Highly-efficient electron ponderomotive acceleration in underdense plasmas
Lorenzo Martelli, Olena Kononenko, Igor Andriyash, Jonathan Wheeler, Julien Gautier, Jean-Philippe Goddet, Amar Tafzi, Ronan Lahaye, Camilla Giaccaglia, Alessan… 展开作者
Lorenzo Martelli, Olena Kononenko, Igor Andriyash, Jonathan Wheeler, Julien Gautier, Jean-Philippe Goddet, Amar Tafzi, Ronan Lahaye, Camilla Giaccaglia, Alessandro Flacco, Vidmantas Tomkus, Migle Mackevičiūtė, Juozas Dudutis, Valdemar Stankevic, Paulius Gečys, Gediminas Račiukaitis, Henri Kraft, Xuan Quyen Dinh, Cédric Thaury
Laser-plasma accelerators represent a promising technology for future compact accelerating systems, enabling the acceleration of tens of pC to above $1\,$GeV over just a few centimeters. Nonetheless, these devices currently lack the stability, beam quality and average current of conventional systems. While many efforts have focused on improving acceleration stability and quality, little progress has been made in increasing the beam's average current, which is essential for future laser-plasma-based applications. In this paper, we investigate a laser-plasma acceleration regime aimed at increasing the beam average current with energies up to few-MeVs, efficiently enhancing the beam charge. We present experimental results on configurations that allow reaching charges of $5-30\,$nC and a maximum conversion efficiency of around $14\,$%. Through comprehensive Particle-In-Cell simulations, we interpret the experimental results and present a detailed study on electron dynamics. From our analysis, we show that most electrons are not trapped in a plasma wave; rather, they experience ponderomotive acceleration. Thus, we prove the laser pulse as the main driver of the particles' energy gain process.
We have studied laser pulse channeling in underdense plasma by means of analytical theory and 3D PIC simulations. The most significant result of this paper is the demonstration of the single fully evacuated stationary channel solution can be reached an asymptotic state in PIC simulations. In the lower density and for a laser power above channeling power, we were able to reproduce in PIC simulations the analytical curve. We showed that single channels are stable structures against symmetric perturbations. We also studied the formation of the ring structure in theory and simulations. An evacuate…
The electron and positron acceleration in the first cycle of a laser-driven wakefield is investigated. Separatrices between different types of the particle motion (confined, reflected by the wakefield or ponderomotive potential and transient) are demonstrated. The ponderomotive acceleration is negligible for electrons but is substantial for positrons. An electron bunch, injected as quasi-monoenergetic, acquires a localized energy spectrum with a cut-off at the maximum energy.
Three-dimensional particle-in-cell simulation is used to investigate the witness proton acceleration in underdense plasma with a short intense Laguerre-Gaussian (LG) laser pulse. Driven by the LG10 laser pulse, a special bubble with an electron pillar on the axis is formed, in which protons can be well-confined by the generated transversal focusing field and accelerated by the longitudinal wakefield. The risk of scattering prior to acceleration with a Gaussian laser pulse in underdense plasma is avoided, and protons are accelerated stably to much higher energy. In simulation, a proton beam has…
The interaction of ultra-intense laser pulses with an underdense plasma is used in laser-plasma acceleration to create compact sources of ultrashort pulses of relativistic electrons and X-rays. The accelerating structure is a plasma wave, or wakefield, that is excited by the laser ponderomotive force, a force that is usually assumed to depend solely on the laser envelope and not on its exact waveform. Here, we use near-single-cycle laser pulses with a controlled carrier-envelope-phase (CEP) to show that the actual waveform of the laser field has a clear impact on the plasma response. We measur…
Analytic model of stable shock-like structures in laser interaction with underdense plasma for identifying of phase and polarization dependent regime of laser wakefield accelerators
In laser-solid interactions, electrons may be generated and subsequently accelerated to energies of the order-of-magnitude of the ponderomotive limit, with the underlying process dominated by direct laser acceleration. Breaking this limit, realized here by a radially-polarized laser pulse incident upon a wire target, can be associated with several novel effects. Three-dimensional Particle-In-Cell simulations show a relativistic intense laser pulse can extract electrons from the wire and inject them into the accelerating field. Anti-dephasing, resulting from collective plasma effects, are shown…
An electron injector concept for laser-plasma accelerator was developed in ref [1] and [2] ; it relies on the use of counter-propagating ultrashort laser pulses. In [2], the scheme is as follows: the pump laser pulse generates a large amplitude laser wakefield (plasma wave). The counter-propagating injection pulse interferes with the pump laser pulse to generate a beatwave pattern. The ponderomotive force of the beatwave is able to inject plasma electrons into the wakefield. We have studied this injection scheme using 1D Particle in Cell (PIC) simulations. The simulations reveal phenomena and …
Relativistic ponderomotive force, uphill acceleration, and transition to chaos
从协变循环平均拉格朗日量出发，导出了点电荷的相对论振荡中心运动方程，并给出了任意强度行波中有质动力的解析表达式。它进一步表明，有质动力的横向和纵波是不同的，在后者中，上坡加速度可以发生。在驻波中，存在一个阈值强度，超过该阈值强度，由于向混沌的转变，长期运动不再能用规则的有质动力来描述。PACS编号：52.20.Dq，05.45.+ b，52.35.MW，52.60.+ H
An effective theory of laser--plasma based particle acceleration is presented. Here we treated the plasma as a continuous medium with an index of refraction $n_{m}$ in which a single electron propagates. Because of the simplicity of this model, we did not need to perform PIC simulations in order to study the properties of the electron acceleration. We studied the properties of the electron motion due to the Lorentz force and the relativistic equations of motion were numerically solved and analysed. We compared our results to PIC simulations and experimental data. Keywords: Underdense plasma; E…
Intense lasers can accelerate electrons to very high energy over a short distance. Such compact accelerators have several potential applications including fast ignition, high energy physics, and radiography. Among the various schemes of laser-based electron acceleration, vacuum laser acceleration has the merits of super-high acceleration gradient and great simplicity. Yet its realization has been difficult because injecting free electrons into the fast-oscillating laser field is not trivial. Here we demonstrate free-electron injection and subsequent vacuum laser acceleration of electrons up to…
We introduce the first approach to volumetrically generate relativistically thermal plasma at gas-jet--accessible density. Using fully kinetic simulations and theory, we demonstrate that two stages of direct laser acceleration driven by two laser pulses in an applied magnetic field can heat a significant plasma volume to multi-MeV average energy. The highest-momentum feature is 2D-isotropic, persists after the interaction, and includes the majority of electrons, enabling experimental access to bulk-relativistic, high-energy-density plasma in an optically diagnosable regime for the first time.
A theoretical study of laser and plasma based electron acceleration is presented. An effective model has been used, in which the presence of an underdense plasma has been taken account via its index of refraction $n_{m}$. In the confines of this model, the basic phenomena can be studied by numerically solving the classical relativistic equations of motion. The key idea of this paper is the application of chirped, bichromatic laser fields. We investigated the advantages and disadvantages of mixing the second harmonic to the original $λ= 800 \, \mathrm{nm}$ wavelength pulse. We performed calcula…
We report the experimental generation of highly energetic carbon ions up to 48 MeV per nucleon by shooting double-layer targets composed of well-controlled slightly underdense plasma (SUP) and ultrathin foils with ultra-intense femtosecond laser pulses. Particle-in-cell simulations reveal that carbon ions residing in the ultrathin foils undergo radiation pressure acceleration and long-time sheath field acceleration in sequence due to the existence of the SUP in front of the foils. Such an acceleration scheme is especially suited for heavy ion acceleration with femtosecond laser pulses. The bre…
A new electron injection scheme is proposed in sub-relativistic plasma wakefield accelerators. A transverse laser ionizes a dopant gas and ponderomotively accelerates the released electrons in the direction of wake propagation. This process enables electron trapping in the wakefield even for a wakefield potential below the trapping threshold. We study the scheme theoretically and by means of particle-in-cell simulations to demonstrate high-quality beam formation and acceleration with sub-micrometer normalized emittances and sub-percent uncorrelated energy spreads.
The oscillation-center Hamiltonian is derived for a relativistic electron injected with an arbitrary momentum in a linearly polarized laser pulse propagating in tenuous plasma, assuming that the pulse length is smaller than the plasma wavelength. For hot electrons generated at collisions with ions under intense laser drive, multiple regimes of ponderomotive acceleration are identified and the laser dispersion is shown to affect the process at plasma densities down to 10^17 cm-3. Assuming a/gamma_g << 1, which prevents net acceleration of the cold plasma, it is also shown that the normalized en…
In laser-plasma experiments, we observed that ion acceleration from the Coulomb explosion of the plasma channel bored by the laser, is prevented when multiple plasma instabilities such as filamentation and hosing, and nonlinear coherent structures (vortices/post-solitons) appear in the wake of an ultrashort laser pulse. The tailoring of the longitudinal plasma density ramp allows us to control the onset of these insabilities. We deduced that the laser pulse is depleted into these structures in our conditions, when a plasma at about 10% of the critical density exhibits a gradient on the order o…
Propagation of relativistically intense azimuthally or radially polarized laser pulses (RPP) in underdense plasmas is demonstrated to be unstable, via 3D particle-in-cell simulation and disregarding the Kerr non-linearity. Strong pulse filamentation occurs for RPP in transversely uniform plasma with an increment, $Γ$, close to the well-known one depending on acceleration, $α$, and modulated density gradient length, $L$, as $Γ\approx (α/L)^{1/2}$. In deep plasma channels the instability vanishes. Electron self-injection and acceleration by the resulting laser pulse wake is explored.
The dynamics of transient electric fields generated by the interaction of high intensity laser pulses with underdense plasmas has been studied experimentally with the proton projection imaging technique. The formation of a charged channel, the propagation of its front edge and the late electric field evolution have been characterised with high temporal and spatial resolution. Particle-in-cell simulations and an electrostatic, ponderomotive model reproduce the experimental features and trace them back to the ponderomotive expulsion of electrons and the subsequent ion acceleration.
Longitudinal ion acceleration from high-intensity (I ~ 10^20 Wcm^-2) laser interactions with helium gas jet targets (n_e ~ 0.04 n_c) have been observed. The ion beam has a maximum energy for He^2+ of approximately 40 MeV and was directional along the laser propagation path, with the highest energy ions being collimated to a cone of less than 10 degrees. 2D particle-in-cell simulations have been used to investigate the acceleration mechanism. The time varying magnetic field associated with the fast electron current provides a contribution to the accelerating electric field as well as providing …
We use particle-in-cell (PIC) simulations and simple analytic models to investigate the laser-plasma interaction known as ponderomotive steepening. When normally incident laser light reflects at the critical surface of a plasma, the resulting standing electromagnetic wave modifies the electron density profile via the ponderomotive force, which creates peaks in the electron density separated by approximately half of the laser wavelength. What is less well studied is how this charge imbalance accelerates ions towards the electron density peaks, modifying the ion density profile of the plasma. Id…
We examine a regime in which a linearly-polarized laser pulse with relativistic intensity irradiates a sub-critical plasma for much longer than the characteristic electron response time. A steady-state channel is formed in the plasma in this case with quasi-static transverse and longitudinal electric fields. These relatively weak fields significantly alter the electron dynamics. The longitudinal electric field reduces the longitudinal dephasing between the electron and the wave, leading to an enhancement of the electron energy gain from the pulse. The energy gain in this regime is ultimately l…
For the purpose of laser wakefield acceleration, it turned out that also the injection of electron bunches longer than a plasma wavelength can generate accelerated femtosecond bunches with relatively low energy spread. This is of high interest because such injecting bunches can be provided, e.g., by state-of-the-art photo cathode RF guns. Here we point out that when an e-bunch is injected in the wakefield it is important to take into account the ponderomotive scattering of the injecting bunch by the laser pulse in the vacuum region located in front of the plasma. At low energies of the injecte…
In laser-wakefield acceleration, an ultra-intense laser pulse is focused into an underdense plasma in order to accelerate electrons to relativistic velocities. In most cases, the pulses consist of multiple optical cycles and the interaction is well described in the framework of the ponderomotive force where only the envelope of the laser has to be considered. But when using single-cycle pulses, the ponderomotive approximation breaks down, and the actual waveform of the laser has to be taken into account. In this paper, we use near-single cycle laser pulses to drive a laser-wakefield accelerato…
It is shown that static longitudinal and transverse electric fields can significantly alter electron acceleration by a long laser beam in a sub-critical plasma, enabling generation of super-ponderomotive electrons. The role of the plasma fields in this regime is not to directly transfer substantial energy to the electron, but rather to reduce the axial dephasing rate between the electron and the laser beam. The reduced dephasing in both cases leads to a subsequent enhancement of the axial momentum and total electron energy. These mechanisms can be relevant to experiments with solid-density tar…
It is shown that electrons with momenta exceeding the `free electron' limit of $m_eca_0^2/2$ can be produced when a laser pulse and a longitudinal electric field interact with an electron via a non-wakefield mechanism. The mechanism consists of two stages: the reduction of the electron dephasing rate $γ-p_x/m_ec$ by an accelerating region of electric field and electron acceleration by the laser via the Lorentz force. This mechanism can, in principle, produce electrons that have longtudinal momenta that is a significant multiple of $m_eca_0^2/2$. 2D PIC simulations of a relatively simple laser-…
The interaction of high intensity laser radiation with mass-limited target exhibits significant enhancement of the ion acceleration when the target is surrounded by an underdense plasma corona, as seen in numerical simulations. The self-generated quasistatic magnetic field squeezes the corona causing the intensification of a subsequent Coulomb explosion of the target. The electric field intensification at the target edges and plasma resonance effects result in the generation of characteristic density holes and further contributes to the ion acceleration.The interaction of high intensity laser …
We study the laser-driven acceleration of electrons from overdense hydrogen clusters to energies of up to 13 MeV in laser forward direction and several hundreds of keV in an outer ring-like structure. The use of cryogenic hydrogen allows for high repetition-rate operation and examination of the influence of source parameters like temperature and gas flow. The outer ring-like structure of accelerated electrons, originating from the interaction, that is robust against the change of laser and target parameters can be observed for low electron densities of ca. 3$\times$10$^{16}$ cm$^{-3}$. For hig…
We report observation of kHz-pulsed-laser-accelerated electron energies up to 3 MeV in the -$k_\text{laser}$ (backward) direction from a 3 mJ laser interacting at normal incidence with a solid density, flowing-liquid target. The electrons/MeV/s.r. >1 MeV recorded here using a mJ-class laser exceeds or equals that of prior super-ponderomotive electron studies employing lasers at lower repetition-rates and oblique incidence. Focal intensity of the 40-fs-duration laser is 1.5 $\cdot$ 10$^{18}$ W cm$^{-2}$, corresponding to only ~80 keV electron ponderomotive energy. Varying laser intensity confir…
An experiment for studying laser self-guiding has been carried out for the high power ultrashort pulse laser interaction with an underdense plasma slab. Formation of an extremely long plasma channel and its bending are observed when the laser pulse power is much higher than the critical power for relativistic self-focusing. The long self-guiding channel formation is accompanied by electron acceleration with a low transverse emittance and high electric current. Particle-in-cell simulations show that laser bending occurs when the accelerated electrons overtake the laser pulse and modify the refr…
We investigate how next-generation laser pulses at 10 PW $-$ 200 PW interact with a solid target in the presence of a relativistically underdense preplasma produced by amplified spontaneous emission (ASE). Laser hole boring and relativistic transparency are strongly restrained due to the generation of electron-positron pairs and $γ$-ray photons via quantum electrodynamics (QED) processes. A pair plasma with a density above the initial preplasma density is formed, counteracting the electron-free channel produced by the hole boring. This pair-dominated plasma can block the laser transport and tr…
This dissertation explores the interaction between high-intensity lasers and plasmas to accelerate electrons and produce radiation via experimental and computational efforts. The laser pulses used in this dissertation have ultrashort duration (< 100 fs), near-infrared to mid-infrared wavelength (0.8 $μ$m, 2 $μ$m, or 3.9 $μ$m), millijoules of energy, and high repetition rates (480 Hz or 20 Hz). The plasma sources applied are from solid-density targets (overdense) or gaseous targets (underdense). With the high-repetition-rate capability, statistical methods are employed to optimize certain aspec…
A strongly mismatched regime of self-guided nonlinear laser-plasma acceleration in the bubble regime is modeled for optimization of Laser to Particle energy efficiency with application to recently proposed laser positron accelerator. The strong mismatch, in contrast with the matched condition, arises from the incident laser spot-size being much larger than that needed for equilibration of the laser ponderomotive and electron-ion charge-separation force in the plasma bubble. This is shown to be favorable for optimization of large self-injected electron charge and ultra-low transverse emittance.…
The mechanism of stochastic electron acceleration in colliding laser waves is investigated by employing proper canonical variables and effective time, such that the new Hamiltonian becomes time independent when the perturbative (weaker) laser wave is absent. The performed analytical analysis clearly reveals the physical picture of stochastic electron dynamics. It shows that when the amplitude of the perturbative laser field exceeds some critical value, stochastic electron acceleration occurs within some electron energy range. The conditions, at which the maximum electron energy gained under st…
We review recent PIC simulation results which show that double-sided irradiation of a thin over- dense plasma slab by ultra-intense laser pulses from both sides can lead to sustained comoving acceleration of surface electrons to energies much higher than the conventional ponderomotive limit. The acceleration stops only when the electrons drift transversely out of the laser beam. We show latest 2.5D results of parameter studies based on finite laser spot size and discuss future laser experiments that can be used to test these results.
We report on new findings in a laser driven enhanced electron beam generation in the multi MeV energy range at moderate relativistic laser intensities and their applications. In our experiment, an intense sub-picosecond laser pulse propagates through a plasma of a near critical electron density (NCD) and direct laser acceleration (DLA) of electrons takes place. The breakthrough toward high current relativistic electron beams became possible due to application of low density polymer foams of sub-mm thickness. In foams, the NCD-plasma was produced by a mechanism of super-sonic ionization. Compar…
The dynamics of electric field generation and radial acceleration of ions by a laser pulse of relativistic intensity propagating in an underdense plasma has been investigated using an one-dimensional electrostatic, ponderomotive model developed to interpret experimental measurements of electric fields [S. Kar et al, New J. Phys. *9*, 402 (2007)]. Ions are spatially focused at the edge of the charge-displacement channel, leading to hydrodynamical breaking, which in turns causes the heating of electrons and an "echo" effect in the electric field. The onset of complete electron depletion in the c…
It is shown that nonlinear interaction between large amplitude circularly polarized EM wave and dusty plasma leads to a nonstationary ponderomotive force which in turn produces a vortex ring, and magnetic field. Then the ensuing vortex ring in the direction of propagation of the pump wave can accelerate the micron-size dust particles which are initially at rest and eventually form a non relativistic dust jet. This effect is purely nonstationary and unlike linear vortices, dust particles do not rotate here. Specifically, it is pointed out that the vortex ring or closed filament can become poten…
A regime of multi-cascade proton acceleration in the interaction of $10^{21}-10^{22}$ W/cm$^2$ laser pulse with a structured target is proposed. The regime is based on the electron charge displacement under the action of laser ponderomotive force and on the effect of relativistically induced slab transparency which allows to realize idea of multi-cascade acceleration. It is shown that a target comprising several properly spaced apart thin foils can optimize the acceleration process and give at the output quasi-monoenergetic beams of protons with energies up to hundreds of MeV with energy sprea…
High-fidelity modeling of plasma-based acceleration (PBA) requires the use of 3D fully nonlinear and kinetic descriptions based on the particle-in-cell (PIC) method. Three-dimensional PIC algorithms based on the quasi-static approximation (QSA) have been successfully applied to efficiently model the beam-plasma interaction. In a QSA-PIC algorithm, the plasma response to a charged particle beam or laser driver is calculated based on self-consistent forces from the QSA form of Maxwell's equations. These fields are then used to advance the charged particle beam or laser forward by a large time st…
We show using particle-in-cell (PIC) simulations and theoretical analysis that a high-quality electron beam whose density is modulated at angstrom scales can be generated directly using density downramp injection in a periodically modulated density in nonlinear plasma wave wakefields. The density modulation turns on and off the injection of electrons at the period of the modulation. Due to the unique longitudinal mapping between the electrons' initial positions and their final trapped positions inside the wake, this results in an electron beam with density modulation at a wavelength orders of …
Magnetic reconnection is a universal process that powers explosive energy release events such as solar flares, geomagnetic substorms, and some astrophysical jets. A characteristic feature of magnetic reconnection is the production of fast reconnection outflow jets near the plasma Alfvén speeds. In eruptive solar flares, dark, finger-shaped plasma downflows moving toward the flare arcade have been commonly regarded as the principal observational evidence for such reconnection-driven outflows. However, they often show a speed much slower than that expected in reconnection theories, challenging t…
Laser pulses of extreme intensities ($I>10^{22}~ \mathrm{W/cm^2}$) are about to become available in the laboratory. The prepulse of such a laser can induce a plasma expansion that generates a low-density channel in near-critical gas jets. We present a study of channel formation and subsequent direct laser acceleration of electrons within the pre-formed channel. Radiation reaction affects the acceleration in several ways. It first interferes with the motion of the return current on the channel walls. In addition, it reduces the radial expelling efficiency of the transverse ponderomotive force, …
Advances in ultra-intense laser technology are enabling, for the first time, relativistic intensities at mid-infrared (mid-IR) wavelengths. Anticipating further experimental research in this domain, we present high-resolution two dimensional Particle-in-Cell (PIC) simulation results using the Large- Scale Plasma (LSP) code that explore intense mid-IR laser interactions with dense targets. We present the results of thirty PIC simulations over a wide range of intensities (0.03 < $a_0$ < 39) and wavelengths (λ =780 nm, 3 μm, and 10 μm). Earlier studies, limited to λ =780 nm and $a_0 \sim$ 1 [1, 2…
We report on the experimental studies of laser driven ion acceleration from double-layer target where a near-critical density target with a few-micron thickness is coated in front of a nanometer thin diamond-like carbon foil. A significant enhancement of proton maximum energies from 12 to ~30 MeV is observed when relativistic laser pulse impinge on the double-layer target under linear polarization. We attributed the enhanced acceleration to superponderomotive electrons that were simultaneously measured in the experiments with energies far beyond the free-electron ponderomotive limit. Our inter…
In addition to the ponderomotive acceleration of highly relativistic electrons at interaction of very short and very intense laser pulses, a further acceleration is derived from the interaction of these electron beams with the spontaneous magnetic fields of about 100 MG. This additional acceleration is the result of a laser-magnetic resonance acceleration (LMRA)[1] around the peak of the azimuthal magnetic field. This causes the electrons to gain energy within a laser period. Using a Gaussian laser pulse, the LMRA acceleration of the electrons depends on the laser polarization. Since this is i…
A planar laser pulse propagating in vacuum can exhibit an extremely large ponderomotive force. This force, however, cannot impart net energy to an electron: As the pulse overtakes the electron, the initial impulse from its rising edge is completely undone by an equal and opposite impulse from its trailing edge. Here we show that planar-like "flying focus" pulses can break this symmetry, imparting relativistic energies to electrons. The intensity peak of a flying focus-a moving focal point resulting from a chirped laser pulse focused by a chromatic lens-can travel at any subluminal velocity, fo…
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…
We show that under appropriate conditions the impact of a very short and intense laser pulse onto a plasma causes the expulsion of surface electrons with high energy in the direction opposite to the one of propagation of the pulse. This is due to the combined effects of the ponderomotive force and the huge longitudinal field arising from charge separation ("slingshot effect"). The effect should also be present with other states of matter, provided the pulse is sufficiently intense to locally cause complete ionization. An experimental test seems to be feasible and, if confirmed, would provide a…
We show through experiments that a transition from laser wakefield acceleration (LWFA) regime to a plasma wakefield acceleration (PWFA) regime can drive electrons up to energies close to the GeV level. Initially, the acceleration mechanism is dominated by the bubble created by the laser in the nonlinear regime of LWFA, leading to an injection of a large number of electrons. After propagation beyond the depletion length, leading to a depletion of the laser pulse, whose transverse ponderomotive force is not able to sustain the bubble anymore, the high energy dense bunch of electrons propagating …
We suggest a novel method for injection of electrons into the acceleration phase of particle accelerators, producing low emittance beams appropriate even for the demanding high energy Linear Collider specifications. In this paper we work out the injection into the acceleration phase of the wake field in a plasma behind a high intensity laser pulse, taking advantage of the laser polarization and focusing. With the aid of catastrophe theory we categorize the injection dynamics. The scheme uses the structurally stable regime of transverse wake wave breaking, when electron trajectory self-intersec…
