Focus on Strong Field Quantum Electrodynamics with high power lasers and particle beams

We present new exact solutions of the Landau–Lifshitz (LL) and higher-order LL equations describing particle motion, with radiation reaction, in intense electromagnetic fields. Through these solutions and others we compare the phenomenological predictions of different equations in the context of the conjectured 'radiation-free direction' (RFD). We confirm analytically in several cases that particle orbits predicted by the LL equation indeed approach the RFD at extreme intensities, and give time-resolved signals of this behaviour in radiation spectra.

By taking the spin and polarization of the electrons, positrons and photons into account in the strong-field QED processes of nonlinear Compton emission and pair production, we find that the growth rate of QED cascades in ultra-intense laser fields can be substantially reduced. While this means that fewer particles are produced, we also found them to be highly polarized. We further find that the high-energy tail of the particle spectra is polarized opposite to that expected from Sokolov–Ternov theory, which cannot be explained by just taking into account spin-asymmetries in the pair production process, but results significantly from 'spin-straggling'. We employ a kinetic equation approach for the electron, positron and photon distributions, each of them spin/polarization-resolved, with the QED effects of photon emission and pair production modelled by a spin/polarization dependent Boltzmann-type collision operator. For photon-seeded cascades, depending on the photon polarization, we find an excess or a shortage of particle production in the early stages of cascade development, which provides a path towards a controlled experiment. Throughout this paper we focus on rotating electric field configuration, which represent an idealized model and allows for a straightforward interpretation of the observed effects.

In a previous paper we showed how higher-order strong-field-QED processes in long laser pulses can be approximated by multiplying sequences of 'strong-field Mueller matrices'. We obtained expressions that are valid for arbitrary field shape and polarization. In this paper we derive practical approximations of these Mueller matrices in the locally-constant- and the locally-monochromatic-field regimes. The spin and polarization can also change due to loop contributions (the mass operator for electrons and the polarization operator for photons). We derive Mueller matrices for these as well, for arbitrary laser polarization and arbitrarily polarized initial and final particles.

The dynamics and radiation of ultrarelativistic electrons in strong counterpropagating laser beams are investigated. Assuming that the particle energy is the dominant scale in the problem, an approximate solution of classical equations of motion is derived and the characteristic features of the motion are examined. A specific regime is found with comparable strong field quantum parameters of the beams, when the electron trajectory exhibits ultrashort spike-like features, which bears great significance to the corresponding radiation properties. An analytical expression for the spectral distribution of spontaneous radiation is derived in the framework of the Baier–Katkov semiclassical approximation based on the classical trajectory. All the analytical results are further validated by exact numerical calculations. We consider a non-resonant regime of interaction, when the laser frequencies in the electron rest frame are far from each other, avoiding stimulated emission. Special attention is devoted to settings when the description of radiation via the local constant field approximation fails and to corresponding spectral features. Periodic and non-periodic regimes are considered, when lab frequencies of the laser waves are always commensurate. The sensitivity of spectra with respect to the electron beam spread, focusing and finite duration of the laser beams is explored.

The process of turning a proton into a neutron, positron and electron-neutrino in a strong plane-wave electromagnetic field is studied. This process is forbidden in vacuum and is seen to feature an exponential suppression factor which is non-perturbative in the field amplitude. The suppression is alleviated when the proton experiences a field strength of about ten times the Schwinger critical field in its rest frame or larger. Around this threshold the lifetime of the proton, in its rest frame, is comparable to the conventional neutron decay lifetime. As the field strength is increased, the proton lifetime becomes increasingly short. We investigate possible scenarios where this process may be observed in the laboratory using an ultra-intense laser and a high-energy proton beam with the conclusion, however, that it would be very challenging to observe this effect in the near future.

The spin effect of electrons/positrons (e⁻/e⁺) and polarization effect of γ photons are investigated in the interaction of two counter-propagating linearly polarized laser pulses of peak intensity 8.9 × 10²³ W cm⁻² with a thin foil target. The processes of nonlinear Compton scattering and nonlinear Breit–Wheeler pair production based on the spin- and polarization-resolved probabilities are implemented into the particle-in-cell (PIC) algorithm by Monte Carlo methods. It is found from PIC simulations that the average degree of linear polarization of emitted γ photons can exceed 50%. This polarization effect leads to a reduced positron yield by about 10%. At some medium positron energies, the reduction can reach 20%. Furthermore, we also observe that the local spin polarization of e⁻/e⁺ leads to a slight decrease of the positron yield about 2% and some anomalous phenomena about the positron spectrum and photon polarization at the high-energy range, due to spin-dependent photon emissions. Our results indicate that spin and polarization effects should be considered in calculating the pair production and laser-plasma interaction with the laser power of 10 PW to 100 PW classes.

A classical model of radiation reaction for the betatron oscillation of an electron in a plasma wakefield accelerator is presented. The maximum energy of the electron due to the longitudinal radiation reaction is found, and the betatron oscillation damping due to both the longitudinal and transverse radiation reaction effects is analyzed. Both theoretical and numerical solutions are shown with good agreements. The regime that the quantum radiation takes effect is also discussed. This model is important for designing future plasma based super accelerators or colliders.

The Landau–Lifshitz (LL) equation has been proposed as the classical equation to describe the dynamics of a charged particle in a strong electromagnetic field when influenced by radiation reaction. Until recently, there has been no clear experimental verification. However, aligned crystals have remedied the situation: here, as in Nielsen et al CERN NA63 Collaboration (2020 Phys. Rev. D 102 052004), we report on a quantitative experimental test of the LL equation by measuring the emission spectra of electrons and positrons penetrating aligned single crystals. The recorded spectra are in remarkable agreement with simulations based on the LL equation of motion with moderate quantum corrections for recoil and, in the case of electrons in axially aligned crystals, spin and reduced radiation intensity.

The forthcoming generation of multi-petawatt lasers opens the way to abundant pair production by the nonlinear Breit–Wheeler process, i.e. the decay of a photon into an electron–positron pair inside an intense laser field. In this paper we explore the optimal conditions for Breit–Wheeler pair production in the head-on collision of a laser pulse with gamma photons. The role of the laser peak intensity versus the focal spot size and shape is examined keeping a constant laser energy to match experimental constraints. A simple model for the soft-shower case, where most pairs originate from the decay of the initial gamma photons, is derived. This approach provides us with a semi-analytical model for more complex situations involving either Gaussian or Laguerre–Gauss (LG) laser beams. We then explore the influence of the order of the LG beams on pair creation. Finally we obtain the result that, above a given threshold, a larger spot size (or a higher order in the case of LG laser beams) is more favorable than a higher peak intensity. Our results match very well with three-dimensional particle-in-cell simulations and can be used to guide upcoming experimental campaigns.

State-of-the-art numerical simulations of quantum electrodynamical (QED) processes in strong laser fields rely on a semiclassical combination of classical equations of motion and QED rates, which are calculated in the locally constant field approximation. However, the latter approximation is unreliable if the amplitude of the fields, a₀, is comparable to unity. Furthermore, it cannot, by definition, capture interference effects that give rise to harmonic structure. Here we present an alternative numerical approach, which resolves these two issues by combining cycle-averaged equations of motion and QED rates calculated in the locally monochromatic approximation. We demonstrate that it significantly improves the accuracy of simulations of photon emission across the full range of photon energies and laser intensities, in plane-wave, chirped and focused background fields.

We study the perspectives of measuring the phenomenon of vacuum birefringence predicted by quantum electrodynamics using an x-ray free-electron laser (XFEL) alone. We devise an experimental scheme allowing two consecutive XFEL pulses to collide under a finite angle, and thus act as both pump and probe field for the effect. The signature of vacuum birefringence is encoded in polarization-flipped signal photons to be detected with high-purity x-ray polarimetry. Our findings for idealized scenarios underline that the discovery potential of solely XFEL-based setups can be comparable to those involving optical high-intensity lasers. For currently achievable scenarios, we identify several key details of the x-ray optical ingredients that exert a strong influence on the magnitude of the desired signatures.

Radiation friction can have a substantial impact on electron dynamics in a transparent target exposed to a strong laser pulse. In particular, by modifying quiver electron motion, it can strongly enhance the longitudinal charge separation field, thus inducing ion acceleration. We present a model and simulation results for such a radiation induced ion acceleration regime and study the scalings of the maximal attainable and average ion energies with respect to the laser and target parameters. We also compare the performance of this mechanism to the conventional ones.

Recent high-intensity laser experiments (Cole et al 2018 Phys. Rev. X 8 011020; Poder et al 2018 Phys. Rev. X 8 031004) have shown evidence of strong radiation reaction in the quantum regime. Experimental evidence of quantum effects on radiation reaction and electron–positron pair cascades has, however, proven challenging to obtain and crucially depends on maximising the quantum parameter of the electron (defined as the ratio of the electric field it feels in its rest frame to the Schwinger field). The quantum parameter can be suppressed as the electrons lose energy by radiation reaction as they traverse the initial rise in the laser intensity. As a result the shape of the intensity temporal envelope becomes important in enhancing quantum radiation reaction effects and pair cascades. Here we show that a realistic laser pulse with a faster rise time on the leading edge, achieved by skewing the temporal envelope, results in curtailing of pair yields as the peak power is reduced. We find a reduction in pair yields by orders of magnitude in contrast to only small reductions reported previously in large-scale particle-in-cell code simulations (Hojbota et al 2018 Plasma Phys. Control. Fusion 60 064004). Maximum pairs per electron are found in colliding 1.5 GeV electrons with a laser wakefield produced envelope 7.90 × 10⁻² followed by a short 50 fs Gaussian envelope, 1.90 × 10⁻², while it is reduced to 8.90 × 10⁻⁵, a factor of 100, for an asymmetric envelope.

The self-consistent modeling of vacuum polarization due to virtual electron-positron fluctuations is of relevance for many near term experiments associated with high intensity radiation sources and represents a milestone in describing scenarios of extreme energy density. We present a generalized finite-difference time-domain solver that can incorporate the modifications to Maxwell's equations due to vacuum polarization. Our multidimensional solver reproduced in one-dimensional configurations the results for which an analytic treatment is possible, yielding vacuum harmonic generation and birefringence. The solver has also been tested for two-dimensional scenarios where finite laser beam spot sizes must be taken into account. We employ this solver to explore different types of laser configurations that can be relevant for future planned experiments aiming to detect quantum vacuum dynamics at ultra-high electromagnetic field intensities.

The laser intensity dependence of nonlinear Compton scattering is discussed in some detail. For sufficiently hard photons with energy ω', the spectrally resolved differential cross section dσ/dω'|_ω'=const, rises from small toward larger laser intensity parameter ξ, reaches a maximum, and falls toward the asymptotic strong-field region. Such a rise and fall of a differential observable is to be contrasted with the monotonously increasing laser intensity dependence of the total probability, which is governed by the soft spectral part. We combine that hard-photon yield from Compton scattering with the seeded Breit–Wheeler pair production in a folding model and obtain a rapidly increasing e⁺e⁻ pair number at ξ ≲ 4. Laser bandwidth effects are quantified in the weak-field limit of the related trident pair production.

Relativistic transparency enables volumetric laser interaction with overdense plasmas and direct laser acceleration of electrons to relativistic velocities. The dense electron current generates a magnetic filament with field strength of the order of the laser amplitude (>10⁵ T). The magnetic filament traps the electrons radially, enabling efficient acceleration and conversion of laser energy into MeV photons by electron oscillations in the filament. The use of microstructured targets stabilizes the hosing instabilities associated with relativistically transparent interactions, resulting in robust and repeatable production of this phenomenon. Analytical scaling laws are derived to describe the radiated photon spectrum and energy from the magnetic filament phenomenon in terms of the laser intensity, focal radius, pulse duration, and the plasma density. These scaling laws are compared to 3D particle-in-cell (PIC) simulations, demonstrating agreement over two regimes of focal radius. Preliminary experiments to study this phenomenon at moderate intensity (a₀ ∼ 30) were performed on the Texas Petawatt Laser. Experimental signatures of the magnetic filament phenomenon are observed in the electron and photon spectra recorded in a subset of these experiments that is consistent with the experimental design, analytical scaling and 3D PIC simulations. Implications for future experimental campaigns are discussed.

Electron–positron pair production via the nonlinear Bethe–Heitler effect in the combined fields of a bare nucleus and a high-intensity laser pulse is studied theoretically. The calculations are performed within the framework of strong-field quantum electrodynamics using a flat-top laser profile with raising and falling edges. This way, the dependence of the pair production process on the precise shape of the laser field is analyzed. Our approach allows us, in particular, to follow the evolution of the created particles' energy spectra from ultra-short few-cycle pulses to the monochromatic infinite pulse-train limit. We show how the various portions of the pulse influence these spectra and determine conditions for which the outcome from a laser pulse closely resembles the predictions from monochromatic theory.

The interaction of light with the quantum-vacuum is predicted to give rise to some of the most fundamental and exotic processes in modern physics, which remain untested in the laboratory to date. Electron–positron pair production from a pure vacuum target, which has yet to be observed experimentally, is possibly the most iconic. The advent of ultra-intense lasers and laser accelerated GeV electron beams provide an ideal platform for the experimental realisation. Collisions of high energy γ-ray photons derived from the GeV electrons and intense laser fields result in detectable pair production rates at field strengths that approach and exceed the Schwinger limit in the centre-of-momentum frame. A detailed experiment has been designed to be implemented at the ATLAS laser at the centre of advanced laser applications. We show full calculations of the expected backgrounds and beam parameters which suggest that single pair events can be reliably generated and detected.

High order harmonic generation by extremely intense, interacting, electromagnetic waves in the quantum vacuum is investigated within the framework of the Heisenberg–Euler formalism. Two intersecting plane waves of finite duration are considered in the case of general polarizations. Detailed finite expressions are obtained for the case where only the first Poincaré invariant does not vanish. Yields of high harmonics in this case are most effective.

Laser–electron beam collisions that aim to generate electron–positron pairs require laser intensities I ≳ 10²¹ W cm⁻², which can be obtained by focusing a 1-PW optical laser to a spot smaller than 10 μm. Spatial synchronization is a challenge because of the Poynting instability that can be a concern both for the interacting electron beam (if laser-generated) and the scattering laser. One strategy to overcome this problem is to use an electron beam coming from an accelerator (e.g., the planned E-320 experiment at FACET-II). Even using a stable accelerator beam, the plane wave approximation is too simplistic to describe the laser–electron scattering. This work extends analytical scaling laws for pair production, previously derived for the case of a plane wave and a short electron beam. We consider a focused laser beam colliding with electron beams of different shapes and sizes. The results take the spatial and temporal synchronization of the interaction into account, can be extended to arbitrary beam shapes, and prescribe the optimization strategies for near-future experiments.

We show that a single laser pulse, traveling through a dense plasma, produces a population of MeV photons of sufficient density to generate a large number of electron–positron pairs via the linear Breit–Wheeler process. While it may be expected that the photons are emitted predominantly in the forward direction, parallel to the laser propagation, we find that a longitudinal plasma electric field drives the emission of photons in the backwards direction. This enables the collision of oppositely directed, MeV-level photons necessary to overcome the mass threshold for the linear Breit–Wheeler process. Our calculations predict the production of 10⁷ electron–positron pairs, per shot, by a laser with peak intensity of just 3 × 10²² W cm⁻². By using only a single laser pulse, the scheme sidesteps the practical difficulties associated with the multiple-laser schemes previously investigated.

We describe a laser–plasma platform for photon–photon collision experiments to measure fundamental quantum electrodynamic processes. As an example we describe using this platform to attempt to observe the linear Breit–Wheeler process. The platform has been developed using the Gemini laser facility at the Rutherford Appleton Laboratory. A laser Wakefield accelerator and a bremsstrahlung convertor are used to generate a collimated beam of photons with energies of hundreds of MeV, that collide with keV x-ray photons generated by a laser heated plasma target. To detect the pairs generated by the photon–photon collisions, a magnetic transport system has been developed which directs the pairs onto scintillation-based and hybrid silicon pixel single particle detectors (SPDs). We present commissioning results from an experimental campaign using this laser–plasma platform for photon–photon physics, demonstrating successful generation of both photon sources, characterisation of the magnetic transport system and calibration of the SPDs, and discuss the feasibility of this platform for the observation of the Breit–Wheeler process. The design of the platform will also serve as the basis for the investigation of strong-field quantum electrodynamic processes such as the nonlinear Breit–Wheeler and the Trident process, or eventually, photon–photon scattering.

A charged particle subject to strong external forces will accelerate, and so radiate energy, inducing a self-force. This phenomenon remains contentious, but advances in laser technology mean we will soon encounter regimes where a more complete understanding is essential. The terms 'self-force' and 'radiation reaction' are often used synonymously, but reflect different aspects of the recoil force. For a particle accelerating in an electromagnetic field, radiation reaction is usually the dominant self-force, but in a scalar field this is not the case, and the total effect of the self-force can be anti-frictional. Aspects of this self-force can be recast in terms of spacetime geometry, and this interpretation illuminates the long-standing enigma of a particle radiating while experiencing no self-force.

X-ray free-electron lasers can generate radiation pulses with extreme peak intensities at short wavelengths. This enables the investigation of laser–matter interactions in a regime of high fields, yet at a non-relativistic ponderomotive potential, where ordinary rules of light–matter interaction may no longer apply and nonlinear processes are starting to become observable. Despite small cross-sections, first nonlinear effects in the hard x-ray regime have recently been observed in solid targets, including x-ray-optical sum-frequency generation (XSFG), x-ray second harmonic generation (XSHG) and two-photon Compton scattering (2PCS). Nonlinear interactions of bound electrons in the x-ray range are fundamentally different from those dominating at optical frequencies. Whereas in the optical regime nonlinearities are predominantly caused by anharmonicities of the atomic potential in the chemical bonds, x-ray nonlinearities far above atomic resonances are expected to be due to nonlinear oscillations of quasi-free electrons, including inner-shell atomic electrons. While the quasi-free-electron model agrees reasonably well with the experimental data for XSFG and XSHG, 2PCS measurements have led to unexpected results: the energy of the nonlinearly scattered photons from non-relativistic electrons shows a substantial unexpected red shift in addition to the Compton shift that is well beyond that predicted by a nonlinear quantum electrodynamics model for free electrons.

A potential explanation for the spectral broadening is based on a previously unexplored scattering process that involves the whole atom rather than just quasi-free electrons. A first simulation that includes the atomic binding potential was successful in describing a broadening of the spectrum of the nonlinearly scattered photons to longer wavelengths for soft x-rays. However, the same model does not show any broadening at hard x-ray wavelengths, which is in agreement with other simulation approaches. To this point no calculation has been able to reproduce the experimentally observed broadening.

Here we present further experimental data of 2PCS for an extended parameter range using additional diagnostics. In particular, we present measurements of the electron momentum distribution during the interaction that strongly suggest that the spectral broadening is not caused by an increased plasma temperature. We extend our measurement of the magnitude of the red shift in beryllium to $> 1.9\enspace \mathrm{k}\mathrm{e}\mathrm{V}$ in addition to the Compton shift expected for free electrons and expand the measurement of the angular distribution to include forward scattering angles. We also present first measurements of 2PCS from diamond.

Measuring signatures of strong-field quantum electrodynamics (SF-QED) processes in an intense laser field is an experimental challenge: it requires detectors to be highly sensitive to single electrons and positrons in the presence of the typically very strong x-ray and γ-photon background levels. In this paper, we describe a particle detector capable of diagnosing single leptons from SF-QED interactions and discuss the background level simulations for the upcoming Experiment-320 at FACET-II (SLAC National Accelerator Laboratory). The single particle detection system described here combines pixelated scintillation LYSO screens and a Cherenkov calorimeter. We detail the performance of the system using simulations and a calibration of the Cherenkov detector at the ELBE accelerator. Single 3 GeV leptons are expected to produce approximately 537 detectable photons in a single calorimeter channel. This signal is compared to Monte-Carlo simulations of the experiment. A signal-to-noise ratio of 18 in a single Cherenkov calorimeter detector is expected and a spectral resolution of 2% is achieved using the pixelated LYSO screens.

High power short pulse lasers provide a promising route to study the strong field effects of the quantum vacuum, for example by direct photon–photon scattering in the all-optical regime. Theoretical predictions based on realistic laser parameters achievable today or in the near future predict scattering of a few photons with colliding Petawatt laser pulses, requiring single photon sensitive detection schemes and very good spatio-temporal filtering and background suppression. In this article, we present experimental investigations of this photon background by employing only a single high power laser pulse tightly focused in residual gas of a vacuum chamber. The focal region was imaged onto a single-photon sensitive, time gated camera. As no detectable quantum vacuum signature was expected in our case, the setup allowed for characterization and first mitigation of background contributions. For the setup employed, scattering off surfaces of imperfect optics dominated below residual gas pressures of 1 × 10⁻⁴ mbar. Extrapolation of the findings to intensities relevant for photon–photon scattering studies is discussed.

Physical scenarios where the electromagnetic fields are so strong that quantum electrodynamics (QED) plays a substantial role are one of the frontiers of contemporary plasma physics research. Investigating those scenarios requires state-of-the-art particle-in-cell (PIC) codes able to run on top high-performance computing (HPC) machines and, at the same time, able to simulate strong-field QED processes. This work presents the PICSAR-QED library, an open-source, portable implementation of a Monte Carlo module designed to provide modern PIC codes with the capability to simulate such processes, and optimized for HPC. Detailed tests and benchmarks are carried out to validate the physical models in PICSAR-QED, to study how numerical parameters affect such models, and to demonstrate its capability to run on different architectures (CPUs and GPUs). Its integration with WarpX, a state-of-the-art PIC code designed to deliver scalable performance on upcoming exascale supercomputers, is also discussed and validated against results from the existing literature.

In this paper we will show that photon–photon collision experiments using extreme lasers can provide measurable effects giving fundamental information about the essence of QED, its Lagrangian. A possible scenario with two counterpropagating ultra-intense lasers for an experiment to detect scattering between optical photons is analyzed. We discuss the importance of the pulse widths and waists, the best scenario for overlapping the beams and signal detection, as well as ways to distinguish the signal from the noise. This would need a high-precision measurement, with control of temporal jitter and noise. We conclude that such experiment is barely feasible at 10²³ W cm⁻² and very promising at 10²⁴ W cm⁻².

The advent of petawatt-class laser systems allows generating electromagnetic fields of unprecedented strength in a controlled environment, driving increasingly more efforts to probe yet unobserved processes through their interaction with the quantum vacuum. Still, the lowest intensity scale governing these effects lies orders of magnitude beyond foreseen capabilities, so that such endeavor is expected to remain extremely challenging. In recent years, however, plasma mirrors have emerged as a promising bridge across this gap, by enabling the conversion of intense infrared laser pulses into coherently focused Doppler harmonic beams lying in the X-UV range. In this work, we present predictions on the quantum vacuum signatures produced when such beams are focused to intensities between 10²⁴ and 10²⁸ W cm⁻², specifically photon–photon scattering and electron–positron pair creation. These signatures are computed via the stimulated vacuum formalism, combined with a model of perfectly focused beam built from PIC-generated harmonics spectra, and implemented on state-of-the-art massively parallel numerical tools. In view of identifying experimentally favorable configurations, we also consider the coupling of the focused harmonic beam with an auxiliary optical beam, and provide comparison with other established schemes. Our results show that a single coherently focused harmonic beam can produce as much scattered photons as two infrared pulses in head-on collision, and confirm that the coupling of the harmonic beam to an auxiliary beam gives rise to significant levels of inelastic scattering, and hence holds the potential to strongly improve the attainable signal to noise ratios in experiments.