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We demonstrate the capability of Flying Focus (FF) laser pulses with $\ell = 1$ orbital angular momentum (OAM) to transversely confine ultra-relativistic charged particle bunches over macroscopic distances while maintaining a tight bunch radius. A FF pulse with $\ell = 1$ OAM creates a radial ponderomotive barrier that constrains the transverse motion of particles and travels with the bunch over extended distances. As compared to freely propagating bunches, which quickly diverge due to their initial momentum spread, the particles co-traveling with the ponderomotive barrier slowly oscillate around the laser pulse axis within the spot size of the pulse. This can be achieved at FF pulse energies that are orders of magnitude lower than required by Gaussian or Bessel pulses with OAM. The ponderomotive trapping is further enhanced by radiative cooling of the bunch resulting from rapid oscillations of the charged particles in the laser field. This cooling decreases the mean square radius and emittance of the bunch during propagation., Comment: 17 pages, 9 figures

The polarization dynamics of electrons including multiple nonlinear Comptonscattering during the interaction of a circularly-polarized ultraintense laserpulse with a counterpropagating ultrarelativistic electron beam isinvestigated. While electron polarization emerges mostly due to spin-flips atphoton emissions, there is a non-radiative contribution to the polarizationwhich stems from the one-loop QED radiative corrections to the self-energy,which admits of a simple physical model. We put forward a method to single outthe non-radiative contribution to the polarization, employing the reflectionregime of the interaction when the radiation reaction is significant. Thepolarization of electrons that penetrate in the forward direction through acolliding laser is shown to be dominated by the loop effect, while thereflected electrons are mostly polarized by spin-flips at photon emissions. Weconfirm this effect by quantum Monte Carlo simulations considering the helicitytransfer from the laser field to the electrons, taking into account theopposite sign of the polarizations induced by the non-radiative loop effect andradiative spin-flip. Our Monte Carlo simulations show a polarization signal ashigh as $\gtrsim 10\%$ from the non-radiative effect, amenable for experimentaldetection with current technology.

Abstract The Landau–Lifshitz equation is widely considered as the equation, which correctly includes the effects of radiation reaction in the classical motion of an electric charge. Here, we provide an approximated analytical solution of the Landau–Lifshitz equation in the presence of a virtually arbitrary electromagnetic field by making the assumptions that the electron’s initial energy is the largest dynamical energy in the problem. We show that in a regime where radiation–reaction effects are a small correction of the Lorentz dynamics, the four-momentum of the electron can be determined perturbatively in the ultrarelativistic limit. We explicitly compute the electron four-momentum up to the first order and in the experimentally relevant case of an ultrashort, tightly focused laser beam as an external field. Graphical abstract

In the presence of an electromagnetic background plane-wave field, electron, positron, and photon states are not stable, because electrons and positrons emit photons and photons decay into electron-positron pairs. This decay of the particle states leads to an exponential damping term in the probabilities of single nonlinear Compton scattering and nonlinear Breit-Wheeler pair production. In this paper we investigate analytically and numerically the probabilities of nonlinear Compton scattering and nonlinear Breit-Wheeler pair production including the particle states' decay. For this we first compute spin- and polarization-resolved expressions of the probabilities, provide some of their asymptotic behaviors and show that the results of the total probabilities are independent of the spin and polarization bases. Then, we present several plots of the total and differential probabilities for different pulse lengths and for different spin and polarization quantum numbers. We observe that it is crucial to take into account the damping of the states in order for the probabilities to stay always below unity and we show that the damping factors also scale with the intensity and pulse duration of the background field. In the case of nonlinear Compton scattering we show numerically that the total probability behaves like a Poissonian distribution in the regime where the photon recoil is negligible. In all considered cases, the kinematic conditions are such that the final particles momenta transverse to the propagation direction of the plane wave are always much smaller than the particles longitudinal momenta and the main spread of the momentum distribution on the transverse plane is along the direction of the plane-wave electric field., 44 pages, 12 figures

Accelerated charges emit both electromagnetic and gravitational radiation. Classically, it was found that the electromagnetic energy spectrum radiated by an electron in a monochromatic plane wave is proportional to the corresponding gravitational one. Quantum mechanically, it was shown that the amplitudes of graviton photoproduction and Compton scattering are proportional to each other at tree level. Here, by combining strong-field QED and quantum gravity, we demonstrate that the amplitude of nonlinear graviton photoproduction in an arbitrary plane wave is proportional to the corresponding amplitude of nonlinear Compton scattering. Also, introducing classical amplitudes we prove that the proportionality relies on the semiclassical nature of the electron's motion in a plane wave and on energy-momentum conservation laws, leading to the same proportionality constant in the classical and quantum case. These results deepen the intertwine between gravity and electromagnetism into both a nonlinear and a quantum level., 6 pages, 1 figure

The solution of the Dirac equation in the presence of an arbitrary plane wave, corresponding to the so-called Volkov states, has provided an enormous insight in strong-field QED. In [Phys. Rev. A \textbf{103}, 076011 (2021)] a new "fully quasiclassical" representation of the Volkov states has been found, which is equivalent to the one known in the literature but which more transparently shows the quasiclassical nature of the quantum dynamics of an electron in a plane-wave field. Here, we derive the corresponding expression of the propagator by constructing it using the fully quasiclassical form of the Volkov states. The found expression allows one, together with the fully quasiclassical expression of the Volkov states, to compute probabilities in strong-field QED in an intense plane wave by manipulating only 2-by-2 rather than 4-by-4 Dirac matrices as in the usual approach. Moreover, apart from the exponential functions featuring the classical action of an electron in a plane wave, the fully quasiclassical Volkov propagator depends only on the electron kinetic four-momentum in the plane wave, which is a gauge-invariant quantity. Finally, we also compute the one-loop tadpole diagram in a plane wave starting from the Volkov propagator and we find that after renormalization it identically vanishes., 25 pages, 2 figure

According to quantum electrodynamics (QED), a strong external field can make the vacuum state decay producing electron-positron pairs. Here we investigate emission of soft photons which accompanies a nonperturbative process of pair production. Our analysis is carried out within the Furry picture to first order in the fine-structure constant. It is shown that the presence of photons in the initial state gives rise to an additional (stimulated) channel of photon emission besides the pure vacuum one. On the other hand, the number of final (signal) photons includes also a negative contribution due to photon absorption within the pair production process. These contributions are evaluated and compared. To obtain quantitative predictions in the domain of realistic field parameters, we employ the WKB approach. We propose to use an optical probe photon beam, whose intensity changes as it traverses a spatial region where a strong electric component of a background laser field is present. It is demonstrated that relative intensity changes on the level of $1 \%$ can be experimentally observed once the intensity of the strong background field exceeds $10^{27}~\text{W/cm}^2$ within a large laser wavelength interval. This finding is expected to significantly support possible experimental investigations of nonlinear QED phenomena in the nonperturbative regime., Comment: 11 pages, 6 figures

In nonlinear Thomson scattering, a relativistic electron reflects and re-radiates the photons of a laser pulse, converting optical light to x rays or beyond. While this extreme frequency conversion offers a promising source for probing high-energy-density materials and driving uncharted regimes of nonlinear quantum electrodynamics, conventional nonlinear Thomson scattering has inherent tradeoffs in its scaling with laser intensity. Here we discover that the ponderomotive control afforded by spatiotemporal pulse shaping enables novel regimes of nonlinear Thomson scattering that substantially enhance the scaling of the radiated power, emission angle, and frequency with laser intensity. By appropriately setting the velocity of the intensity peak, a spatiotemporally shaped pulse can increase the power radiated by orders of magnitude. The enhanced scaling with laser intensity allows for operation at significantly lower electron energies and can eliminate the need for a high-energy electron accelerator., Comment: 23 pages, 4 figures

Radiation reaction (RR) is the oldest still-unsolved problem in electrodynamics. In addition to conceptual difficulties in its theoretical formulation, the requirement of exceedingly large charge accelerations has thus far prevented its unambiguous experimental identification. Here, we show how measurable RR effects in a laser-electron interaction can be achieved through the use of flying focus pulses (FFPs). By allowing the focus to counterpropagate with respect to the pulse phase velocity, a FFP overcomes the intrinsic limitation of a conventional laser Gaussian pulse (GP) that limits its focus to a Rayleigh range. For an electron initially also counterpropagating with respect to the pulse phase velocity, an extended interaction length with the laser peak intensity is achieved in a FFP. As a result, the same RR deceleration factors are obtained, but at FFP laser powers orders of magnitude lower than for ultrashort GPs with the same energy. This renders the proposed setup much more stable than those using GPs and allows for more accurate \emph{in situ} diagnostics. Using the Landau-Lifshitz equation of motion, we show numerically and analytically that the capability of emerging laser systems to deliver focused FFPs will allow for a clear experimental identification of RR., 13 pages, 5 figures

The present thesis investigates the phenomenological implications of the quasiclassical representation of the Volkov states and radiative corrections for the nonlinear Compton scattering. Firstly, the quasiclassical states are extracted as a solution of the Dirac equation in the presence of a plane wave background. In contrast to the usual Volkov states, the new quasiclassical solutions have the advantage of having a spinorial structure identical to the WKB wave functions. In exchange, instead of using 4-by-4 matrices in order to perform computations, one can now manipulate 2-by-2 matrices which are more flexible. Hence, several computations in the literature are sure to be further simplified. In order to showcase this explicitly, upon extracting the quasiclassical solutions, the spin polarization vector is firstly computed and afterwards the propagator is evaluated where as showcased, due to the equivalence of the quasiclassical solutions with the Volkov states, the result is the same. In consequence, we investigate the renormalization of the tadpole in the presence of an external plane wave and showcase explicitly that after renormalization, it identically vanishes. As a final note, we compute the renormalized mass operator and its contribution to the probability amplitude of the nonlinear Compton scattering process at one-loop for an arbitrary plane wave background.

The intensity peak of a "flying focus" travels at a programmable velocityover many Rayleigh ranges while maintaining a near-constant profile. Assessingthe extent to which these features can enhance laser-based applicationsrequires an accurate description of the electromagnetic fields. Here we presentexact analytical solutions to Maxwell's equations for the electromagneticfields of a constant-velocity flying focus, generalized for arbitrarypolarization and orbital angular momentum. The approach combines the complexsource-point method, which transforms multipole solutions into beam-likesolutions, with the Lorentz invariance of Maxwell's equations. Propagating thefields backward in space reveals the space-time profile that an opticalassembly must produce to realize these fields in the laboratory. Comparisonswith simpler paraxial solutions provide conditions for their reliable use whenmodeling a flying focus.

When dense high-energy lepton bunches collide, the beam particles can experience rest-frame electromagnetic fields which greatly exceed the QED critical one. Here it is demonstrated that beamstrahlung efficiently converts lepton energy to high-energy photons in this so-called supercritical QED regime, as the single-photon emission spectrum exhibits a pronounced peak close to the initial lepton energy. It is also shown that the observation of this high-energy peak in the photon spectrum requires one to mitigate multiple photon emissions during the interaction. Otherwise, the photon recoil induces strong correlations between subsequent emissions which soften the photon spectrum and suppress the peak. The high-energy peak in the photon spectrum constitutes a unique observable of photon emission in the supercritical QED regime, and provides decisive advantages for the realization of an efficient multi-TeV laserless gamma-gamma collider based on electron-electron collisions., Comment: 11 pages, 4 figures. Published version is Open Access

Volkov states are exact solutions of the Dirac equation in the presence of an arbitrary plane wave. Volkov states, as well as free photon states, are not stable in the presence of the background plane-wave field but "decay" as electrons/positrons can emit photons and photons can transform into electron-positron pairs. By using the solutions of the corresponding Schwinger-Dyson equations within the locally-constant field approximation, we compute the probabilities of nonlinear single Compton scattering and nonlinear Breit-Wheeler pair production by including the effects of the decay of electron, positron, and photon states. As a result, we find that the probabilities of these processes can be expressed as the integral over the light-cone time of the known probabilities valid for stable states per unit of light-cone time times a light-cone time-dependent exponential damping function for each interacting particle. The exponential function for an incoming (outgoing) either electron/positron or photon at each light-cone time corresponds to the total probability that either the electron/positron emits a photon via nonlinear Compton scattering or the photon transforms into an electron-positron pair via nonlinear Breit-Wheeler pair production until that light-cone time (from that light-cone time on). It is interesting that the exponential damping terms depend not only on the particles momentum but also on their spin (for electrons/positrons) and polarization (for photons). This additional dependence on the discrete quantum numbers prevents the application of the electron/positron spin and photon polarization sum-rules, which significantly simplify the computations in the perturbative regime., Comment: 31 pages, 5 figures

New journal of physics 24(1), 015002 (2022). doi:10.1088/1367-2630/ac4283, Published by IOP, [London]

Accelerated charges emit electromagnetic radiation and the consequent energy-momentum loss alters their trajectory. This phenomenon is known as radiation reaction and the Landau-Lifshitz (LL) equation is the classical equation of motion of the electron, which takes into account radiation-reaction effects in the electron trajectory. By using the analytical solution of the LL equation in an arbitrary plane wave, we compute the analytical expression of the classical emission spectrum via nonlinear Thomson scattering including radiation-reaction effects. Both the angularly-resolved and the angularly-integrated spectra are reported, which are valid in an arbitrary plane wave. Also, we have obtained a phase-dependent expression of the electron dressed mass, which includes radiation-reaction effects. Finally, the corresponding spectra within the locally constant field approximation have been derived., 18 pages, no figures

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., Comment: 34 pages, 11 figures, submitted to New J. Phys

If a charge is hit by a superstrong laser pulse, such as those that can be created with state-of-the-art laser technology, it experiences an extreme acceleration causing the motion of the charge to be strongly affected by its own emission of radiation. In classical electrodynamics this effect can be taken into account by adding a new force term (also called radiation reaction) to the equation of motion of the charge in addition to the Lorentz force. Here we show how the radiation reaction force can be used to control the deflection of a relativistic beam of electrons colliding headon with a plane-wave laser pulse as well as in the head-on and oblique incidence collision with a tightly focused laser pulse. In addition, strong-field QED effects are also considered by correcting the classical radiation reaction force with a quantum factor, leading to a semiclassical treatment. All of this is done by performing analytic calculations and by numerical integration with a fourth order Runge-Kutta method, which is tested against the analytic result of the plane wave case.

Available laser technology is opening the possibility of testing QED experimentally in the so-called strong-field regime. This calls for developing theoretical tools to investigate strong-field QED processes in electromagnetic fields of complex spacetime structure. Here, we propose a scheme to compute electron wave functions in tightly focused laser beams by taking into account exactly the complex spacetime structure of the fields. The scheme is solely based on the validity of the Wentzel-Kramers-Brillouin (WKB) approximation and the resulting wave functions, unlike previously proposed ones [Phys. Rev. Lett. \textbf{113}, 040402 (2014)], do not rely on approximations on the classical electron trajectory. Moreover, a consistent procedure is indicated to take into account higher-order quantum effects within the WKB approach depending on higher-and-higher powers of the Planck constant. In the case of a plane-wave background field the found wave functions exactly reduce to the Volkov states, which are then written in a new and fully quasiclassical form. Finally, by using the leading-order WKB wave functions to compute the probabilities of nonlinear Compton scattering and nonlinear Breit-Wheeler pair production, it is explicitly shown that, if additionally the energies of the charges are sufficiently large that the latter are not significantly deflected by the field, the corresponding Baier's formulas are exactly reproduced for an otherwise arbitrary classical electron/positron trajectory., 49 pages, no figures. Misprints corrected in Eqs. (B2) and (B3)

The elastic scattering of two real photons in vacuum is one of the most elusive of the fundamentally new processes predicted by quantum electrodynamics. This explains why, although it was first predicted more than eighty years ago, it has so far remained undetected. Here we show that in present-day facilities, the elastic scattering of two real photons can become detectable far off axis in an asymmetric photon-photon collider setup. This may be obtained within one day of operation time by colliding 1 mJ extreme ultraviolet pulses with the broadband gamma-ray radiation generated in nonlinear Compton scattering of ultrarelativistic electron beams with terawatt-class optical laser pulses operating at a 10 Hz repetition rate. In addition to the investigation of elastic photon-photon scattering, this technique allows us to unveil or constrain new physics that could arise from the coupling of photons to yet undetected particles, therefore opening new avenues for searches of physics beyond the standard model., 8 pages, 5 figures. Published paper is Open Access

Upcoming experiments on the interaction of electrons with intense laser fields are envisaged to become more and more accurate, which calls for theoretical computations of rates and probabilities with correspondingly higher precision. In strong-field QED this requires the knowledge of radiative corrections to be added to leading-order results. Here, we first derive the mass operator in momentum space of an off-shell electron in the presence of an arbitrary plane wave. By taking the average of the mass operator in momentum space over an on-shell electron state, we obtain a new representation, equivalent to but more compact than the known one computed in [Sov. Phys. JETP \textbf{42}, 400 (1975)]. Moreover, we use the obtained mass operator to determine the electron mass shift in an arbitrary plane wave, which generalizes the already known expression in a constant crossed field. The spin-dependent part of the electron mass shift can be related to the anomalous magnetic moment of the electron in the plane wave. We show that within the locally constant field approximation it is possible to conveniently define a local expression of the electron anomalous magnetic moment, which reduces to the known expression in a constant crossed field. Beyond the locally constant field approximation, however, the interaction between the electron and the plane wave is non-local such that it is not possible to conveniently introduce an electron anomalous magnetic moment., Comment: 22 pages, 3 figures

The value of the anomalous magnetic moment of the electron is the most accurately verified prediction of Quantum Electrodynamics (QED). Upcoming QED experiments on the interaction of electrons with intense laser fields open up the way of checking whether this high degree of agreement for the value of the electron anomalous magnetic moment persists in intense background fields. The possibility of experimentally verifying the expression for the anomalous magnetic moment of the electron in intense laser fields calls for computing radiative corrections beyond the leading-order result, that already includes the background field exactly. While in vacuum QED the anomalous magnetic moment is extracted from the vertex diagram for which the external photon provides the magnetic field interacting with the electron, in the strong field case the mass operator is used, where the magnetic field of the plane wave is exploited instead. Hence, in the thesis, the renormalized momentum space mass operator for an off-shell electron in the presence of an arbitrary plane-wave background is computed in light-cone coordinates, which have the advantage of making transparent the conserved quantities. Sandwiching between on-shell electron states, a new representation, more compact than the one known from the literature [VS75], is obtained. Solving the Schwinger-Dyson equation for the electron, in which the determined mass operator is inserted, the electron mass shift in an arbitrary plane wave is obtained. The expression for the electron mass shift generalizes the already known expressions from the literature [VS71; Rit70] for the constant crossed field case. The spin-dependent part of the electron mass shift is related to the anomalous magnetic moment of the electron in the plane wave. In the locally constant field approximation, the anomalous magnetic moment of the electron is extracted and reduces to Schwinger’s famous result when the background is removed. However, due to the non-local dependence of the electron mass shift on the field, it is not generally possible to define a local expression of the electron anomalous magnetic moment in an arbitrary plane

Sources of high-energy photons have important applications in almost all areas of research. However, the photon flux and intensity of existing sources is strongly limited for photon energies above a few hundred keV. Here we show that a high-current ultrarelativistic electron beam interacting with multiple submicrometer-thick conducting foils can undergo strong self-focusing accompanied by efficient emission of gamma-ray synchrotron photons. Physically, self-focusing and high-energy photon emission originate from the beam interaction with the near-field transition radiation accompanying the beam-foil collision. This near field radiation is of amplitude comparable with the beam self-field, and can be strong enough that a single emitted photon can carry away a significant fraction of the emitting electron energy. After beam collision with multiple foils, femtosecond collimated electron and photon beams with number density exceeding that of a solid are obtained. The relative simplicity, unique properties, and high efficiency of this gamma-ray source open up new opportunities for both applied and fundamental research including laserless investigations of strong-field QED processes with a single electron beam., Comment: 17 pages, 11 figures, matches published article

The process of electron-positron annihilation into two photons in the presence of an intense classical plane wave of an arbitrary shape is investigated analytically by employing light-cone quantization and by taking into account the effects of the plane wave exactly. We introduce a general description of second-order 2-to-2 scattering processes in a plane-wave background field, indicating the necessity of considering the localization of the colliding particles and achieving that by means of wave packets. We define a local cross section in the background field, which generalizes the vacuum cross section and which, though not being directly an observable, allows for a comparison between the results in the plane wave and in vacuum without relying on the shape of the incoming wave packets. Two possible cascade or two-step channels have been identified in the annihilation process and an alternative way of representing the two-step and one-step contributions via a "virtuality" integral has been found. Finally, we compute the total local cross section to leading order in the coupling between the electron-positron field and the quantized photon field, excluding the interference between the two leading-order diagrams arising from the exchange of the two final photons, and express it in a relatively compact form. In contrast to processes in a background field initiated by a single particle, the pair annihilation into two photons, in fact, also occurs in vacuum. Our result naturally embeds the vacuum part and reduces to the vacuum expression, known in the literature, in the case of a vanishing laser field., 26 pages, 2 figures

The process of emission of electromagnetic radiation does not occur instantaneously but it is "formed" over a finite time known as radiation formation time. In the ultrarelativistic regime, the corresponding (longitudinal) formation length is given by the formation time times the speed of light and controls several features of radiation. Here, we elucidate the importance of the transverse formation length (TFL) by investigating nonlinear Compton scattering by an electron initially counterpropagating with respect to a \emph{flying focus} laser beam. The TFL is related to the transverse size of the radiation formation "volume" and, unlike the longitudinal formation length, has a quantum origin. Being the TFL typically of the order of the Compton wavelength, where any laser field can be assumed to be approximately uniform, related quantum interference effects have been ignored. However, we show analytically that if the focus in a flying focus beam with $n_L\gg 1$ cycles moves at the speed of light and backwards with respect to the beam propagation direction, the effects of the TFL undergo a large enhancement proportional to $n_L$ and may substantially alter the differential emission probability for feasible flying focus pulses., 23 pages

QED cascades are complex avalanche processes of hard photon emission and electron-positron pair creation driven by ultra-strong electromagnetic fields. They play a fundamental role in astrophysical environments such as a pulsars' magnetosphere, rendering an earth-based implementation with intense lasers attractive. In the literature, QED cascades were also predicted to limit the attainable intensity in a set-up of colliding laser beams in a tenuous gas such as the residual gas of a vacuum chamber, therefore severely hindering experiments at extreme field intensities. Here, we demonstrate that the onset of QED cascades may be either prevented even at intensities around $10^{26}\text{ W/cm$^{2}$}$ with tightly focused laser pulses and low-$Z$ gases, or facilitated at intensities below $10^{24}\text{ W/cm$^{2}$}$ with enlarged laser focal areas or high-$Z$ gases. These findings pave the way for the control of novel experiments such as the generation of pure electron-positron-photon plasmas from laser energy, and for probing QED in the extreme-intensity regime where the quantum vacuum becomes unstable., 11 pages, 3 figures, 1 table

In this paper we show how to recast the results of the semiclassical method of Baier, Katkov and Strakhovenko for pair production, including the possibility of specifying all the spin states and photon polarization, in a form that is suitable for numerical implementation. In this case, a new type of integral appears in addition to the ones required for the radiation emission process. We compare the resulting formulas with those obtained for a short pulse plane wave external field by using the Volkov state. We investigate the applicability of the local constant field approximation for the proposed upcoming experiments at FACET II at SLAC and LUXE at DESY. Finally, we provide results on the dependence of the pair production rate on the relative polarization between a linearly polarized laser pulse and a linearly polarized incoming high energy photon. We observe that even in the somewhat intermediate multiphoton regime of these experiments, there is roughly a factor of 2 difference between the pair production rates corresponding to the two relative photon polarizations, as predicted by Ritus in the monochromatic highly multiphoton weak field limit. This finding is of interest in light of the vacuum birefringence of QED.

We compute the general expression of the one-loop vertex correction in an arbitrary plane-wave background field for the case of two on-shell external electrons and an off-shell external photon. The properties of the vertex corrections under gauge transformations of the plane-wave background field and of the radiation field are studied. Concerning the divergences of the vertex correction, the infrared one is cured by assigning a finite mass to the photon, whereas the ultraviolet one is shown to be renormalized exactly as in vacuum. Finally, the corresponding expression of the vertex correction within the locally-constant crossed field is also derived and the high-field asymptotic is shown to scale according to the Ritus-Narozhny conjecture., Comment: 42 pages, 5 figures

This work consists of two fields of study involving the interaction of light with matter and light with light. The first part explores the interaction of a superintense laser pulse with an ultrathin solid density foil. The radiation pressure exerted by the laser pulse can be so strong that, in principle, the whole foil is accelerated. This results in the generation of dense, high-flux and collimated and quasimonoenergetic ion beams. However, the onset of transverse instabilities damages the foil, thus resulting in ion spectral broadening. Simple analytical modeling is supported by particle-in-cell (PIC) simulations to strategize methods for instability suppression and ion-beam quality improvement. The second part puts forward a method for detecting the purely quantum electrodynamic process of elastic scattering of real photons in vacuum. Monte-Carlo simulations are used to study the feasibility of detection of this yet undetected process. An experimental setup comprising of a high energy gamma-ray beam colliding with an extreme ultraviolet (XUV) pulse or a free-electron laser (FEL) is utilized. This clean and controllable setup exploits the high gamma photon energies and large laser photon flux for enhancing the probability of scattering events.

We show how the semiclassical formulas for radiation emission of Baier, Katkov and Strakhovenko for arbitrary initial and final spins of the electron and arbitrary polarization of the emitted photon can be rewritten in a form which numerically converges quickly. We directly compare the method in the case of a background plane wave with the result obtained by using the Volkov state solution of the Dirac equation, and confirm that we obtain the same result. We then investigate the interaction of a circularly polarized short laser pulse scattering with GeV electrons and see that the finite duration of the pulse leads to a lower transfer of circular polarization than that predicted by the known formulas in the monochromatic case. We also see how the transfer of circular polarization from the laser beam to the gamma ray beam is gradually deteriorated as the laser intensity increases, entering the nonlinear regime. However, this is shown to be recovered if the scattered photon beam is collimated to only allow for passage of photons emitted with angles smaller than 1/γ with respect to the initial electron direction, where γ is the approximately constant Lorentz factor of the electron. The obtained formulas also allow us to answer questions regarding radiative polarization of the emitting particles. In this respect we briefly discuss an application of the present approach to the case of a bent crystal and high-energy positrons.

We report on experimental spectra of photons radiated by 50 GeV positrons crossing silicon single crystals of thicknesses 1.1 mm, 2.0 mm, 4.2 mm, and 6.2 mm at sufficiently small angles to the (110) planes that their motion effectively is governed by the continuum crystal potential. The experiment covers a new regime of interaction where each positron emits several hard photons, whose recoil are not negligible and which are formed on lengths where the variation of the crystal field cannot be ignored. As a result neither the single-photon semiclassical theory of Baier et al. nor the conventional cascade approach to multiple hard photon emissions (quantum radiation reaction) based on the local constant field approximation are able to reproduce the experimental results. After developing a theoretical scheme which incorporates the essential physical features of the experiments, i.e., multiple emissions, photon recoil and background field variation within the radiation formation length, we show that it provides results in convincing agreement with the data.

The impact of a laser field on the process of photon radiation by an ultra-relativistic electron in an atomic field is investigated. The angular distribution and the spectrum of the radiated photon are derived. By means of the quasiclassical approximation, the obtained results are exact in the parameters of the laser field and the atomic field. It is shown that the impact of the laser field is significant even for fairly average values of the laser field parameters routinely achievable nowadays. Therefore, an experimental observation of the influence of the laser field on bremsstrahlung in the atomic field is a very feasible task., 15 pages, 1 figure

Approximate solutions of the Dirac equation are found for ultrarelativistic particles moving in a periodic potential, which depends only on one coordinate, transverse to the largest component of the momentum of the incoming particle. As an example we employ these solutions to calculate the radiation emission of positrons and electrons trapped in the planar potential found between the (110) planes in Silicon. This allows us to compare with the semi-classical method of Baier, Katkov and Strakhovenko, which includes the effect of spin and photon recoil, but neglects the quantization of the transverse motion. For high-energy electrons, the high-energy part of the angularly integrated photon energy spectrum calculated with the found wave functions differs from the corresponding one calculated with the semi-classical method. However, for lower particle energies it is found that the angularly integrated emission energy spectra obtained via the semi-classical method is in fairly good agreement with the full quantum calculation except that the positions of the harmonic peaks in photon energy and the photon emission angles are shifted.

High-flux polarized particle beams are of critical importance for the investigation of spin-dependent processes, such as in searches of physics beyond the Standard Model, as well as for scrutinizing the structure of solids and surfaces in material science. Here we demonstrate that kiloampere polarized electron beams can be produced via laser-wakefield acceleration from a gas target. A simple theoretical model for determining the electron beam polarization is presented and supported with self-consistent three-dimensional particle-in-cell simulations that incorporate the spin dynamics. By appropriately choosing the laser and gas parameters, we show that the depolarization of electrons induced by the laser-wakefield-acceleration process can be as low as 10%. Compared to currently available sources of polarized electron beams, the flux is increased by four orders of magnitude., 6 pages, 3 figures

The local-constant-field approximation (LCFA) is an essential theoretical tool for investigating strong-field QED phenomena in background electromagnetic fields with complex spacetime structure. In our previous work [Phys.~Rev.~A~\textbf{98}, 012134 (2018)] we have analyzed the shortcomings of the LCFA in nonlinear Compton scattering at low emitted photon energies for the case of a background plane-wave field. Here, we generalize that analysis to background fields, which can feature a virtually arbitrary spacetime structure. In addition, we provide an explicit and simple implementation of an improved expression of the nonlinear Compton scattering differential probability that solves the main shortcomings of the standard LCFA in the infrared region, and is suitable for background electromagnetic fields with arbitrary spacetime structure such as those occurring in particle-in-cell simulations. Finally, we carry out a systematic procedure to calculate the probability of nonlinear Compton scattering per unit of emitted photon light-cone energy and of nonlinear Breit-Wheeler pair production per unit of produced positron light-cone energy beyond the LCFA in a plane-wave background field, which allows us to identify the limits of validity of this approximation quantitatively., Comment: 15 pages, 3 figures

In the realm of laser-plasma interactions, if the laser intensity is strong enough, quantum effects play a significant role. Due to the large separation between the length scale at which quantum electrodynamic processes form and both the typical separation between particles in a plasma and the wavelength of optical lasers, it is possible in many situations of interest to take into account quantum electrodynamic processes in a fairly straightforward way. If one considers plasmas of increasingly large densities, the presence of many particles can render potentially unavoidable a full quantum treatment of the dynamics. Here, two kinds of multi-particle effects are discussed within strong-field Quantum Electrodynamics. First, we show how a correct description of coherence effects in the radiation emitted by a two-electron wave packet in a strong laser field requires a quantum treatment also if the quantum nonlinearity parameter of the system is much smaller than unity. Secondly, we indicate that at solid-state densities the presence of several particles within the formation region of radiation by an electron in a strong electromagnetic field may alter the emission probability itself, such that in general it is not possible to disentangle collective effects from quantum effects.

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., 22 pages, 2 figures. To appear in the Focus issue "Strong Field Quantum Electrodynamics with high power lasers and particle beams" of New Journal of Physics

Quantum electrodynamics in an intense plane-wave field is considered within the framework of light-cone quantization. In this context, high-energy vacuum birefringence and dichroism in an intense laser field are investigated. In particular, a setup is analyzed, in which probe gamma photons are generated via Compton backscattering, propagate through an intense laser pulse, and are subsequently detected via pair production in matter. The polarization of the photon beam is characterized by the Stokes parameters, and their change due to vacuum birefringence and dichroism is determined. The magnitude of the polarization effects is assessed for upcoming high-power laser facilities. Optimal parameters and regimes are identified, and the required statistics and the duration of the experiment in order to confirm the prediction of quantum electrodynamics are estimated. Furthermore, an approach for the treatment of the bispinor part of scattering amplitudes in a plane-wave field is introduced. Simplified expressions for the vertex functions, arising from the interaction terms of the lightfront Hamiltonian, are obtained. It is demonstrated that with the developed technique the evaluation of the gamma-matrix traces for scattering in an external plane-wave field can be performed in a relatively straightforward way and the final results can be written in a compact form.

We study the high-energy behaviour of QED in a strong plane wave electromagnetic background field generated by a laser pulse. Earlier calculations in this field hinted that under this circumstances the coupling constant of QED may increase with the 2/3-power of the energy scale for high energies and not logarithmic like in normal vacuum QED. Nevertheless, this calculations were performed in the limit of low laser frequencies or constant-crossed-fields. We show in this work that this limit does not commute with the high-energy limit and thus the power-law scaling just pertains to the constant-crossed field limit. Further we calculate the asymptotic expression of the polarization and mass operator in a strong laser pulse in the limit of high energetic photons and electrons, respectively, and obtain that they scale double logarithmic with the energy scale. Using this we show that also the probability for non-linear Breit-Wheeler pair production and for non-linear Compton scattering scales logarithmic with the energy like in vacuum QED.

We investigate the second order process of two photons being emitted by a high-energy electron dressed in the strong background electric field found between the planes in a crystal. The strong crystalline field combined with ultrarelativistic electrons is one of very few cases where the Schwinger field can be experimentally achieved in the electron's rest frame. The radiation being emitted, the so-called channeling radiation, is a well studied phenomenon. However, only the first order diagram corresponding to emission of a single photon has been studied so far. We elaborate on how the two-photon emission process should be understood in terms of a two-step versus a one-step process, i.e., if one can consider one photon being emitted after the other, or if there is also a contribution where the two photons are emitted ``simultaneously.'' From the calculated full probability we see that the two-step contribution is simply the product of probabilities for single photon emission while the additional one-step terms are, mainly, interferences due to several possible intermediate virtual states. These terms can contribute significantly when the crystal is thin. Therefore, in addition, we see how one can, for a thick crystal, calculate multiple photon emissions quickly by neglecting the one-step terms, which represents a solution of the problem of quantum radiation reaction in a crystal beyond the usually applied constant field approximation. We explicitly calculate an example of 180 GeV electrons in a thin silicon crystal and argue why it is, for experimental reasons, more feasible to see the one-step contribution in a crystal experiment than in a laser experiment.

Analytical calculations of radiative corrections in strong-field QED have hinted that in the presence of an intense plane wave the effective coupling of the theory in the high-energy sector may increase as the $(2/3)$-power of the energy scale. These findings have raised the question of their compatibility with the corresponding logarithmic increase of radiative corrections in QED in vacuum. However, all these analytical results in strong-field QED have been obtained within the limiting case of a background constant crossed field. Starting from the polarization operator and the mass operator in a general plane wave, we show that the constant-crossed-field limit and the high-energy limit do not commute with each other and identify the physical parameter discriminating between the two alternative limits orders. As a result, we find that the power-law scaling at asymptotically large energy scales pertains strictly speaking only to the case of a constant crossed background field, whereas high-energy radiative corrections in a general plane wave depend logarithmically on the energy scale as in vacuum. However, we also confirm the possibility of testing the ``power-law'' regime experimentally by means of realistic setups involving, e.g., high-power lasers or high-density electron-positron bunches., 29 pages, 4 figures

We investigate the radiation emitted by an ultrarelativistic electron traveling in a 1-dimensional parabolic potential. Having in mind a simplified model for beamstrahlung, we consider the realistic case of the electron motion being highly directional, with the transverse momentum being much smaller than the longitudinal one. In this case we can find solutions of the Dirac equation and we calculate exactly the radiation emission using first-order perturbation theory. We compare the results obtained to that obtained via the semi-classical method of Baier and Katkov which includes quantum effects due to photon recoil in the radiation emission but ignores the quantum nature of the electron motion. On the one hand, we confirm a prediction of the semi-classical method that the emission spectrum should coincide with that in the case of a linearly polarized monochromatic wave. On the other hand, however, we find that the semi-classical method does not yield the exact result when the quantum number describing the transverse motion becomes small. In this way, we address quantitatively the problem of the limits of validity of the semi-classical method, which is known, generally speaking, to be applicable for large quantum numbers. Finally, we also discuss which beam conditions would be necessary to enter the studied regime where also the motion of the particles must be considered quantum mechanically to yield the correct spectrum.

The description of the dynamics of an electron in an external electromagnetic field of arbitrary intensity is one of the most fundamental outstanding problems in electrodynamics. Remarkably, to date there is no unanimously accepted theoretical solution for ultra-high intensities and little or no experimental data. The basic challenge is the inclusion of the self-interaction of the electron with the field emitted by the electron itself - the so-called radiation reaction force. We report here on the experimental evidence of strong radiation reaction, in an all-optical experiment, during the propagation of highly relativistic electrons (maximum energy exceeding 2 GeV) through the field of an ultra-intense laser (peak intensity of $4\times10^{20}$ W/cm$^2$). In their own rest frame, the highest energy electrons experience an electric field as high as one quarter of the critical field of quantum electrodynamics and are seen to lose up to 30% of their kinetic energy during the propagation through the laser field. The experimental data show signatures of quantum effects in the electron dynamics in the external laser field, potentially showing departures from the constant cross field approximation.

Laser pulses traveling through a plasma can feature group velocities significantly differing from the speed of light in vacuum. This modifies the well-known Volkov states of an electron inside a strong laser-field from the vacuum case and consequently all quantum electrodynamical effects triggered by the electron. Here we present an in-depth study of the basic process of photon emission by an electron scattered from an intense short laser pulse inside a plasma, labeled nonlinear Compton scattering, based on modified Volkov solutions derived from first principles. Consequences of the nonlinear, plasma-dressed laser dispersion on the Compton spectra of emitted photons and implications for high-intensity laser-plasma experiments are pointed out., 6 pages, 4 figures

Bright sources of high energy electromagnetic radiation are widely employed in fundamental research as well as in industry and medicine. This steadily growing interest motivated the construction of several facilities aiming at the realisation of sources of intense X- and gamma-ray pulses. To date, free electron lasers and synchrotrons provide intense sources of photons with energies up to 10-100 keV. Facilities under construction based on incoherent Compton back scattering of an optical laser pulse off an electron beam are expected to yield photon beams with energy up to 19.5 MeV and peak brilliance in the range 10$^{20}$-10$^{23}$ photons s$^{-1}$ mrad$^{-2}$ mm$^{-2}$ per 0.1% bandwidth. Here, we demonstrate a novel mechanism based on the strongly amplified synchrotron emission which occurs when a sufficiently dense electron beam interacts with a millimetre thickness solid target. For electron beam densities exceeding approximately $3\times10^{19}\text{ cm$^{-3}$}$ filamentation instability occurs with the self-generation of 10$^{7}$-10$^{8}$ gauss magnetic fields where the electrons of the beam are trapped. This results into a giant amplification of synchrotron emission with the production of collimated gamma-ray pulses with peak brilliance above $10^{25}$ photons s$^{-1}$ mrad$^{-2}$ mm$^{-2}$ per 0.1% bandwidth and photon energies ranging from 200 keV up to several hundreds MeV. These findings pave the way to compact, high-repetition-rate (kHz) sources of short (30 fs), collimated (mrad) and high flux ($>10^{12}$ photons/s) gamma-ray pulses., Full-text access to a view-only version of the published paper by the following SharedIt link: https://rdcu.be/LGtC This is part of the Springer Nature Content Sharing Initiative (https://www.springernature.com/gp/researchers/sharedit). Enhanced PDF features such as annotation tools, one-click supplements, citation file exports and article metrics are freely available

If an electric charge is accelerated by a sufficiently intense electromagnetic field, the effects of the radiation emitted by the charge on the charge dynamics (radiation reaction) cannot be ignored. Here we show that classical radiation-reaction effects alter qualitatively and quantitatively the infrared behavior of the spectrum of the radiation emitted by an electron in the presence of an intense electromagnetic plane wave (nonlinear Thomson scattering). An analytical expression of the infrared limit of nonlinear Thomson scattering is provided, which includes radiation-reaction effects and is valid for an arbitrary plane wave. Apart from their own conceptual importance and as a signature of classical radiation reaction, these results provide the limiting expression of the corresponding and yet unknown exact infrared behavior of strong-field QED in an intense plane wave., 27 pages, 1 figure

Quantum radiation reaction is the influence of multiple photon emissions from a charged particle on the particle's dynamics, characterized by a significant energy-momentum loss per emission. Here we report experimental radiation emission spectra from ultrarelativistic positrons in silicon in a regime where quantum radiation reaction effects dominate the positron's dynamics. Our analysis shows that while the widely used quantum approach is overall the best model, it does not completely describe all the data in this regime. Thus, these experimental findings may prompt seeking more generally valid methods to describe quantum radiation reaction. This experiment is a fundamental test of quantum electrodynamics in a regime where the dynamics of charged particles is strongly influenced not only by the external electromagnetic fields but also by the radiation field generated by the charges themselves and where each photon emission may significantly reduce the energy of the charge., The experimental evidence of radiation reaction has so far been elusive. Here the authors provide the signature of radiation reaction in quantum electrodynamics by observing the radiation reaction effects when high-energy positrons emit radiation while propagating through a silicon crystal.

Volkov states and Volkov propagator are the basic analytical tools to investigate QED processes occurring in the presence of an intense plane-wave electromagnetic field. In the present paper we provide alternative and relatively simple proofs of the completeness and of the orthonormality at a fixed time of the Volkov states. Concerning the completeness, we exploit some known properties of the Green's function of the Dirac operator in a plane wave, whereas the orthonormality of the Volkov states is proved, relying only on a geometric argument based on the Gauss theorem in four dimensions. In relation with the completeness of the Volkov states, we also study some analytical properties of the Green's function of the Dirac operator in a plane wave, which we explicitly prove to coincide with the Volkov propagator in configuration space. In particular, a closed-form expression in terms of modified Bessel functions and Hankel functions is derived by means of the operator technique in a plane wave and different asymptotic forms are determined. Finally, the transformation properties of the Volkov propagator under general gauge transformations and a general gauge-invariant expression of the so-called dressed mass in configuration space are presented., 25 pages, no figures

A number of analytical and numerical studies has been performed to investigate the onset and the development of QED cascades in the collision of two counterpropagating laser pulses as a function of the laser intensity. However, it has been recently demonstrated [M. Tamburini et al., Sci. Rep. 7, 5694 (2017)] that the onset of QED cascades is also strongly influenced by the structure of the laser pulses, such as the laser pulse waist radius. Here we investigate how QED cascades are affected by: (a) the laser pulse duration, (b) the presence of a relative delay for the peak of the laser pulses to reach the focus, (c) the existence of a mismatch between the laser focal axis of the two laser pulses. This is especially important as, in realistic laboratory conditions, fluctuations may arise in the temporal and point stability of the lasers., Comment: 10 pages, 5 figures, 2 tables. Accepted for publication in Physics of Plasmas

The process of nonlinear electron-positron pair production by an electron colliding with an arbitrary plane wave electromagnetic field (nonlinear trident pair production) is studied analytically and numerically. Special emphasis is put on the properties of the transition amplitude. In fact, its original expression as resulting from applying the Wick's theorem turns out to be divergent and not to manifestly fulfill gauge invariance. By restoring the latter, the amplitude is regularized and investigated in different regimes. In particular, the amplitude is divided into a two-step and a one-step contributions, depending on the scaling dependence on the laser pulse duration. The corresponding contributions to the positron angular distribution spectra and the resulting interference terms are studied numerically emphasizing the possibility of measuring experimentally the contribution of the one-step contribution., Comment: 21 pages, 6 figures

In this work we study Nonlinear Compton Scattering, one of the most fundamental processes of Quantum Electrodynamics in a strong electromagnetic field background. One can imagine Nonlinear Compton Scattering as a process where a free electron scatters with a laser field, and while doing so it generates radiation. With the imminent inauguration of some Petawatt laser facilities, Nonlinear Compton Scattering will be routinely tested, especially in order to understand the dynamics of plasmas interacting with strong fields. Despite its promising applications, this process has always been studied for single particles with a well-defined initial momentum. We will show which effects arise when initially one or multiple electrons are in a wave packet state; in particular, we will be interested in which modifications are brought about by quantum effects, and which instead have a classical explanation. Moreover, in the multi-particle case, we will focus on the coherence of the emitted radiation, and calculate how quantum effects limit the frequencies at which the radiation can be coherent even at a regime typically associated with Classical Electrodynamics.