Advanced strategies for ion acceleration using high power lasers
A. Macchi, A. Sgattoni, S. Sinigardi, M. Borghesi, M. Passoni
备注：
Invited paper from plenary talk at the 40th European Physical Society Conference on Plasma Physics (Espoo, Finland, July 1-5, 2013). To be submitted to Plasma Physics and Controlled Fusion (special EPS issue). 4 figures. 2nd version implements corrections
A short overview of laser-plasma acceleration of ions is presented. The focus is on some recent experimental results and related theoretical work on advanced regimes. These latter include in particular target normal sheath acceleration using ultrashort low-energy pulses and structured targets, radiation pressure acceleration of both thick and ultrathin targets, and collisionless shock acceleration in moderate density plasmas. For each approach, open issues and the need and potential for further developments are briefly discussed.
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 present an analytical theory that reveals the importance of the longitudinal laser electric field in the resonant acceleration of relativistic electrons by the tightly confined laser beam. It is shown that this field always counterworks to the laser transverse component and effectively decreases the final energy gain of electrons through direct laser acceleration mechanism. This effect is demonstrated by carrying out the particle-in-cell simulations in the setup where the wakefield in the plasma bubble is compensated by the longitudinal laser electric field experienced by the accelerated el…
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…
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 concept of a hybrid laser wakefield/direct laser plasma accelerator is proposed. Relativistic electrons undergoing resonant betatron oscillations inside the plasma bubble created by a laser pulse are accelerated by gaining energy directly from the laser pulse and from its plasma wake. The resulting bifurcated phase space of self-injected plasma electrons contains a population that experiences wakefield acceleration beyond the standard one-dimensional limit because of the multi-dimensional nature of its motion that reduces the phase slippage between the electrons and the wake.
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…
Laser ion acceleration is a promising concept for generation of fast ions using a compact laser-solid interaction setup. In this study, we theoretically investigate the feasibility of ion acceleration from the interaction of petawatt-scale laser pulses with a structured target that embodies a micron-scale channel filled with relativistically transparent plasma. Using 2D and 3D Particle-In-Cell (PIC) simulations and theoretical estimates, we show that it is possible to generate GeV protons with high volumetric charge and quasi-monoenergetic feature in the energy spectrum. We interpret the accel…
We propose a new approach to high-intensity laser-driven electron acceleration in a plasma. Here, we demonstrate that a plasma wave generated by a stimulated forward-scattering of an incident laser pulse can be in a longest acceleration phase with an incident laser wave. This is why the plasma wave has the maximum amplification coefficient which is determined by the breakdown (overturn) electric field in which the acceleration of injected relativistic beam electrons occurs. We estimate qualitatively the acceleration parameters of relativistic electrons in the field of a plasma wave generated a…
An experimental study on 55fs laser driven plasma accelerator using mixed gas-jet target with varying plasma density is used to identify the role of different acceleration mechanisms, viz. Direct Laser Acceleration (DLA) and wakefield. At lower electron density electron acceleration could be attributed mainly to DLA with ionization induced injection. With increase in density, increasing role of wakefield was observed leading to hybrid regime, and at densities higher than self-injection threshold, observed experimentally for He target contribution of DLA and wakefield was found to be comparable…
We demonstrate that hybrid laser wakefield and direct acceleration (LWDA) can be significantly improved by using two laser pulses with different polarizations or frequencies. The improvement entails higher energy and charge of the accelerated electrons, as well as weaker sensitivity to the time delay between the leading (pump) pulse responsible for generating the wakefield, and the trailing laser pulse responsible for direct laser acceleration (DLA). When the two laser pulses have the same frequency, it is shown that it is advantageous to have their polarization states orthogonal to each other…
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.
An approach using topology reveals a new understanding and knowledge of laser particle acceleration. Laser pulse irradiation on a thin-foil target is examined using two-dimensional particle-in-cell simulations. Through topology, laser ion acceleration schemes are classified depending on whether the deformed target shape after laser irradiation is homeomorphic with respect to the initial target. High energy ions are generated with high-efficiency when the deformed target shape is non-homeomorphic. In this case, the target thickness greatly affects the obtained ion energy. However, when the defo…
In this work, we will show through three-dimensional particle-in-cell simulations that direct laser acceleration in laser a wakefield accelerator can generate sub-femtosecond electron bunches. Two simulations were done with two laser pulse durations, such that the shortest laser pulse occupies only a fraction of the first bubble, whereas the longer pulse fills the entire first bubble. In the latter case, as the trapped electrons moved forward and interacted with the high intensity region of the laser pulse, micro-bunching occurred naturally, producing 0.5 fs electron bunches. This is not obser…
The excitation of nonlinear electrostatic waves, such as shock and solitons, by ultraintense laser interaction with overdense plasmas and related ion acceleration are investigated by numerical simulations. Stability of solitons and formation of shock waves is strongly dependent on the velocity distribution of ions. Monoenergetic components in ion spectra are produced by "pulsed" reflection from solitary waves. Possible relevance to recent experiments on "shock acceleration" is discussed.
We propose a new approach to high-intensity relativistic laser-driven electron acceleration in a plasma. Here, we demonstrate that a plasma wave generated by a stimulated forward-scattering of an incident laser pulse can be in the longest acceleration phase with injected relativistic beam electrons. This is why the plasma wave has the maximum amplification coefficient which is determined by the acceleration time and the breakdown (overturn) electric field in which the acceleration of the injected beam electrons occurs. We must note that for the longest acceleration phase the relativity of the …
In this proceeding, we show that when the drive laser pulse overlaps the trapped electrons in a laser wakefield accelerator (LWFA), those electrons can gain energy from direct laser acceleration (DLA) over extended distances despite the evolution of both the laser and the wake. Through simulations, the evolution of the properties of both the laser and the electron beam is quantified, and then the resonance condition for DLA is examined in the context of this change. We find that although the electrons produced from the LWFA cannot continuously satisfy the DLA resonance condition, they neverthe…
A scenario for the enhanced laser-driven ion acceleration from a thin solid target at high laser intensity is considered, where the target is enclosed in a reflecting cavity. The laser pulse reflected from the target is redirected towards the target by reflection at the inner cavity wall. This scenario is discussed in the context of sub-wavelength foil acceleration in the radiation pressure regime, when plasma dynamics is known to be reasonably well described by the light-sail model. A semi-analytic formula is presented that describes the effect of cavity reflections in one-dimensional geometr…
For the laser wakefield acceleration, suppression of beam energy spread while keeping sufficient charge is one of the key challenges. In order to achieve this, we propose bichromatic laser ionization injection with combined laser wavelengths of $2.4\rm μm$ and $0.8\rm μm$ for wakefield excitation and for triggering electron injection via field ionization, respectively. A laser pulse at $2.4\rm μm$ wavelength enables one to drive an intense acceleration structure with relatively low laser power. To further reduce the requirement of laser power, we also propose to use carbon dioxide as the worki…
As one of the leading acceleration mechanisms in laser-driven underdense plasmas, direct laser acceleration (DLA) is capable of producing high-energy-density electron beams in a plasma channel for many applications. However, the mechanism relies on highly nonlinear particle-laser resonances, rendering its modeling and control to be very challenging. Here, we report on novel physics of the particle resonances and, based on that, define a potential path toward more controlled DLA. Key findings are acquired by treating the electron propagation angle independently within a comprehensive model. Thi…
Particle energy chirp is shown to be a useful instrument in the staging laser wake field acceleration directed to generation of high-quality dense electron beams. The chirp is a necessary tool to compensate non-uniformity of acceleration field in longitudinal direction and achieve essential reduction of energy dispersion. This is demonstrated via particle-in-cell simulations exploiting the splitting technique for plasma and beam electrons. Properly chosen beam chirps allow decrease in the energy dispersion of order of magnitude in every single stage during acceleration to the GeV energy range.
A remarkable ion energy increase is demonstrated by several-stage post-acceleration in a laser plasma interaction. Intense short-pulse laser generates a strong current by high-energy electrons accelerated, when an intense short-pulse laser illuminates a plasma target. The strong electric current creates a strong magnetic field along the high-energy electron current in plasma. During the increase phase of the magnetic field, the longitudinal inductive electric field is induced for the forward ion acceleration by the Faraday law. The inductive acceleration and the target-normal sheath accelerati…
Relativistic laser wakefield acceleration is characterized by an unsurpassed accelerating gradient, which is very suitable for electron acceleration over short distances and could be a promising candidate for next-generation compact accelerators. However, using this technique for positron acceleration is still challenging because positively charged particles are naturally defocused in nonlinear wakefields. Here we propose and numerically demonstrate a scheme to accelerate an externally injected positron beam in a nonlinear laser wakefield in a regime where a tail wave is formed behind density …
The acceleration of ions in the interaction of high intensity laser pulses with overdense plasmas is investigated with particle-in-cell simulations. For circular polarization of the laser pulses, high-density ion bunches moving into the plasma are generated at the laser-plasma interaction surface. A simple analytical model accounts for the numerical observations and provides scaling laws for the ion bunch energy and generation time as a function of pulse intensity and plasma density.
The experimental study of the plasma projectile acceleration in the laser-induced cavity pressure acceleration (LICPA) scheme is reported. In the experiment performed at the kilojoule PALS laser facility, the parameters of the projectile were measured using interferometry, a streak camera and ion diagnostics, and the measurements were supported by two-dimensional hydrodynamic simulations. It is shown that in the LICPA accelerator with a 200-J laser driver, a 4 microgram gold plasma projectile is accelerated to the velocity of 140 km/s with the energetic acceleration efficiency of 15-19 percent…
Theoretical study of heavy ion acceleration from ultrathin (<200 nm) gold foils irradiated by a short pulse laser is presented. Using two dimensional particle-in-cell simulations the time history of the laser bullet is examined in order to get insight into the laser energy deposition and ion acceleration process. For laser pulses with intensity , duration 32 fs, focal spot size 5 mkm and energy 27 Joules the calculated reflection, transmission and coupling coefficients from a 20 nm foil are 80 %, 5 % and 15 %, respectively. The conversion efficiency into gold ions is 8 %. Two highly collimated…
We consider the Directed Coulomb Explosion regime of ion acceleration from ultra-thin double layer (high Z/low Z) mass limited targets. In this regime the laser pulse evacuated the electrons from the irradiated spot and accelerates the remaining ion core in the direction of the laser pulse propagation. Then the moving ion core explodes due to the excess of positive charge forming a moving charge separation field that accelerates protons from the second layer. The utilization of the mass limited targets increases the effectiveness of the acceleration. It is also shown that different parameters …
Theoretical study of heavy ion acceleration from an ultrathin (20 nm) gold foil irradiated by sub-picosecond lasers is presented. Using two dimensional particle-in-cell simulations we identified two highly efficient ion acceleration schemes. By varying the laser pulse duration we observed a transition from Radiation Pressure Acceleration to the Breakout Afterburner regime akin to light ions. The underlying physics and ion acceleration regimes are similar to that of light ions, however, nuances of the acceleration process make the acceleration of heavy ions more challenging. Two laser systems a…
The radiation pressure acceleration (RPA) of charged particles has been considered a challenging task in laser particle acceleration. Laser-driven proton/ion acceleration has attracted considerable interests due to its underlying physics and potential for applications such as high-energy density physics, ultrafast radiography, and cancer therapy. Among critical issues to overcome the biggest challenge is to produce energetic protons using an efficient acceleration mechanism. The proton acceleration by radiation pressure is considerably more efficient than the conventional target normal sheath …
A short overview of the theory of acceleration of thin foils driven by the radiation pressure of superintense lasers is presented. A simple criterion for radiation pressure dominance at intensities around $5 \times 10^{20} \mbox{W cm}^{-2}$ is given, and the possibility for fast energy gain in the relativistic regime is discussed.
The characteristics of a MeV ion source driven by superintense, ultrashort laser pulses with circular polarization are studied by means of particle-in-cell simulations. Predicted features include high efficiency, large ion density, low divergence and the possibility of femtosecond duration. A comparison with the case of linearly polarized pulses is made.
Propagation of short and ultra-intense laser pulses in a semi-infinite space of overdense hydrogen plasma is analyzed via fully-relativistic, real geometry particle-in-cell (PIC) simulations including radiation friction. The relativistic transparency and hole-boring regimes are found to be sensitive to the transverse plasma field, backward light reflection, and laser pulse filamentation. For laser intensities approaching $I\sim10^{24}$ W/cm$^2$ the direct laser acceleration of protons, along with ion Coulomb explosion, results in their injection into the acceleration phase of the compressed el…
In the effort of achieving high-energetic ion beams from the interaction of ultrashort laser pulses with a plasma, volumetric acceleration mechanisms beyond Target Normal Sheath Acceleration have gained attention. A relativisticly intense laser can turn a near critical density plasma slowly transparent, facilitating a synchronized acceleration of ions at the moving relativistic critical density front. While simulations promise extremely high ion energies in in this regime, the challenge resides in the realization of a synchronized movement of the ultra-relativistic laser pulse ($a_0\gtrsim 30$…
We demonstrate that electrons can be efficiently accelerated to high energy in spatially non-uniform, intense laser fields. Laser non-uniformities occur when a perfect plane wave reflects off a randomly perturbed surface. By solving for three-dimensional particle trajectories in the electromagnetic field of a randomly perturbed laser, we are able to generate electron energy spectra with temperatures well above the ponderomotive scaling, as observed in many experiments. The simulations show that high electron energies can be achieved by the laser fields alone, without the need for plasma fields…
We report a laser wakefield acceleration of electron beams up to 130 MeV from laser-driven 4-mm long nitrogen gas jet. By using a moderate laser intensity (3.5*10^18 W.cm^(-2)) and relatively low plasma densities (0.8*10^18 cm^(-3) to 2.7*10^18 cm^(-3)) we have achieved a stable regime for laser propagation and consequently a stable generation of electron beams. We experimentally studied the dependence of the drive laser energy on the laser-plasma channel and electron beam parameters. The quality of the generated electron beams is discussed within the framework of the ionization-induced inject…
A new electron acceleration mechanism is identified that develops when a relativistically intense laser irradiates the wedge of an over-dense plasma. This induces a diffracted electromagnetic wave with a significant longitudinal electric field that accelerates electrons from the plasma over long distances to relativistic energies. Well collimated, highly-charged (nC) electron bunches with energies up to 100's MeV are obtained using a laser beam with $I λ_0^2 =3.5\times 10^{19}\,{\rm W μm^2/cm^2}$. Multi-dimensional particle-in-cell simulations, supported by a simple analytical model, confirm t…
Accelerating particles to relativistic energies over very short distances using lasers has been a long standing goal in physics. Among the various schemes proposed for electrons, vacuum laser acceleration has attracted considerable interest and has been extensively studied theoretically because of its appealing simplicity: electrons interact with an intense laser field in vacuum and can be continuously accelerated, provided they remain at a given phase of the field until they escape the laser beam. But demonstrating this effect experimentally has proved extremely challenging, as it imposes str…
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…
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, …
A new analytical approach for bubble deformation was used for optimization of the electron acceleration in the 3D highly nonlinear laser wake-field regime. Injection of the electron bunch with initial velocity in the bubble was considered in the inhomogeneous plasma with linearly density ramp. The researchers show that deformation of the bubble shape has an efficient role on the trapping of the electrons in the acceleration region. The influence of the linearly density ramp on the electron bunch trapping ratio and its mean energy was considered by the numerical method.
Ion acceleration driven by superintense laser pulses is attracting an impressive and steadily increasing effort. Motivations can be found in the potential for a number of foreseen applications and in the perspective to investigate novel regimes as far as available laser intensities will be increasing. Experiments have demonstrated in a wide range of laser and target parameters the generation of multi-MeV proton and ion beams with unique properties such as ultrashort duration, high brilliance and low emittance. In this paper we give an overview of the state-of-the art of ion acceleration by las…
We explore the physics of electron acceleration in a plasma medium in an effective field theory framework. Employing a multiple Compton scattering mechanism, it is found that the acceleration can be sustained in such a medium so as to attain the energies up to the order of $O(100 \rm{MeV})$ within a centimeter. Also, the collimation and mono-energetic electron spectrum can be obtained by proper tuning of the plasma parameters with the photon frequency. The present work is potentially useful in understanding the physics of laser-plasma accelerators.
Scaling laws of ion acceleration in ultrathin foils driven by radiation pressure of intense laser pulses are investigated by theoretical analysis and two-dimensional particle-in-cell simulations. Considering the instabilities are inevitable during laser plasma interaction, the maximum energy of ions should have two contributions: the bulk acceleration driven by radiation pressure and the sheath acceleration in the moving foil reference induced by hot electrons. A theoretical model is proposed to quantitatively explain the results that the cutoff energy and energy spread are larger than the pre…
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…
We show analytically and through three-dimensional particle-in-cell simulations that non-linear wakefields driven by Laguerre-Gaussian laser pulses can lead to hollow electron self-injection and positron acceleration. We find that higher order lasers can drive donut shaped blowout wakefields with strong positron accelerating gradients comparable to those of a spherical bubble. Corresponding positron focusing forces can be more than an order of magnitude stronger than electron focusing forces in a spherical bubble. Required laser intensities and energies to reach the non-linear donut shaped blo…
We analyze the motion of the plasma critical layer by two different processes in the relativistic-electron laser-plasma interaction regime ($a_0>1$). The differences are highlighted when the critical layer ions are stationary in contrast to when they move with it. Controlling the speed of the plasma critical layer in this regime is essential for creating low-$β$ traveling acceleration structures of sufficient laser-excited potential for laser ion accelerators (LIA). In Relativistically Induced Transparency Acceleration (RITA) scheme the heavy plasma-ions are fixed and only trace-density light-…
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.
Particle-in-cell (PIC) simulation results of sustained acceleration of electron-positron (e+e-) plasmas by comoving electromagnetic (EM) pulses are presented. When a thin slab of overdense e+e- plasma is irradiated with linear-polarized ultra-intense short laser pulses from both sides, the pulses are transmitted when the plasma is compressed to thinner than ~ 2 relativistic skin depths. A fraction of the plasma is then captured and efficiently accelerated by self-induced JxB forces. For 1 micron laser and 1021Wcm-2 intensity, the maximum energy exceeds GeV in a picosecond.
We have investigated the role that the transverse electric field of the laser plays in the acceleration of electrons in a laser wakefield accelerator (LWFA) operating in the quasi-blowout regime through particle-in-cell code simulations. In order to ensure that longitudinal compression and/or transverse focusing of the laser pulse is not needed before the wake can self-trap the plasma electrons, we have employed the ionization injection technique. Furthermore, the plasma density is varied such that at the lowest densities, the laser pulse occupies only a fraction of the first wavelength of the…
In the Coulomb explosion acceleration regime, an ion bunch with a narrow energy range exhibits a thin shell shape with a certain diameter. The ion cloud has a layered structure of these ion bunches with different energies. The divergences of the ion bunch in the laser inclination direction and perpendicular to it are different in an oblique incidence laser. This indicates that the smaller the spot diameter of the laser pulse, the larger the divergence of the ion beam. In addition, theoretical formulas for the radius of the generated ion beam and the energy spectrum are derived, and they are sh…
While laser-plasma accelerators have demonstrated a strong potential in the acceleration of electrons up to giga-electronvolt energies, few experimental tools for studying the acceleration physics have been developed. In this paper, we demonstrate a method for probing the acceleration process. A second laser beam, propagating perpendicular to the main beam is focused in the gas jet few nanosecond before the main beam creates the accelerating plasma wave. This second beam is intense enough to ionize the gas and form a density depletion which will locally inhibit the acceleration. The position o…
A method based on laser wakefield acceleration with controlled ionization injection triggered by another frequency-tripled laser is proposed, which can produce electron bunches with low energy spread. As two color pulses co-propagate in the background plasma, the peak amplitude of the combined laser field is modulated in time and space during the laser propagation due to the plasma dispersion. Ionization injection occurs when the peak amplitude exceeds certain threshold. The threshold is exceeded for limited duration periodically at different propagation distances, leading to multiple ionizati…
We present a setup for highly polarized proton beams using two parallel propagating laser pulses that have a carrier envelope phase difference of $π$. This mechanism is examined utilizing particle-in-cell simulations and compared to a single-pulse setup commonly used for magnetic vortex acceleration. We find that the use of the dual-pulse setup allows for peak energies of 124 MeV and good angular spread for two pulses with normalized laser vector potential $a_0 = 100$. Compared to a single pulse, we further observe higher polarization of the accelerated bunch.
High frequency modulations appearing in the kinetic energy distribution of laser accelerated ions are proposed for retrieving the acceleration field dynamics at femtosecond time scale. Such an approach becomes possible if the laser-cycling field modulates the particle density in the ion spectra and produces quasi time stamps for analysis. We investigate target and laser parameters determining this effect and discuss the dependencies of the observed modulation. Our findings refine a basic mechanism, the Target Normal Sheath Acceleration, where an intense and ultrafast laser pulse produces a ver…
