It is possible using current high intensity laser facilities to reach the quantum radiation reaction regime for energetic electrons. An experiment using a wakefield accelerator to drive GeV electrons into a counterpropagating laser pulse would demonstrate the increase in the yield of high energy photons caused by the stochastic nature of quantum synchrotron emission: we show that a beam of $10^9$ 1 GeV electrons colliding with a 30 fs laser pulse of intensity $10^{22}~\text{Wcm}^{-2}$ will emit 6300 photons with energy greater than 700 MeV, $60\times$ the number predicted by classical theory.
From the development of the electron theory by H. A. Lorentz in 1906, many authors have tried to reformulate this model named "radiation reaction". P. A. M. Dirac derived the relativistic-classical electron model in 1938, which is now called the Lorentz-Abraham-Dirac model. But this model has the big difficulty of the run-away solution. Recently, this equation has become important for ultra-intense laser-electron (plasma) interactions. Therefore, it is desirable to stabilize this model of the radiation reaction for estimations. Via my recent research, I found a stabilized model of radiation re…
{A simple electrodynamic model is developed to define plasma-field structures in self-consistent ultra-relativistic laser-plasma interactions when the radiation reaction effects come into play. An exact analysis of a circularly polarized laser interacting with plasmas is presented. We define fundamental notations such as nonlinear dielectric permittivity, ponderomotive and dissipative forces acting in a plasma. Plasma-field structures arising during the ultra-relativisitc interactions are also calculated. Based on these solutions we show that about 50% of laser energy can be converted into gam…
Stimulated Raman scattering of an ultra-intense laser pulse in plasmas is studied by perturbatively including the leading order term of the Landau-Lifshitz radiation reaction force in the equation of motion for plasma electrons. In this approximation, radiation reaction force causes phase shift in nonlinear current densities that drive the two Raman sidebands (anti-Stokes and Stokes waves), manifesting itself into the nonlinear mixing of two sidebands. This mixing results in a strong enhancement in the growth of the forward Raman scattering instability.
In the laser --- electron beam head-on interaction electron energy can decrease due to radiation reaction, i.e. emission of photons. For 10--100~fs laser pulses and for the laser field strength up to the pair photoproduction threshold, it is shown that one can calculate the resulting electron and photon spectra as if the electron beam travels through a constant magnetic field. The strength of this constant field and the interaction time are found as functions of the laser field amplitude and duration. Using of constant field approximation can make a theoretical analysis of stochasticity of the…
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 …
We propose a new method of detecting radiation reaction effects in the motion of particles subjected to laser pulses of moderate intensity and long duration. The effect becomes sizeable for particles that gain almost no energy through the interaction with the laser pulse.
Radiation reaction effects on ion acceleration in laser foil interaction are investigated via analytical modeling and multi-dimensional particle-in-cell simulations. We find the radiation effects are important in the area where some electrons move backwards due to static charge separation field at the laser intensity of 1022 W=cm2. Radiation reaction tends to impede these backwards motion. In the optical transparency region ion acceleration is enhanced when the radiation effects are considered.
A classical model of radiation reaction for the betatron oscillation of an electron in a plasma wakefield accelerator is presented. The maximum energy of the electron due to the longitudinal radiation reaction is found, and the betatron oscillation damping due to both the longitudinal and transverse radiation reaction effects is analyzed. Both theoretical and numerical solutions are shown with good agreements. The regime that the quantum radiation takes effect is also discussed. This model is important for designing future plasma based super accelerators or colliders.
Radiation reaction effects in the interaction of an electron bunch with a superstrong focused ultrashort laser pulse are investigated in the quantum radiation dominated regime. The angle-resolved Compton scattering spectra are calculated in laser pulses of variable duration using a semi-classical description for the radiation dominated dynamics and a full quantum treatment for the emitted radiation. In dependence of the laser pulse duration we find signatures of quantum radiation reaction in the radiation spectra, which are characteristic for the focused laser beam and visible in the qualitati…
Non-linear cascade scattering of intense, tightly focused laser pulses by relativistic electrons is studied numerically in the classical approximation including the radiation damping for the quantum parameter hwx-ray/E<1 and an arbitrary radiation parameter Kai. The electron energy loss, along with its side scattering by the ponderomotive force, makes the scattering in the vicinity of high laser field nearly impossible at high electron energies. The use of a second, co-propagating laser pulse as a booster is shown to solve this problem.
The fission-fusion reaction mechanism was proposed in order to generate extremely neutron-rich nuclei close to the waiting point N = 126 of the rapid neutron capture nucleosynthesis process (r-process). The production of such isotopes and the measurement of their nuclear properties would fundamentally help to increase the understanding of the nucleosynthesis of the heaviest elements in the universe. Major prerequisite for the realization of this new reaction scheme is the development of laser-based acceleration of ultra-dense heavy ion bunches in the mass range of A = 200 and above. In this pa…
The radiation pressure acceleration regime of laser ion acceleration requires high intensity laser pulses to function efficiently. Moreover the foil should be opaque for incident radiation during the interaction to ensure maximum momentum transfer from the pulse to the foil, which requires proper matching of the target to the laser pulse. However, in the ultrarelativistic regime, this leads to large acceleration distances, over which the high laser intensity for a Gaussian laser pulse must be maintained. It is shown that proper tailoring of the laser pulse profile can significantly reduce the …
We investigate the feasibility of using laser accelerated protons/deuterons for positron emission tomography (PET) isotope production by means of the nuclear reactions $^{11}$B($p,n$)$^{11}$C and $^{10}$B($d,n$)$^{11}$C. The second reaction has a positive Q-value and no energy threshold. One can, therefore, make use of the lower energy part of the laser-generated deuterons, which includes the majority of the accelerated deuterons. The $^{11}$C produced from the reaction $^{10}$B($d,n$)$^{11}$C is estimated to be 7.4 $\times$ 10$^{9}$ per laser-shot at the Titan laser at Lawrence Livermore Nati…
A novel scheme for generating powerful terahertz (THz) radiation based on laser-solid interactions is proposed. When a $p$-polarized femtosecond laser impinges obliquely on a plane solid target and the target partially blocks the laser energy, surface electrons are extracted out and accelerated by the laser fields, forming a low-divergence electron beam. A half-cycle THz radiation pulse is emitted simultaneously as the beam passes by the edge of the target, due to coherent diffraction radiation. Our particle-in-cell simulations show that the relativistic THz pulse can have an energy of a few t…
The advent of high-intensity pulsed laser technology enables the generation of extreme states of matter under conditions that are far from thermal equilibrium. This in turn could enable different approaches to generating energy from nuclear fusion. Relaxing the equilibrium requirement could widen the range of isotopes used in fusion fuels permitting cleaner and less hazardous reactions that do not produce high energy neutrons. Here we propose and implement a means to drive fusion reactions between protons and boron-11 nuclei, by colliding a laser-accelerated proton beam with a laser-generated …
Under the presence of ultra high intensity lasers or other intense electromagnetic fields the motion of particles in the ultrarelativistic regime can be severely affected by radiation reaction. The standard particle-in-cell (PIC) algorithms do not include radiation reaction effects. Even though this is a well known mechanism, there is not yet a definite algorithm nor a standard technique to include radiation reaction in PIC codes. We have compared several models for the calculation of the radiation reaction force, with the goal of implementing an algorithm for classical radiation reaction in t…
The radiation reaction effects on electron dynamics in counter-propagating circularly polarized laser beams are investigated through the linearization theorem and the results are in great agreement with numeric solutions. For the first time, the properties of fixed points in electron phase-space were analyzed with linear stability theory, showing that center nodes will become attractors if the classical radiation reaction is considered. Electron dynamics are significantly affected by the properties of the fixed points and the electron phase-space densities are found to be increasing exponentia…
We report a laser-driven neutron source with high yield ($>10^8$/J) and high peak flux ($>10^{25}$/cm$^2$/s) derived from high-temperature deuteron-deuteron fusion reactions. The neutron yield and the fusion temperature ($\sim 200$ keV) in our experiment are respectively two orders of magnitude and one order of magnitude higher than any previous laser-induced D-D fusion reaction. The high-temperature plasma is generated from thin ($\sim 2\,μ$m), solid-density deuterium targets, produced by a cryogenic jet, irradiated by a 140 fs, 130 J petawatt laser with an F/3 off-axis parabola and a plasma …
Relativistic electrons, accelerated by the laser ponderomotive force, can be focused onto a high-Z convertor to generate high-brightness beams of gamma-rays, which in turn can be used to induce photonuclear reactions. In this work, the possibility of photo-transmutation of long-lived radionuclide Cs-135 by laser-plasma driven electron source has been demonstrated through Geant4 simulations. High energy electron generation, bremsstrahlung and photonuclear reaction have been observed at four different laser intensities of 10^{20} W/cm^2, 5 times 10^{20} W/cm^2, 10^{21} W/cm^2 and 5 times 10^{21}…
Radiation Reaction (RR) effects in the interaction of an ultra-intense laser pulse with a thin plasma foil are investigated analytically and by two-dimensional (2D3P) Particle-In-Cell (PIC) simulations. It is found that the radiation reaction force leads to a significant electron cooling and to an increased spatial bunching of both electrons and ions. A fully relativistic kinetic equation including RR effects is discussed and it is shown that RR leads to a contraction of the available phase space volume. The results of our PIC simulations are in qualitative agreement with the predictions of th…
Due to screening effects, nuclear reactions in astrophysical plasmas may behave differently than in the laboratory. The possibility to determine the magnitude of these screening effects in colliding laser-generated plasmas is investigated theoretically, having as a starting point a proposed experimental setup with two laser beams at the Extreme Light Infrastructure facility. A laser pulse interacting with a solid target produces a plasma through the Target Normal Sheath Acceleration scheme, and this rapidly streaming plasma (ion flow) impacts on a secondary plasma created by the interaction of…
In the interaction of laser pulses of extreme intensity ($>10^{23}~{\rm W cm}^{-2}$) with high-density, thick plasma targets, simulations show significant radiation friction losses, in contrast to thin targets for which such losses are negligible. We present an analytical calculation, based on classical radiation friction modeling, of the conversion efficiency of the laser energy into incoherent radiation in the case when a circularly polarized pulse interacts with a thick plasma slab of overcritical initial density. By accounting for three effects including the influence of radiation losses o…
The effects of radiation reaction force on laser driven auto-resonant particle acceleration scheme are studied using Landau-Lifshitz equation of motion. These studies are carried out for both linear as well as circularly polarized laser fields in the presence of static axial magnetic field. From the parametric study, a radiation reaction dominated region has been identified in which the particle dynamics is greatly effected by this force. In the radiation reaction dominated region the two significant effects on particle dynamics are seen viz., (1) saturation in energy gain by the initially res…
Polarization and radiation reaction (RR) effects in the interaction of a superintense laser pulse (I > 10^23 W/cm^2) with a thin plasma foil are investigated with three dimensional particle-in-cell (PIC) simulations. For a linearly polarized laser pulse, strong anisotropies such as the formation of two high-energy clumps in the plane perpendicular to the propagation direction and significant radiation reactions effects are observed. On the contrary, neither anisotropies nor significant radiation reaction effects are observed using circularly polarized laser pulses, for which the maximum ion en…
Using full-scale 3D particle-in-cell simulations we show that the radiation reaction dominated regime can be reached in an all optical configuration through the collision of a $\sim$1 GeV laser wakefield accelerated (LWFA) electron bunch with a counter propagating laser pulse. In this configuration radiation reaction significantly reduces the energy of the particle bunch, thus providing clear experimental signatures for the process with currently available lasers. We also show that the transition between classical and quantum radiation reaction could be investigated in the same configuration w…
The dynamics of energetic particles in strong electromagnetic fields can be heavily influenced by the energy loss arising from the emission of radiation during acceleration, known as radiation reaction. When interacting with a high-energy electron beam, today's lasers are sufficiently intense to explore the transition between the classical and quantum radiation reaction regimes. We report on the observation of radiation reaction in the collision of an ultra-relativistic electron beam generated by laser wakefield acceleration ($\varepsilon > 500$ MeV) with an intense laser pulse ($a_0 > 10$). W…
Radiation reaction (RR) effects on the acceleration of a thin plasma foil by a superintense laser pulse in the radiation pressure dominated regime are investigated theoretically. A simple suitable approximation of the Landau-Lifshitz equation for the RR force and a novel leapfrog pusher for its inclusion in particle-in-cell simulations are provided. Simulations for both linear and circular polarization of the laser pulse are performed and compared. It is found that at intensities exceeding $10^{23} \Wcm$ the radiation reaction force strongly affects the dynamics for a linearly polarized laser …
In this paper, we investigate the evolution of the energy spread and the divergence of electron beams while they interact with different laser pulses at intensities where quantum effects and radiation reaction are of relevance. The interaction is modeled with a QED-PIC code and the results are compared with those obtained with a standard PIC code with the addition of a classical radiation reaction module and with theoretical predictions. While classical radiation reaction is a continuous process, in QED, radiation emission is stochastic. The two pictures reconcile in the limit when the emitted…
The production of intense neutron beams via thermonuclear reactions in laser-generated plasmas is investigated theoretically. So far, state-of-the-art neutron beams are produced via laser-induced particle acceleration leading to high-energy particle beams that subsequently interact with a secondary target. Here we show that neutron beams of two orders of magnitude narrower bandwidth can be obtained from thermonuclear reactions in plasmas generated by Petawatt-class lasers. The intensity of such neutron beams is about one or two orders of magnitude lower than the one of the state-of-the-art las…
Charged particles accelerated by electromagnetic fields emit radiation, which must, by the conservation of momentum, exert a recoil on the emitting particle. The force of this recoil, known as radiation reaction, strongly affects the dynamics of ultrarelativistic electrons in intense electromagnetic fields. Such environments are found astrophysically, e.g. in neutron star magnetospheres, and will be created in laser-matter experiments in the next generation of high-intensity laser facilities. In many of these scenarios, the energy of an individual photon of the radiation can be comparable to t…
Coherently enhanced radiation friction in laser-plasma collisions
ELI Beamlines facility, The Extreme Light Infrastructure ERIC（极轻基础设施欧洲研究联盟 ELI 光束线设施）；National Research Nuclear University MEPhI（俄罗斯国家核研究医科大学 MEPhI）；Institute of Applied Physics of the Russian Academy of Sciences（俄罗斯科学院应用物理研究所）；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术学院）；FNSPE, Czech Technical University in Prague（捷克布拉格理工大学 FNSPE）
Today's high-intensity laser facilities produce short pulses can, in tight focus, reach peak intensities of $10^{22}\,\mathrm{Wcm}^{-2}$ and, in long focus, wakefield-accelerate electrons to GeV energies. The radiation-reaction--dominated regime, where the recoil from stochastic photon emission becomes significant, can be reached in the collision of such an electron beam with an intense short pulse. Measuring the total energy emitted in gamma rays or the presence of a prominent depletion zone in the electron beam's post-collision energy spectrum would provide strong evidence of radiation react…
Spectral red-shifting of high power laser pulses propagating through underdense plasma can be a source of ultrashort mid-infrared (MIR) radiation. During propagation, a high power laser pulse drives large amplitude plasma waves, depleting the pulse energy. At the same time, the large amplitude plasma wave provides a dynamic dielectric response that leads to spectral shifting. The loss of laser pulse energy and the approximate conservation of laser pulse action imply that spectral red-shifts accompany the depletion. In this paper, we investigate, through simulation, the parametric dependence of…
The diffraction broadening of the intense laser radiation restricts its efficient use in many applications. Proposed in the present work is a method for laser radiation guiding in a density channel formed in plasma by a relativistic electron beam. The conditions and parameters of the relativistic beam ensuring the guiding by means of the proposed method have been examined.
Ion beams generated with ultra-intense lasers-plasma accelerators hold promises to provide compact and affordable beams of relativistic ions. One of the most efficient acceleration setups was demonstrated to be direct acceleration by the laser's radiation pressure. Due to plasma instabilities developing in the ultra-thin foils required for radiation pressure acceleration, however, it is challenging to maintain stable acceleration over long distances. Recent studies demonstrated, on the other hand, that specially tailored laser pulses can shorten the required acceleration distance suppressing t…
The evolution of an electron beam colliding head-on with a strong plane-wave field is investigated in the framework of strong-field QED including radiation-reaction effects due to photon emission. Employing a kinetic approach to describe the electron and the photon distribution it is shown that at a given total laser fluence the final electron distribution depends on the shape of the laser envelope and on the pulse duration, in contrast to the classical predictions of radiation reaction based on the Landau-Lifshitz equation. Finally, it is investigated how the pair-creation process leads to a …
The inexorable development of ever more powerful laser systems has re-ignited interest in electromagnetic radiation reaction and its significance for the collective behaviour of charged matter interacting with intense electromagnetic fields. The classical radiation reaction force on a point electron is non-conservative, and this has led some authors to question the validity of methods used to model ultra-intense laser-matter interactions including radiation reaction. We explain why such concern is unwarranted.
A quantum plasma screening model based on the density matrix formalism is used to investigate theoretically the thermonuclear reactions $^{13}$C($α$, $n$)$^{16}$O and $^2$H($d$, $n$)$^3$He in laser-generated plasmas over a large range of densities and temperatures. For cold and dense (solid-state density) plasmas, our results show that quantum effects can enhance the plasma screening for thermonuclear reactions up to one order of magnitude compared to the classical case. This result can have impact on nuclear astrophysics predictions, and also may play a role for fusion energy gain prospects. …
We study electron acceleration within a sub-critical plasma channel irradiated by an ultra-intense laser pulse ($a_0>100$ or $I>10^{22}~\mathrm{W/cm^2}$). In this regime, radiation reaction significantly alters the electron dynamics. This has an effect not only on the maximum attainable electron energy but also on the phase-matching process between betatron motion and electron oscillations in the laser field. Our study encompasses analytical description, test-particle calculations and 2-dimensional particle-in-cell simulations. We show single-stage electron acceleration to multi-GeV energies w…
When an ultrarelativistic electron beam collides with a sufficiently intense laser pulse, radiation-reaction effects can strongly alter the beam dynamics. In the realm of classical electrodynamics, radiation reaction has a beneficial effect on the electron beam as it tends to reduce its energy spread. Here, we show that when quantum effects become important, radiation reaction induces the opposite effect, i.e., the electron beam spreads out after interacting with the laser pulse. We identify the physical origin of this opposite tendency in the intrinsic stochasticity of photon emission, which …
Although, for current laser pulse energies, the weakly nonlinear regime of LWFA is known to be the optimal for reaching the highest possible electron energies, the capabilities of upcoming large laser systems will provide the possibility of running highly nonlinear regimes of laser pulse propagation in underdense or near-critical plasmas. Using an extended particle-in-cell (PIC) model that takes into account all the relevant physics, we show that such regimes can be implemented with external guiding for a relatively long distance of propagation and allow for the stable transformation of laser …
Ultra-strong laser pulses can be so intense that an electron in the focused beam loses significant energy due to gamma-photon emission while its motion deviates via the radiation back-reaction. Numerical methods and tools designed to simulate radiation-dominated and QED-strong laser-plasma interactions are summarized here.
An intense, short laser pulse incident on a transparent dielectric can excite electrons from valence to the conduction band. As these electrons undergo scattering, both from phonons and ions, they emit bremsstrahlung radiation. Here we present a theory of bremsstrahlung emission appropriate for laser pulse-dielectric interactions. Simulations of the interaction, incorporating this theory, illustrate characteristics of the radiation (power, energy and spectra) for arbitrary ratios of electron collision frequency to radiation frequency. The conversion efficiency of laser pulse energy into bremss…
With the recent advances in laser technology, experimental investigation of radiation reaction phenomena is at last becoming a realistic prospect. A pedagogical introduction to electromagnetic radiation reaction is given with the emphasis on matter driven by ultra-intense lasers. Single-particle, multi-particle, classical and quantum aspects are all addressed.
The dynamics of nuclear reaction in plasma is a fundamental issue in many high energy density researches, such as the astrophysical reactions and the inertial confinement fusion. The effective reaction cross-sections and ion stopping power in plasma need to be taken into account to analyze the reactivity. In this research, we have experimentally investigated the from D-D reactions from interactions between deuteron beams and deuterated polystyrene (CD) plasma, driven by two laser pulses respectively. The neutron yields, plasma density and deuteron energy loss in plasma have been measured, and …
Accelerated charges radiate, and therefore must lose energy. The impact of this energy loss on particle motion, called radiation reaction, becomes significant in intense-laser matter interactions, where it can reduce collision energies, hinder particle acceleration schemes, and is seemingly unavoidable. Here we show that this common belief breaks down in short laser pulses, and that energy losses and radiation reaction can be controlled and effectively switched off by appropriate tuning of the pulse length. This "quenching" of emission is impossible in classical physics, but becomes possible i…
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…
Analytical theory of coherent radiation and radiation friction in laser-plasma collisions
ELI Beamlines facility, The Extreme Light Infrastructure ERIC（极亮基础设施欧洲研究联合体 ELI光束线设施）；National Research Nuclear University MEPhI（莫斯科国立核研究大学 MEPhI）；Institute of Applied Physics of the Russian Academy of Sciences（俄罗斯科学院应用物理研究所）；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术学院）；Deutsches Elektronen–Synchrotron DESY（德国电子同步加速器 DESY）；FNSPE, Czech Technical University in Prague（捷克布拉格理工大学 FNSPE）
The emission from an electron in the field of a relativistically strong laser pulse is analyzed. At pulse intensities of J > 2 10^22 W/cm2 the emission from counter-propagating electrons is modified by the effects of Quantum ElectroDynamics (QED), as long as the electron energy is sufficiently high: E > 1 GeV. The radiation force experienced by an electron is for the first time derived from the QED principles and its applicability range is extended towards the QED-strong fields.
High-intensity X-ray sources are invaluable tools, enabling experiments at the forefront of our understanding of materials science, chemistry, biology, and physics. Laser-plasma electron accelerators are sources of high-intensity X-rays, as electrons accelerated in wakefields emit short-wavelength radiation due to betatron oscillations. While applications such as phase-contrast imaging with these betatron sources have already been demonstrated, others would require higher photon number and would benefit from increased tunability. In this paper we demonstrate, through detailed 3D simulations, a…
We consider nonlinear interaction of superpower laser pulses of relativistic intensities with nanolayers and solid-plasma-targets towards the production of high energy-density electron bunches along with nuclear radiation (hard $% γ$-quanta and positron fluxes). It is shown that petawatt lasers are capable of producing via two-target scheme high density field free electron/positron bunches and substantial amounts of $γ$-quanta with energies up to $200$ MeV. For actual supershort and tightly focused--strongly nonplane ultrarelativistic laser pulses of linear and circular polarizations 3D3V prob…
Plasmas created by high-intensity lasers are often subject to the formation of kinetic-streaming instabilities, such as the Weibel instability, which lead to the spontaneous generation of high-amplitude, tangled magnetic fields. These fields typically exist on small spatial scales, i.e. "sub-Larmor scales". Radiation from charged particles moving through small-scale electromagnetic (EM) turbulence has spectral characteristics distinct from both synchrotron and cyclotron radiation, and it carries valuable information on the statistical properties of the EM field structure and evolution. Consequ…
Backward terahertz radiation can be produced by a high-intensity laser normally incident upon an underdense plasma. It is found that terahertz radiation is generated by electrons refluxing along the bubble shell. These shell electrons have similar dynamic trajectories and emit backward radiations to vacuum. This scheme has been proved through electron dynamic calculations as well as by using an ionic sphere model. In addition, the bubble shape is found to influence the radiation frequency, and this scheme can be implemented in both uniform and up-ramp density gradient plasma targets. The terah…
The effects of coherently enhanced radiation reaction on the motion of subwavelength electron bunches in interaction with intense laser pulses are analyzed. The radiation reaction force behaves as a radiation pressure in the laser beam direction, combined with a viscous force in the perpendicular direction. Due to Coulomb expansion of the electron bunch, coherent radiation reaction effects only occur in the initial stage of the laser-bunch interaction while the bunch is still smaller than the wavelength. It is shown that this initial stage can have observable effects on the trajectory of the b…
