Recent Developments and Applications of the Beam Simulation Code WARP
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Response to FESAC survey, non-fusion connections to Fusion Energy Sciences. Applications of the FES-supported beam and plasma simulation code, Warp
The Fusion Energy Sciences Advisory Committee’s subcommittee on non-fusion applications (FESAC NFA) is conducting a survey to obtain information from the fusion community about non-fusion work that has resulted from their DOE-funded fusion research. The subcommittee has requested that members of the community describe recent developments connected to the activities of the DOE Office of Fusion Energy Sciences. Two questions in particular were posed by the subcommittee. This document contains the authors’ responses to those questions.
43 PARTICLE ACCELERATORS↗
Computational Methods in the Warp Code Framework for Kinetic Simulations of Particle Beams and Plasmas
Abstract not provided
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Particle-in-cell/accelerator code for space-charge dominated beam simulation
Warp is a multidimensional discrete-particle beam simulation program designed to be applicable where the beam space-charge is non-negligible or dominant. It is being developed in a collaboration among LLNL, LBNL and the University of Maryland. It was originally designed and optimized for heave ion fusion accelerator physics studies, but has received use in a broader range of applications, including for example laser wakefield accelerators, e-cloud studies in high enery accelerators, particle traps and other areas. At present it incorporates 3-D, axisymmetric (r,z) planar (x-z) and transverse slice (x,y) descriptions, with both electrostatic and electro-magnetic fields, and a beam envelope model. The code is guilt atop the Python interpreter language.
Grote, D. P.↗
Space-Charge Compensation Using Electron Columns at IOTA
Beam loss due to space charge is a major problem at current and future high intensity particle accelerators. The space charge force can be compensated for proton or ion beams by creating a column of electrons with a charge distribution matched to that of the beam, maintaining electron-proton stability. The column is created by the beam ionizing short sections of high pressure gas. The ionization electrons are then shaped appropriately using electric and magnetic fields. The Integrable Optics Test Accelerator (IOTA) at Fermilab is a test bed for beam loss and instability mitigation techniques. Simulations using the particle-in-cell code, Warp, have been made to track the evolution of both the electron column and the beam over multiple passes. A 2.5 MeV proton beamline is under construction at IOTA, to be used to study the effect of the electron column on a space charge dominated beam.
43 PARTICLE ACCELERATORS↗
Sirepo - Warp
Sirepo is an open source framework for cloud computing. The graphical user interface (GUI) for Sirepo, also known as the client, executes in any HTML5 compliant web browser on any computing platform, including tablets. The client is built in JavaScript, making use of the following open source libraries: Bootstrap, which is fundamental for cross-platform web applications; AngularJS, which provides a model–view–controller (MVC) architecture and GUI components; and D3.js, which provides interactive plots and data-driven transformations. The Sirepo server is built on the following Python technologies: Flask, which is a lightweight framework for web development; Jin-ja, which is a secure and widely used templating language; and Werkzeug, a utility library that is compliant with the WSGI standard. We use Nginx as the HTTP server and proxy, which provides a scalable event-driven architecture. The physics codes supported by Sirepo execute inside a Docker container. One of the codes supported by Sirepo is Warp. Warp is a particle-in-cell (PIC) code de-signed to simulate high-intensity charged particle beams and plasmas in both the electrostatic and electromagnetic regimes, with a wide variety of integrated physics models and diagnostics. At pre-sent, Sirepo supports a small subset of Warp’s capabilities. Warp is open source and is part of the Berkeley Lab Accelerator Simulation Toolkit.
Nagler, Robert↗
Sirepo - Warp
Sirepo is an open source framework for cloud computing. The graphical user interface (GUI) for Sirepo, also known as the client, executes in any HTML5 compliant web browser on any computing platform, including tablets. The client is built in JavaScript, making use of the following open source libraries: Bootstrap, which is fundamental for cross-platform web applications; AngularJS, which provides a model–view–controller (MVC) architecture and GUI components; and D3.js, which provides interactive plots and data-driven transformations. The Sirepo server is built on the following Python technologies: Flask, which is a lightweight framework for web development; Jin-ja, which is a secure and widely used templating language; and Werkzeug, a utility library that is compliant with the WSGI standard. We use Nginx as the HTTP server and proxy, which provides a scalable event-driven architecture. The physics codes supported by Sirepo execute inside a Docker container. One of the codes supported by Sirepo is Warp. Warp is a particle-in-cell (PIC) code de-signed to simulate high-intensity charged particle beams and plasmas in both the electrostatic and electromagnetic regimes, with a wide variety of integrated physics models and diagnostics. At pre-sent, Sirepo supports a small subset of Warp’s capabilities. Warp is open source and is part of the Berkeley Lab Accelerator Simulation Toolkit.
Nagler, Robert↗
Progress towards the development of a realistic electron cyclotron resonance ion source extraction model
In this paper, an ongoing effort to provide a simulation and design tool for electron cyclotron resonance ion source extraction and low energy beam transport is described and benchmarked against experimental results. Utilizing the particle-in-cell code WARP, a set of scripts has been developed: A semiempirical method of generating initial conditions, a 2D-3D hybrid method of plasma extraction and a simple beam transport deck. Measured emittances and beam profiles of uranium and helium beams are shown and the influence of the sextupole part of the plasma confinement field is investigated. The results are compared to simulations carried out using the methods described above. The results show that the simulation model (with some additional refinements) represents highly charged, well-confined ions well, but that the model is less applicable for less confined, singly charged ions.
43 PARTICLE ACCELERATORS↗
Simulations of Field-Emission Electron Beams from CNT Cathodes in RF Photoinjectors
Average field emission currents of up to 700 mA were produced by Carbon Nano Tube (CNT) cathodes in a 1.3 GHz RF gun at Fermilab High Brightness Electron Source Lab. (HBESL). The CNT cathodes were manufactured at Xintek and tested under DC conditions at RadiaBeam. The electron beam intensity as well as the other beam properties are directly related to the time-dependent electric field at the cathode and the geometry of the RF gun. This report focuses on simulations of the electron beam generated through field-emission and the results are compared with experimental measurements. These simulations were performed with the time-dependent Particle In Cell (PIC) code WARP.
43 PARTICLE ACCELERATORS↗
Multipass Simulations of Space Charge Compensation using Electron Columns at IOTA
Defocusing repulsive forces due to self space charge fields lead to degradation of high-intensity particle beams. Being of particular concern for low- and medium-energy proton beams, they result in emittance growth, beam halo formation, and beam loss. They set stringent limits on the intensity of frontier accelerators; therefore, the mitigation of space charge effects is a crucial challenge to improve proton beam intensity. The space charge effects in a positively charged proton beam can be effectively compensated using negatively charged electron columns. In this paper, we present the results of simulations using Synergia of the Electron Column lattice for IOTA. Beam loss due to space charge effects and aperture restrictions have been studied, as well as bunch formation and matching using an adiabatic ramp of the RF cavity. The results show the need for space charge compensation, and provide the basis for integration of the Synergia and Warp codes in order to form a complete simulation of space charge compensation using an Electron Column in IOTA.
43 PARTICLE ACCELERATORS↗
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.
43 PARTICLE ACCELERATORS↗
Advanced Simulation Tools for Muon-Based Accelerators
The project developed new software tools incorporating the most accurate theoretical calculations and experimental data available for crucial and not-yet-considered physics processes specific to muon accelerators. These new tools were applied to modeling muon ionization cooling channels for a muon collider or a neutrino factory, the facilities that have the potential to discover and explore new exciting fundamental physics but require the development of demanding technologies and innovative concepts. G4beamline, COSY Infinity, and WARP computer codes are particularly well-suited for addressing muon accelerator modeling problems. G4beamline was chosen for its flexibility and modularity, and for being one of the de facto standard codes used by the muon accelerator community. COSY was selected for speed, ability to take into account high-order nonlinear effects essential for the large beams under consideration, and availability of built-in optimization tools. WARP was chosen for its space charge calculation capabilities, speed and flexibility of implementing new lattice elements such as RF cavities. This final technical report summarizes the efforts on implementing advanced new tools in these computer codes addressing the shortcomings in modeling muon physics processes and using these tools to model muon ionization cooling channels.
43 PARTICLE ACCELERATORS↗
Modeling laser-driven electron acceleration using WARP with Fourier decomposition
WARP is used with the recent implementation of the Fourier decomposition algorithm to model laser-driven electron acceleration in plasmas. Simulations were carried out to analyze the experimental results obtained on ionization-induced injection in a gas cell. The simulated results are in good agreement with the experimental ones, confirming the ability of the code to take into account the physics of electron injection and reduce calculation time. We present a detailed analysis of the laser propagation, the plasma wave generation and the electron beam dynamics.
43 PARTICLE ACCELERATORS↗
Warp-X: A new exascale computing platform for beam–plasma simulations
Turning the current experimental plasma accelerator state-of-the-art from a promising technology into mainstream scientific tools depends critically on high-performance, high-fidelity modeling of complex processes that develop over a wide range of space and time scales. As part of the U.S. Department of Energy's Exascale Computing Project, a team from Lawrence Berkeley National Laboratory, in collaboration with teams from SLAC National Accelerator Laboratory and Lawrence Livermore National Laboratory, is developing a new plasma accelerator simulation tool that will harness the power of future exascale supercomputers for high-performance modeling of plasma accelerators. We present the various components of the codes such as the new Particle-In-Cell Scalable Application Resource (PICSAR) and the redesigned adaptive mesh refinement library AMReX, which are combined with redesigned elements of the Warp code, in the new WarpX software. Lastly, the code structure, status, early examples of applications and plans are discussed.
43 PARTICLE ACCELERATORS↗
Toward fully self-consistent simulation of the interaction of E-Clouds and beams with WARP-POSINST
To predict the evolution of electron clouds and their effect on the beam, the high energy physics community has relied so far on the complementary use of 'buildup' and 'single/multi-bunch instability' reduced descriptions. The former describes the evolution of electron clouds at a given location in the ring, or 'station', under the influence of prescribed beams and external fields [1], while the latter (sometimes also referred as the 'quasi-static' approximation [2]) follows the interaction between the beams and the electron clouds around the accelerator with prescribed initial distributions of electrons, assumed to be concentrated at a number of discrete 'stations' around the ring. Examples of single bunch instability codes include HEADTAIL [3], QuickPIC [4, 5], and PEHTS [6]. By contrast, a fully self-consistent approach, in which both the electron cloud and beam distributions evolve simultaneously under their mutual influence without any restriction on their relative motion, is required for modeling the interaction of high-intensity beams with electron clouds for heavy-ion beam-driven fusion and warm-dense matter science. This community has relied on the use of Particle-In-Cell (PIC) methods through the development and use of the WARP-POSINST code suite [1, 7, 8]. The development of novel numerical techniques (including adaptive mesh refinement, and a new 'drift-Lorentz' particle mover for tracking charged particles in magnetic fields using large time steps) has enabled the first application of WARP-POSINST to the fully self-consistent modeling of beams and electron clouds in high energy accelerators [9], albeit for only a few betatron oscillations. It was recently observed [10] that there exists a preferred frame of reference which minimizes the number of computer operations needed to simulate the interaction of relativistic objects. This opens the possibility of reducing the cost of fully self-consistent simulations for the interaction of ultrarelativistic beams with electron cloud by orders of magnitude. The computational cost of the fully self-consistent mode is then predicted to be comparable to that of the quasi-static mode, assuming that several stations per betatron period are needed. During the workshop, there was some debate about the number of stations per betatron period that are needed when using the quasi-static mode. The argument was made that if there is less than one station per betatron period, then artificial resonances can be triggered and the resulting emittance growth provides an upper bound. The emittance growth thus obtained will fall either above or below the operational requirements of the machine. In the latter case, one can conclude that the electron effect that has been simulated is of no concern. However, if the emittance growth that was obtained is above the threshold, then the results become inconclusive, and simulations which resolve the betatron motion are then needed. In this case, according to [10], the fully self-consistent approach becomes an option. The aim of this paper is to investigate whether this option is indeed practical.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Note on numerical study of the beam energy spread in NDCX-I
The kinetic energy spread (defined here as the standard deviation of the beam particle energies) sets the ultimate theoretical limit on the longitudinal compression that can be attained on NDCX-I and NDCX-II. Experimental measurements will inevitably include the real influences on the longitudinal phase space of the beam due to injector and accelerator field imperfections1. These induced energy variations may be the real limit to the longitudinal compression in an accelerator. We report on a numerical investigation of the energy spread evolution in NDCX-I; these studies do not include all the real imperfections, but rather are intended to confirm that there are no other intrinsic mechanisms (translaminar effects, transverse-longitudinal anisotropy instability, etc.) for significant broadening of the energy distribution. We have performed Warp simulations that use a realistic Marx voltage waveform which was derived from experimental measurements (averaged over several shots), a fully-featured model of the accelerating and focusing lattice, and new diagnostics for computing the local energy spread (and temperature) that properly account for linear correlations that arise from the discrete binning along each physical dimension (these capabilities reproduce and extend those of the earlier HIF code BPIC). The new diagnostics allow for the calculation of multi-dimensional maps of energy spread and temperature in 2-D axisymmetric or 3-D Cartesian space at selected times. The simulated beam-line was terminated at z = 3 m by a conducting plate, so as to approximately reproduce the experimental conditions at the entrance of the spectrometer that was used for mapping the longitudinal phase space. Snapshots of the beam projection and current, as well as the Marx waveform and history of beam kinetic energy collected at the end plate, are shown in Fig. 1. A two-dimensional axisymmetric map of energy spread from simulations of a typical NDCX-I configuration is shown in Fig. 2 (a). The energy spread starts at 0.1 eV at the source and rapidly rises to a few eV, then fluctuates between a fraction of an eV and tens of eV, ending near the exit in a range of a few eV at the outer edge of the beam to a few tens of eV near the axis. The higher value on-axis is associated with greater numerical noise there, due to the axisymmetric geometry of the calculation, resulting in poorer simulation-particle statistics at small radius. A scatter plot of the macroparticles kinetic energy (KE) versus radius (R) and longitudinal position (0.28 m < z < 3 m) colored by local energy spread is shown in Fig. 2 (b). As expected, there is a correlation of the kinetic energy with radius that is clearly visible at z = 2.8 m and vanishes at the metal plate at z = 3 m. More snapshots from simulations varying the time step, grid resolution and number of macroparticles are given in Appendix II. The macro-particles were collected at the exit plate and their kinetic energy history is plotted in Fig. 3 (left) and contrasted to an experimental measurement using a streak camera shown in Fig. 3. For some types of measurements, averaging over several pulses to improve signal-to-noise will contribute an additional spread that may not be present on any single beam pulse. The upper bound for the energy spread is in the range of a few 100 eV for the experiment while in the range of a few eV for the reported Warp simulations. The Marx voltage exhibits variations in the range of up to several hundreds of volts, playing a significant role in the experimentally measured energy spread, which may account for the difference between the experimental and the simulated bounds.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Simulation Results of a Feedback Control System to Damp Electron Cloud Single-Bunch Transverse Instabilities In The Cern SPS
Transverse Single-Bunch Instabilities due to the Electron Cloud effect are limiting the operation at high current of the SPS at CERN. Recently a high-bandwidth Feedback System has been proposed as a possible solution to stabilize the beam and is currently under study. We analyze the dynamics of the bunch actively damped with a simple model of the Feedback in the macro-particle code WARP, in order to investigate the limitations of the System such as the minimum amount of power required to maintain stability. We discuss the feedback model, report on simulation results and present our plans for further development of the numerical model.
43 PARTICLE ACCELERATORS↗
Direct Numerical Modeling of E-Cloud Driven Instability of a Bunch Train in the CERN SPS
The simulation package WARP-POSINST was recently upgraded for handling multiple bunches and modeling concurrently the electron cloud buildup and its effect on the beam, allowing for direct self-consistent simulation of bunch trains generating, and interacting with, electron clouds. We have used the WARP-POSINST package on massively parallel supercomputers to study the buildup and interaction of electron clouds with a proton bunch train in the CERN SPS accelerator. Results suggest that a positive feedback mechanism exists between the electron buildup and the e-cloud driven transverse instability, leading to a net increase in predicted electron density. Electron clouds have been shown to trigger fast growing instabilities on proton beams circulating in the SPS and other accelerators. So far, simulations of electron cloud buildup and their effects on beam dynamics have been performed separately. This is a consequence of the large computational cost of the combined calculation due to large space and time scale disparities between the two processes. We have presented the latest improvements of the simulation package WARP-POSINST for the simulation of self-consistent ecloud effects, including mesh refinement, and generation of electrons from gas ionization and impact at the pipe walls. We also presented simulations of two consecutive bunches interacting with electrons clouds in the SPS, which included generation of secondary electrons. The distribution of electrons in front of the first beam was initialized from a dump taken from a preceding buildup calculation using the POSINST code. In this paper, we present an extension of this work where one full batch of 72 bunches is simulated in the SPS, including the entire buildup calculation and the self-consistent interaction between the bunches and the electrons.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗