Local Constant Field Approximation Research Articles

Kinetic theory for spin-polarized relativistic plasmas

The investigation of spin and polarization effects in ultra-high intensity laser–plasma and laser–beam interactions has become an emergent topic in high-field science recently. In this paper, we derive a relativistic kinetic description of spin-polarized plasmas, where quantum-electrodynamics effects are taken into account via Boltzmann-type collision operators under the local constant field approximation. The emergence of anomalous precession is derived from one-loop self-energy contributions in a strong background field. We are interested, in particular, in the interplay between radiation reaction effects and the spin polarization of the radiating particles. For this, we derive equations for spin-polarized quantum radiation reaction from moments of the spin-polarized kinetic equations. By comparing with the classical theory, we identify and discuss the spin-dependent radiation reaction terms and radiative contributions to spin dynamics.

SFQEDtoolkit: A high-performance library for the accurate modeling of strong-field QED processes in PIC and Monte Carlo codes

Strong-field quantum electrodynamics (SFQED) processes are central in determining the dynamics of particles and plasmas in extreme electromagnetic fields such as those present in the vicinity of compact astrophysical objects or generated with ultraintense lasers. SFQEDtoolkit is an open source library designed to allow users for a straightforward implementation of SFQED processes in existing particle-in-cell (PIC) and Monte Carlo codes. Through advanced function approximation techniques, high-energy photon emission and electron-positron pair creation probability rates and energy distributions are calculated within the locally-constant-field approximation (LCFA) as well as with more advanced models [Phys. Rev. A 99, 022125 (2019)]. SFQEDtoolkit is designed to provide users with high-performance and high-accuracy, and neat examples showing its usage are provided. In the near future, SFQEDtoolkit will be enriched to model the angular distribution of the generated particles, i.e., beyond the commonly employed collinear emission approximation, as well as to model spin and polarization dependent SFQED processes. Notably, the generality and flexibility of the presented function approximation approach makes it suitable to be employed in other areas of physics, chemistry and computer science. Program summaryProgram Title: SFQEDtoolkit (version 1.0)CPC Library link to program files:https://doi.org/10.17632/j7mhj3cg3m.1Developer's repository link:https://github.com/QuantumPlasma/SFQEDtoolkitLicensing provisions: GPLv3Programming language: C++, FortranNature of problem: The accurate simulation of strong-field QED processes in the interaction of particles or plasmas with strong electromagnetic fields is critical for present and future experiments with ultraintense lasers as well as to unveil the dynamics around compact astrophysical objects. State-of-the-art PIC and Monte Carlo codes implement strong-field QED processes by means of lookup tables, where the approximated function is evaluated on a fixed set of points. This typically results in numerical artifacts such as stairlike structures in the approximated function, and in a reduced efficiency when large size lookup tables are necessary. An easily implementable open-source accurate and efficient simulation tool is required to address problems at the high-intensity frontier of plasma physics and astrophysics.Solution method: Strong-field QED process rates and particle distributions are calculated by leveraging advanced approximation methods based on variable and function transformation, asymptotic expansions as well as Chebyshev polynomial expansions. This provides a numerically-stable and efficient approach that allows us to overcome all limitations of existing methods based on standard lookup tables.

Precision Measurement of Trident Production in Strong Electromagnetic Fields.

We demonstrate experimentally that the trident process e^{-}→e^{-}e^{+}e^{-} in a strong external field, with a spatial extension comparable to the effective radiation length, is well understood theoretically. The experiment, conducted at CERN, probes values for the strong field parameter χ up to 2.4. Experimental data and theoretical expectations using the local constant field approximation show remarkable agreement over almost 3 orders of magnitude in yield.

Particle Production in Strong Electromagnetic Fields and Local Approximations

We investigate the phenomenon of electron–positron pair production in intense external backgrounds within the strong-field regime. We perform nonperturbative calculations by solving the quantum kinetic equations, and obtain the momentum distributions of particles created and the total number of pairs. In particular, we analyze the validity of the locally constant field approximation (LCFA), which represents a powerful method for treating inhomogeneous external backgrounds. We consider a combination of two consecutive time-dependent Sauter pulses and thoroughly examine the effects of quantum interference and the role of the Pauli exclusion principle. It is shown that the latter can be approximately incorporated within the LCFA when computing the momentum distributions, while the closed-form LCFA expression for the total particle yield completely disregards Pauli blocking. It is demonstrated that in the presence of multiple turning points of classical electron trajectories, one observes interference patterns in the particle spectra, and the LCFA may significantly overestimate the number of pairs. To further elaborate this issue, we perform the analogous calculations in the case of scalar QED. It is shown that the quantum statistics effects enhance the number of bosons produced.

Electron spin- and photon polarization-resolved probabilities of strong-field QED processes

A derivation of fully polarization-resolved probabilities is provided for high-energy photon emission and electron-positron pair production in ultrastrong laser fields. The probabilities resolved in both electron spin and photon polarization of incoming and outgoing particles are indispensable for developing QED Monte Carlo and QED-particle-in-cell codes, aimed at the investigation of polarization effects in nonlinear QED processes in ultraintense laser-plasma and laser-electron beam interactions, and other nonlinear QED processes in external ultrastrong fields, which involve multiple elementary processes of a photon emission and pair production. The quantum operator method introduced by Baier and Katkov is employed for the calculation of probabilities within the quasiclassical approach and the local constant field approximation. The probabilities for the ultrarelativistic regime are given in a compact form and are suitable to describe polarization effects in strong laser fields of arbitrary configuration, rendering them very well suited for applications.

Higher fidelity simulations of nonlinear Breit\u2013Wheeler pair creation in intense laser pulses

When a photon collides with a laser pulse, an electron-positron pair can be produced via the nonlinear Breit–Wheeler process. A simulation framework has been developed to calculate this process, which is based on a ponderomotive approach that includes strong-field quantum electrodynamical effects via the locally monochromatic approximation (LMA). Here we compare simulation predictions for a variety of observables, in different physical regimes, with numerical evaluation of exact analytical results from theory. For the case of a focussed laser background, we also compare simulation with a high-energy theory approximation. These comparisons are used to quantify the accuracy of the simulation approach in calculating harmonic structure, which appears in the lightfront momentum and angular spectra of outgoing particles, and the transition from multi-photon to all-order pair creation. Calculation of the total yield of pairs over a range of intensity parameters is also used to assess the accuracy of the locally constant field approximation (LCFA).

Total yield of electron-positron pairs produced from vacuum in strong electromagnetic fields: Validity of the locally constant field approximation

The widely used locally constant field approximation (LCFA) can be utilized in order to derive a simple closed-form expression for the total number of particles produced in the presence of a strong electromagnetic field of a general spatiotemporal configuration. A usual justification for this approximate approach is the requirement that the external field vary slowly in space and time. In this investigation, we examine the validity of the LCFA by comparing its predictions to the results obtained by means of exact nonperturbative numerical techniques. To benchmark the LCFA in the regime of small field amplitudes and low frequencies, we employ a semiclassical approach. As a reference, we consider a standing electromagnetic wave oscillating both in time and space as well as two spatially uniform field configurations: Sauter pulse and oscillating electric field. Performing a thorough numerical analysis, we identify the domain of the field parameters where the approximation is well justified. In particular, it is demonstrated that the Keldysh parameter itself is not a relevant quantity governing the accuracy of the LCFA. It is also found that for field amplitudes close to the Schwinger critical value, the LCFA may overestimate the particle yield. We discuss how this effect is related to the Pauli exclusion principle and quantum interference.

Generation of polarized positron beams via collisions of ultrarelativistic electron beams

A novel scheme is proposed for generating a polarized positron beam via multiphoton Breit-Wheeler process during the collision of a 10 GeV, pC seeding electron beam with the other 1 GeV, nC driving electron beam. The driving beam provides the strong self-generated field, and a suitable transverse deviation distance between two beams enables the field experienced by the seeding beam to be unipolar, which is crucial for realizing the positron polarization. We employ the particle simulation with a Monte-Carlo method to calculate the spin- and polarization-resolved photon emission and electron-positron pair production in the local constant field approximation. Our simulation results show that a highly polarized positron beam with polarization above $40\%$ can be generated in several femtoseconds, which is robust with respect to parameters of two electron beams. Based on an analysis of the influence of $\gamma$-photon polarization on the polarized pair production, we find that a polarized seeding beam of the proper initial polarization can further improve the positron polarization to $60\%$.

First-order strong-field QED processes including the damping of particle states

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.

Ultrarelativistic electrons in counterpropagating laser beams

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.

Anomalous violation of the local constant field approximation in colliding laser beams

The local constant field approximation (LCFA) is widely used in the study of QED effects in laser-matter interactions, with the justification that the classical strong-field parameter of the impinging laser beam is large. Here, the failure of this conjecture is demonstrated for an electron interacting with strong counterpropagating laser waves due to the emergence of an additional small time scale in the electron dynamics. Moreover, we identify a class of anomalous LCFA violation in which electrons turn sharply and leave the radiation formation zone much earlier than in the LCFA estimation. In contrast to previous observations of LCFA violation in a single laser beam, resulting in new low-harmonic peaks in the spectrum, here deviations from LCFA results are seen across the whole spectrum. A similar phenomenon is also demonstrated for an electron colliding with an ultrashort laser pulse. These results indicate the necessity of amending laser-plasma kinetic simulations in multiple beam laser configurations.Received 13 March 2020Revised 8 June 2020Accepted 9 February 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.013214Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasHigh intensity laser-plasma interactionsQuantum electrodynamicsStrong electromagnetic field effectsAccelerators & BeamsPlasma PhysicsGeneral Physics

Вакуумное двулучепреломление в поле плоской электромагнитной волны

We study the process of vacuum birefringence in a strong electromagnetic field: a probe photon changes its polarization while traversing a counterpropagating laser beam. To describe this phenomenon, we calculate the polarization tensor in the field of a plane monochromatic wave to leading order with respect to its amplitude. The main goal of the study is to compare the results with the data obtained within the locally constant field approximation (LCFA). Here we identify the domain of the LCFA applicability in the case of a plane-wave external background. It is shown that the frequency of the probe photon and that of the external field are symmetrically involved in the relative uncertainty. The exact treatment of the spatiotemporal dependence beyond the LCFA becomes necessary at the energy scale 0.1-1 MeV.

Generation of highly-polarized high-energy brilliant γ-rays via laser-plasma interaction

The generation of highly polarized high-energy brilliant γ-rays via laser–plasma interaction is investigated in the quantum radiation-reaction regime. We employ a quantum electrodynamics particle-in-cell code to describe spin-resolved electron dynamics semiclassically and photon emission and polarization quantum mechanically in the local constant field approximation. As an ultrastrong linearly polarized (LP) laser pulse irradiates a near-critical-density (NCD) plasma followed by an ultrathin planar aluminum target, the electrons in the NCD plasma are first accelerated by the driving laser to ultrarelativistic energies and then collide head-on with the laser pulse reflected by the aluminum target, emitting brilliant LP γ-rays via nonlinear Compton scattering with an average polarization of about 70% and energy up to hundreds of MeV. Such γ-rays can be produced with currently achievable laser facilities and will find various applications in high-energy physics and laboratory astrophysics.

Production of Highly Polarized Positron Beams via Helicity Transfer from Polarized Electrons in a Strong Laser Field.

The production of a highly polarized positron beam via nonlinear Breit-Wheeler processes during the interaction of an ultraintense circularly polarized laser pulse with a longitudinally spin-polarized ultrarelativistic electron beam is investigated theoretically. A new MonteCarlo method employing fully spin-resolved quantum probabilities is developed under the local constant field approximation to include three-dimensional polarization effects in strong laser fields. The produced positrons are longitudinally polarized through polarization transferred from the polarized electrons by the medium of high-energy photons. The polarization transfer efficiency can approach 100% for the energetic positrons moving at smaller deflection angles. This method simplifies the postselection procedure to generate high-quality positron beams in further applications. In a feasible scenario, a highly polarized (40%-65%), intense (10^{5}-10^{6}/bunch), collimated (5-70mrad) positron beam can be obtained in a femtosecond timescale. The longitudinally polarized positron sources are desirable for applications in high-energy physics and material science.

Uniform locally constant field approximation for photon-seeded pair production

A challenge to upcoming experiments that plan to collide a particle beam with laser pulses of moderate intensity is how to correctly incorporate quantum effects into simulation frameworks. Using a uniform approach, we extend the widely-used locally constant field approximation (LCFA) to derive an improved rate of photon-seeded pair creation (the nonlinear Breit-Wheeler process). By benchmarking our "ULCFA" expressions with the lightfront spectrum of: i) exact analytical results and ii) numerical integration of the QED probability for short pulses, we show that our extended approach remains accurate at smaller values of the intensity parameter than the standard LCFA.

Numerical approach to the semiclassical method of pair production for arbitrary spins and photon polarization

In this paper we show how to recast the results of the semiclassical method of Baier, Katkov & 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 intensity regime of these experiments, there is roughly a factor of $2$ difference between the pair production rates corresponding to the two relative photon polarizations, which is of interest in light of the vacuum birefringence of QED.

Vortex γ rays from scattering laser bullets off ultrarelativistic electrons

Generation of high-flux vortex γ -ray pulses is investigated in the interaction of ultraintense Bessel–Bessel laser bullets colliding head-on with ultrarelativistic electron bunches in the quantum radiation-dominated regime. In the simulations, a semiclassical Monte–Carlo method is used, based on the radiation probabilities in the local constant field approximation, to describe the electron motion and emission of radiation. Characteristics of the driving laser pulse (orbital angular momentum and nondiffracting spatial and temporal structures) are transferred to the emitted γ rays by nonlinear Compton scattering.

Photon emission in strong fields beyond the locally-constant field approximation

We investigate a fundamental nonlinear process of vacuum photon emission in the presence of strong electromagnetic fields going beyond the locally-constant field approximation (LCFA), i.e., providing the exact treatment of the spatiotemporal inhomogeneities of the external field. We examine a standing electromagnetic wave formed by high-intensity laser pulses and benchmark the approximate predictions against the results obtained by means of a precise approach evaluating both the tadpole (reducible) and vertex (irreducible) contributions. It is demonstrated that the previously used approximate methods may fail to properly describe the quantitative characteristics of each of the two terms. In the case of the tadpole contribution, the LCFA considerably underestimates the number of photons emitted for sufficiently high frequency of the external field. The vertex term predicts emission of a great number of soft photons whose spectrum is no longer isotropic in contrast to the LCFA results. A notable difference among the photon yields along different spatial directions, which is not captured by the LCFA, represents an important signature for experimental studies of the photon emission process. Since this feature takes place unless the Keldysh parameter is much larger than unity, it can also be used in indirect observation of the Schwinger mechanism.

Polarized Positron Beams via Intense Two-Color Laser Pulses.

The generation of ultrarelativistic polarized positrons during the interaction of an ultrarelativistic electron beam with a counterpropagating two-color petawatt laser pulse is investigated theoretically. Our MonteCarlo simulation, based on a semiclassical model, incorporates photon emissions and pair productions, using spin-resolved quantum probabilities in the local constant field approximation, and describes the polarization of electrons and positrons for the pair production and photon emission processes, as well as the classical spin precession in between. The main reason for the polarization is shown to be the spin asymmetry of the pair production process in strong external fields, combined with the asymmetry of the two-color laser field. Employing a feasible scenario, we show that highly polarized positron beams, with a polarization degree of ζ≈60%, can be produced in a femtosecond timescale, with a small angular divergence, ∼74 mrad, and high density, ∼10^{14} cm^{-3}. The laser-driven polarized positron source raises hope for providing an alternative for high-energy physics studies.

Quantum radiation reaction in aligned crystals beyond the local constant field approximation

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.