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Radiation reaction describes the effective force experienced by an accelerated charge due to radiation emission. Quantum effects dominate charge dynamics and radiation production[1][2] for charges accelerated by fields with strengths approaching the Schwinger field, $\mathbf{E_{sch}=}$\textbf{\SI[detect-weight]{1.3e18}{\volt\per\metre}[3]. Such fields exist in extreme astrophysical environments such as pulsar magnetospheres[4], may be accessed by high-power laser systems[5-7], dense particle beams interacting with plasma[8], crystals[9], and at the interaction point of next generation particle colliders[10]. Classical radiation reaction theories do not limit the frequency of radiation emitted by accelerating charges and omit stochastic effects inherent in photon emission[11], thus demanding a quantum treatment. Two quantum radiation reaction models, the quantum-continuous[12] and quantum-stochastic[13] models, correct the former issue, while only the quantum-stochastic model incorporates stochasticity[12]. Such models are of fundamental importance, providing insight into the effect of the electron self-force on its dynamics in electromagnetic fields. The difficulty of accessing conditions where quantum effects dominate inhibited previous efforts to observe quantum radiation reaction in charged particle dynamics with high significance. We report the first direct, high significance $(>5{\sigma})$ observation of strong-field radiation reaction on charged particles. Furthermore, we obtain strong evidence favouring the quantum radiation reaction models, which perform equivalently, over the classical model. Robust model comparison was facilitated by a novel Bayesian framework which inferred collision parameters. This framework has widespread utility for experiments where parameters governing lepton-laser collisions cannot be directly measured, including those using conventional accelerators., Comment: 31 pages, 14 figures

Plasma based acceleration is considered a promising concept for the next generation of linear electron-positron colliders. Despite the great progress achieved over last twenty years in laser technology, laser and beam driven particle acceleration, and special target availability, positron acceleration remains significantly underdeveloped if compared to electron acceleration. This is due to both the specifics of the plasma-based acceleration, and the lack of adequate positron sources tailored for the subsequent plasma based acceleration. Here a positron source based on the collision of a high energy electron beam with a high intensity laser pulse is proposed. The source relies on the subsequent multi-photon Compton and Breit-Wheeleer processes to generate an electron-positron pair out of a high energy photon emitted by an electron. Due to the strong dependence of the Breit-Wheeler process rate on photon energy and field strength, positrons are created with low divergence in a small volume around the peak of the laser pulse. The resulting low emittance in the submicron range potentially makes such positron source interesting for collider applications., Comment: 28 pages, 10 figures, 2 tables

Current experiments investigating radiation reaction employ high energy electron beams together with tightly focused laser pulses in order to reach the quantum regime, as expressed through the quantum nonlinearity parameter $\chi$. Such experiments are often complicated by the large number of latent variables, including the precise structure of the electron bunch. Here we examine a correlation between the electron spatial and energy distributions, called an energy chirp, investigate its significance to the laser-electron beam interaction and show that the resulting effect cannot be trivially ignored when analysing current experiments. In particular, we show that the energy chirp has a large effect on the second moment of the electron energy, but a lesser impact on the first electron energy moment or the photon critical energy. These results show the importance of improved characterisation and control over electron bunch parameters on a shot-to-shot basis in such experiments., Comment: 8 pages, 8 figures

The availability of ever stronger, laser-generated electromagnetic fields underpins continuing progress in the study and application of nonlinear phenomena in basic physical systems, ranging from molecules and atoms to relativistic plasmas and quantum electrodynamics. This raises the question: how far will we be able to go with future lasers? One exciting prospect is the attainment of field strengths approaching the Schwinger critical field $E_\text{cr}$ in the laboratory frame, such that the field invariant $E^2 - c^2B^2 > E_\text{cr}^2$ is reached. The feasibility of doing so has been questioned, on the basis that cascade generation of dense electron-positron plasma would inevitably lead to absorption or screening of the incident light. Here we discuss the potential for future lasers to overcome such obstacles, by combining the concept of multiple colliding laser pulses with that of frequency upshifting via a tailored laser-plasma interaction. This compresses the electromagnetic field energy into a region of nanometer size and attosecond duration, which increases the field magnitude at fixed power but also suppresses pair cascades. Our results indicate that 10-PW-class laser facilities could be capable of reaching $E_\text{cr}$. Such a scenario opens up prospects for experimental investigation of phenomena previously considered to occur only in the most extreme environments in the Universe.

The dynamics of charged particles in electromagnetic fields is an essential component of understanding the most extreme environments in our Universe. In electromagnetic fields of sufficient magnitude, radiation emission dominates the particle motion and effects of nonlinear quantum electrodynamics (QED) are crucial, which triggers electron-positron pair cascades and counterintuitive particle-trapping phenomena. As a result of recent progress in laser technology, high-power lasers provide a platform to create and probe such fields in the laboratory. With new large-scale laser facilities on the horizon and the prospect of investigating these hitherto unexplored regimes, we review the basic physical processes of radiation reaction and QED in strong fields, how they are treated theoretically and in simulation, the new collective dynamics they unlock, recent experimental progress and plans, as well as possible applications for high-flux particle and radiation sources., Comment: 62 pages, 35 figures; as submitted to Rev. Mod. Phys

Electrons at the surface of a plasma that is irradiated by a laser with intensity in excess of $10^{23}~\mathrm{W}\mathrm{cm}^{-2}$ are accelerated so strongly that they emit bursts of synchrotron radiation. Although the combination of high photon and electron density and electromagnetic field strength at the plasma surface makes particle-particle interactions possible, these interactions are usually neglected in simulations of the high-intensity regime. Here we demonstrate an implementation of two such processes: photon absorption and stimulated emission. We show that, for plasmas that are opaque to the laser light, photon absorption would cause complete depletion of the multi-keV region of the synchrotron photon spectrum, unless compensated by stimulated emission. Our results motivate further study of the density dependence of QED phenomena in strong electromagnetic fields., Comment: 20 pages, 4 figures; accepted version

An ultrarelativistic electron beam passing through an intense laser pulse emits radiation around its direction of propagation into a characteristic angular profile. Here we show that measurement of the variances of this profile in the planes parallel and perpendicular to the laser polarization, and the mean initial and final energies of the electron beam, allows the intensity of the laser pulse to be inferred in way that is independent of the model of the electron dynamics. The method presented applies whether radiation reaction is important or not, and whether it is classical or quantum in nature, with accuracy of a few per cent across three orders of magnitude in intensity. It is tolerant of electron beams with broad energy spread and finite divergence. In laser-electron beam collision experiments, where spatiotemporal fluctuations cause alignment of the beams to vary from shot to shot, this permits inference of the laser intensity at the collision point, thereby facilitating comparisons between theoretical calculations and experimental data., Comment: 9 pages, 6 figures; merged supplementary material and main body, to appear in Phys Rev Accel Beams

Apart from maximizing the strength of optical electromagnetic fields achievable at high-intensity laser facilities, the collision of several phase-matched laser pulses has been theoretically identified as a trigger of and way to study various phenomena. These range from the basic processes of strong-field quantum electrodynamics to the extraordinary dynamics of the generated electron-positron plasmas. This has paved the way for several experimental proposals aimed at both fundamental studies of matter at extreme conditions and the creation of particle and radiation sources. Because of the unprecedented capabilities of such sources they have the potential to open up new opportunities for experimental studies in nuclear and quark-gluon physics. We here perform a systematic analysis of different regimes and opportunities achievable with the concept of multiple-colliding laser pulses (MCLP), for both current and upcoming laser facilities. We reveal that several distinct regimes could be within reach of multi-PW laser facilities., Comment: 15 pages, 12 figures

Classical theories of radiation reaction predict that the electron motion is confined to the plane defined by the electron's instantaneous momentum and the force exerted by the external electromagnetic field. However, in the quantum radiation reaction regime, where the recoil exerted by individual quanta becomes significant, the electron can scatter `out-of-plane', as the photon is emitted into a cone with finite opening angle. We show that Monte Carlo implementation of an angularly resolved emission rate leads to substantially improved agreement with exact QED calculations of nonlinear Compton scattering. Furthermore, we show that the transverse recoil caused by this finite beaming, while negligible in many high-intensity scenarios, can be identified in the increase in divergence, in the plane perpendicular to the polarization, of a high-energy electron beam that interacts with a linearly polarized, ultraintense laser., Comment: 8 pages, 5 figures; accepted for publication in Phys Rev A

The reflection of intense laser radiation from solids appears as a result of relativistic dynamics of the electrons driven by both incoming and self-generated electromagnetic fields at the periphery of the emerging dense plasma. In the case of highly-relativistic motion, electrons tend to form a thin oscillating layer, which makes it possible to model the interaction and obtain the temporal structure of the reflected radiation. The modelling reveals the possibility and conditions for producing singularly intense and short XUV bursts of radiation, which are interesting for many applications. However, the intensity and duration of the XUV bursts, as well as the high-energy end of the harmonic spectrum, depends on the thickness of the layer and its internal structure which are not assessed by such macroscopic modelling. Here we analyse the microscopic physics of this layer and clarify how its parameters are bound and how this controls outlined properties of XUV bursts., Comment: 9 pages, 5 figures

As an alternative to Compton backscattering and bremsstrahlung, the process of colliding high-energy electron beams with strong laser fields can more efficiently provide both cleaner and brighter source of photons in the multi-GeV range for fundamental studies in nuclear and quark-gluon physics. In order to favor the emission of high-energy quanta and minimize their decay into electron-positron pairs the fields must not only be sufficiently strong, but also well localized. We here examine these aspects and develop the concept of a laser-particle collider tailored for high-energy photon generation. We show that the use of multiple colliding laser pulses with 0.4 PW of total power is capable of converting more than 18% of the initial multi-GeV electron beam energy into photons, each of which carries more than half of the electron energy., Comment: 6 pages, 4 figures

It is conjectured that all perturbative approaches to quantum electrodynamics (QED) break down in the collision of a high-energy electron beam with an intense laser, when the laser fields are boosted to `supercritical' strengths far greater than the critical field of QED. As field strengths increase toward this regime, cascades of photon emission and electron-positron pair creation are expected, as well as the onset of substantial radiative corrections. Here we identify the important role played by the collision angle in mitigating energy losses to photon emission that would otherwise prevent the electrons reaching the supercritical regime. We show that a collision between an electron beam with energy in the tens of GeV and a laser pulse of intensity $10^{24}~\text{W}\text{cm}^{-2}$ at oblique, or even normal, incidence is a viable platform for studying the breakdown of perturbative strong-field QED. Our results have implications for the design of near-term experiments as they predict that certain quantum effects are enhanced at oblique incidence., Comment: 8 pages, 4 figures; merged supplementary material and main body, updated references; to appear in NJP

The recoil associated with photon emission is key to the dynamics of ultrarelativistic electrons in strong electromagnetic fields, as are found in high-intensity laser-matter interactions and astrophysical environments such as neutron star magnetospheres. When the energy of the photon becomes comparable to that of the electron, it is necessary to use quantum electrodynamics (QED) to describe the dynamics accurately. However, computing the appropriate scattering matrix element from strong-field QED is not generally possible due to multiparticle effects and the complex structure of the electromagnetic fields. Therefore these interactions are treated semiclassically, coupling probabilistic emission events to classical electrodynamics using rates calculated in the locally constant field approximation. Here we provide comprehensive benchmarking of this approach against the exact QED calculation for nonlinear Compton scattering of electrons in an intense laser pulse. We find agreement at the percentage level between the photon spectra, as well as between the models' predictions of absorption from the background field, for normalized amplitudes $a_0 > 5$. We discuss possible routes towards improved numerical methods and the implications of our results for the study of QED cascades., Comment: 12 pages, 7 figures; accepted for publication in Physics of Plasmas

Collisions between high intensity laser pulses and energetic electron beams are now used to measure the transition between the classical and quantum regimes of light-matter interactions. However, the energy spectrum of laser-wakefield-accelerated electron beams can fluctuate significantly from shot to shot, making it difficult to clearly discern quantum effects in radiation reaction, for example. Here we show how this can be accomplished in only a single laser shot. A millimeter-scale pre-collision drift allows the electron beam to expand to a size larger than the laser focal spot and develop a correlation between transverse position and angular divergence. In contrast to previous studies, this means that a measurement of the beam's energy-divergence spectrum automatically distinguishes components of the beam that hit or miss the laser focal spot and therefore do and do not experience radiation reaction.

Electron-positron pairs are produced through the Breit-Wheeler process when energetic photons traverse electromagnetic fields of sufficient strength. Here we consider a possible experimental geometry for observation of pair creation in the highly nonlinear regime, in which bremsstrahlung of an ultrarelativistic electron beam in a high-$Z$ target is used to produce $\gamma$ rays that collide with a counterpropagating laser pulse. We show how the target thickness may be chosen to optimize the yield of Breit-Wheeler positrons, and verify our analytical predictions with simulations of the cascade in the material and in the laser pulse. The electron beam energy and laser intensity required are well within the capability of today's high-intensity laser facilities., Comment: 12 pages, 5 figures

Advances in the generation of relativistic intensity pulses with wavelengths in the X-ray regime, through high harmonic generation from near-critical plasmas, opens up the possibility of X-ray driven wakefield acceleration. The similarity scaling laws for laser plasma interaction suggest that X-rays can drive wakefields in solid materials providing TeV/cm gradients, resulting in electron and photon beams of extremely short duration. However, the wavelength reduction enhances the quantum parameter $\chi$, hence opening the question of the role of non-scalable physics, e.g., the effects of radiation reaction. Using three dimensional Particle-In-Cell simulations incorporating QED effects, we show that for the wavelength $\lambda=5\,$nm and relativistic amplitudes $a_0=10$-100, similarity scaling holds to a high degree, combined with $\chi\sim 1$ operation already at moderate $a_0\sim 50$, leading to photon emissions with energies comparable to the electron energies. Contrasting to the generation of photons with high energies, the reduced frequency of photon emission at X-ray wavelengths (compared to at optical wavelengths) leads to a reduction of the amount of energy that is removed from the electron population through radiation reaction. Furthermore, as the emission frequency approaches the laser frequency, the importance of radiation reaction trapping as a depletion mechanism is reduced, compared to at optical wavelengths for $a_0$ leading to similar $\chi$., Comment: 9 pages, 7 figures

Showers of $\gamma$-rays and positrons are produced when a high-energy electron beam collides with a super-intense laser pulse. We present scaling laws for the electron beam energy loss, the $\gamma$-ray spectrum, and the positron yield and energy that are valid in the non-linear, radiation-reaction--dominated regime. As an application we demonstrate that by employing the collision of a $>$GeV electron beam with a laser pulse of intensity $>5\times10^{21}\,\text{Wcm}^{-2}$, today's high-intensity laser facilities are capable of producing $O(10^4)$ positrons per shot via light-by-light scattering., Comment: 12 pages, 9 figures; eq 5 and references corrected

The dynamics of energetic particles in strong electromagnetic fields can be heavily influenced by the energy loss arising from the emission of radiation during acceleration, known as radiation reaction. When interacting with a high-energy electron beam, today's lasers are sufficiently intense to explore the transition between the classical and quantum radiation reaction regimes. We report on the observation of radiation reaction in the collision of an ultra-relativistic electron beam generated by laser wakefield acceleration ($\varepsilon > 500$ MeV) with an intense laser pulse ($a_0 > 10$). We measure an energy loss in the post-collision electron spectrum that is correlated with the detected signal of hard photons ($\gamma$-rays), consistent with a quantum (stochastic) description of radiation reaction. The generated $\gamma$-rays have the highest energies yet reported from an all-optical inverse Compton scattering scheme, with critical energy $\varepsilon_{\rm crit} > $ 30 MeV., Comment: 11 pages, 9 figures, accepted for publication in PRX

Two signatures of quantum effects on radiation reaction in the collision of a ~GeV electron-beam with a high-intensity (>3x10^20W/cm^2) laser-pulse have been considered. We show that the decrease in the average energy of the electron-beam may be used to measure the Gaunt factor g for synchrotron emission. We derive an equation for the evolution of the variance in the energy of the electron-beam in the quantum regime, i.e. quantum efficiency parameter eta > 0.1$. We show that the evolution of the variance may be used as a direct measure of the quantum stochasticity of the radiation reaction and determine the parameter regime where this is observable. For example, stochastic emission results in a 25% increase in the standard deviation of the energy spectrum of a GeV electron beam, 1 fs after it collides with a laser pulse of intensity 10^21 W/cm^2. This effect should therefore be measurable using current high-intensity laser systems.

Pulses of extreme ultraviolet (XUV) light, with wavelengths between 10 and 100$\,$nm, can be used to image and excite ultra-fast phenomena such as the motion of atomic electrons. Here we show that the illumination of plasma with near-critical electron density may be used as a source of relativistically intense XUV radiation, providing the means for novel XUV-pump--XUV-probe experiments in the non-linear regime. We describe how the optimal regime may be reached by tailoring the laser-target interaction parameters and by the presence of preplasma. Our results indicate that currently available laser facilities are capable of producing XUV pulses with duration $\sim 10~\text{fs}$, brilliance in excess of $10^{23}$ photons/s/mm$^2$/mrad$^2$ (0.1% bandwidth) and intensity $I\lambda^2 \gtrsim 10^{19}~\text{W}\text{cm}^{-2}\mu\text{m}^2$., Comment: 11 pages, 9 figures; additional theoretical comparisons and analysis of density ramps

One aim of upcoming high-intensity laser facilities is to provide new high-flux gamma-ray sources. Electromagnetic cascades may serve for this, but are known to limit both field strengths and particle energies, restricting efficient production of photons to sub-GeV energies. Here we show how to create a directed GeV photon source, enabled by a controlled interplay between the cascade and anomalous radiative trapping. Using advanced 3D QED particle-in-cell (PIC) simulations and analytic estimates, we show that the concept is feasible for planned peak powers of 10 PW level. A higher peak power of 40 PW can provide $10^9$ photons with GeV energies in a well-collimated 3 fs beam, achieving peak brilliance ${9 \times 10^{24}}$ ph s$^{-1}$mrad$^{-2}$mm$^{-2}$/0.1${\%}$BW. Such a source would be a powerful tool for studying fundamental electromagnetic and nuclear processes.

Absorption covers the physical processes which convert intense photon flux into energetic particles when a high-power laser illuminates optically-thick matter. It underpins important petawatt-scale applications today, e.g., medical-quality proton beam production. However, development of ultra-high-field applications has been hindered since no study so far has described absorption throughout the entire transition from the classical to the quantum electrodynamical (QED) regime of plasma physics. Here we present a model of absorption that holds over an unprecedented six orders-of-magnitude in optical intensity and lays the groundwork for QED applications of laser-driven particle beams. We demonstrate 58% efficient \gamma-ray production at $1.8\times 10^{25}~\mathrm{W~ cm^{-2}}$ and the creation of an anti-matter source achieving $4\times 10^{24}\ \mathrm{positrons}\ \mathrm{cm^{-3}}$, $10^{6}~\times$ denser than of any known photonic scheme. These results will find applications in scaled laboratory probes of black hole and pulsar winds, \gamma-ray radiography for materials science and homeland security, and fundamental nuclear physics., Comment: 10 pages, 5 figures

We study the effects of laser pulse focussing on the spectral properties of Thomson scattered radiation. Modelling the laser as a paraxial beam we find that, in all but the most extreme cases of focussing, the temporal envelope has a much bigger effect on the spectrum than the focussing itself. For the case of ultra-short pulses, where the paraxial model is no longer valid, we adopt a sub-cycle vector beam description of the field. It is found that the emission harmonics are blue shifted and broaden out in frequency space as the pulse becomes shorter. Additionally the carrier envelope phase becomes important, resulting in an angular asymmetry in the spectrum. We then use the same model to study the effects of focussing beyond the limit where the paraxial expansion is valid. It is found that fields focussed to sub-wavelength spot sizes produce spectra that are qualitatively similar to those from sub-cycle pulses due to the shortening of the pulse with focussing. Finally, we study high-intensity fields and find that, in general, the focussing makes negligible difference to the spectra in the regime of radiation reaction., Comment: 14 pages, 17 figures

We extend the existing theoretical model for determining the characteristic features of magnetic deflagration in nanomagnet crystals. For the first time, all energy levels are accounted for calculation of the the Zeeman energy, the deflagration velocity, and other parameters. It reduces the final temperature and significantly changes the propagation velocity of the spin-flipping front. We also consider the effect of a strong transverse magnetic field, and show that the latter significantly modifies the spin-state structure, leading to an uncertainty concerning the activation energy of the spin flipping. Our front velocity prediction for a crystal of Mn$_{12}$-acetate in a longitudinal magnetic field is in much better agreement with experimental data than the previous reduced-model results.

The interaction of charged particles and photons with intense electromagnetic fields gives rise to multi-photon Compton and Breit-Wheeler processes. These are usually described in the framework of the external field approximation, where the electromagnetic field is assumed to have infinite energy. However, the multi-photon nature of these processes implies the absorption of a significant number of photons, which scales as the external field amplitude cubed. As a result, the interaction of a highly charged electron bunch with an intense laser pulse can lead to significant depletion of the laser pulse energy, thus rendering the external field approximation invalid. We provide relevant estimates for this depletion and find it to become important in the interaction between fields of amplitude $a_0 \sim 10^3$ and electron bunches with charges of the order of 10 nC., Comment: 5 pages, 3 captioned figures, version to appear in PRL

The magnetic instability at the front of the spin avalanche in a crystal of molecular magnets is considered. This phenomenon reveals similar features with the Darrieus-Landau instability, inherent to classical combustion flame fronts. The instability growth rate and the cut-off wavelength are investigated with respect to the strength of the external magnetic field, both analytically in the limit of an infinitely thin front and numerically for finite-width fronts. The presence of quantum tunneling resonances is shown to increase the growth rate significantly, which may lead to a possible transition from deflagration to detonation regimes. Different orientations of the crystal easy axis are shown to exhibit opposite stability properties. In addition, we suggest experimental conditions that could evidence the instability and its influence on the magnetic deflagration velocity.

We consider the emission spectrum of high-energy electrons in an intense laser field. At high intensities ($a_0\sim200$) we find that the QED theory predicts a narrower angular spread of emissions than the classical theory. This is due to the classical theory overestimating the energy loss of the particles, resulting in them becoming more susceptible to reflection in the laser pulse., Comment: 7 pages, 6 figures

Experimentally detected ultrafast spin-avalanches spreading in crystals of molecular (nano)magnets (Decelle et al., Phys. Rev. Lett. 102, 027203 (2009)), have been recently explained in terms of magnetic detonation (Modestov et al., Phys. Rev. Lett. 107, 207208 (2011)). Here magnetic detonation structure is investigated by taking into account transport processes of the crystals such as thermal conduction and volume viscosity. In contrast to the previously suggested model, the transport processes result in smooth profiles of the most important thermodynamical crystal parameters - such as temperature, density and pressure - all over the magnetic detonation front including the leading shock, which is one of the key regions of magnetic detonation. In the case of zero volume viscosity, thermal conduction leads to an isothermal discontinuity instead of the shock, for which temperature is continuous while density and pressure experience jump., Comment: 11 pages, 14 figures

We review common extensions of particle-in-cell (PIC) schemes which account for strong field phenomena in laser-plasma interactions. After describing the physical processes of interest and their numerical implementation, we provide solutions for several associated methodological and algorithmic problems. We propose a modified event generator that precisely models the entire spectrum of incoherent particle emission without any low-energy cutoff, and which imposes close to the weakest possible demands on the numerical time step. Based on this, we also develop an adaptive event generator that subdivides the time step for locally resolving QED events, allowing for efficient simulation of cascades. Further, we present a new and unified technical interface for including the processes of interest in different PIC implementations. Two PIC codes which support this interface, PICADOR and ELMIS, are also briefly reviewed.

We perform a numerical study of the interaction of a high-intensity laser pulse with a nano-structured target. In particular, we study a target where the nano-structuring increases the absorption rate as compared to the flat target case. The transport of electrons within the target, and in particular in the nano-structure, is analysed. It is shown that it is indeed possible, using a terawatt class laser, to light up a nano-scale Christmas tree. Due to the form of the tree we achieve very strong edge fields, in particular at the top where the star is located. Such edge fields, as here located at ion rich spots, makes strong acceleration gradients possible. It also results in a nice, warm glow suitable for the holiday season., Comment: 3 pages, 4 figures