155 research outputs found
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
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