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We demonstrate through high-fidelity particle-in-cell simulations a simple approach for efficiently generating 20+ GeV electron beams with the necessary charge, energy spread, and emittance for use as the injector for an electron arm of a future linear collider or a next generation XFEL. The self-focusing of an unmatched, relatively low quality, drive beam results in self-injection by elongating the wakefield excited in the nonlinear blowout regime. Over pump depletion distances, the drive beam dynamics and self-loading from the injected beam leads to extremely high quality and high energy output beams. For plasma densities of $10^{18} \ \text{cm}^{-3}$, PIC simulation results indicate that self-injected beams with $0.52 \ \text{nC}$ of charge can be accelerated to $\sim 20$ GeV energies with projected energy spreads, $\lesssim 1\%$ within the beam core, slice normalized emittances as low as $110 \ \text{nm}$, a peak normalized brightness $\gtrsim 10^{19} \ \text{A}/\text{m}^2/\text{rad}^2$, and energy transfer efficiencies $\gtrsim 54\%$.

This study documents several correlations observed during the first run of the plasma wakefield acceleration experiment E300 conducted at FACET-II, using a single drive electron bunch. The established correlations include those between the measured maximum energy loss of the drive electron beam and the integrated betatron x-ray signal, the calculated total beam energy deposited in the plasma and the integrated x-ray signal, among three visible light emission measuring cameras, and between the visible plasma light and x-ray signal. The integrated x-ray signal correlates almost linearly with both the maximum energy loss of the drive beam and the energy deposited into the plasma, demonstrating its usability as a measure of energy transfer from the drive beam to the plasma. Visible plasma light is found to be a useful indicator of the presence of wake at three locations that overall are two meters apart. Despite the complex dynamics and vastly different timescales, the x-ray radiation from the drive bunch and visible light emission from the plasma may prove to be effective non-invasive diagnostics for monitoring the energy transfer from the beam to the plasma in future high-repetition-rate experiments., Comment: 20 pages, 6 figures

The emergence of multi-petawatt laser facilities is expected to push forward the maximum energy gain that can be achieved in a single stage of a LWFA to tens of GeV, which begs the question - is it likely to impact particle physics by providing a truly compact particle collider? Colliders have very stringent requirements on beam energy, acceleration efficiency and beam quality. In this article, we propose a LWFA scheme that can for the first time simultaneously achieve hitherto unrealized acceleration efficiency from the laser to the electron beam of >20% and a sub-one percent energy spread using a stepwise plasma structure and a nonlinearly chirped laser pulse. Three-dimensional high-fidelity simulations show that the nonlinear chirp can effectively mitigate the laser waveform distortion and lengthen the acceleration distance. This combined with an inter-stage rephasing process in the stepwise plasma can triple the beam energy gain compared to that in a uniform plasma for a fixed laser energy thereby dramatically increasing the efficiency. A dynamic beam loading effect can almost perfectly cancel the energy chirp that arises during the acceleration, leading to the sub-percent energy spread. This scheme is highly scalable and can be applied to peta-watt LWFA scenarios. Scaling laws are obtained that suggest electron beams with energy gain of >100 GeV, charge of 2 nC, and with an energy spread <1% can be realized with a high laser pulse to particle beam energy transfer efficiency in a LWFA driven by a peta-watt laser, which could be the basis for a proof of concept of one arm of a future electron-positron collider.

Intense spatial or spatiotemporal vortex pulses from the extreme ultraviolet to soft X-ray spectral windows are expected to provide new degrees of freedom for a variety of key applications since they carry longitudinal or transverse orbital angular momentum (OAM), respectively. Plasma-based high harmonic generation driven by a near-infrared spatial or spatiotemporal optical vortex offers a promising route to such novel light sources. However, the energy conversion efficiency from the incident vortex beam to the vortex harmonics is rather low because of the limited driving intensities available in practice. Here, we propose and demonstrate through simulations that by adding a readily available relativistic Gaussian pump beam as a source of energy, the energy conversion efficiency can be increased by several orders of magnitude. In addition, the proposed scheme allows independent control over the frequency and OAM of the vortex harmonics.

The past decade has seen tremendous progress in the production and utilization of vortex and vector laser pulses. Although both are considered as structured light beams, the vortex lasers have helical phase fronts and phase singularities, while the vector lasers have spatially variable polarization states and polarization singularities. In contrast to the vortex pulses that carry orbital angular momentum (OAM), the vector laser pulses have a complex spin angular momentum (SAM) and OAM coupling. Despite many potential applications enabled by such pulses, the generation of high-power/-intensity vortex and vector beams remains challenging. Here, we demonstrate using theory and three-dimensional simulations that the strongly-coupled stimulated Brillouin scattering (SC-SBS) process in plasmas can be used as a promising amplification technique with up to 65% energy transfer efficiency from the pump beam to the seed beam for both vortex and vector pulses. We also show that SC-SBS is strongly polarization-dependent in plasmas, enabling an all-optical polarization control of the amplified seed beam. Additionally, the interaction of such structured lasers with plasmas leads to various angular momentum couplings and decouplings that produce intense new light structures with controllable OAM and SAM. This scheme paves the way for novel optical devices such as plasma-based amplifiers and light field manipulators.

Laser wakefield accelerators (LWFAs) have electric fields that are orders of magnitude larger than those of conventional accelerators, promising an attractive, small-scale alternative for next-generation light sources and lepton colliders. The maximum energy gain in a single-stage LWFA is limited by dephasing, which occurs when the trapped particles outrun the accelerating phase of the wakefield. Here, we demonstrate that a single space-time structured laser pulse can be used for ionization injection and electron acceleration over many dephasing lengths in the bubble regime. Simulations of a dephasingless laser wakefield accelerator driven by a 6.2-J laser pulse show 25 pC of injected charge accelerated over 20 dephasing lengths (1.3 cm) to a maximum energy of 2.1 GeV. The space-time structured laser pulse features an ultrashort, programmable-trajectory focus. Accelerating the focus, reducing the focused spot-size variation, and mitigating unwanted self-focusing stabilize the electron acceleration, which improves beam quality and leads to projected energy gains of 125 GeV in a single, sub-meter stage driven by a 500-J pulse., Comment: 18 pages, 4 figures

The quality of electron beams produced from plasma-based accelerators, i.e., normalized brightness and energy spread, has made transformative progress in the past several decades in both simulation and experiment. Recently, full-scale particle-in-cell (PIC) simulations have shown that electron beams with unprecedented brightness ($10^{20}\sim10^{21}~\mathrm{A}/\mathrm{m}^2/\mathrm{rad}^2$) and $0.1\sim 1$ MeV energy spread can be produced through controlled injection in a slowly expanding bubble that arises when a particle beam or laser pulse propagates in density gradient, or when a particle beam self-focuses in uniform plasma or has a superluminal flying focus. However, in previous simulations of work on self-injection triggered by an evolving laser driver in a uniform plasma, the resulting beams did not exhibit comparable brightnesses and energy spreads. Here, we demonstrate through the use of large-scale high-fidelity PIC simulations that a slowly expanding bubble driven by a laser pulse in a uniform plasma can indeed produce self-injected electron beams with similar brightnesses and energy spreads as for an evolving bubble driven by an electron beam driver. We consider laser spot sizes roughly equal to the matched spot sizes in a uniform plasma and find that the evolution of the bubble occurs naturally through the evolution of the laser. The effects of the electron beam quality on the choice of physical as well as numerical parameters, e.g. grid sizes and field solvers used in the PIC simulations are presented. It is found that this original and simplest injection scheme can produce electron beams with beam quality exceeding that of the more recent concepts.

Plasmas are a compelling medium for particle acceleration owing to their natural ability to sustain electric fields that are orders of magnitude larger than those available in conventional radio-frequency accelerators. Plasmas are also unique amongst accelerator technologies in that they respond differently to beams of opposite charge. The asymmetric response of a plasma to highly-relativistic electron and positron beams arises from the fact that plasmas are composed of light, mobile electrons and heavy, stationary ions. Hollow channel plasma acceleration is a technique for symmetrizing the response of the plasma, such that it works equally well for high-energy electron and positron beams. In the experiment described here, we demonstrate the generation of a positron beam-driven wake in an extended, annular plasma channel, and acceleration of a second trailing witness positron bunch by the wake. The leading bunch excites the plasma wakefield and loses energy to the plasma, while the witness bunch experiences an accelerating field and gains energy, thus providing a proof-of-concept for hollow channel acceleration of positron beams. At a bunch separation of 330 um, the accelerating gradient is 70 MV/m, the transformer ratio is 0.55, and the energy transfer efficiency is 18% for a drive-to-witness beam charge ratio of 5:1.

In a laser wakefield accelerator (LWFA), an intense laser pulse excites a plasma wave that traps and accelerates electrons to relativistic energies. When the pulse overlaps the accelerated electrons, it can enhance the energy gain through direct laser acceleration (DLA) by resonantly driving the betatron oscillations of the electrons in the plasma wave. The particle-in-cell (PIC) algorithm, although often the tool of choice to study DLA, contains inherent errors due to numerical dispersion and the time staggering of the electric and magnetic fields. Further, conventional PIC implementations cannot reliably disentangle the fields of the plasma wave and laser pulse, which obscures interpretation of the dominant acceleration mechanism. Here, a customized field solver that reduces errors from both numerical dispersion and time staggering is used in conjunction with a field decomposition into azimuthal modes to perform PIC simulations of DLA in an LWFA. Comparisons with traditional PIC methods, model equations, and experimental data show improved accuracy with the customized solver and convergence with an order-of-magnitude fewer cells. The azimuthal-mode decomposition reveals that the most energetic electrons receive comparable energy from DLA and LWFA., Comment: 10 pages, 5 figures, to submit to Physics of Plasmas

Accelerator-based X-ray free-electron lasers (XFELs) are the latest addition to the revolutionary tools of discovery for the 21st century. The two major components of an XFEL are an accelerator-produced electron beam and a magnetic undulator which tend to be kilometer-scale long and expensive. Here, we present an ultra-compact scheme to produce 10s of attosecond X-ray pulses with several GW peak power utilizing a novel aspect of the FEL instability using a highly chirped, pre-bunched and ultra-bright electron beam from a plasma-based accelerator interacting with an optical undulator. The self-selection of electrons from the combination of a highly chirped and pre-bunched beam leads to the stable generation of attosecond X-ray pulses. Furthermore, two-color attosecond pulses with sub-femtosecond separation can be produced by adjusting the energy distribution of the electron beam so that multiple FEL resonances occur at different locations within the beam. Such a tunable coherent attosecond X-ray sources may open up a new area of attosecond science enabled by X-ray attosecond pump/probe techniques., Comment: 8 pages, 4 figures

Plasma wakefield acceleration in the nonlinear blowout regime has been shown to provide high acceleration gradients and high energy transfer efficiency while maintaining great beam quality for electron acceleration. In contrast, research on positron acceleration in this regime is still in a preliminary stage. We find that an on-axis electron filament can be self-consistently formed and maintained by loading an intense positron beam at the back of the electron beam driven blowout cavity. Via an analytic model and fully nonlinear simulations, we show this coaxial electron filament not only can focus the positron beam but changes the loaded longitudinal wakefield in a distinctly different way from electron beam loading in the blowout regime. Using simulations, we demonstrate that a high charge positron beam can be accelerated with tens of percent energy transfer from wake to positrons, percent level induced energy spread and several mm$\cdot$mrad normalized emittance, while significantly depleting the energy of the electron drive beam. This concept can be extended to simultaneous acceleration of electron and positron beams and high transformer ratio positron acceleration as well.

We derive the kinetic theory of fluctuations in physically and numerically stable particle-in-cell (PIC) simulations of electrostatic plasmas. The starting point is the single-time correlations at the simulation start between the statistical fluctuations of weighted densities of macroparticle centers in the plasma particle phase-space. The single-time correlations at all time steps and in each spatial grid cell are then determined from the Laplace-Fourier transforms of the discretized Klimontovich-like equation for the macroparticles and Maxwell's equations for the fields as computed by modern PIC codes. We recover the expressions for the electrostatic field and the plasma particle density fluctuation autocorrelations spectra as well as the kinetic equations describing the average evolution of PIC-simulated plasma particles, first derived by Langdon in 1970, using a macroparticle test approach perturbing a discretized Vlasovian plasma and then averaging the obtained physical quantity over the initial macroparticle velocity distribution. We generalize and extend these results to the modern algorithms in PIC codes and using arbitrary macroparticle weights. Analytical estimates of statistical fluctuations single-time correlation amplitudes are derived as a function of the plasma simulation parameters, using the central limit theorem in the limit of a large number of macroparticles per cell. The theory is then used to analyze the ensemble averaging technique of PIC simulations where statistical averages are performed over ensembles of PIC simulations, modeling the same plasma physics problem but using different statistical realizations of the initial distribution functions of the macroparticles., Comment: 38 pages, 11 figures

Spatiotemporal control refers to a class of optical techniques for structuring a laser pulse with coupled space-time dependent properties, including moving focal points, dynamic spot sizes, and evolving orbital angular momenta. Here we introduce the concept of arbitrarily structured laser (ASTRL) pulses which generalizes these techniques. The ASTRL formalism employs a superposition of prescribed pulses to create a desired electromagnetic field structure. Several examples illustrate the versatility of ASTRL pulses to address a range of laser-based applications., Comment: 6 pages, 2 figures

High-gradient and high-efficiency acceleration in plasma-based accelerators has been demonstrated, showing its potential as the building block for a future collider operating at the energy frontier of particle physics. However, generating and accelerating the required spin-polarized beams in such a collider using plasma-based accelerators has been a long-standing challenge. Here we show that the passage of a highly relativistic, high-current electron beam through a single-species (ytterbium) vapor excites a nonlinear plasma wake by primarily ionizing the two outer 6s electrons. Further photoionization of the resultant Yb2+ ions by a circularly polarized laser injects the 4f14 electrons into this wake generating a highly spin-polarized beam. Combining time-dependent Schrodinger equation simulations with particle-in-cell simulations, we show that a sub-femtosecond, high-current (4 kA) electron beam with up to 56% net spin polarization can be generated and accelerated to 15 GeV in just 41 cm. This relatively simple scheme solves the perplexing problem of producing spin-polarized relativistic electrons in plasma-based accelerators., Comment: 3 figures

This paper discusses how to improve the Boris pusher used to advance relativistic charged particles in fixed electromagnetic fields. We first derive a simpler solution to a flaw previously discovered by others. We then derive a new analytic Boris pusher that is a minor modification to the original split-time scheme, except for the calculation of {\gamma}. This analytic pusher assumes that the change of {\gamma} during a particle advance is small. It is less accurate than the pusher derived by Fei Li et. al., but is nearly twice as fast. We will discuss when it is advantageous and when it is not., Comment: 15 pages, 4 figures

Plasma is an attractive medium for generating strong microscopic magnetic structures and tunable electromagnetic radiation with predictable topologies due to its extraordinary ability to sustain and manipulate high currents and strong fields. Here, using theory and simulations, we show efficient generation of multi-megagauss magnetic and tunable optical vortices when a sharp relativistic ionization front (IF) passes through a relatively long-wavelength Laguerre-Gaussian (LG) laser pulse with orbital angular momentum (OAM). The optical vortex is frequency upshifted within a wide spectral range simply by changing the plasma density and compressed in duration. The topological charges of both vortices can be manipulated by controlling the OAM mode of the incident LG laser and/or by controlling the topology and density of the IF. For relatively high (low) plasma densities, most energy of the incident LG laser pulse is converted to the magnetic (optical) vortex.

Generation and amplification of magnetic fields in plasmas is a long-standing topic that is of great interest to both plasma and space physics. The electron Weibel instability is a well-known mechanism responsible for self-generating magnetic fields in plasmas with temperature anisotropy and has been extensively investigated in both theory and simulations, yet experimental verification of this instability has been challenging. Recently, we demonstrated a new experimental platform that enables the controlled initialization of highly nonthermal and/or anisotropic plasma electron velocity distributions via optical-field ionization. Using an external electron probe bunch from a linear accelerator, the onset, saturation and decay of the self-generated magnetic fields due to electron Weibel instability were measured for the first time to our knowledge. In this paper, we will first present experimental results on time-resolved measurements of the Weibel magnetic fields in non-relativistic plasmas produced by Ti:Sapphire laser pulses (0.8 $\mu m$) and then discuss the feasibility of extending the study to quasi-relativistic regime by using intense $\rm CO_2$ (e.g., 9.2 $\mu m$) lasers to produce much hotter plasmas., Comment: 22 pages, 10 figures

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 step. Since the time step is not limited by the regular Courant-Friedrichs-Lewy condition that constrains a standard 3D fully electromagnetic PIC code, a 3D QSA-PIC code can achieve orders of magnitude speedup in performance. Recently, a new hybrid QSA-PIC algorithm that combines another speedup technique known as azimuthal Fourier decomposition has been proposed and implemented. This hybrid algorithm decomposes the electromagnetic fields, charge and current density into azimuthal harmonics and only the Fourier coefficients need to be updated, which can significantly reduce the algorithmic complexity. Modeling the laser-plasma interaction in a full 3D PIC algorithm is very computationally expensive due to the enormous disparity of physical scales to be resolved. In the QSA the laser is modeled using the ponderomotive guiding center (PGC) approach. We describe how to implement a PGC algorithm compatible with the QSA PIC algorithms based on the azimuthal mode expansion. This algorithm permits time steps orders of magnitude larger than the cell size and it can be asynchronously parallelized. Details on how this is implemented into the QSA PIC code that utilizes an azimuthal mode expansion, QPAD, are also described.

Due to the highly nonlinear nature of the beam-loading, it is at present not possible to analytically determine the beam parameters needed in a two-bunch plasma wakefield accelerator for maintaining a low energy spread. Therefore in this paper, by using the Broyden-Fletcher-Goldfarb-Shanno algorithm for the parameter scanning with the code QuickPIC and the polynomial regression together with k-fold cross-validation method, we obtain two fitting formulas for calculating the parameters of tri-Gaussian electron beams when minimizing the energy spread based on the beam-loading effect in a nonlinear plasma wakefield accelerator. One formula allows the optimization of the normalized charge per unit length of a trailing beam to achieve the minimal energy spread, i.e. the optimal beam-loading. The other one directly gives the transformer ratio when the trailing beam achieves the optimal beam-loading. A simple scaling law for charges of drive beams and trailing beams is obtained from the fitting formula, which indicates that the optimal beam-loading is always achieved for a given charge ratio of the two beams when the length and separation of two beams and the plasma density are fixed. The formulas can also help obtain the optimal plasma densities for the maximum accelerated charge and the maximum acceleration efficiency under the optimal beam-loading respectively. These two fitting formulas will significantly enhance the efficiency for designing and optimizing a two-bunch plasma wakefield acceleration stage.

Bremsstrahlung x-rays generated in laser-solid interactions can be used as light sources for high-energy-density science. We present electron and x-ray spectra from particle-in-cell and Monte Carlo simulations, varying laser pulse intensity and duration at fixed energy of 200$\,$J. Superponderomotive electron temperatures are observed at low intensity; a new temperature scaling is given that depends on pulse duration and density scale length. Short, high-intensity pulses create low-divergence electron beams before self-generated magnetic fields evolve, resulting in more forward-going MeV x-rays., Comment: 6 pages, 5 figures

We propose a novel positron beam loading regime in a hollow plasma channel that can efficiently accelerate $e^+$ beam with high gradient and narrow energy spread. In this regime, the $e^+$ beam coincides with the drive $e^-$ beam in time and space and their net current distribution determines the plasma wakefields. By precisely shaping the beam current profile and loading phase according to explicit expressions, three-dimensional Particle-in-Cell (PIC) simulations show that the acceleration for $e^+$ beam of $\sim$nC charge with $\sim$GV/m gradient, $\lesssim$0.5% induced energy spread and $\sim$50% energy transfer efficiency can be achieved simultaneously. Besides, only tailoring the current profile of the more tunable $e^-$ beam instead of the $e^+$ beam is enough to obtain such favorable results. A theoretical analysis considering both linear and nonlinear plasma responses in hollow plasma channels is proposed to quantify the beam loading effects. This theory agrees very well with the simulation results and verifies the robustness of this beam loading regime over a wide range of parameters.

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 ($\sim$30 nm rad), high current ($\sim$ 17 kA), low slice energy-spread ($\sim$0.1%) and therefore high normalized brightness ($>10^{19}$ A/rad$^2$/m$^2$) in a plasma of density $\sim10^{19}$ 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/rad$^2$/m$^2$.

An extended thermal particle boundary condition is devised to more efficiently and accurately model laser-plasma interactions in overdense plasmas. Particle-in-cell simulations of such interactions require many particles per cell, and a large region of background plasma is often necessary to correctly mimic a semi-infinite plasma and avoid electron refluxing from a truncated plasma. For long-pulse lasers of many picoseconds, such constraints can become prohibitively expensive. Here, an extended particle boundary condition (absorber) is designed that instantaneously stops and re-emits energetic particles streaming toward the simulation boundary over a defined region, allowing sufficient time and space for a suitably cool return current to develop in the background plasma. Tunable parameters of the absorber are explained, and simulations using the absorber with a 3-ps laser are shown to accurately reproduce those of a causally separated boundary while requiring only 20% the number of particles., Comment: 12 pages, 9 figures

An improved description for nonlinear plasma wakefields with phase velocities near the speed of light is presented and compared against fully kinetic particle-in-cell simulations. These wakefields are excited by intense particle beams or lasers pushing plasma electrons radially outward, creating an ion bubble surrounded by a sheath of electrons characterized by the source term $S \equiv -\frac{1}{en_p}(\rho-J_z/c)$ where $\rho$ and $J_z$ are the charge and axial current densities. Previously, the sheath source term was described phenomenologically with a positive-definite function, resulting in a positive definite wake potential. In reality, the wake potential is negative at the rear of the ion column which is important for self-injection and accurate beam loading models. To account for this, we introduce a multi-sheath model in which the source term, $S$, of the plasma wake can be negative in regions outside the ion bubble. Using this model, we obtain a new expression for the wake potential and a modified differential equation for the bubble radius. Numerical results obtained from these equations are validated against particle-in-cell simulations for unloaded and loaded wakes. The new model provides accurate predictions of the shape and duration of trailing bunch current profiles that flatten plasma wakefields. It is also used to design a trailing bunch for a desired longitudinally varying loaded wakefield. We present beam loading results for laser wakefields and discuss how the model can be improved for laser drivers in future work. Finally, we discuss differences between the predictions of the multi- and single-sheath models for beam loading., Comment: 25 pages, 15 figures

In situ generation of a high-energy, high-current, spin-polarized electron beam is an outstanding scientific challenge to the development of plasma-based accelerators for high-energy colliders. In this Letter we show how such a spin-polarized relativistic beam can be produced by ionization injection of electrons of certain atoms with a circularly polarized laser field into a beam-driven plasma wakefield accelerator, providing a much desired one-step solution to this challenge. Using time-dependent Schr\"odinger equation (TDSE) simulations, we show the propensity rule of spin-dependent ionization of xenon atoms can be reversed in the strong-field multi-photon regime compared with the non-adiabatic tunneling regime, leading to high total spin-polarization. Furthermore, three-dimensional particle-in-cell (PIC) simulations are incorporated with TDSE simulations, providing start-to-end simulations of spin-dependent strong-field ionization of xenon atoms and subsequent trapping, acceleration, and preservation of electron spin-polarization in lithium plasma. We show the generation of a high-current (0.8 kA), ultra-low-normalized-emittance (~37 nm), and high-energy (2.7 GeV) electron beam within just 11 cm distance, with up to ~31% net spin polarization. Higher current, energy, and net spin-polarization beams are possible by optimizing this concept, thus solving a long-standing problem facing the development of plasma accelerators., Comment: 4 figures

The binary Monte Carlo (MC) collision algorithm is a standard and robust method to include binary Coulomb collision effects in particle-in-cell (PIC) simulations of plasmas. Here, we show that the coupling between PIC and MC algorithms can give rise to (nonphysical) numerical heating of the system, that significantly exceeds that observed when these algorithms operate independently. We argue that this deleterious effect results from an inconsistency between the particle motion associated with MC-collisions and the work performed by the collective electromagnetic field on the PIC grid. This inconsistency manifests as the (artificial) stochastic production of electromagnetic energy, which ultimately heats the plasma particles. The MC-induced numerical heating can significantly impact the evolution of the simulated system for long simulation times ($\gtrsim 10^3$ collision periods, for typical numerical parameters). We describe the source of the MC-induced numerical heating analytically and discuss strategies to minimize it.

Plasma wakefield acceleration in the blowout regime is particularly promising for high-energy acceleration of electron beams because of its potential to simultaneously provide large acceleration gradients and high energy transfer efficiency while maintaining excellent beam quality. However, no equivalent regime for positron acceleration in plasma wakes has been discovered to-date. We show that after a short propagation distance, an asymmetric electron beam drives a stable wakefield in a hollow plasma channel that can be both accelerating and focusing for a positron beam. A high charge positron bunch placed at a suitable distance behind the drive bunch can beam-load or flatten the longitudinal wakefield and enhance the transverse focusing force, leading to high-efficiency and narrow energy spread acceleration of the positrons. Three-dimensional quasi-static particle-in-cell (PIC) simulations show that over 30% energy extraction efficiency from the wake to the positrons and 1% level energy spread can be simultaneously obtained, and further optimization is feasible.

This paper discusses numerical and experimental results on frequency downshifting and upshifting of a 10 $\mu$m infrared laser to cover the entire wavelength (frequency) range from $\lambda$=1-150 $\mu$m ($\nu$=300-2 THz) using two different plasma techniques. The first plasma technique utilizes frequency downshifting of the drive laser pulse in a nonlinear plasma wake. Based on this technique, we have proposed and demonstrated that in a tailored plasma structure multi-millijoule energy, single-cycle, long-wavelength IR (3-20 $\mu$m) pulses can be generated by using an 810 nm Ti:sapphire drive laser. Here we extend this idea to the THz frequency regime. We show that sub-joule, terawatts, single-cycle terahertz (2-12 THz, or 150-25 $\mu$m) pulses can be generated by replacing the drive laser with a picosecond 10 $\mu$m CO$_2$ laser and a different shaped plasma structure. The second plasma technique employs frequency upshifting by colliding a CO$_2$ laser with a rather sharp relativistic ionization front created by ionization of a gas in less than half cycle (17 fs) of the CO$_2$ laser. Even though the electrons in the ionization front carry no energy, the frequency of the CO$_2$ laser can be upshifted due to the relativistic Doppler effect as the CO$_2$ laser pulse enters the front. The wavelength can be tuned from 1-10 $\mu$m by simply changing the electron density of the front. While the upshifted light with $5 <\lambda(\mu$m$)< 10$ propagates in the forward direction, that with $1 <\lambda(\mu$m$)< 5$ is back-reflected. These two plasma techniques seem extremely promising for covering the entire molecular fingerprint region., Comment: 7 figures

The temporal evolution of the magnetic field associated with electron thermal Weibel instability in optical-field ionized plasmas is measured using ultrashort (1.8 ps), relativistic (45 MeV) electron bunches from a linear accelerator. The self-generated magnetic fields are found to self-organize into a quasi-static structure consistent with a helicoid topology within a few ps and such a structure lasts for tens of ps in underdense plasmas. The measured growth rate agrees well with that predicted by the kinetic theory of plasmas taking into account collisions. Magnetic trapping is identified as the dominant saturation mechanism., Comment: Accepted for publication in Physical Review Letters

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 magnitude shorter than the plasma density modulation. The ponderomotive force of two counter propagating lasers of the same frequency can generate a density modulation at half the laser wavelength. Assuming a laser wavelength of $0.8\micro\meter$, fully self-consistent OSIRIS PIC simulations show that this scheme can generate high quality beams modulated at wavelengths between 10s and 100 angstroms. Such beams could produce fully coherent, stable, hundreds of GW X-rays by going through a resonant undulator., Comment: 6 pages, 4 figures

When a fs duration and hundreds of kA peak current electron beam traverses the vacuum and high-density plasma interface a new process, that we call relativistic transition radiation (R-TR) generates an intense $\sim100$ as pulse containing $\sim$ TW power of coherent VUV radiation accompanied by several smaller fs duration satellite pulses. This pulse inherits the radial polarization of the incident beam field and has a ring intensity distribution. This R-TR is emitted when the beam density is comparable to the plasma density and the spot size much larger than the plasma skin depth. Physically, it arises from the return current or backward relativistic motion of electrons starting just inside the plasma that Doppler up-shifts the emitted photons. The number of R-TR pulses is determined by the number of groups of plasma electrons that originate at different depths within the first plasma wake period and emit coherently before phase mixing., Comment: 5 pages, 4 figures

Next-generation high-power lasers that can be focused to intensities exceeding 10^23 W/cm^2 are enabling new physics and applications. The physics of how these lasers interact with matter is highly nonlinear, relativistic, and can involve lowest-order quantum effects. The current tool of choice for modeling these interactions is the particle-in-cell (PIC) method. In strong fields, the motion of charged particles and their spin is affected by radiation reaction. Standard PIC codes usually use Boris or its variants to advance the particles, which requires very small time steps in the strong-field regime to obtain accurate results. In addition, some problems require tracking the spin of particles, which creates a 9D particle phase space (x, u, s). Therefore, numerical algorithms that enable high-fidelity modeling of the 9D phase space in the strong-field regime are desired. We present a new 9D phase space particle pusher based on analytical solutions to the position, momentum and spin advance from the Lorentz force, together with the semi-classical form of RR in the Landau-Lifshitz equation and spin evolution given by the Bargmann-Michel-Telegdi equation. These analytical solutions are obtained by assuming a locally uniform and constant electromagnetic field during a time step. The solutions provide the 9D phase space advance in terms of a particle's proper time, and a mapping is used to determine the proper time step for each particle from the simulation time step. Due to the analytical integration, the constraint on the time step needed to resolve trajectories in ultra-high fields can be greatly reduced. We present single-particle simulations and full PIC simulations to show that the proposed particle pusher can greatly improve the accuracy of particle trajectories in 9D phase space for given laser fields. A discussion on the numerical efficiency of the proposed pusher is also provided.

Plasma-based accelerators (PBAs) driven by either intense lasers (laser wakefield accelerators, LWFAs) or particle beams (plasma wakefield accelerators, PWFAs), can accelerate charged particles at extremely high gradients compared to conventional radio-frequency (RF) accelerators. In the past two decades, great strides have been made in this field, making PBA a candidate for next-generation light sources and colliders. However, these challenging applications necessarily require beams with good stability, high quality, controllable polarization and excellent reproducibility. To date, such beams are generated only by conventional RF accelerators. Therefore, it is important to demonstrate the injection and acceleration of beams first produced using a conventional RF accelerator, by a PBA. In some recent studies on LWFA staging and external injection-acceleration in PWFA only a very small fraction (from below 0.1% to few percent) of the injected charge (the coupling efficiency) was accelerated. For future colliders where beam energy will need to be boosted using multiple stages, the coupling efficiency per stage must approach 100%. Here we report the first demonstration of external injection from a photocathode-RF-gun-based conventional linear accelerator (LINAC) into a LWFA and subsequent acceleration without any significant loss of charge or degradation of quality, which is achieved by properly shaping and matching the beam into the plasma structure. This is an important step towards realizing a high-throughput, multi-stage, high-energy, hybrid conventional-plasma accelerator.

A customized finite-difference field solver for the particle-in-cell (PIC) algorithm that provides higher fidelity for wave-particle interactions in intense electromagnetic waves is presented. In many problems of interest, particles with relativistic energies interact with intense electromagnetic fields that have phase velocities near the speed of light. Numerical errors can arise due to (1) dispersion errors in the phase velocity of the wave, (2) the staggering in time between the electric and magnetic fields and between particle velocity and position and (3) errors in the time derivative in the momentum advance. Errors of the first two kinds are analyzed in detail. It is shown that by using field solvers with different $\mathbf{k}$-space operators in Faraday's and Ampere's law, the dispersion errors and magnetic field time-staggering errors in the particle pusher can be simultaneously removed for electromagnetic waves moving primarily in a specific direction. The new algorithm was implemented into OSIRIS by using customized higher-order finite-difference operators. Schemes using the proposed solver in combination with different particle pushers are compared through PIC simulation. It is shown that the use of the new algorithm, together with an analytic particle pusher (assuming constant fields over a time step), can lead to accurate modeling of the motion of a single electron in an intense laser field with normalized vector potentials, $eA/mc^2$, exceeding $10^4$ for typical cell sizes and time steps.

Furthering our understanding of many of today's interesting problems in plasma physics---including plasma based acceleration and magnetic reconnection with pair production due to quantum electrodynamic effects---requires large-scale kinetic simulations using particle-in-cell (PIC) codes. However, these simulations are extremely demanding, requiring that contemporary PIC codes be designed to efficiently use a new fleet of exascale computing architectures. To this end, the key issue of parallel load balance across computational nodes must be addressed. We discuss the implementation of dynamic load balancing by dividing the simulation space into many small, self-contained regions or "tiles," along with shared-memory (e.g., OpenMP) parallelism both over many tiles and within single tiles. The load balancing algorithm can be used with three different topologies, including two space-filling curves. We tested this implementation in the code OSIRIS and show low overhead and improved scalability with OpenMP thread number on simulations with both uniform load and severe load imbalance. Compared to other load-balancing techniques, our algorithm gives order-of-magnitude improvement in parallel scalability for simulations with severe load imbalance issues., Comment: 13 pages, 7 figures, submitted to Computer Physics Communications

The 3D quasi-static particle-in-cell (PIC) algorithm is a very efficient method for modeling short-pulse laser or relativistic charged particle beam-plasma interactions. In this algorithm, the plasma response to a non-evolving laser or particle beam is calculated using Maxwell's equations based on the quasi-static approximate equations that exclude radiation. The plasma fields are then used to advance the laser or beam forward using a large time step. The algorithm is many orders of magnitude faster than a 3D fully explicit relativistic electromagnetic PIC algorithm. It has been shown to be capable to accurately model the evolution of lasers and particle beams in a variety of scenarios. At the same time, an algorithm in which the fields, currents and Maxwell equations are decomposed into azimuthal harmonics has been shown to reduce the complexity of a 3D explicit PIC algorithm to that of a 2D algorithm when the expansion is truncated while maintaining accuracy for problems with near azimuthal symmetry. This hybrid algorithm uses a PIC description in r-z and a gridless description in $\phi$. We describe a novel method that combines the quasi-static and hybrid PIC methods. This algorithm expands the fields, charge and current density into azimuthal harmonics. A set of the quasi-static field equations are derived for each harmonic. The complex amplitudes of the fields are then solved using the finite difference method. The beam and plasma particles are advanced in Cartesian coordinates using the total fields. Details on how this algorithm was implemented using a similar workflow to an existing quasi-static code, QuickPIC, are presented. The new code is called QPAD for QuickPIC with Azimuthal Decomposition. Benchmarks and comparisons between a fully 3D explicit PIC code, a full 3D quasi-static code, and the new quasi-static PIC code with azimuthal decomposition are also presented.

The particle-in-cell (PIC) method is widely used to model the self-consistent interaction between discrete particles and electromagnetic fields. It has been successfully applied to problems across plasma physics including plasma based acceleration, inertial confinement fusion, magnetically confined fusion, space physics, astrophysics, high energy density plasmas. In many cases the physics involves how relativistic particles are generated and interact with plasmas. However, when relativistic particles stream across the grid both in vacuum and in plasma there are many numerical issues that may arise which can lead to incorrect physics. We present a detailed analysis of how discretized Maxwell solvers used in PIC codes can lead to numerical errors to the fields that surround particles that move at relativistic speeds across the grid. Expressions for the axial electric field as integrals in k space are presented. Two types of errors to these expressions are identified. The first arises from errors to the numerator of the integrand and leads to unphysical fields that are antisymmetric about the particle. The second arises from errors to the denominator of the integrand and lead to Cerenkov like radiation in "vacuum". These fields are not anti-symmetric, extend behind the particle, and cause the particle to accelerate or decelerate depending on the solver and parameters. The unphysical fields are studied in detail for two representative solvers - the Yee solver and the FFT based solver. A solution for eliminating these unphysical fields by modifying the k operator in the axial direction is also presented. Using a customized finite difference solver, this solution was successfully implemented into OSIRIS. Results from the customized solver are also presented. This solution will be useful for a beam of particles that all move in one direction with a small angular divergence., Comment: 38 pages, 8 figures

Three-dimensional (3D) simulations of electron beams propagating in high energy density (HED) plasmas using the quasi-static Particle-in-Cell (PIC) code QuickPIC demonstrate a significant increase in stopping power when beam electrons mutually interact via their wakes. Each beam electron excites a plasma wave wake of wavelength $\sim2\pi c/\omega_{pe}$, where $c$ is the speed of light and $\omega_{pe}$ is the background plasma frequency. We show that a discrete collection of electrons undergoes a beam-plasma like instability caused by mutual particle-wake interactions that causes electrons to bunch in the beam, even for beam densities $n_b$ for which fluid theory breaks down. This bunching enhances the beam's stopping power, which we call "correlated stopping," and the effect increases with the "correlation number" $N_b \equiv n_b (c/\omega_{pe})^3$. For example, a beam of monoenergetic 9.7 MeV electrons with $N_b=1/8$, in a cold background plasma with $n_e=10^{26}$ cm$^{-3}$ (450 g cm$^{-3}$ DT), has a stopping power of $2.28\pm0.04$ times the single-electron value, which increases to $1220\pm5$ for $N_b=64$. The beam also experiences transverse filamentation, which eventually limits the stopping enhancement., Comment: 10 pages, 8 figures, accepted by Physical Review E

The availability of intense, ultrashort coherent radiation sources in the infrared region of the spectrum is enabling the generation of attosecond X-ray pulses via high harmonic generation, pump-probe experiments in the "molecular fingerprint" region and opening up the area of relativistic-infrared nonlinear optics of plasmas. These applications would benefit from multi-millijoule single-cycle pulses in the mid to long wavelength infrared (LW-IR) region. Here we present a new scheme capable of producing tunable relativistically intense, single-cycle infrared pulses from 5-14$\mu$m with a 1.7% conversion efficiency based on a photon frequency downshifting scheme that uses a tailored plasma density structure. The carrier-envelope phase (CEP) of the LW-IR pulse is locked to that of the drive laser to within a few percent. Such a versatile tunable IR source may meet the demands of many cutting-edge applications in strong-field physics and greatly promote their development., Comment: 6 figures

The Faraday effect, caused by a magnetic-field-induced change in the optical properties, takes place in a vast variety of systems from a single atomic layer of graphenes to huge galaxies. Currently, it plays a pivot role in many applications such as the manipulation of light and the probing of magnetic fields and material's properties. Basically, this effect causes a polarization rotation of light during its propagation along the magnetic field in a medium. Here, we report an extreme case of the Faraday effect where a linearly polarized ultrashort laser pulse splits in time into two circularly polarized pulses of opposite handedness during its propagation in a highly magnetized plasma. This offers a new degree of freedom for manipulating ultrashort and ultrahigh power laser pulses. Together with technologies of ultra-strong magnetic fields, it may pave the way for novel optical devices, such as magnetized plasma polarizers. In addition, it may offer a powerful means to measure strong magnetic fields in laser-produced plasmas., Comment: 18 pages, 5 figures

In this paper we present a customized finite-difference-time-domain (FDTD) Maxwell solver for the particle-in-cell (PIC) algorithm. The solver is customized to effectively eliminate the numerical Cerenkov instability (NCI) which arises when a plasma (neutral or non-neutral) relativistically drifts on a grid when using the PIC algorithm. We control the EM dispersion curve in the direction of the plasma drift of a FDTD Maxwell solver by using a customized higher order finite difference operator for the spatial derivative along the direction of the drift ($\hat 1$ direction). We show that this eliminates the main NCI modes with moderate $\vert k_1 \vert$, while keeps additional main NCI modes well outside the range of physical interest with higher $\vert k_1 \vert$. These main NCI modes can be easily filtered out along with first spatial aliasing NCI modes which are also at the edge of the fundamental Brillouin zone. The customized solver has the possible advantage of improved parallel scalability because it can be easily partitioned along $\hat 1$ which typically has many more cells than other directions for the problems of interest. We show that FFTs can be performed locally to current on each partition to filter out the main and first spatial aliasing NCI modes, and to correct the current so that it satisfies the continuity equation for the customized spatial derivative. This ensures that Gauss' Law is satisfied. We present simulation examples of one relativistically drifting plasmas, of two colliding relativistically drifting plasmas, and of nonlinear laser wakefield acceleration (LWFA) in a Lorentz boosted frame that show no evidence of the NCI can be observed when using this customized Maxwell solver together with its NCI elimination scheme.

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 $2.4\rm \mu m$ and $0.8\rm \mu m$ for wakefield excitation and for triggering electron injection via field ionization, respectively. A laser pulse at $2.4\rm \mu m$ 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 working gas medium, where carbon acts as the injection element. Our full three dimensional particle-in-cell simulations show that electron beams at the GeV energy level with both low energy spreads (around one percent) and high charges (several tens of picocoulomb) can be obtained by this scheme with laser parameters achievable in the near future., Comment: 5 pages, 4 figures