arXiv subjects

Ricardo A. Fonseca

Publications and source records attributed to Ricardo A. Fonseca.

At least 19 recordsLinked to original sources

arXiv2023

Particle-in-cell simulations of pulsar magnetospheres: transition between electrosphere and force-free regimes

Global particle-in-cell (PIC) simulations of pulsar magnetospheres are performed with a volume, surface and pair production-based plasma injection schemes to systematically investigate the transition between electrosphere and force-free pulsar magnetospheric regimes. A new extension of the PIC code OSIRIS to model pulsar magnetospheres using a two-dimensional axisymmetric spherical grid is presented. The sub-algorithms of the code and thorough benchmarks are presented in detail, including a new first-order current deposition scheme that conserves charge to machine precision. It is shown that all plasma injection schemes produce a range of magnetospheric regimes. Active solutions can be obtained with surface and volume injection schemes when using artificially large plasma injection rates, and with pair production-based plasma injection for sufficiently large separation between kinematic and pair production energy scales.

astro-ph.HE↗

arXiv2021

Accurately simulating nine-dimensional phase space of relativistic particles in strong fields

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.

physics.comp-ph↗

arXiv2020

A new field solver for modeling of relativistic particle-laser interactions using the particle-in-cell algorithm

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.

physics.comp-ph↗

arXiv2020

Dynamic load balancing with enhanced shared-memory parallelism for particle-in-cell codes

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.

physics.comp-ph↗

arXiv2019

On numerical errors to the fields surrounding a relativistically moving particle in PIC codes

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.

physics.plasm-ph↗

arXiv2019

Are we ready to transfer optical light to gamma-rays?

Scattering relativistic electrons with optical lasers can result in a significant frequency upshift for the photons, potentially producing $γ$-rays. This is what linear Compton scattering taught us. Ultra-intense lasers offer nowadays a new paradigm where multi-photon absorption effects come into play. These effects can result in higher harmonics, higher yields and also electron-positron pairs. This article intends to discriminate the different laser scenarios that have been proposed over the past years as well as to give scaling laws for future experiments. The energy conversion from laser or particles to high-frequency photons is addressed for both the well-known counter propagating electron beam-laser interaction and for Quantum-electrodynamics cascades triggered by various lasers. Constructing bright and energetic gamma-ray sources in controlled conditions is within an ace of seeing the light of day.

physics.plasm-ph↗

arXiv2019

Extremely intense laser-based electron acceleration in a plasma channel

Laser pulses of extreme intensities ($I>10^{22}~ \mathrm{W/cm^2}$) are about to become available in the laboratory. The prepulse of such a laser can induce a plasma expansion that generates a low-density channel in near-critical gas jets. We present a study of channel formation and subsequent direct laser acceleration of electrons within the pre-formed channel. Radiation reaction affects the acceleration in several ways. It first interferes with the motion of the return current on the channel walls. In addition, it reduces the radial expelling efficiency of the transverse ponderomotive force, leading to the radiative trapping of particles near the channel axis. These particles then interact with the peak laser intensity and can attain multi-GeV energies.

physics.plasm-ph↗

arXiv2018

Fully kinetic large scale simulations of the collisionless Magnetorotational instability

We present two-dimensional particle-in-cell (PIC) simulations of the fully kinetic collisionless magnetorotational instability (MRI) in weakly magnetized (high $β$) pair plasma. The central result of this numerical analysis is the emergence of a self-induced turbulent regime in the saturation state of the collisionless MRI, which can only be captured for large enough simulation domains. One of the underlying mechanisms for the development of this turbulent state is the drift-kink instability (DKI) of the current sheets resulting from the nonlinear evolution of the channel modes. The onset of the DKI can only be observed for simulation domain sizes exceeding several linear MRI wavelengths. The DKI, together with ensuing magnetic reconnection, activate the turbulent motion of the plasma in the late stage of the nonlinear evolution of the MRI. At steady state, the magnetic energy has an MHD-like spectrum with a slope of $k^{-5/3}$ for $kρ<1$ and $k^{-3}$ for sub-Larmor scale ($kρ>1$). We also examine the role of the collisionless MRI and associated magnetic reconnection in the development of pressure anisotropy. We study the stability of the system due to this pressure anisotropy, observing the development of mirror instability during the early-stage of the MRI. We further discuss the importance of magnetic reconnection for particle acceleration during the turbulence regime. In particular, consistent with reconnection studies, we show that at late times the kinetic energy presents a characteristic slope of $ε^{-2}$ in the high-energy region.

astro-ph.HE↗

arXiv2016

Quantum radiation reaction in head-on laser-electron beam interaction

In this paper, we investigate the evolution of the energy spread and the divergence of electron beams while they interact with different laser pulses at intensities where quantum effects and radiation reaction are of relevance. The interaction is modeled with a QED-PIC code and the results are compared with those obtained with a standard PIC code with the addition of a classical radiation reaction module and with theoretical predictions. While classical radiation reaction is a continuous process, in QED, radiation emission is stochastic. The two pictures reconcile in the limit when the emitted photons energy is small compared to the energy of the emitting electrons. The energy spread of the electron distribution function always tends to decrease with classical radiation reaction, whereas the stochastic QED emission can also enlarge it. These two tendencies compete in the QED-dominated regime. Our analysis, supported by the QED module, reveals an upper limit to the maximal attainable energy spread due to stochasticity that depends on laser intensity and the electron beam average energy. Beyond this limit, the energy spread decreases. These findings are verified for different laser pulse lengths ranging from short ~ 30 fs pulses presently available to the long ~ 150 fs pulses expected in the near-future laser facilities, and compared with a theoretical model. Our results also show that near future experiments will be able to probe this transition and to demonstrate the competition between enhanced QED induced energy spread and energy spectrum narrowing from classical radiation reaction.

physics.plasm-ph↗

arXiv2016

Electron - positron cascades in multiple-laser optical traps

We present an analytical and numerical study of multiple-laser QED cascades induced with linearly polarised laser pulses. We analyse different polarisation orientations and propose a configuration that maximises the cascade multiplicity and favours the laser absorption. We generalise the analytical estimate for the cascade growth rate previously calculated in the field of two colliding linearly polarised laser pulses and account for multiple laser interaction. The estimate is verified by a comprehensive numerical study of four-laser QED cascades across a range of different laser intensities with QED PIC module of OSIRIS. We show that by using four linearly polarised 30 fs laser pulses, one can convert more than 50 % of the total energy to gamma-rays already at laser intensity $I\simeq10^{24}\ \mathrm{W/cm^2}$. In this configuration, the laser conversion efficiency is higher compared with the case with two colliding lasers.

physics.plasm-ph↗

arXiv2016

Controlling the Numerical Cerenkov Instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction

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.

physics.comp-ph↗

arXiv2016

Classical Radiation Reaction in Particle-In-Cell Simulations

Under the presence of ultra high intensity lasers or other intense electromagnetic fields the motion of particles in the ultrarelativistic regime can be severely affected by radiation reaction. The standard particle-in-cell (PIC) algorithms do not include radiation reaction effects. Even though this is a well known mechanism, there is not yet a definite algorithm nor a standard technique to include radiation reaction in PIC codes. We have compared several models for the calculation of the radiation reaction force, with the goal of implementing an algorithm for classical radiation reaction in the Osiris framework, a state-of-the-art PIC code. The results of the different models are compared with standard analytical results, and the relevance/advantages of each model are discussed. Numerical issues relevant to PIC codes such as resolution requirements, application of radiation reaction to macro particles and computational cost are also addressed. The Landau and Lifshitz reduced model is chosen for implementation.

physics.plasm-ph↗

arXiv2015

Laser absorption via QED cascades in counter propagating laser pulses

A model for laser light absorption in electron-positron plasmas self-consistently created via QED cascades is described. The laser energy is mainly absorbed due to hard photon emission via nonlinear Compton scattering. The degree of absorption depends on the laser intensity and the pulse duration. The QED cascades are studied with multi-dimensional particle-in-cell simulations complemented by a QED module and a macro-particle merging algorithm that allows to handle the exponential growth of the number of particles. Results range from moderate-intensity regimes ($\sim$ 10 PW) where the laser absorption is negligible, to extreme intensities (> 100 PW) where the degree of absorption reaches 80%. Our study demonstrates good agreement between the analytical model and simulations. The expected properties of the hard photon emission and the generated pair-plasma are investigated, and the experimental signatures for near-future laser facilities are discussed.

physics.plasm-ph↗

arXiv2015

Lorentz boosted frame simulation of Laser wakefield acceleration in quasi-3D geometry

When modeling laser wakefield acceleration (LWFA) using the particle-in-cell (PIC) algorithm in a Lorentz boosted frame, the plasma is drifting relativistically at $β_b c$ towards the laser, which can lead to a computational speedup of $\sim γ_b^2=(1-β_b^2)^{-1}$. Meanwhile, when LWFA is modeled in the quasi-3D geometry in which the electromagnetic fields and current are decomposed into a limited number of azimuthal harmonics, speedups are achieved by modeling three dimensional problems with the computation load on the order of two dimensional $r-z$ simulations. Here, we describe how to combine the speed ups from the Lorentz boosted frame and quasi-3D algorithms. The key to the combination is the use of a hybrid Yee-FFT solver in the quasi-3D geometry that can be used to effectively eliminate the Numerical Cerenkov Instability (NCI) that inevitably arises in a Lorentz boosted frame due to the unphysical coupling of Langmuir modes and EM modes of the relativistically drifting plasma in these simulations. In addition, based on the space-time distribution of the LWFA data in the lab and boosted frame, we propose to use a moving window to follow the drifting plasma to further reduce the computational load. We describe the details of how the NCI is eliminated for the quasi-3D geometry, the setups for simulations which combine the Lorentz boosted frame and quasi-3D geometry, the use of a moving window, and compare the results from these simulations against their corresponding lab frame cases. Good agreement is obtained, particularly when there is no self-trapping, which demonstrates it is possible to combine the Lorentz boosted frame and the quasi-3D algorithms when modeling LWFA to achieve unprecedented speedups.

physics.plasm-ph↗

arXiv2015

Shock formation in electron-ion plasmas: mechanism and timing

We analyse the full shock formation process in electron-ion plasmas in theory and simulations. It is accepted that electromagnetic shocks in initially unmagnetised relativistic plasmas are triggered by the filamentation instability. However, the transition from the first unstable phase to the quasi-steady shock is still missing. We derive a theoretical model for the shock formation time, taking into account the filament merging in the non-linear phase of the filamentation instability. This process is much slower than in electron-positron pair shocks, so that the shock formation is longer by a factor proportional to sqrt(m_i/m_e) ln(m_i/m_e).

astro-ph.HE↗

arXiv2015

Mitigation of numerical Cerenkov radiation and instability using a hybrid finite difference-FFT Maxwell solver and a local charge conserving current deposit

A hybrid Maxwell solver for fully relativistic and electromagnetic (EM) particle-in-cell (PIC) codes is described. In this solver, the EM fields are solved in $k$ space by performing an FFT in one direction, while using finite difference operators in the other direction(s). This solver eliminates the numerical Cerenkov radiation for particles moving in the preferred direction. Moreover, the numerical Cerenkov instability (NCI) induced by the relativistically drifting plasma and beam can be eliminated using this hybrid solver by applying strategies that are similar to those recently developed for pure FFT solvers. A current correction is applied for the charge conserving current deposit to correctly account for the EM calculation in hybrid Yee-FFT solver. A theoretical analysis of the dispersion properties in vacuum and in a drifting plasma for the hybrid solver is presented, and compared with PIC simulations with good agreement obtained. This hybrid solver is applied to both 2D and 3D Cartesian and quasi-3D (in which the fields and current are decomposed into azimuthal harmonics) geometries. Illustrative results for laser wakefield accelerator simulation in a Lorentz boosted frame using the hybrid solver in the 2D Cartesian geometry are presented, and compared against results from 2D UPIC-EMMA simulation which uses a pure spectral Maxwell solver, and from OSIRIS 2D lab frame simulation using the standard Yee solver. Very good agreement is obtained which demonstrates the feasibility of using the hybrid solver for high fidelity simulation of relativistically drifting plasma with no evidence of the numerical Cerenkov instability.

physics.comp-ph↗

arXiv2015

Elimination of the numerical Cerenkov instability for spectral EM-PIC codes

When using an electromagnetic particle-in-cell (EM-PIC) code to simulate a relativistically drifting plasma, a violent numerical instability known as the numerical Cerenkov instability (NCI) occurs. The NCI is due to the unphysical coupling of electromagnetic waves on a grid to wave-particle resonances, including aliased resonances, i.e., $ω+ 2πμ/Δt=(k_1+ 2πν_1/Δx_1)v_0$, where $μ$ and $ν_1$ refer to the time and space aliases and the plasma is drifting relativistically at velocity $v_0$ in the $\hat{1}$-direction. Recent studies have shown that an EM-PIC code which uses a spectral field solver and a low pass filter can eliminate the fastest growing modes of the NCI. Based on these studies a new spectral PIC code for studying laser wakefield acceleration (LWFA) in the Lorentz boosted frame was developed. However, we show that for parameters of relevance for LWFA simulations in the boosted frame, a relativistically drifting plasma is susceptible to a host of additional unstable modes with lower growth rates, and that these modes appear when the fastest growing unstable modes are filtered out. We show that these modes are most easily identified as the coupling between modes which are purely transverse (EM) and purely longitudinal (Langmuir) in the rest frame of the plasma for specific time and space aliases. We rewrite the dispersion relation of the drifting plasma for a general field solver and obtain analytic expressions for the location and growth rate for each unstable mode, i.e, for each time and space aliased resonances. We show for the spectral solver that when the fastest growing mode is eliminated a new mode at the fundamental resonance ($μ=ν_1=0$) can be seen. (Please check the whole abstract in the paper).

physics.plasm-ph↗

arXiv2014

Particle Merging Algorithm for PIC Codes

Particle-in-cell merging algorithms aim to resample dynamically the six-dimensional phase space occupied by particles without distorting substantially the physical description of the system. Whereas various approaches have been proposed in previous works, none of them seemed to be able to conserve fully charge, momentum, energy and their associated distributions. We describe here an alternative algorithm based on the coalescence of N massive or massless particles, considered to be close enough in phase space, into two new macro-particles. The local conservation of charge, momentum and energy are ensured by the resolution of a system of scalar equations. Various simulation comparisons have been carried out with and without the merging algorithm, from classical plasma physics problems to extreme scenarios where quantum electrodynamics is taken into account, showing in addition to the conservation of local quantities, the good reproducibility of the particle distributions. In case where the number of particles ought to increase exponentially in the simulation box, the dynamical merging permits a considerable speedup, and significant memory savings that otherwise would make the simulations impossible to perform.

physics.plasm-ph↗