Particle-in-cell Code Research Articles

Two-dimensionals-polarized solitary waves in plasmas. II. Stability, collisions, electromagnetic bursts, and post-soliton evolution

The dynamics of two-dimensional s-polarized solitary waves is investigated with the aid of particle-in-cell (PIC) simulations. Instead of the usual excitation of the waves with a laser pulse, the PIC code was directly initialized with the numerical solutions from the fluid plasma model. This technique allows the analysis of different scenarios including the theoretical problems of the solitary wave stability and their collision as well as features already measured during laser-plasma experiments such as the emission of electromagnetic bursts when the waves reach the plasma-vacuum interface, or their expansion on the ion time scale, usually named post-soliton evolution. Waves with a single density depression are stable whereas multihump solutions decay to several waves. Contrary to solitons, two waves always interact through a force that depends on their relative phases, their amplitudes, and the distance between them. On the other hand, the radiation pattern at the plasma-vacuum interface was characterized, and the evolution of the diameter of different waves was computed and compared with the "snow plow" model.

A generalized implicit algorithm for multi-dimensional particle-in-cell simulations in Cartesian geometry

An implicit multi-dimensional particle-in-cell (PIC) code is developed to study the interaction of ultrashort pulse lasers with matter. The algorithm is based on current density decomposition and is only marginally more complicated compared to explicit PIC codes, but it completely eliminates grid heating and possesses good energy conserving properties with relaxed time step and grid resolution. This is demonstrated in a test case study, in which high-energy protons are generated from a thin carbon foil at solid density using linear and circular polarizations. The grid heating rate is estimated to be 1–10 eV/ps.

Fine-sorting one-dimensional particle-in-cell algorithm with Monte-Carlo collisions on a graphics processing unit

Particle-in-cell (PIC) simulations with Monte-Carlo collisions are used in plasma science to explore a variety of kinetic effects. One major problem is the long run-time of such simulations. Even on modern computer systems, PIC codes take a considerable amount of time for convergence. Most of the computations can be massively parallelized, since particles behave independently of each other within one time step. Current graphics processing units (GPUs) offer an attractive means for execution of the parallelized code. In this contribution we show a one-dimensional PIC code running on NVIDIA® GPUs using the CUDA™ environment. A distinctive feature of the code is that size of the cells that the code uses to sort the particles with respect to their coordinates is comparable to size of the grid cells used for discretization of the electric field. Hence, we call the corresponding algorithm “fine-sorting”. Implementation details and optimization of the code are discussed and the speed-up compared to classical CPU approaches is computed.

Multi-beam effects on backscatter and its saturation in experiments with conditions relevant to ignition

To optimize the coupling to indirect drive targets in the National Ignition Campaign (NIC) at the National Ignition Facility [E. Moses et al., Phys. Plasmas 16, 041006 (2009)], a model of stimulated scattering produced by multiple laser beams is used. The model has shown that scatter of the 351 nm beams can be significantly enhanced over single beam predictions in ignition relevant targets by the interaction of the multiple crossing beams with a millimeter scale length, 2.5 keV, 0.02−0.05 × critical density, plasma. The model uses a suite of simulation capabilities and its key aspects are benchmarked with experiments at smaller laser facilities. The model has also influenced the design of the initial targets used for NIC by showing that both the stimulated Brillouin scattering (SBS) and stimulated Raman scattering (SRS) can be reduced by the reduction of the plasma density in the beam intersection volume that is caused by an increase in the diameter of the laser entrance hole (LEH). In this model, a linear wave response leads to a small gain exponent produced by each crossing quad of beams (<∼1 per quad) which amplifies the scattering that originates in the target interior where the individual beams are separated and crosses many or all other beams near the LEH as it exits the target. As a result all 23 crossing quads of beams produce a total gain exponent of several or greater for seeds of light with wavelengths in the range that is expected for scattering from the interior (480 to 580 nm for SRS). This means that in the absence of wave saturation, the overall multi-beam scatter will be significantly larger than the expectations for single beams. The potential for non-linear saturation of the Langmuir waves amplifying SRS light is also analyzed with a two dimensional, vectorized, particle in cell code (2D VPIC) that is benchmarked by amplification experiments in a plasma with normalized parameters similar to ignition targets. The physics of cumulative scattering by multiple crossing beams that simultaneously amplify the same SBS light wave is further demonstrated in experiments that benchmark the linear models for the ion waves amplifying SBS. The expectation from this model and its experimental benchmarks is shown to be consistent with observations of stimulated Raman scatter in the first series of energetic experiments with ignition targets, confirming the importance of the multi-beam scattering model for optimizing coupling.

Characterization and focusing of light ion beams generated by ultra-intensely irradiated thin foils at the kilojoule scale

We present the first observations of focused multi-MeV carbon ion beams generated using ultra-intense shortpulse laser interactions with thin hemispherical (400μm radius) targets. The experiments were performed at the Trident laser facility (80 J, 0.6 ps, 2×1020W/cm2) at Los Alamos National Laboratory and at the Omega EP (extended performance) facility (1 kJ, 10 ps, 5×1018W/cm2) at the Laboratory for Laser Energetics. The targets were chemical vapor deposition diamond, hemi-shells and were heated to remove contaminants. The ion beam focusing was characterized by tracing the projection of a witness mesh in the ion beam on a lithium fluoride nuclear activation detector. From the data, we infer that the divergence of the beam changes as a function of time. We present a 2-D isothermal model to explain the dynamics. We also present discrepancies in the peak proton and carbon ion energies from the two facilities. The implication of which is a fundamental difference in the temporal evolution of the beams from the two facilities. Simulations using the hybrid particle in cell code, Lsp were performed and compared with the experiments.

Particle-in-cell mode beam dynamics simulation of the low energy beam transport for the SSC-linac injector

A new SSC-linac system (injector into separated sector cyclotron) is being designed in the HIRFL (heavy ion research facility of Lanzhou). As part of SSC-Linac, the LEBT (low energy beam transport) consists of seven solenoids, four quadrupoles, a bending magnet and an extra multi-harmonic buncher. The total length of this segment is about 7 meters. The beam dynamics in this LEBT has been studied using three-dimensional PIC (particle-in-cell) code BEAMPATH. The simulation results show that the continuous beam from the ion source is first well analyzed by a charge-to-mass selection system, and the beam of the selected charge-to-mass ratio is then efficiently pre-bunched by a multi-harmonic buncher and optimally matched into the RFQ (radio frequency quadrupole) for further acceleration. The principles and effects of the solenoid collimation channel are discussed, and it could limit the beam emittance by changing the aperture size.

Kinetic simulations of a deuterium-tritium Z pinch with >1016 neutron yield

Fully kinetic, collisional, and electromagnetic simulations of the time evolution of an imploding and burning Z pinch plasma have been performed. Using the implicit particle-in-cell (PIC) code, multidimensional (1D and 3D) simulations of deuterium and deuterium-tritium Z pinches provide insight into the mechanisms of neutron production. The PIC code allows non-Maxwellian particle distributions, simulates finite mean-free-path effects, performs self-consistent calculations of anomalous resistivity, and permits charge separation. At low pinch current, neutron production is dominated by high energy ions driven by instabilities. The instabilities produce a power-law ion-energy distribution function in the distribution tail. At higher currents with deuterium-tritium fuel, the vast majority of the neutrons is thermonuclear in origin and neutron yield follows an I4 neutron yield scaling with current. High-current, multidimension simulations (up to 40 MA with > 1016 neutron yield) suggest that the fraction of thermonuclear neutrons increases with current and the strong dependence of neutron yield with current will continue at still higher currents. Scenarios for fusion breakeven and possible ignition in the 40–80 MA regime are discussed.

A Three-Dimensional Particle-in-Cell Simulation of Quasi-Perpendicular Shock on Fujitsu FX1 Cluster

The high-specification computational power of Japan Aerospace Exploration Agency's new supercomputer system, called Fujitsu FX1 cluster, enables us to perform really macroscale 3-D situations with full particle plasma simulation [particle-in-cell (PIC) method]. A fully 3-D kinetic approach to collisionless shock problems, which is one of the most important problems in the space plasma science, is possible, and a challenging run is being executed for a pioneering study of the topic. About 0.4 billion grids are allocated for the electromagnetic fields, and about 0.1 trillion particles are loaded into the simulation run. The computational efficiency of the PIC code is about 8% of the peak performance (4.6 Tflops) using 5776 CPU cores (57 Tflops). The simulation parameters were selected to simulate ESA's Cluster-II spacecraft observational result reported by Seki (in 2009). The full mass ratio mi/me = 1840 was taken for this simulation, and almost one ion inertia length square could be allocated for the simulation. In this simulation, a quite complicated wave activity is found in the shock foot region. In this paper, comparing 3-D results with 2-D simulation results, a 3-D nature of shock transition region of quasi-perpendicular shock is reported.

Field ionization model implemented in Particle In Cell code and applied to laser-accelerated carbon ions

A novel numerical modeling of field ionization in PIC (Particle In Cell) codes is presented. Based on the quasistatic approximation of the ADK (Ammosov Delone Krainov) theory and implemented through a Monte Carlo scheme, this model allows for multiple ionization processes. Two-dimensional PIC simulations are performed to analyze the cut-off energies of the laser-accelerated carbon ions measured on the UHI 10 Saclay facility. The influence of the target and the hydrocarbon pollutant composition on laser-accelerated carbon ion energies is demonstrated.

PIC Codes in New Processors: A Full Relativistic PIC Code in CUDA-Enabled Hardware With Direct Visualization

Kinetic plasma simulations using an electromagnetic particle-in-cell (PIC) algorithm have become the tool of choice for numerical modeling of several astrophysical and laboratory scenarios, ranging from astrophysical shocks and plasma shell collisions, to high-intensity laser-plasma interactions, with applications to fast ignition and particle acceleration. However, fully relativistic kinetic codes are computationally intensive, and new computing paradigms are required for one-to-one direct modeling of these scenarios. In this paper, we look at the use of modern graphics processing units for PIC algorithm calculations, discussing the implementation of a fully relativistic PIC code using NVIDIA's Compute Unified Device Architecture, also allowing one for simultaneous visualization of simulation results with negligible impact on performance. Details on the algorithm implementation are given, focusing on grid-particle interpolation and current deposition and also on the direct visualization routines. Finally, we present results from a test simulation of an electron/positron plasma shell collision, focusing on code validation and performance evaluation.

HPC Parallel Programming Model for Gyrokinetic MHD Simulation

The 3-dimensional gyrokinetic PIC (particle-in-cell) code for MHD simulation, Gpic-MHD, was installed on SR16000 (“Plasma Simulator”), which is a scalar cluster system consisting of 8,192 logical cores. The Gpic-MHD code advances particle and field quantities in time. In order to distribute calculations over large number of logical cores, the total simulation domain in cylindrical geometry was broken up into NDD-r × NDD-z (number of radial decomposition times number of axial decomposition) small domains including approximately the same number of particles. The axial direction was uniformly decomposed, while the radial direction was non-uniformly decomposed. NRP replicas (copies) of each decomposed domain were used (“particle decomposition”). The hybrid parallelization model of multi-threads and multi-processes was employed: threads were parallelized by the auto-parallelization and NDD-r ×NDD-z ×NRP processes were parallelized by MPI (message-passing interface). The parallelization performance of Gpic-MHD was investigated for the medium size system of Nr × Nθ × Nz = 1025 × 128 × 128 mesh with 4.196 or 8.192 billion particles. The highest speed for the fixed number of logical cores was obtained for two threads, the maximum number of NDD-z, and optimum combination of NDD-r and NRP. The observed optimum speeds demonstrated good scaling up to 8,192 logical cores.

Quantitative Evaluation of Ion Kinetic Effect in Magnetic Field Inflation by the Injection of a Plasma Jet

The steady state of dipolar magnetic field expansion is examined by injecting a plasma jet from the center of the dipolar magnetic field (magnetic inflation). Using a two-dimensional hybrid particle-in-cell (PIC) code taking into account the finite Larmor radius effect, we examine the magnetic field inflation process when Argon (Ar) plasma is injected into a dipole magnetic field generated by a simple hoop coil; the plasma is injected within an angle of 30° in the polar direction. Compared to ideal magneto hydrodynamics (MHD) results, the results obtained using the hybrid PIC code are more accurate since the finite ion Larmor radius effect decreases the flow of magnetic flux with respect to the flow of the plasma jet.

Dark-current-free petawatt laser-driven wakefield accelerator based on electron self-injection into an expanding plasma bubble

A dark-current-free plasma accelerator driven by a short (⩽150 fs) self-guided petawatt laser pulse is proposed. The accelerator uses two plasma layers, one of which, short and dense, acts as a thin nonlinear lens. It is followed by a long rarefied plasma (∼1017 electrons cm−3) in which background electrons are trapped and accelerated by a nonlinear laser wakefield. The pulse overfocused by the plasma lens diffracts in low-density plasma as in vacuum and drives in its wake a rapidly expanding electron density bubble. The expanding bubble effectively traps initially quiescent electrons. The trapped charge given by quasi-cylindrical three-dimensional particle-in-cell (PIC) simulations (using the CALDER-Circ code) is ∼1.3 nC. When laser diffraction saturates and self-guiding begins, the bubble transforms into a bucket of a weakly nonlinear non-broken plasma wave. Self-injection thus never resumes, and the structure remains free of dark current. The CALDER-Circ modelling predicts a few π mm mrad normalized transverse emittance of electron beam accelerated in the first wake bucket. Test-particle modelling of electron acceleration over 9 cm (using the quasistatic PIC code WAKE) sets the upper limit of energy gain 2.6 GeV with ∼2% relative spread.

Two-dimensional particle-in-cell simulations of transport in a magnetized electronegative plasma

Particle transport in a uniformly magnetized electronegative plasma is studied in two-dimensional (2D) geometry with insulating (dielectric) boundaries. A 2D particle-in-cell (PIC) code is employed, with the results compared to analytic one-dimensional models that approximate the end losses as volume losses. A modified oxygen reaction set is used to scale to the low densities used in PIC codes and also to approximately model other gases. The principal study is the limiting of the transverse electron flow due to strong electron magnetization. The plasma in the PIC calculation is maintained by axial currents that vary across the transverse dimension. For a cosine current profile nearly uniform electron temperature is obtained, which at the B-fields studied (600–1200 G) give a small but significant fraction (0.25 or less) of electron to negative ion transverse loss. For a more transverse-confined current, and approximating the higher mass and attachment reaction rate of iodine, the fraction of electron to negative ion transverse loss can be made very small. The models which have been constructed reasonably approximate the PIC results and indicate that the cross-field transport is nearly classical.

Kinetic Simulations of Type II Radio Burst Emission Processes

AbstractUsing a fully relativistic, 3D particle in cell code we have studied Langmuir- and electromagnetic wave processes in a CME foreshock plasma with counterstreaming electron beams. Langmuir wave excitation in resonance with the plasma frequency is observed, with timescales in accordance with theoretical predictions. However, no three wave interaction leading to emission of electromagnetic waves were detectable within the timeframe of our simulations.

Peak Coalescence, Spontaneous Loss of Coherence, and Quantification of the Relative Abundances of Two Species in the Plasma Regime: Particle-In-Cell Modeling of Fourier Transform Ion Cyclotron Resonance Mass Spectrometry

Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS) is often limited by space-charge effects. Previously, particle-in-cell (PIC) simulations have been used to understand these effects on FTICR-MS signals. However, none have extended fully into the space-charge dominated (plasma) regime. We use a two-dimensional (2-D) electrostatic PIC code, which facilitates work at very high number densities at modest computational cost to study FTICR-MS in the plasma regime. In our simulation, we have observed peak coalescence and the rapid loss of signal coherence, two common experimental problems. This demonstrates that a 2-D model can simulate these effects. The 2-D code can handle a larger numbers of particles and finer spatial resolution than can currently be addressed by 3-D models. The PIC method naturally takes into account image charge and space charge effects in trapped-ion mass spectrometry. We found we can quantify the relative abundances of two closely spaced (such as (7)Be(+) and (7)Li(+)) species in the plasma regime even when their peaks have coalesced. We find that the frequency of the coalesced peak shifts linearly according to the relative abundances of these species. Space charge also affects more widely spaced lines. Singly-ionized (7)BeH and (7)Li have two separate peaks in the plasma regime. Both the frequency and peak area vary nonlinearly with their relative abundances. Under some conditions, the signal exhibited a rapid loss of coherence. We found that this is due to a high order diocotron instability growing in the ion cloud.

70% Efficient Relativistic Magnetron With Axial Extraction of Radiation Through a Horn Antenna

At the Nagaoka University of Technology (Japan), Daimon and Jiang used particle-in-cell (PIC) code simulations to demonstrate that the electronic efficiency of the A6 magnetron with axial extraction can be increased from 3% up to 37% applying different diffraction outputs, from tapered cavities in a conical horn antenna to modified expanded ones that improve magnetron matching with the antenna. This paper presents PIC code simulation results for the modified magnetron design using a transparent cathode, in contrast with Daimon and Jiang's simulations that used a solid explosive emission cathode. Furthermore, by further optimizing the magnetron parameters, we demonstrate an efficiency approaching 70% with gigawatt radiation power for an applied voltage of 400 kV. By maintaining a synchronous interaction of electrons with the operating wave, we found that the radiation power increases as the square of the diode voltage up to a diode voltage of 800 kV with short rise time that does not exceed 20 ns. In addition, we show that using a transparent cathode promotes avoiding the regime of hard excitation of magnetrons.

Sheath effects on DEMETER ion drift measurements

The “Instrument d’Analyse du Plasma” on DEMETER includes an ion drift meter used to measure the direction of the incoming ram plasma ( Berthelier et al., 2006a, b ). Given the velocity of the satellite, and expected flow velocities of plasma along DEMETER's orbit, it is estimated that at mid latitudes, the direction of incident plasma as measured by IAP should be within approximately 2° of the ram direction. Yet, significantly larger angular deviations are measured routinely. An important assumption made in the interpretation of onboard instruments, such as IAP, is that neither the spacecraft nor the instrument significantly perturb the plasma that is being measured. In view of the large observed angular deviations, this paper examines the possible effect of the electrostatic sheath surrounding IAP. This is done with the 3D PIC simulation code PTetra. The model uses a full 3D particle in cell code with unstructured tetrahedral mesh capable of accurately representing the satellite geometry. The mesh is also adaptive so as to provide a fine spatial resolution in the vicinity of the particle sensor where it is needed, and a coarse resolution in regions where plasma parameters vary over a longer scale length. Calculation results show that while particle deflection associated with the electrostatic sheath near IAP can account for appreciable angular deflections for representative ionospheric plasmas, they are typically smaller than the ones observed. Additionally, the model is unable to reproduce the latitudinal dependence of the observed large deflection angles. It is concluded that sheath effects may cause appreciable distortions on the IAP type of ion flow meter instruments, and on other particle sensors in general. The larger observed deviations and their latitudinal dependence, however, must be attributable to other physical processes not accounted for in the model.

Electron Optics System of a 100-MW S-Band Klystron

This paper presents the design and experimental results of the electron optics system for use in an S-band 100-MW high-peak-power klystron. The gun operating voltage is 415 kV with a beam current of 535 A. For the design of the gun, special emphasis is placed on the geometric layout of the electrodes to ensure a moderate voltage gradient, reasonable cathode loading, and accurate beam perveance. The beam-focusing system is a space-charge balanced flow type with a solenoidal magnet structure. The magnetic field at the center of the cathode is 60 G, and the longitudinal magnetic field in the interaction region is in the range of 1.0-1.38 kG. The electron optics system design was accomplished with SUPERFISH, EGUN, and a Particle-in-Cell (PIC) code. Simulation results indicate that the gun has a voltage gradient lower than 220 kV/cm and excellent beam transport characteristics with a beam-to-tunnel radial fill factor of less than 0.75. The focusing beam trajectories simulated by EGUN and the PIC code both have good laminarity. Two prototypes based on a simplified RF design (not intended to achieve full RF power) were fabricated in order to demonstrate the beam optics, and the measured beam transport is in agreement with predictions made by simulation codes. RF circuit simulation designs with the 1-D large-signal code KLY_12 and the PIC code are also presented.

Numerical Rebuilding of SMART-1 Hall Effect Thruster Plasma Plume

The SMART-1 flight data provided an excellent opportunity for extending validation of plume prediction codes to actual flight conditions. This paper will present the results obtained for the numerical simulation of the SMART-1 plasma plume using the PICPluS particle in cell code, which had been previously validated using ground experiment data. This activity can be considered as the first important step in the direction of a full in-flight validation for the code models and algorithms. A description of the implemented physical models is provided, followed by simulation results of experimental data from Alta's tests and from the literature. Finally, the results of the code application to the SMART-1 mission are presented, focusing on the simulation of retarding potential analyzer measurement, spacecraft floating potential, and interaction of the plasma field with the satellite (in particular the solar array). The results show that, although the possibility of dangerous interaction between the electric propulsion system and the spacecraft is very limited, a number of complex phenomena arise due to the use of the electric propulsion system in orbit. For example, the interaction between the plume and the solar array orientation leads to complex patterns for the spacecraft floating potential. Eventually, full three-dimensional simulation is therefore needed to accurately model this kind of phenomena with a realistic description of the involved geometries.