David P. Grote

Three-dimensional particle simulation of heavy-ion fusion beams

The beams in a heavy‐ion‐beam‐driven inertial fusion (HIF) accelerator are collisionless, nonneutral plasmas, confined by applied magnetic and electric fields. These space‐charge‐dominated beams must be focused onto small (few mm) spots at the fusion target, and so preservation of a small emittance is crucial. The nonlinear beam self‐fields can lead to emittance growth, and so a self‐consistent field description is needed. To this end, a multidimensional particle simulation code, warp [Friedman et al., Part. Accel. 37‐38, 131 (1992)], has been developed and is being used to study the transport of HIF beams. The code’s three‐dimensional (3‐D) package combines features of an accelerator code and a particle‐in‐cell plasma simulation. Novel techniques allow it to follow beams through many accelerator elements over long distances and around bends. This paper first outlines the algorithms employed in warp. A number of applications and corresponding results are then presented. These applications include studies ...

The WARP Code: Modeling High Intensity Ion Beams

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 ...

Three-dimensional simulations of high-current beams in induction accelerators with WARP3d

For many issues relevant to acceleration and propagation of heavy-ion beams for inertial confinement fusion, understanding the behavior of the beam requires the self-consistent inclusion of the self-fields of the beams in multiple dimensions. For these reasons, the three-dimensional simulation code WARP3d A.Friedman was developed. The code combines the particle-in-cell plasma simulation technique with a realistic description of the elements which make up an accelerator. In this paper, the general structure of the code is reviewed and details of two ongoing applications are presented along with a discussion of simulation techniques used. The most important results of this work are presented.

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.

Recirculating induction accelerators as drivers for heavy ion fusion

A two‐year study of recirculating induction heavy ion accelerators as low‐cost driver for inertial‐fusion energy applications was recently completed. The projected cost of a 4 MJ accelerator was estimated to be about

Simulation of heavy ion beams with a semi-Lagrangian Vlasov solver

500 M (million) and the efficiency was estimated to be 35%. The principal technology issues include energy recovery of the ramped dipole magnets, which is achieved through use of ringing inductive/capacitive circuits, and high repetition rates of the induction cell pulsers, which is accomplished through arrays of field effect transistor (FET) switches. Principal physics issues identified include minimization of particle loss from interactions with the background gas, and more demanding emittance growth and centroid control requirements associated with the propagation of space‐charge‐dominated beams around bends and over large path lengths. In addition, instabilities such as the longitudinal resistive instability, beam‐breakup instability and betatron‐orbit instability were found to be controllable with careful design.

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

Abstract We introduce the semi-Lagrangian Vlasov method, which computes the distribution function of the particles on a grid in phase space, to beam propagation in a uniform focusing channel. With this new tool, we study halo formation in a mismatched thermal beam, and the evolution of an initial semi-Gaussian beam. For the latter problem comparisons are made with the Particle-In-Cell code WARP.

Computational methods in the Warp code framework for kinetic simulations of particle beams and plasmas

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.

Overview of US heavy ion fusion research

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 Neds contributions to plasma simulation and to the careers of those he mentored.