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 Warp's 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.

/pdf/novel-methods-in-the-particle-in-cell-accelerator-code-12ncjuusih.pdf

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

The Warp code, developed for heavy‐ion driven inertial fusion energy studies, is used to model high intensity ion (and electron) beams Significant capability has been incorporated in Warp, allowing nearly all sections of an accelerator to be modeled, beginning with the source Warp has as its core an explicit, three‐dimensional, particle‐in‐cell model Alongside this is a rich set of tools for describing the applied fields of the accelerator lattice, and embedded conducting surfaces (which are captured at sub‐grid resolution) Also incorporated are models with reduced dimensionality: an axisymmetric model and a transverse “slice” model The code takes advantage of modern programming techniques, including object orientation, parallelism, and scripting (via Python) It is at the forefront in the use of the computational technique of adaptive mesh refinement, which has been particularly successful in the area of diode and injector modeling, both steady‐state and time‐dependent In the presentation, some of the major aspects of Warp will be overviewed, especially those that could be useful in modeling ECR sources Warp has been benchmarked against both theory and experiment Recent results will be presented showing good agreement of Warp with experimental results from the STS500 injector test stand Additional information can be found on the web page http://hiflblgov/theory/WARP_summaryhtml

/pdf/the-warp-code-modeling-high-intensity-ion-beams-5b2dnchvqg.pdf

The WARP Code: Modeling High Intensity Ion Beams

The Warp code (and its framework of associated tools) was initially developed for particle-in-cell simulations of space-charge-dominated ion beams in accelerators, for heavy-ion-driven inertial fusion energy, and related experiments. It has found a broad range of applications, including nonneutral plasmas in traps, stray electron clouds in accelerators, laser-based acceleration, and the focusing of ion beams produced when short-pulse lasers irradiate foil targets. We summarize novel methods used in Warp, including: time-stepping conducive to diagnosis and particle injection; an interactive Python-Fortran-C structure that enables scripted and interactive user steering of runs; a variety of geometries (3-D $x$ , $y$ , $z$ ; 2-D $r$ , $z$ ; 2-D $x$ , $y$ ); electrostatic and electromagnetic field solvers; a cut-cell representation for internal boundaries; the use of warped coordinates for bent beam lines; adaptive mesh refinement, including a capability for time-dependent space-charge-limited flow from curved surfaces; models for accelerator lattice elements (magnetic or electrostatic quadrupole lenses, accelerating gaps, etc.) at user-selectable levels of detail; models for particle interactions with gas and walls; moment/envelope models that support sophisticated particle loading; a drift-Lorentz mover for rapid tracking through regions of strong and weak magnetic field; a Lorentz-boosted frame formulation with a Lorentz-invariant modification of the Boris mover; an electromagnetic solver with tunable dispersion and stride-based digital filtering; and a pseudospectral electromagnetic solver. Warp has proven useful for a wide range of applications, described very briefly herein. It is available as an open-source code under a BSD license. This paper describes material presented during the Prof. Charles K. (Ned) Birdsall Memorial Session of the 2013 IEEE Pulsed Power and Plasma Science Conference. In addition to our overview of the computational methods used in Warp, we summarize a few aspects of Ned's contributions to plasma simulation and to the careers of those he mentored.

Computational Methods in the Warp Code Framework for Kinetic Simulations of Particle Beams and Plasmas

CHAOS: An octree-based PIC-DSMC code for modeling of electron kinetic properties in a plasma plume using MPI-CUDA parallelization

(150 word max) We present a first-of-kind mesh-refined (MR) massively parallel Particle-In-Cell (PIC) code for kinetic plasma simulations optimized on the Frontier, Fugaku, Summit, and Perlmutter supercomputers. Major innovations, implemented in the WarpX PIC code, include: (i) a three level parallelization strategy that demonstrated performance portability and scaling on millions of A64FX cores and tens of thousands of AMD and Nvidia GPUs (ii) a groundbreaking mesh refinement capability that provides between 1.5 x to 4 x savings in computing requirements on the science case reported in this paper, (iii) an efficient load balancing strategy between multiple MR levels. The MR PIC code enabled 3D simulations of laser-matter interactions on Frontier, Fugaku, and Summit, which have so far been out of the reach of standard codes. These simulations helped remove a major limitation of compact laser-based electron accelerators, which are promising candidates for next generation high-energy physics experiments and ultra-high dose rate FLASH radiotherapy. 

Pushing the Frontier in the Design of Laser-Based Electron Accelerators with Groundbreaking Mesh-Refined Particle-In-Cell Simulations on Exascale-Class Supercomputers

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 domain, 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 examples of application in Heavy Ion Fusion and related fields which illustrate the effectiveness of the approach. We also report on the status of a collaboration under way at Lawrence Berkeley National Laboratory between the Applied Numerical Algorithms Group (ANAG) and the Heavy Ion Fusion group to upgrade ANAG's mesh refinement library Chombo to include the tools needed by Particle-In-Cell simulation codes.

/pdf/application-of-adaptive-mesh-refinement-to-particle-in-cell-3xhkcvn9io.pdf

Application of adaptive mesh refinement to particle-in-cell simulations of plasmas and beams

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 domain, a method which has proven to be effective in other areas (e.g., fluid dynamics simulations) is the mesh refinement technique. A brief discussion of the challenges posed by coupling this technique with plasma particle-in-cell simulations is given, followed by a presentation of examples of application in heavy ion fusion and related fields which illustrate the effectiveness of the approach. Finally, a report is given on the status of a collaboration under way at Lawrence Berkeley National Laboratory between the Applied Numerical Algorithms Group (ANAG) and the Heavy Ion Fusion group to upgrade ANAG’s mesh refinement library Chombo to include the tools needed by particle-in-cell simulation codes.

/pdf/application-of-adaptive-mesh-refinement-to-particle-in-cell-4osf263x25.pdf

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Application of adaptive mesh refinement to particle-in-cell simulations of plasmas and beams

Application of adaptive mesh refinement to particle-in-cell simulations of plasmas and beams