Jean-Luc Vay

Novel methods in the Particle-In-Cell accelerator Code-Framework Warp

The Particle-In-Cell (PIC) Code-Framework Warp is being developed by the Heavy Ion Fusion Science Virtual National Laboratory (HIFS-VNL) to guide the development of accelerators that can deliver beams suitable for high-energy density experiments and implosion of inertial fusion capsules. It is also applied in various areas outside the Heavy Ion Fusion program to the study and design of existing and next-generation high-energy accelerators, including the study of electron cloud effects and laser wakefield acceleration for example. This paper presents an overview of Warps capabilities, summarizing recent original numerical methods that were developed by the HIFS-VNL (including PIC with adaptive mesh refinement, a large-timestep ?drift-Lorentz? mover for arbitrarily magnetized species, a relativistic Lorentz invariant leapfrog particle pusher, simulations in Lorentz-boosted frames, an electromagnetic solver with tunable numerical dispersion and efficient stride-based digital filtering), with special emphasis on the description of the mesh refinement capability. Selected examples of the applications of the methods to the abovementioned fields are given.

Numerical methods for instability mitigation in the modeling of laser wakefield accelerators in a Lorentz-boosted frame

Modeling of laser-plasma wakefield accelerators in an optimal frame of reference [1] has been shown to produce orders of magnitude speed-up of calculations from first principles. Obtaining these speedups required mitigation of a high-frequency instability that otherwise limits effectiveness. In this paper, methods are presented which mitigated the observed instability, including an electromagnetic solver with tunable coefficients, its extension to accommodate Perfectly Matched Layers and Friedmans damping algorithms, as well as an efficient large bandwidth digital filter. It is observed that choosing the frame of the wake as the frame of reference allows for higher levels of filtering or damping than is possible in other frames for the same accuracy. Detailed testing also revealed the existence of a singular time step at which the instability level is minimized, independently of numerical dispersion. A combination of the techniques presented in this paper prove to be very efficient at controlling the instability, allowing for efficient direct modeling of 10GeV class laser plasma accelerator stages. The methods developed in this paper may have broader application, to other Lorentz-boosted simulations and Particle-In-Cell simulations in general.

Numerical stability of relativistic beam multidimensional PIC simulations employing the Esirkepov algorithm

Rapidly growing numerical instabilities routinely occur in multidimensional particle-in-cell computer simulations of plasma-based particle accelerators, astrophysical phenomena, and relativistic charged particle beams. Reducing instability growth to acceptable levels has necessitated higher resolution grids, high-order field solvers, current filtering, etc. except for certain ratios of the time step to the axial cell size, for which numerical growth rates and saturation levels are reduced substantially. This paper derives and solves the cold beam dispersion relation for numerical instabilities in multidimensional, relativistic, electromagnetic particle-in-cell programs employing either the standard or the Cole–Karkkainnen finite difference field solver on a staggered mesh and the common Esirkepov current-gathering algorithm. Good overall agreement is achieved with previously reported results of the WARP code. In particular, the existence of select time steps for which instabilities are minimized is explained. Additionally, an alternative field interpolation algorithm is proposed for which instabilities are almost completely eliminated for a particular time step in ultra-relativistic simulations.

A domain decomposition method for pseudo-spectral electromagnetic simulations of plasmas

Summary form only given. Particle-In-Cell (PIC) has been the method of choice for the last fifty years for modeling plasmas that include kinetic effects. The most popular electromagnetic formulation uses finite difference discretization of Maxwells equations in both space and time (FDTD), which produces fast solvers that scale well in parallel, but suffers from various anomalous numerical effects resulting from discretization, field staggering, and numerical dispersion. Pseudo-spectral methods, which advance fields in Fourier space, offer a number of advantages over FDTD algorithms. In particular, Habers Pseudo-Spectral Analytical Time-Domain (PSATD) algorithm1 has dispersion-free propagation and no Courant limit in vacuum. Yet, pseudo-spectral solvers have not been widely used, due in part to the difficulty for efficient parallelization owing to global communications associated with global FFTs. We present a novel method2 for the parallelization of electromagnetic pseudo-spectral solvers that requires only local FFTs and exchange of local guard cell data between neighboring regions, by taking advantage of the properties of DFTs, the linearity of Maxwells equations and the finite speed of light. Although this requires a small approximation, test results show that no significant error is made on the test cases such as single electromagnetic pulse expansion, or Particle-In-Cell simulations of the wakefield formation in a laser plasma accelerator. Extension to other equations beyond electromagnetic PIC will be discussed.

Mesh refinement for particle-in-cell plasma simulations: Applications to - and benefits for - heavy ion fusion

The numerical simulation of the driving beams in a heavy ion fusion power plant is a challenging task, and simulation of the power plant as a whole, or even of the driver, is not yet possible. Despite the rapid progress in computer power, past and anticipated, one must consider the use of the most advanced numerical techniques, if we are to reach our goal expeditiously. One of the difficulties of these simulations resides in the disparity of scales, in time and in space, which must be resolved. When these disparities are in distinctive zones of the simulation region, a method which has proven to be effective in other areas (e.g., fluid dynamics simulations) is the mesh refinement technique. They discuss the challenges posed by the implementation of this technique into plasma simulations (due to the presence of particles and electromagnetic waves). They will present the prospects for and projected benefits of its application to heavy ion fusion. In particular to the simulation of the ion source and the final beam propagation in the chamber. A collaboration project is under way at LBNL between the Applied Numerical Algorithms Group (ANAG) and the HIF group to couple the Adaptive Mesh Refinement (AMR) library (CHOMBO) developed by the ANAG group to the Particle-In-Cell accelerator code WARP developed by the HIF-VNL. They describe their progress and present their initial findings.

Numerical stability analysis of the pseudo-spectral analytical time-domain PIC algorithm

The pseudo-spectral analytical time-domain (PSATD) particle-in-cell (PIC) algorithm solves the vacuum Maxwell?s equations exactly, has no Courant time-step limit (as conventionally defined), and offers substantial flexibility in plasma and particle beam simulations. It is, however, not free of the usual numerical instabilities, including the numerical Cherenkov instability, when applied to relativistic beam simulations. This paper derives and solves the numerical dispersion relation for the PSATD algorithm and compares the results with corresponding behavior of the more conventional pseudo-spectral time-domain (PSTD) and finite difference time-domain (FDTD) algorithms. In general, PSATD offers superior stability properties over a reasonable range of time steps. More importantly, one version of the PSATD algorithm, when combined with digital filtering, is almost completely free of the numerical Cherenkov instability for time steps (scaled to the speed of light) comparable to or smaller than the axial cell size.

Applying the Roofline Performance Model to the Intel Xeon Phi Knights Landing Processor

The Roofline Performance Model is a visually intuitive method used to bound the sustained peak floating-point performance of any given arithmetic kernel on any given processor architecture. In the Roofline, performance is nominally measured in floating-point operations per second as a function of arithmetic intensity (operations per byte of data). In this study we determine the Roofline for the Intel Knights Landing (KNL) processor, determining the sustained peak memory bandwidth and floating-point performance for all levels of the memory hierarchy, in all the different KNL cluster modes. We then determine arithmetic intensity and performance for a suite of application kernels being targeted for the KNL based supercomputer Cori, and make comparisons to current Intel Xeon processors. Cori is the National Energy Research Scientific Computing Center’s (NERSC) next generation supercomputer. Scheduled for deployment mid-2016, it will be one of the earliest and largest KNL deployments in the world.

Suppressing the numerical Cherenkov instability in FDTD PIC codes

A procedure for largely suppressing the numerical Cherenkov instability in finite difference time-domain (FDTD) particle-in-cell (PIC) simulations of cold, relativistic beams is derived, and residual growth rates computed and compared with WARP code simulation results. Sample laser-plasma acceleration simulation output is provided to further validate the new procedure.

Implementations of mesh refinement schemes for Particle-In-Cell plasma simulations

Plasma simulations are often rendered challenging by the disparity of scales in time and in space which must be resolved. When these disparities are in distinctive zones of the simulation region, a method which has proven to be effective in other areas (e.g. fluid dynamics simulations) is the mesh refinement technique. We briefly discuss the challenges posed by coupling this technique with plasma Particle-In-Cell simulations and present two implementations in more detail, with examples.

Vlasov simulations of beams with a moving grid

Vlasov simulations can for some situations be a valuable alternative to PIC simulations for the study of intense beam propagation. However, as they rely on a phase-space grid which is fixed for the whole simulation, important computing effort can be wasted in zones where no particles are present at some given time. In order to overcome this drawback, we introduce here a new method which makes use of a phase-space grid which is uniform at any given time, but moves in time according to the evolution of the envelope of the beam.