Enabling Lorentz boosted frame particle-in-cell simulations of laser wakefield acceleration in quasi-3D geometry

Yu, Peicheng; Xu, Xinlu; Davidson, Anthony; Tableman, Adam; Dalichaouch, Thamine; Li, Fēi; Meyers, Michael; An, Weiming; Tsung, F. S.; Decyk, Viktor K.; Fiúza, Frederico; Vieira, Jorge; Fonseca, Ricardo; Lü, Wei; Silva, Luı́s O.; Mori, W. B.

doi:10.1016/j.jcp.2016.04.014

Cited by 11 publications

(8 citation statements)

References 33 publications

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“…The use of the grid and finite difference time operators essentially means that the grid can be viewed as a medium where the dispersion relation of light is modified. In addition, there has been recent work on identifying and mitigating or eliminating what is referred to as the numerical Cerenkov instability (NCI) [9,10,11,12,13,14,15,16,17,18,19] that arises from the coupling between the electromagnetic and plasma beam modes. These schemes include using a variety of different Maxwell solvers including solvers that customize the representation of spatial derivatives in wave number space [19].…”

Section: Introductionmentioning

confidence: 99%

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

Tsung

et al. 2020

Journal of Computational Physics

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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 (those with high relativistic γ factors) 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 numer-ator 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. Although the Cerenkov fields are absent, the space charge fields are still present in the fundamental Brillouin zone for the FFT based solvers. In addition, the Cerenkov fields are present in higher order zones for the FFT based solvers. Comparison between the analytical solutions and OSIRIS results are presented. 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.

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Section: Introductionmentioning

confidence: 99%

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

Tsung

et al. 2020

Journal of Computational Physics

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“…The first two are based on the assumption that all relevant waves move forward with velocities near the speed of light, e.g., no radiation propagates backwards. Some of these methods can be combined [35].…”

Section: Introductionmentioning

confidence: 99%

“…The quasi-3D method has been implemented into some fully explicit 3D PIC codes [32,33,34] and used to study laser [14,40] and beam [11] plasma interactions. It also been successfully combined with the boosted frame method [35]. However, the azimuthal mode expansion has not been combined with the QSA method or implemented into a quasi-static PIC code.…”

Section: Introductionmentioning

confidence: 99%

A quasi-static particle-in-cell algorithm based on an azimuthal Fourier decomposition for highly efficient simulations of plasma-based acceleration: QPAD

Li,

An,

Decyk

et al. 2020

Preprint

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The three-dimensional (3D) quasi-static particle-in-cell (PIC) algorithm is a very efficient method for modeling short-pulse laser or relativistic charged particle beam-plasma interactions. In this algorithm, the plasma response, i.e., plasma wave wake, to a nonevolving laser or particle beam is calculated using a set of Maxwell's equations based on the quasi-static approximate equations that exclude radiation. The plasma fields are then used to advance the laser or beam forward using a large time step. The algorithm is many orders of magnitude faster than a 3D fully explicit relativistic electromagnetic PIC algorithm. It has been shown to be capable to accurately model the evolution of lasers and particle beams in a variety of scenarios. At the same time, an algorithm in which the fields, currents and Maxwell equations are decomposed into azimuthal harmonics has been shown to reduce the complexity of a 3D explicit PIC algorithm to that of a 2D algorithm when the expansion is truncated while maintaining accuracy for problems with near azimuthal symmetry. This hybrid algorithm uses a PIC description in r-z and a gridless description in φ. We describe a novel method that combines the quasi-static and hybrid PIC methods. This algorithm expands the fields, charge and current density into azimuthal harmonics. A set of the quasi-static field equations are derived for each harmonic. The complex amplitudes of the fields are then solved using the finite difference method. The beam and plasma particles are advanced in Cartesian coordinates using the total fields. Details on how this algorithm was implemented using a similar workflow to an existing quasi-static code, QuickPIC, are presented. The new code is called QPAD for QuickPIC with Azimuthal Decomposition. Benchmarks and comparisons between a fully 3D explicit PIC code (OSIRIS), a full 3D quasi-static code

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“…These simulations are extremely computationally intensive, due to the need to resolve the evolution of a driver (laser or particle beam) and an accelerated beam into a structure that is orders of magnitude longer and wider than the accelerated beam. Hence, various techniques or reduced models have been developed to allow multidimensional simulations at manageable computational costs: quasistatic approximation [10][11][12][13][14], ponderomotive guiding center (PGC) models [11,12,[14][15][16], simulation in an optimal Lorentz boosted frame [17][18][19][20][21][22][23][24][25][26][27][28][29], expanding the fields into a truncated series of azimuthal modes [30][31][32][33][34], fluid approximation [12,15,35] and scaled parameters [36,37].…”

Section: Introductionmentioning

confidence: 99%

Simulation of plasma accelerators with the Particle-In-Cell method

Vay¹

2020

Preprint

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We present the standard electromagnetic Particle-in-Cell method, starting from the discrete approximation of derivatives on a uniform grid. The application to second-order, centered, finite-difference discretization of the equations of motion and of Maxwell's equations is then described in one dimension, followed by two and three dimensions. Various algorithms are presented, for which we discuss the stability and accuracy, introducing and elucidating concepts like "numerical stochastic heating", "CFL limit" and "numerical dispersion". The coupling of the particles and field quantities via interpolation at various orders is detailed, together with its implication on energy and momentum conserving. Special topics of relevance to the modeling of plasma accelerators are discussed, such as moving window, optimal Lorentz boosted frame, the numerical Cherenkov instability and its mitigation. Examples of simulations of laser-driven and particle beam-driven accelerators are given, including with mesh refinement. We conclude with a discussion on high-performance computing and a brief outlook.

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Enabling Lorentz boosted frame particle-in-cell simulations of laser wakefield acceleration in quasi-3D geometry

Cited by 11 publications

References 33 publications

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

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

A quasi-static particle-in-cell algorithm based on an azimuthal Fourier decomposition for highly efficient simulations of plasma-based acceleration: QPAD

Simulation of plasma accelerators with the Particle-In-Cell method

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