Bradley Allan Shadwick

Electron self-injection into an evolving plasma bubble: Quasi-monoenergetic laser-plasma acceleration in the blowout regime

An electron density bubble driven in a rarefied uniform plasma by a slowly evolving laser pulse goes through periods of adiabatically slow expansions and contractions. Bubble expansion causes robust self-injection of initially quiescent plasma electrons, whereas stabilization and contraction terminate self-injection thus limiting injected charge; concomitant phase space rotation reduces the bunch energy spread. In regimes relevant to experiments with hundred terawatt- to petawatt-class lasers, bubble dynamics and, hence, the self-injection process are governed primarily by the driver evolution. Collective transverse fields of the trapped electron bunch reduce the accelerating gradient and slow down phase space rotation. Bubble expansion followed by stabilization and contraction suppresses the low-energy background and creates a collimated quasi-monoenergetic electron bunch long before dephasing. Nonlinear evolution of the laser pulse (spot size oscillations, self-compression, and front steepening) can also cause continuous self-injection, resulting in a large dark current, degrading the electron beam quality.

Variational formulation of particle algorithms for kinetic E&M plasma simulations

Summary form only given. Recent developments of a novel variational technique [1-4] for rigorously deriving discrete, self-consistent equations for electromagnetic particle codes will be discussed. The primary advantage of the Lagrangian formulation is the connection between symmetries of the system and conservation laws, which in the present case resolves the grid-heating issue. However, the approach also simplifies coordinate transformations and enables the particle method to be formulated in moving window coordinates and a cylindrical geometry with a truncated Fourier decomposition in angle. For some laser-plasma interaction scenarios, these lead to significant computational savings as compared to the lab frame. New time advance integrators were developed in both the lab frame coordinate system and the moving window. A comparison of symplectic methods to more straightforward explicit and implicit methods allow us to make conclusions about the limits of phase-space fidelity in macro-particle methods.

Laser plasma acceleration with a negatively chirped pulse: all-optical control over dark current in the blowout regime

Recentexperimentswith100terawatt-class,sub-50femtosecondlaser pulses show that electrons self-injected into a laser-driven electron density bubble can be accelerated above 0.5gigaelectronvolt energy in a sub-centimetre- length rarefied plasma. To reach this energy range, electrons must ultimately outrun the bubble and exit the accelerating phase; this, however, does not ensure high beam quality. Wake excitation increases the laser pulse band- width by red-shifting its head, keeping the tail unshifted. Anomalous group velocity dispersion of radiation in plasma slows down the red-shifted head, compressing the pulse into a few-cycle-long piston of relativistic intensity. Pulse transformation into a piston causes continuous expansion of the bubble, trapping copious numbers of unwanted electrons (dark current) and producing a poorly collimated, polychromatic energy tail, completely dominating the electron spectrum at the dephasing limit. The process of piston formation can be mitigated by using a broad-bandwidth (corresponding to a few-cycle transform-limited duration), negatively chirped pulse. Initial blue-shift of the pulse leading edge compensates for the nonlinear frequency red-shift and delays the piston formation, thus significantly suppressing the dark current, making

Nonlinear laser energy depletion in laser-plasma accelerators

Energy depletion of intense, short-pulse lasers via excitation of plasma waves is investigated numerically and analytically. The evolution of a resonant laser pulse proceeds in two phases. In the first phase, the pulse steepens, compresses, and frequency red-shifts as energy is deposited in the plasma. The second phase of evolution occurs after the pulse reaches a minimum length at which point the pulse rapidly lengthens, losing resonance with the plasma. Expressions for the rate of laser energy loss and rate of laser red-shifting are derived and are found to be in excellent agreement with the direct numerical solution of the laser field evolution coupled to the plasma response. Both processes are shown to have the same characteristic length-scale. In the high intensity limit, for nearly-resonant Gaussian laser pulses, this scale length is shown to be independent of laser intensity.

Generation of tunable, 100–800 MeV quasi-monoenergetic electron beams from a laser-wakefield accelerator in the blowout regime

In this paper, we present results on a scalable high-energy electron source based on laser wakefield acceleration. The electron accelerator using 30–80 TW, 30 fs laser pulses, operates in the blowout regime, and produces high-quality, quasi-monoenergetic electron beams in the range 100–800 MeV. These beams have angular divergence of 1–4 mrad, and 5%–25% energy spread, with a resulting brightness 1011 electrons mm−2 MeV−1 mrad−2. The beam parameters can be tuned by varying the laser and plasma conditions. The use of a high-quality laser pulse and appropriate target conditions enables optimization of beam quality, concentrating a significant fraction of the accelerated charge into the quasi-monoenergetic component.

Spectral bandwidth reduction of Thomson scattered light by pulse chirping

Based on single particle tracking in the framework of classical Thomson scattering with incoherent superposition, we developed a relativistic, three-dimensional numerical model that calculates and quantifies the characteristics of emitted radiation when a relativistic electron beam interacts with an intense laser pulse. This model has been benchmarked against analytical expressions, based on the plane wave approximation to the laser field, derived by Esarey et al. [Phys. Rev. E 48, 3003 (1993)]. For laser pulses of sufficient duration, we find that the scattered radiation spectrum is broadened due to interferences arising from the pulsed nature of the laser. We find that by appropriately chirping the scattering laser pulse, spectral broadening can be minimized, and the peak on-axis brightness of the emitted radiation is increased by a factor of approximately 5.

Variational formulation of macro-particle plasma simulation algorithms

A variation formulation of macro-particle kinetic plasma models is discussed. In the electrostatic case, the use of symplectic integrators is investigated and found to offer advantages over typical generic methods. For the electromagnetic case, gauge invariance and momentum conservation are considered in detail. It is shown that, while the symmetries responsible for these conservation laws are broken in the presence of a spatial grid, the conservation laws hold in an average sense. The requirements for exact invariance are explored and it is shown that one viable option is to represent the potentials with a truncated Fourier basis.

Computationally efficient methods for modelling laser wakefield acceleration in the blowout regime

Electron self-injection and acceleration until dephasing in the blowout regime is studied for a set of initial conditions typical of recent experiments with 100-terawatt-class lasers. Two different approaches to computationally efficient, fully explicit, 3D particle-in-cell modelling are examined. First, the Cartesian code vorpal (Nieter, C. and Cary, J. R. 2004 VORPAL: a versatile plasma simulation code. J. Comput. Phys. 196, 538) using a perfect-dispersion electromagnetic solver precisely describes the laser pulse and bubble dynamics, taking advantage of coarser resolution in the propagation direction, with a proportionally larger time step. Using third-order splines for macroparticles helps suppress the sampling noise while keeping the usage of computational resources modest. The second way to reduce the simulation load is using reduced-geometry codes. In our case, the quasi-cylindrical code calder-circ (Lifschitz, A. F. et al. 2009 Particle-in-cell modelling of laser-plasma interaction using Fourier decomposition. J. Comput. Phys. 228(5), 1803-1814) uses decomposition of fields and currents into a set of poloidal modes, while the macroparticles move in the Cartesian 3D space. Cylindrical symmetry of the interaction allows using just two modes, reducing the computational load to roughly that of a planar Cartesian simulation while preserving the 3D nature of the interaction. This significant economy of resources allows using fine resolution in the direction of propagation and a small time step, making numerical dispersion vanishingly small, together with a large number of particles per cell, enabling good particle statistics. Quantitative agreement of two simulations indicates that these are free of numerical artefacts. Both approaches thus retrieve the physically correct evolution of the plasma bubble, recovering the intrinsic connection of electron self-injection to the nonlinear optical evolution of the driver.

Variational Formulation of Macroparticle Models for Electromagnetic Plasma Simulations

A variational method is used to derive a self-consistent macroparticle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work, discretization of the electromagnetic Low Lagrangian is performed via a reduction of the phase-space distribution function onto a collection of finite-sized macroparticles of arbitrary shape and discretization of field quantities onto a spatial grid. This approach may be used with lab frame coordinates or moving window coordinates; the latter can greatly improve computational efficiency for studying some types of laser-plasma interactions. The primary advantage of the variational approach is the preservation of Lagrangian symmetries, which in our case leads to energy conservation and thus avoids difficulties with grid heating. In addition, this approach decouples particle size from grid spacing and relaxes restrictions on particle shape, leading to low numerical noise. The variational approach also guarantees consistent approximations in the equations of motion and is amenable to higher order methods in both space and time. We restrict our attention to the 1.5-D case (one coordinate and two momenta). Simulations are performed with the new models and demonstrate energy conservation and low noise.

Electron Self-Injection into an Evolving Plasma Bubble: The Way to a Dark Current Free GeV-Scale Laser Accelerator

A time-varying electron density bubble created by the radiation pressure of a tightly focused petawatt laser pulse traps electrons of ambient rarefied plasma and accelerates them to a GeV energy over a few-cm distance. Expansion of the bubble caused by the shape variation of the self-guided pulse is the primary cause of electron self-injection in strongly rarefied plasmas (ne ∼ 10 17 cm −3 ). Stabilization and contraction of the bubble extinguishes the injection. After the bubble stabilization, longitudinal non-uniformity of the accelerating gradient results in a rapid phase space rotation that produces a quasi-monoenergetic bunch well before the de-phasing limit. Combination of reduced and fully self-consistent (first-principle) 3-D PIC simulations complemented with the Hamiltonian diagnostics of electron phase space shows that the bubble dynamics and the self-injection process are governed primarily by the driver evolution; collective transverse fields of the trapped electron bunch reduce the accelerating gradient, slow down phase space rotation, and result in a formation of monoenergetic electron beam with higher energy than test-particle modeling predicts.