Variational Formulation of Macro-Particle Models for Electromagnetic Plasma Simulations

A variational method is used to derive a self-consistent macro-particle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work [E. G. Evstatiev and B. A. Shadwick, J. Comput. Phys., vol. 245, pp. 376-398, 2013], the discretization of the electromagnetic Low Lagrangian is performed via a reduction of the phase-space distribution function onto a collection of finite-sized macro-particles of arbitrary shape and discretization of field quantities onto a spatial grid. This approach may be used with both 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. Additionally, 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 1-1/2 dimensional case (one coordinate and two momenta). Simulations are performed with the new models and demonstrate energy conservation and low noise.Comment: IEEE Transaction on Plasma Science (TPS) Special Issue: Plenary and Invited Papers of the Pulsed Power and Plasma Science Conference (PPPS 2013

Exactly Conservative Integrators

Traditional numerical discretizations of conservative systems generically yield an artificial secular drift of any nonlinear invariants. In this work we present an explicit nontraditional algorithm that exactly conserves these invariants. We illustrate the general method by applying it to the three-wave truncation of the Euler equations, the Lotka--Volterra predator--prey model, and the Kepler problem. This method is discussed in the context of symplectic (phase space conserving) integration methods as well as nonsymplectic conservative methods. We comment on the application of our method to general conservative systems.Comment: 30 pages, postscript (1.3MB). Submitted to SIAM J. Sci. Comput

Optically controlled laser–plasma electron accelerator for compact gamma-ray sources

Generating quasi-monochromatic, femtosecond γ-ray pulses via Thomson scattering (TS) demands exceptional electron beam (e-beam) quality, such as percent-scale energy spread and five-dimensional brightness over 1016 Am–2.We show that near-GeV e-beams with these metrics can be accelerated in a cavity of electron density, driven with an incoherent stack of Joule-scale laser pulses through ammsize, dense plasma (n0 ~ 1019 cm−3). Changing the time delay, frequency difference, and energy ratio of the stack components controls the e-beam phase space on the femtosecond scale, while the modest energy of the optical driver helps afford kHz-scale repetition rate at manageable average power. Blue-shifting one stack component by a considerable fraction of the carrier frequency makes the stack immune to self-compression. This, in turn, minimizes uncontrolled variation in the cavity shape, suppressing continuous injection of ambient plasma electrons, preserving a single, ultra-bright electron bunch. In addition, weak focusing of the trailing component of the stack induces periodic injection, generating, in a single shot, a train of bunches with controllable energy spacing and femtosecond synchronization. These designer e-beams, inaccessible to conventional acceleration methods, generate, via TS, gigawatt γ-ray pulses (or multi-color pulse trains) with the mean energy in the range of interest for nuclear photonics (4–16MeV), containing over 106 photons within a microsteradian-scale observation cone

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, three-dimensional particle-in-cell modelling are examined. First, the Cartesian code VORPAL 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 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 the two simulations indicates that they are free of numerical artefacts. Both approaches thus retrieve physically correct evolution of the plasma bubble, recovering the intrinsic connection of electron self-injection to the nonlinear optical evolution of the driver

An Exactly Conservative Integrator for the n-Body Problem

The two-dimensional n-body problem of classical mechanics is a non-integrable Hamiltonian system for n > 2. Traditional numerical integration algorithms, which are polynomials in the time step, typically lead to systematic drifts in the computed value of the total energy and angular momentum. Even symplectic integration schemes exactly conserve only an approximate Hamiltonian. We present an algorithm that conserves the true Hamiltonian and the total angular momentum to machine precision. It is derived by applying conventional discretizations in a new space obtained by transformation of the dependent variables. We develop the method first for the restricted circular three-body problem, then for the general two-dimensional three-body problem, and finally for the planar n-body problem. Jacobi coordinates are used to reduce the two-dimensional n-body problem to an (n-1)-body problem that incorporates the constant linear momentum and center of mass constraints. For a four-body choreography, we find that a larger time step can be used with our conservative algorithm than with symplectic and conventional integrators.Comment: 17 pages, 3 figures; to appear in J. Phys. A.: Math. Ge

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 fully relativistic, three dimensional numerical code that calculates and quantifies the characteristics of emitted radiation when a relativistic electron beam collides head-on with a focused counter-propagating intense laser field. The developed code has been benchmarked against analytical expressions, based on the plane wave approximation to the laser field, derived in (1). For sufficiently long duration laser pulses, we find that the scattered radiation spectrum is broadened due to interferences arising from the pulsed nature of the laser. We show that by appropriately chirping the scattering laser pulse, the spectral broadening could be minimized.Comment: 11 pages, 3 figures, 25 reference