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DOE OSTI2014

Inertia driven radial breathing and nonlinear relaxation in cylindrically confined pure electron plasma

The dynamics of cylindrically trapped electron plasma has been investigated using a newly developed 2D Electrostatic PIC code that uses unapproximated, mass-included equations of motion for simulation. Exhaustive simulations, covering the entire range of Brillouin ratio, were performed for uniformly filled circular profiles in rigid rotor equilibrium. The same profiles were then loaded away from equilibrium with an initial value of rigid rotation frequency different from that required for radial force balance. Both these sets of simulations were performed for an initial zero-temperature or cold load of the plasma with no spread in either angular velocity or radial velocity. The evolution of the off-equilibrium initial conditions to a steady state involve radial breathing of the profile that scales in amplitude and algebraic growth with Brillouin fraction. For higher Brillouin fractions, the growth of the breathing mode is followed by complex dynamics of spontaneous hollow density structures, excitation of poloidal modes, leading to a monotonically falling density profile.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2015

Inertia driven radial breathing and nonlinear relaxation in cylindrically confined pure electron plasma

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Dispersion and the speed-limited particle-in-cell algorithm

This paper discusses temporally continuous and discrete forms of the speed-limited particle-in-cell (SLPIC) method first treated by Werner et al. [Phys. Plasmas 25, 123512 (2018)]. The dispersion relation for a 1D1V electrostatic plasma whose fast particles are speed-limited is derived and analyzed. By examining the normal modes of this dispersion relation, we show that the imposed speed-limiting substantially reduces the frequency of fast electron plasma oscillations while preserving the correct physics of lower-frequency plasma dynamics (e.g. ion acoustic wave dispersion and damping). We then demonstrate how the timestep constraints of conventional electrostatic particle-in-cell methods are relaxed by the speed-limiting approach, thus enabling larger timesteps and faster simulations. Here, these results indicate that the SLPIC method is a fast, accurate, and powerful technique for modeling plasmas wherein electron kinetic behavior is nontrivial (such that a fluid/Boltzmann representation for electrons is inadequate) but evolution is on ion timescales.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2020

Anomalous Ion Heating and Pole Erosion in the 12.5-kW Hall Effect Rocket with Magnetic Shielding (HERMeS)

Wear measurements of the inner pole cover in HERMeS have shown as much as ten times higher erosion rates than past numerical simulations predicted. Also, measurements of ion velocity distribution functions (IVDF) suggest that ion heating occurs near the chamfered regions of the acceleration channel and around the inner pole surface. In our companion paper we present theoretical evidence that the plasma conditions in this region can excite instabilities in the lower hybrid frequency. Here, we provide further evidence of their presence through comparisons between numerical simulations and measurements. After including in the 2-D axisymmetric hydrodynamic-PIC code Hall2De an idealized model of the ion temperature based on a scaling with the lower hybrid frequency, we find the agreement between the computed and measured IVDF is significantly improved. In addition, the computed erosion rates at the inner pole surface are now in close agreement with wear test measurements.

Frieman, Jason↗

DOE OSTI2013

Pedestal fueling simulations with a coupled kinetic plasma–kinetic neutral transport code

The simplified neutral transport routine in the guiding center ion–electron-neutral neoclassical PIC code XGC0 has been replaced by one that calls the Monte Carlo neutral transport code DEGAS2. This provides a more realistic treatment of neutral atoms in the tokamak edge plasma and allows detailed atomic physics and plasma–material interaction processes to be incorporated into the simulations. The spatial profile of the neutral particle source used in DEGAS2 is determined from the fluxes of XGC0 ions to the material surfaces, and DEGAS2 is run in a time dependent manner synchronized with XGC0. The kinetic plasma–kinetic neutral transport capability is demonstrated with example pedestal fueling simulations.

Materials Science↗

DOE OSTI2013

Kinetic simulation of the O-X conversion process in dense magnetized plasmas

One scheme for heating a dense magnetized plasma core, such as in a tokamak, involves launching an ordinary (O) electromagnetic wave at the low density edge. It is converted to a reflected extraordinary (X) electromagnetic wave under certain conditions, and then transformed into an electron Bernstein wave able to reach high density regions inaccessible to most other waves. The O-X mode conversion is important in heating and diagnostic processes in different devices such as tokamaks, stellarators, and some types of pinches. The goal of this study has been to demonstrate that the kinetic particle-in-cell (PIC) scheme is suitable for modeling the O-X conversion process as the first step toward a more complete simulation of O-X-B heating. The O-X process is considered and simulated with a kinetic particle model for parameters of the TJ-II stellarator using the PIC code, XOOPIC. This code is able to model the non-monotonic density and the magnetic profile of the TJ-II stellarator. It can also statistically represent the self-consistent distribution function of the plasma, which has not been possible in previous fluid models. By considering the electric and magnetic components of launched and reflected waves, the O-mode and X-mode waves can be detected, and the O-X conversion can be demonstrated. In this work, the optimum angle for conversion efficiency, as predicted by the previous theory and experimentally confirmed, is used. Via considering the power of the launched O-mode wave and the converted X-mode wave, the efficiency of 63% for O-X conversion for the optimum theoretical launch angle of 47{sup ∘} is obtained, which is in good agreement with efficiencies computed via full-wave simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

An unsupervised machine-learning checkpoint-restart algorithm using Gaussian mixtures for particle-in-cell simulations

We propose an unsupervised machine-learning checkpoint-restart (CR) algorithm for particle-in-cell (PIC) algorithms using Gaussian mixtures (GM). The algorithm compresses the particle population per spatial cell by constructing a velocity distribution function using GM. Particles are reconstructed at restart time by local resampling of the Gaussians. To guarantee fidelity of the CR process, we ensure the exact preservation of invariants such as charge, momentum, and energy for both compression and reconstruction stages, everywhere on the mesh. We also ensure the preservation of Gauss' law after particle reconstruction by exactly matching the density profile at restart time. As a result, the GM CR algorithm is shown to provide a clean, conservative restart capability while potentially affording orders of magnitude savings in input/output requirements. Here, we demonstrate the algorithm using a recently developed exactly energy- and charge-conserving PIC algorithm using both electrostatic and electromagnetic tests. The tests demonstrate not only a high-fidelity CR capability, but also its potential for enhancing the fidelity of the PIC solution for a given particle resolution.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Challenges in simulating beam dynamics of dielectric laser acceleration

Dielectric Laser Acceleration (DLA) achieves the highest gradients among structure-based electron accelerators. The use of dielectrics increases the breakdown field limit, and thus the achievable gradient, by a factor of at least 10 in comparison to metals. Experimental demonstrations of DLA in 2013 led to the Accelerator on a Chip International Program (ACHIP), funded by the Gordon and Betty Moore Foundation. In ACHIP, our main goal is to build an accelerator on a silicon chip, which can accelerate electrons from below 100 keV to above 1 MeV with a gradient of at least 100 MeV/m. For stable acceleration on the chip, magnet-only focusing techniques are insufficient to compensate the strong acceleration defocusing. Thus, spatial harmonic and Alternating Phase Focusing (APF) laser-based focusing techniques have been developed. Additionally, we have developed the simplified symplectic tracking code DLAtrack6D, which makes use of the periodicity and applies only one kick per DLA cell, which is calculated by the Fourier coefficient of the synchronous spatial harmonic. Due to coupling, the Fourier coefficients of neighboring cells are not entirely independent and a field flatness optimization (similarly as in multi-cell cavities) needs to be performed. The simulation of the entire accelerator on a chip by a Particle In Cell (PIC) code is possible, but impractical for optimization purposes. Finally, we have also outlined the treatment of wake field effects in attosecond bunches in the grating within DLAtrack6D, where the wake function is computed by an external solver.

43 PARTICLE ACCELERATORS↗

NASA NTRS2017

The Heliopause Electrostatic Rapid Transit System (HERTS) - Design, Trades, and Analyses Performed in a Two Year NASA Investigation of Electric Sail Propulsion Systems

Personnel from NASA's MSFC have been investigating the feasibility of an advanced propulsion system known as the Electric Sail (E-Sail) for future scientific exploration missions. This team initially won a NASA Space Technology Mission Directorate (STMD) Phase I NASA Innovative Advanced Concept (NIAC) award and then a two-year follow-on Phase II NIAC award in October 2015. This paper documents the findings from this three-year investigation. An Electric sail, a propellant-less propulsion system, uses solar wind ions to rapidly travel either to deep space or the inner solar system. Scientific spacecraft could reach Pluto in ~5 years, or the boundary of the solar system in ten to twelve years compared to the thirty-five plus years the Voyager spacecraft took. The team's recent focuses have been: 1) Developing a Particle in Cell (PIC) numeric engineering model from MSFC's experimental data on the interaction between simulated solar wind and a charged bare wire that can be applied to a variety of missions, 2) Determining what missions could benefit from this revolutionary propulsion system, 3) Conceptualizing spacecraft designs for various tasks: to reach the solar system's edge, to orbit the sun as Heliophysics sentinels, or to examine a multitude of asteroids.

Wiegmann, Bruce M.↗

NASA NTRS2017

Findings from NASA's 2015-2017 Electric Sail Investigations

Personnel from NASA's MSFC have been investigating the feasibility of an advanced propulsion system known as the Electric Sail (E-Sail) for future scientific exploration missions. This team initially won a NASA Space Technology Mission Directorate (STMD) Phase I NASA Innovative Advanced Concept (NIAC) award and then a two-year follow-on Phase II NIAC award in October 2015. This paper documents the findings from this three-year investigation. An Electric sail, a propellant-less propulsion system, uses solar wind ions to rapidly travel either to deep space or the inner solar system. Scientific spacecraft could reach Pluto in approx. 5 years, or the boundary of the solar system in ten to twelve years compared to the thirty-five plus years the Voyager spacecraft took. The team's recent focuses have been: 1) Developing a Particle in Cell (PIC) numeric engineering model from MSFC's experimental data on the interaction between simulated solar wind and a charged bare wire that can be applied to a variety of missions, 2) Determining what missions could benefit from this revolutionary propulsion system, 3) Conceptualizing spacecraft designs for various tasks: to reach the solar system's edge, to orbit the sun as Heliophysics sentinels, or to examine a multitude of asteroids.

Wiegmann, Bruce M.↗

DOE OSTI2015

Conformal Electromagnetic Particle in Cell: A Review

We review conformal (or body-fitted) electromagnetic particle-in-cell (EM-PIC) numerical solution schemes. Included is a chronological history of relevant particle physics algorithms often employed in these conformal simulations. We also provide brief mathematical descriptions of particle-tracking algorithms and current weighting schemes, along with a brief summary of major time-dependent electromagnetic solution methods. Several research areas are also highlighted for recommended future development of new conformal EM-PIC methods.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

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

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 non-evolving 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. Additionally, 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 algorithmic 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 . 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 is 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 (QuickPIC), and the new quasi-static PIC code with azimuthal decomposition (QPAD) are also presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2018

Numerical Simulation of Ion Transport in a Nano-Electrospray Ion Source at Atmospheric Pressure

Understanding ion transport properties from the ion source to the mass spectrometer (MS) is essential for optimizing device performance. Numerical simulation helps in understanding of ion transport properties and, furthermore, facilitates instrument design. In contrast to previously reported numerical studies, ion transport simulations in a continuous injection mode whilst considering realistic space-charge effects have been carried out. The flow field was solved using Reynolds-averaged Navier-Stokes (RANS) equations, and a particle-in-cell (PIC) method was applied to solve a time-dependent electric field with local charge density. A series of ion transport simulations were carried out at different cone gas flow rates, ion source currents, and capillary voltages. A force evaluation analysis reveals that the electric force, the drag force, and the Brownian force are the three dominant forces acting on the ions. Both the experimental and simulation results indicate that cone gas flow rates of ≤250 slph (standard liter per hour) are important for high ion transmission efficiency, as higher cone gas flow rates reduce the ion signal significantly. The simulation results also show that the ion transmission efficiency reduces exponentially with an increased ion source current. Additionally, the ion loss due to space-charge effects has been found to be predominant at a higher ion source current, a lower capillary voltage, and a stronger cone gas counterflow. The interaction of the ion driving force, ion opposing force, and ion dispersion is discussed to illustrate ion transport mechanism in the ion source at atmospheric pressure. .

42 ENGINEERING↗

DOE OSTI2014

Noiseless Vlasov–Poisson simulations with linearly transformed particles

We introduce a deterministic discrete-particle simulation approach, the Linearly-Transformed Particle-In-Cell (LTPIC) method, that employs linear deformations of the particles to reduce the noise traditionally associated with particle schemes. Formally, transforming the particles is justified by local first order expansions of the characteristic flow in phase space. In practice the method amounts of using deformation matrices within the particle shape functions; these matrices are updated via local evaluations of the forward numerical flow. Because it is necessary to periodically remap the particles on a regular grid to avoid excessively deforming their shapes, the method can be seen as a development of Denavit's Forward Semi-Lagrangian (FSL) scheme (Denavit, 1972 [8]). However, it has recently been established (Campos Pinto, 2012 [20]) that the underlying Linearly-Transformed Particle scheme converges for abstract transport problems, with no need to remap the particles; deforming the particles can thus be seen as a way to significantly lower the remapping frequency needed in the FSL schemes, and hence the associated numerical diffusion. To couple the method with electrostatic field solvers, two specific charge deposition schemes are examined, and their performance compared with that of the standard deposition method. Finally, numerical 1d1v simulations involving benchmark test cases and halo formation in an initially mismatched thermal sheet beam demonstrate some advantages of our LTPIC scheme over the classical PIC and FSL methods. Benchmarked test cases also indicate that, for numerical choices involving similar computational effort, the LTPIC method is capable of accuracy comparable to or exceeding that of state-of-the-art, high-resolution Vlasov schemes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1990

Simulation studies of electron acceleration by ion ring distributions in solar flares

A 2.5-dimensional fully relativistic EM, particle-in-cell code (PIC) is used to investigate a potential electron acceleration mechanism in solar flares. The free energy is provided by ions which have a ring velocity distribution about the magnetic-field direction. Ion rings may be produced by perpendicular shocks, which could in turn be generated by the super-Alfvenic motion of magnetic flux tubes emerging from the photosphere or by coronal mass ejections. Such ion distributions are known to be unstable to the generation of lower hybrid waves, which have phase velocities in excess of the electron thermal speed parallel to the field and can, therefore, resonantly accelerate electrons in that direction. The simulations show the transfer of perpendicular ion energy to energetic electrons via lower hybrid wave turbulence. With plausible ion ring velocities, the process can account for the observationally inferred fluxes and energies of non-thermal electrons during the impulsive phase of flares.

Mcclements, K. G.↗

NASA NTRS2017

The Heliopause Electrostatic Rapid Transit System (HERTS) Design, Trades, and Analyses Performed in a Two Year NASA Investigation of Electric Sail Propulsion Systems

The Heliopause Electrostatic Rapid Transit System (HERTS) was one of the seven total Phase II NASA Innovative Advanced Concepts (NIAC) that was down-selected in 2015 for continued funding and research. In Phase I our team learned that a spacecraft propelled by an Electric Sail (E-Sail) can travel great astronomical distances, such as to the Heliopause region of the solar system (approx. 100 to 120 AU) in approximately one quarter of the time (10 years) versus the time it took the Voyager spacecraft launched in 1977 (36 years). The completed work within the Phase II NIAC funded effort builds upon the work that was done in the Phase I NIAC and is focused on: 1) Testing of plasma interaction with a charged wire in a MSFC simulated solar environment vacuum test chamber. 2) Development of a Particle-in-Cell (PIC) models that are validated in the plasma testing and used to extrapolate to the E-Sail propulsion system design. 3) Conceptual design of a Technology Demonstration Mission (TDM) spacecraft developed to showcase E-Sail propulsion systems. 4) Down selection of both: a) Materials for a multi km length conductor and, b) Best configuration of the proposed conductor deployment subsystem. This paper will document the findings to date (June, 2017) of the above focused areas.

Wiegmann, Bruce M.↗

DOE OSTI2014

Fluid preconditioning for Newton–Krylov-based, fully implicit, electrostatic particle-in-cell simulations

A recent proof-of-principle study proposes an energy- and charge-conserving, nonlinearly implicit electrostatic particle-in-cell (PIC) algorithm in one dimension [9]. The algorithm in the reference employs an unpreconditioned Jacobian-free Newton–Krylov method, which ensures nonlinear convergence at every timestep (resolving the dynamical timescale of interest). Kinetic enslavement, which is one key component of the algorithm, not only enables fully implicit PIC as a practical approach, but also allows preconditioning the kinetic solver with a fluid approximation. This study proposes such a preconditioner, in which the linearized moment equations are closed with moments computed from particles. Effective acceleration of the linear GMRES solve is demonstrated, on both uniform and non-uniform meshes. The algorithm performance is largely insensitive to the electron–ion mass ratio. Numerical experiments are performed on a 1D multi-scale ion acoustic wave test problem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Modern gyrokinetic particle-in-cell simulation of fusion plasmas on top supercomputers

The Gyrokinetic Toroidal Code at Princeton (GTC-P) is a highly scalable and portable particle-in-cell (PIC) code. It solves the 5D Vlasov-Poisson equation featuring efficient utilization of modern parallel computer architectures at the petascale and beyond. Motivated by the goal of developing a modern code capable of dealing with the physics challenge of increasing problem size with sufficient resolution, new thread-level optimizations have been introduced as well as a key additional domain decomposition. GTC-P's multiple levels of parallelism, including inter-node 2D domain decomposition and particle decomposition, as well as intra-node shared memory partition and vectorization have enabled pushing the scalability of the PIC method to extreme computational scales. In this paper, we describe the methods developed to build a highly parallelized PIC code across a broad range of supercomputer designs. This particularly includes implementations on heterogeneous systems using NVIDIA GPU accelerators and Intel Xeon Phi (MIC) co-processors and performance comparisons with state-of-the-art homogeneous HPC systems such as Blue Gene/Q. New discovery science capabilities in the magnetic fusion energy application domain are enabled, including investigations of Ion-Temperature-Gradient (ITG) driven turbulence simulations with unprecedented spatial resolution and long temporal duration. Performance studies with realistic fusion experimental parameters are carried out on multiple supercomputing systems spanning a wide range of cache capacities, cache-sharing configurations, memory bandwidth, interconnects and network topologies. Furthermore, these performance comparisons using a realistic discovery-science-capable domain application code provide valuable insights on optimization techniques across one of the broadest sets of current high-end computing platforms worldwide.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗