Ultrabright Electron Bunch Injection in a Plasma Wakefield Driven by a Superluminal Flying Focus Electron Beam

We propose a new method for self-injection of high-quality electron bunches in the plasma wakefield structure in the blowout regime utilizing a "flying focus" produced by a drive beam with an energy chirp. In a flying focus the speed of the density centroid of the drive bunch can be superluminal or subluminal by utilizing the chromatic dependence of the focusing optics. We first derive the focal velocity and the characteristic length of the focal spot in terms of the focal length and an energy chirp. We then demonstrate using multidimensional particle-in-cell simulations that a wake driven by a superluminally propagating flying focus of an electron beam can generate GeV-level electron bunches with ultralow normalized slice emittance (∼30  nm rad), high current (∼17  kA), low slice energy spread (∼0.1%), and therefore high normalized brightness (>10^{19}  A/m^{2}/rad^{2}) in a plasma of density ∼10^{19}  cm^{-3}. The injection process is highly controllable and tunable by changing the focal velocity and shaping the drive beam current. Near-term experiments at FACET II where the capabilities to generate tens of kA, <10  fs drivers are planned, could potentially produce beams with brightness near 10^{20}  A/m^{2}/rad^{2}.

Electron acceleration at oblique angles via stimulated Raman scattering at laser irradiance >10^{16}Wcm^{-2}μm^{2}

The generation of hot, directional electrons via laser-driven stimulated Raman scattering (SRS) is a topic of great importance in inertial confinement fusion (ICF) schemes. Little recent research has been dedicated to this process at high laser intensity, in which back, side, and forward scatter simultaneously occur in high energy density plasmas, of relevance to, for example, shock ignition ICF. We present an experimental and particle-in-cell (PIC) investigation of hot electron production from SRS in the forward and near-forward directions from a single speckle laser of wavelength λ_{0}=1.053μm, peak laser intensities in the range I_{0}=0.2-1.0×10^{17}Wcm^{-2} and target electron densities between n_{e}=0.3-1.6%n_{c}, where n_{c} is the plasma critical density. As the intensity and density are increased, the hot electron spectrum changes from a sharp cutoff to an extended spectrum with a slope temperature T=34±1keV and maximum measured energy of 350 keV experimentally. Multidimensional PIC simulations indicate that the high energy electrons are primarily generated from SRS-driven electron plasma wave phase fronts with k vectors angled ∼50^{∘} with respect to the laser axis. These results are consistent with analytical arguments that the spatial gain is maximized at an angle which balances the tendency for the growth rate to be larger for larger scattered light wave angles until the kinetic damping of the plasma wave becomes important. The efficiency of generated high energy electrons drops significantly with a reduction in either laser intensity or target electron density, which is a result of the rapid drop in growth rate of Raman scattering at angles in the forward direction.

Three-dimensional particle-in-cell modeling of parametric instabilities near the quarter-critical density in plasmas

The nonlinear regime of laser-plasma interactions including both two-plasmon decay (TPD) and stimulated Raman scattering (SRS) instabilities has been studied in three-dimensional (3D) particle-in-cell simulations with parameters relevant to the inertial confinement fusion (ICF) experiments. SRS and TPD develop in the same region in plasmas, and the generation of fast electrons can be described accurately with only the full model including both SRS and TPD. The growth of instabilities in the linear stage is found to be in good agreement with analytical theories. In the saturation stage the low-frequency density perturbations driven by the daughter waves of the SRS side scattering can saturate the TPD and consequently inhibit the fast-electron generation. The fast-electron flux in 3D modeling is up to an order of magnitude smaller than previously reported in 2D TPD simulations, bringing it close to the results of ICF experiments.

Role of Direct Laser Acceleration of Electrons in a Laser Wakefield Accelerator with Ionization Injection

We show the first experimental demonstration that electrons being accelerated in a laser wakefield accelerator operating in the forced or blowout regimes gain significant energy from both the direct laser acceleration (DLA) and the laser wakefield acceleration mechanisms. Supporting full-scale 3D particle-in-cell simulations elucidate the role of the DLA of electrons in a laser wakefield accelerator when ionization injection of electrons is employed. An explanation is given for how electrons can maintain the DLA resonance condition in a laser wakefield accelerator despite the evolving properties of both the drive laser and the electrons. The produced electron beams exhibit characteristic features that are indicative of DLA as an additional acceleration mechanism.

Formation of Ultrarelativistic Electron Rings from a Laser-Wakefield Accelerator

Ultrarelativistic-energy electron ring structures have been observed from laser-wakefield acceleration experiments in the blowout regime. These electron rings had 170-280 MeV energies with 5%-25% energy spread and ∼10  pC of charge and were observed over a range of plasma densities and compositions. Three-dimensional particle-in-cell simulations show that laser intensity enhancement in the wake leads to sheath splitting and the formation of a hollow toroidal pocket in the electron density around the wake behind the first wake period. If the laser propagates over a distance greater than the ideal dephasing length, some of the dephasing electrons in the second period can become trapped within the pocket and form an ultrarelativistic electron ring that propagates in free space over a meter-scale distance upon exiting the plasma. Such a structure acts as a relativistic potential well, which has applications for accelerating positively charged particles such as positrons.

Improving the self-guiding of an ultraintense laser by tailoring its longitudinal profile

Self-guiding of an ultraintense laser requires the refractive index to build up rapidly to a sufficient value before the main body of the pulse passes by. We show that placing a low-intensity precursor in front of the main pulse mitigates the diffraction of its leading edge and facilitates reaching a self-guided state that remains stable for more than 10 Rayleigh lengths. Furthermore, this precursor slows the phase slippage between the trapped electrons and the wakefield and leads to an accelerating structure that is more stable, contains more energy, and is sustained longer. Examples from three-dimensional particle-in-cell simulations show that the conversion efficiency from the laser to the self-trapped electrons increases by an order of magnitude when using the precursor.

Anomalously hot electrons due to rescatter of stimulated Raman scattering in the kinetic regime

Using particle-in-cell simulations, we examine hot electron generation from electron plasma waves excited by stimulated Raman scattering and rescattering in the kinetic regime where the wave number times the Debye length (kλ(D)) is >/~0.3 for backscatter. We find that for laser and plasma conditions of possible relevance to experiments at the National Ignition Facility, anomalously energetic electrons can be produced through the interaction of a discrete spectrum of plasma waves generated from stimulated Raman scattering (back and forward scatter), rescatter, and the Langmuir decay of the rescatter-generated plasma waves. Electrons are bootstrapped in energy as they propagate into plasma waves with progressively higher phase velocities.

Generating energetic electrons through staged acceleration in the two-plasmon-decay instability in inertial confinement fusion

A new hot-electron generation mechanism in two-plasmon-decay instabilities is described based on a series of 2D, long-term (~10 ps) particle-in-cell and fluid simulations under parameters relevant to inertial confinement fusion. The simulations show that significant laser absorption and hot-electron generation occur in the nonlinear stage. The hot electrons are stage accelerated from the low-density region to the high-density region. New modes with small phase velocities develop in the low-density region in the nonlinear stage and form the first stage for electron acceleration. Electron-ion collisions are shown to significantly reduce the efficiency of this acceleration mechanism.

Self-guided laser wakefield acceleration beyond 1 GeV using ionization-induced injection

The concepts of matched-beam, self-guided laser propagation and ionization-induced injection have been combined to accelerate electrons up to 1.45 GeV energy in a laser wakefield accelerator. From the spatial and spectral content of the laser light exiting the plasma, we infer that the 60 fs, 110 TW laser pulse is guided and excites a wake over the entire 1.3 cm length of the gas cell at densities below 1.5 × 10(18) cm(-3). High-energy electrons are observed only when small (3%) amounts of CO2 gas are added to the He gas. Computer simulations confirm that it is the K-shell electrons of oxygen that are ionized and injected into the wake and accelerated to beyond 1 GeV energy.

Effects of plasma wave packets and local pump depletion in stimulated Raman scattering

Through one-dimensional and two-dimensional (2D) particle-in-cell simulations of stimulated Raman scattering (SRS), we show that nonlinear plasma wave packets that are created during SRS and convect through the system after saturation can have a dramatic effect on the recurrence of the instability. The recurrence rate is shown to depend on the propagation speed and frequency content of these packets. Furthermore, SRS can be driven to higher amplitudes via backscattered light traveling between packets. In 2D, the influence of the plasma wave packets is also seen, but the average reflectivity is substantially less due to geometric effects and transverse localization of the packets.

Growth and saturation of convective modes of the two-plasmon decay instability in inertial confinement fusion

Particle-in-cell (PIC) and fluid simulations of two-plasmon decay (TPD) instability under conditions relevant to inertial confinement fusion show the importance of convective modes. Growing at the lower density region, the convective modes can cause pump depletion and are energetically dominant in the nonlinear stage. The PIC simulations show that TPD saturates due to ion density fluctuations, which can turn off TPD by raising the instability threshold through mode coupling.

Beam loading in the nonlinear regime of plasma-based acceleration

A theory that describes how to load negative charge into a nonlinear, three-dimensional plasma wakefield is presented. In this regime, a laser or an electron beam blows out the plasma electrons and creates a nearly spherical ion channel, which is modified by the presence of the beam load. Analytical solutions for the fields and the shape of the ion channel are derived. It is shown that very high beam-loading efficiency can be achieved, while the energy spread of the bunch is conserved. The theoretical results are verified with the particle-in-cell code OSIRIS.

Observation of synchrotron radiation from electrons accelerated in a petawatt-laser-generated plasma cavity

The dynamics of plasma electrons in the focus of a petawatt laser beam are studied via measurements of their x-ray synchrotron radiation. With increasing laser intensity, a forward directed beam of x rays extending to 50 keV is observed. The measured x rays are well described in the synchrotron asymptotic limit of electrons oscillating in a plasma channel. The critical energy of the measured synchrotron spectrum is found to scale as the Maxwellian temperature of the simultaneously measured electron spectra. At low laser intensity transverse oscillations are negligible as the electrons are predominantly accelerated axially by the laser generated wakefield. At high laser intensity, electrons are directly accelerated by the laser and enter a highly radiative regime with up to 5% of their energy converted into x rays.

Laser-wakefield acceleration of monoenergetic electron beams in the first plasma-wave period

Beam profile measurements of laser-wakefield accelerated electron bunches reveal that in the monoenergetic regime the electrons are injected and accelerated at the back of the first period of the plasma wave. With pulse durations ctau >or= lambda(p), we observe an elliptical beam profile with the axis of the ellipse parallel to the axis of the laser polarization. This increase in divergence in the laser polarization direction indicates that the electrons are accelerated within the laser pulse. Reducing the plasma density (decreasing ctau/lambda(p)) leads to a beam profile with less ellipticity, implying that the self-injection occurs at the rear of the first period of the plasma wave. This also demonstrates that the electron bunches are less than a plasma wavelength long, i.e., have a duration <25 fs. This interpretation is supported by 3D particle-in-cell simulations.

Space-charge effects in the current-filamentation or Weibel instability

We consider how an unmagnetized plasma responds to an incoming flux of energetic electrons. We assume a return current is present and allow for the incoming electrons to have a different transverse temperature than the return current. To analyze this configuration we present a nonrelativistic theory of the current-filamentation or Weibel instability for rigorously current-neutral and nonseparable distribution functions, f(0)(p(x), p(y), p(z)) is not equal to f(x)(p(x))f(y)(p(y))f(z)(p(z)). We find that such distribution functions lead to lower growth rates because of space-charge forces that arise when the forward-going electrons pinch to a lesser degree than the colder, backward-flowing electrons. We verify the growth rate, range of unstable wave numbers, and the formation of the density filaments using particle-in-cell simulations.

Global simulation for laser-driven MeV electrons in fast ignition

A comprehensive examination of the interaction of a picosecond-long ignition pulse on high-density (40 times critical density) pellets using a two-dimensional particle-in-cell model is described. The global geometry consists of a 50 mum diameter pellet surrounded by a corona which is isolated by a vacuum region from the boundary. For cone-attached targets, as much as 67% of the incident laser energy is absorbed with 12% sent forward as fast electrons in a 23 degrees cone. The current filaments are driven by the Weibel instability of the forward-going fast electron flux and its return current with the ions playing an important role of neutralizing the space charge. No global current filament coalescence has been observed. The electron distribution function obeys a power law, which begins at E approximately 0.2 MeV and falls off as E-(2-3).

Near-GeV-energy laser-wakefield acceleration of self-injected electrons in a centimeter-scale plasma channel

The first three-dimensional, particle-in-cell (PIC) simulations of laser-wakefield acceleration of self-injected electrons in a 0.84 cm long plasma channel are reported. The frequency evolution of the initially 50 fs (FWHM) long laser pulse by photon interaction with the wake followed by plasma dispersion enhances the wake which eventually leads to self-injection of electrons from the channel wall. This first bunch of electrons remains spatially highly localized. Its phase space rotation due to slippage with respect to the wake leads to a monoenergetic bunch of electrons with a central energy of 0.26 GeV after 0.55 cm propagation. At later times, spatial bunching of the laser enhances the acceleration of a second bunch of electrons to energies up to 0.84 GeV before the laser pulse intensity is significantly reduced.

Monoenergetic beams of relativistic electrons from intense laser-plasma interactions

High-power lasers that fit into a university-scale laboratory can now reach focused intensities of more than 10(19) W cm(-2) at high repetition rates. Such lasers are capable of producing beams of energetic electrons, protons and gamma-rays. Relativistic electrons are generated through the breaking of large-amplitude relativistic plasma waves created in the wake of the laser pulse as it propagates through a plasma, or through a direct interaction between the laser field and the electrons in the plasma. However, the electron beams produced from previous laser-plasma experiments have a large energy spread, limiting their use for potential applications. Here we report high-resolution energy measurements of the electron beams produced from intense laser-plasma interactions, showing that--under particular plasma conditions--it is possible to generate beams of relativistic electrons with low divergence and a small energy spread (less than three per cent). The monoenergetic features were observed in the electron energy spectrum for plasma densities just above a threshold required for breaking of the plasma wave. These features were observed consistently in the electron spectrum, although the energy of the beam was observed to vary from shot to shot. If the issue of energy reproducibility can be addressed, it should be possible to generate ultrashort monoenergetic electron bunches of tunable energy, holding great promise for the future development of 'table-top' particle accelerators.

Dynamics of a supersonic plume moving along a magnetized plasma

A particle-in-cell code is used to investigate the evolution of a density plume moving through a background plasma with supersonic speed directed along the confinement magnetic field. For scale lengths representative of laboratory and auroral phenomena, the major nonlinear effects identified by the present simulations are the formation of a bipolar current system from the ballistic electrons, the appearance of transient potential layers, and the carving of deep density cavities. A 3D magnetic topology is generated by the self-consistent ballistic and diamagnetic currents that accompany highly localized potential layers.

Generation of ultra-intense single-cycle laser pulses by using photon deceleration

A scheme to generate single-cycle laser pulses is presented based on photon deceleration in underdense plasmas. This robust and tunable process is ideally suited for lasers above critical power because it takes advantage of the relativistic self-focusing of these lasers and the nonlinear features of the plasma wake. The mechanism is demonstrated by particle-in-cell simulations in three and 2(1/2) dimensions, resulting in pulse shortening up to a factor of 4, thus making it feasible to generate few-femtosecond single-cycle pulses in the optical to IR domain with intensities I > 10(20) W/cm(2) by using present-day laser technology.

Learning in recurrent finite difference networks

A recurrent learning algorithm based on a finite difference discretization of continuous equations for neural networks is derived. This algorithm has the simplicity of discrete algorithms while retaining some essential characteristics of the continuous equations. In discrete networks learning smooth oscillations is difficult if the period of oscillation is too large. The network either grossly distorts the waveforms or is unable to learn at all. We show how the finite difference formulation can explain and overcome this problem. Formulas for learning time constants and time delays in this framework are also presented.