that the quadrupolar interaction between the active electrons manifests itself as a level shift, for which a quantitative experiment/theory comparison has been carried out. The autoionization process has also been demonstrated, although no quantitative comparison with calculations has yet been made.
In fact, the estimated lifetime is very long and does not take into account the details of the experimental situation, notably the presence of a static electric field.
Microwave spectrum for the atomic transition between circular strontium states eint 51c → eint 49c, where eint is the state of the inner electron. For the black (resp. red) curve eint is the 5s1/2 mj (resp. 4d3/2 mj) state. In the2nd case, the quadrupolar interaction between electrons is manifested by a separation into two components corresponding to the values 3/2 and 1/2 of the modulus |mj|.
(From the SCiRQ proposal Appel à projets 2023, ANR-23-CE47-0008)
Bibliography
- R. P. Feynman, “Simulating physics with computers”, Int. J. Theor. Phys. 21 467 (1982).
- A. Muni, L. Lachaud, A. Couto, M. Poirier, R. C. Texeira, J.-M. Raimond, M. Brune, and S. Gleyzes, “Optical coherent manipulation of alkaline-earth circular Rydberg states”, Nature Phys. 18 502 (2022).
https://cea.hal.science/hal-03481615v1