Gregory R. Werner

Dielectric laser accelerators

We describe recent advances in the study of particle acceleration using dielectric near-field structures driven by infrared lasers, which we refer to as Dielectric Laser Accelerators. Implications for high energy physics and other applications are discussed.

A stable FDTD algorithm for non-diagonal, anisotropic dielectrics

A stable FDTD algorithm is developed for simulating Maxwell’s equations in anisotropic dielectric materials with principal axes not aligned with the grid. The algorithm is stable because the finite-difference operator that converts D to E is symmetric and positive semidefinite; for contrast, a previously developed asymmetric algorithm is shown to suffer from late-time instabilities. The presented algorithm has second-order error for continuous dielectric materials, and the error can be reduced to third-order by Richardson extrapolation. Applied to dielectrics with sharp interfaces, the algorithm has first-order error, even when averaging the dielectric within partially filled grid cells. However, averaging the dielectric permits Richardson extrapolation to obtain second-order error.

The Extent of Power-Law Energy Spectra in Collisionless Relativistic Magnetic Reconnection in Pair Plasmas

Using two-dimensional particle-in-cell simulations, we characterize the energy spectra of particles accelerated by relativistic magnetic reconnection (without guide field) in collisionless electron–positron plasmas, for a wide range of upstream magnetizations σ and system sizes L. The particle spectra are well-represented by a power law

On the Distribution of Particle Acceleration Sites in Plasmoid-Dominated Relativistic Magnetic Reconnection

{\gamma }^{-\alpha }

Non-thermal particle acceleration in collisionless relativistic electron–proton reconnection

, with a combination of exponential and super-exponential high-energy cutoffs, proportional to σ and L, respectively. As a result, for large L and σ, the power-law index α approaches about 1.2.

Kinetic Turbulence in Relativistic Plasma: From Thermal Bath to Nonthermal Continuum

The Crab Nebula was formed after the collapse of a massive star about a thousand years ago, leaving behind a pulsar that inflates a bubble of ultra-relativistic electron-positron pairs permeated with magnetic field. The observation of brief but bright flares of energetic gamma rays suggests that pairs are accelerated to PeV energies within a few days; such rapid acceleration cannot be driven by shocks. Here, it is argued that the flares may be the smoking gun of magnetic dissipation in the Nebula. Using 2D and 3D particle-in-cell simulations, it is shown that the observations are consistent with relativistic magnetic reconnection, where pairs are subject to strong radiative cooling. The Crab flares may highlight the importance of relativistic magnetic reconnection in astrophysical sources.

A more accurate, stable, FDTD algorithm for electromagnetics in anisotropic dielectrics

We investigate the distribution of particle acceleration sites, independently of the actual acceleration mechanism, during plasmoid-dominated, relativistic collisionless magnetic reconnection by analyzing the results of a particle-in-cell numerical simulation. The simulation is initiated with Harris-type current layers in pair plasma with no guide magnetic field, negligible radiative losses, no initial perturbation, and using periodic boundary conditions. We find that the plasmoids develop a robust internal structure, with colder dense cores and hotter outer shells, that is recovered after each plasmoid merger on a dynamical time scale. We use spacetime diagrams of the reconnection layers to probe the evolution of plasmoids, and in this context we investigate the individual particle histories for a representative sample of energetic electrons. We distinguish three classes of particle acceleration sites associated with (1) magnetic X-points, (2) regions between merging plasmoids, and (3) the trailing edges of accelerating plasmoids. We evaluate the contribution of each class of acceleration sites to the final energy distribution of energetic electrons -- magnetic X-points dominate at moderate energies, and the regions between merging plasmoids dominate at higher energies. We also identify the dominant acceleration scenarios, in order of decreasing importance -- (1) single acceleration between merging plasmoids, (2) single acceleration at a magnetic X-point, and (3) acceleration at a magnetic X-point followed by acceleration in a plasmoid. Particle acceleration is absent only in the vicinity of stationary plasmoids. The effect of magnetic mirrors due to plasmoid contraction does not appear to be significant in relativistic reconnection.

A second-order 3D electromagnetics algorithm for curved interfaces between anisotropic dielectrics on a Yee mesh

A variant of the filter-diagonalization method, using targeted excitation to filter out unwanted modes, can extract exactly or nearly degenerate eigenmodes and frequencies from time-domain simulations. Excitation provides a particularly simple way to produce filtered states with already-existing time-domain simulations, while requiring minimal storage space. Moreover, using broader excitations that cover the entire range of desired frequencies requires just one-fifth as much computation as using narrow excitations. With this method, almost any time-domain code can be easily turned into an efficient eigenmode solver with little or no change to the code. To distinguish M degenerate modes requires running at least M different simulations, so the computational effort is proportional to the size of the degeneracy, no matter how closely-spaced the modes; however, from those M simulations many other non-degenerate modes can also be extracted with high accuracy, without much extra effort. This method allows relatively simple FDTD algorithms to compete with frequency-domain solvers, offering advantages of simplicity, flexibility and ease of implementation; also, it scales to very large problems and massively parallel computation, and it can be used to extract high-frequency modes without first having to identify lower-frequency modes. The accuracy of this method is demonstrated by finding eigenmodes and frequencies of an electromagnetic resonant cavity.