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The Vlasov--Poisson system describes the time evolution of a plasma in the so-called collisionless regime. The investigation of a high-temperature plasma that is influenced by an exterior magnetic field is one of the most significant aspects of thermonuclear fusion research. In this paper, we formulate and analyze a kinetic optimal control problem for the Vlasov--Poisson system where the control is represented by an external magnetic field. The main goal of such optimal control problems is to confine the plasma to a certain region in phase space. We first investigate the optimal control problem in terms of mathematical analysis, i.e., we show the existence of at least one global minimizer and rigorously derive a first-order necessary optimality condition for local minimizers by the adjoint approach. Then we build a Monte Carlo framework to solve the state equations as well as the adjoint equations by means of a particle-in-cell method, and we apply a nonlinear conjugate gradient method to solve the optimization problem. Eventually, we present numerical experiments that successfully validate our optimization framework. [ABSTRACT FROM AUTHOR]

The thermal evolution of the Earth’s interior and its dynamic effects are the focus of Earth sciences. However, the commonly adopted grid-based temperature solver is usually prone to numerical oscillations, especially in the presence of sharp thermal gradients, such as when modeling subducting slabs and rising plumes. This phenomenon prohibits the correct representation of thermal evolution and may cause incorrect implications of geodynamic processes. After examining several approaches for removing these numerical oscillations, we show that the Lagrangian method provides an ideal way to solve this problem. In this study, we propose a particle-in-cell method as a strategy for improving the solution to the energy equation and demonstrate its effectiveness in both one-dimensional and three-dimensional thermal problems, as well as in a global spherical simulation with data assimilation. We have implemented this method in the open-source finite-element code CitcomS, which features a spherical coordinate system, distributed memory parallel computing, and data assimilation algorithms.

Kinetic simulations have been performed on an Inertial Electrostatic Confinement Fusion (IECF) device. These simulations were performed using the particle-in-cell (PIC) method to analyze the behavior of ions in an IEC device and the effects of some parameters on the Confinement Time (CT). CT is an essential factor that significantly contributes to the IEC's performance as a nuclear fusion device. Using the PIC method, the geometry of a two-grided device with variable grid radius, the number of cathode grid rings, variable pressure and different dielectric thickness for the feed stalk was simulated. In this research, with the development of previous works, the interaction of particles was simulated and compared with previous results. The simulation results are in good agreement with the previous results. In these simulations, it was found that with the increase of the dielectric thickness of the feed stalk, the electric field was weakened and as a result, the confinement time was reduced. On the other hand, with the increase of the cathode radius, the confinement time increased. Using the results, an IEC device can be designed with higher efficiency and more optimal CT for ions.

We present a three-dimensional model for numerical simulation of beam-plasma dynamics in an open magnetic trap. For specific parameters, it may be possible to observe a magnetic field push-out by the injecting particles and the formation of a configuration required for the plasma confinement (diamagnetic mode). For an axially symmetric case in cylindrical coordinates, it was shown that the diamagnetic configuration is possible; however, the complex non-linear nature of the processes in the diamagnetic trap and the decisive role of kinetic effects require the use of three-dimensional numerical simulation. Based on the results of the simulation, it will be possible to determine the required conditions for the formation and stability of the diamagnetic configuration. [ABSTRACT FROM AUTHOR]

High frequency (HF) capacitively coupled plasmas (CCPs) are ubiquitous, having several industrial applications, especially in the semiconductor industry. Inductive heating effects within these plasmas play an important role and therefore understanding them is key to improve industrial applications. For this purpose kinetic research, using particle-in-cell (PIC) codes, offers significant opportunity to study, and improve, industrial plasma processes that operate at the atomic level. However, PIC codes commonly used for CCPs are electrostatic and thus cannot be used to simulate electromagnetically induced currents. Therefore we have developed EPOCH-LTP, a 1D PIC code with a current heating model, that enables the simulation of inductive heating effects in HF CCPs. First simulation results, from an HF CCP (60 MHz) operated at 1 mTorr of argon, show that inductive currents couple most of their power to the electrons at the interface between the bulk plasma and the sheath. Furthermore, the simulation of a dual-frequency CCP, where a HF inductive current and a low-frequency (LF) voltage waveform at 400 kHz are applied, have shown a synergy between the HF and LF waveforms that increase the inductive heating rate. [ABSTRACT FROM AUTHOR]

We demonstrate the possibility of using an XCELS [1] laser pulse propagating in a plasma of near-critical density in the regime of relativistic self-trapping to accelerate a large number of electrons with an energy of about 0.2 to 2 GeV with a record charge, almost up to 0.1 μC. An even greater charge is concentrated in electrons with an energy of ∼100 MeV. This opens up new prospects for using such electron bunches to produce ultra-high-brightness sources of gamma radiation and to obtain a high yield of products of photonuclear reactions and nuclear cascades. [ABSTRACT FROM AUTHOR]

Particle‐based simulations of the Vlasov equation typically require a large number of particles, which leads to a high‐dimensional system of ordinary differential equations. Solving such systems is computationally very expensive, especially when simulations for many different values of input parameters are desired. In this work, we compare several model reduction techniques and demonstrate their applicability to numerical simulations of the Vlasov equation. The necessity of symplectic model reduction algorithms is illustrated with a simple numerical experiment. [ABSTRACT FROM AUTHOR]

Dispersion-free ultra-high order FFT-based Maxwell solvers have recently proven to be paramount to a large range of applications, including the high-fidelity modeling of high-intensity laser–matter interactions with Particle-In-Cell (PIC) codes. To enable a massively parallel scaling of these solvers, a novel parallelization technique was recently proposed, which consists in splitting the simulation domain into several processor sub-domains, with guard regions appended at each sub-domain boundary. Maxwell's equations are advanced independently on each sub-domain using local shared-memory FFTs (instead of a single distributed global FFT). This implies small truncation errors at sub-domain boundaries, the amplitude of which depends on guard regions sizes and order of the Maxwell solver. For moderate guard region sizes, this ’local’ technique proved to be highly scalable on up to a million cores and notably enabled the 3D modelingof so-called plasma mirrors, for which 8 guard cells only were enough to prevent truncation error growth. Yet, for other applications, the required number of guard cells might be much higher, which would severely limit the parallel efficiency of this technique due to the large volume of guard cells to be exchanged between sub-domains. In this context, we propose a novel parallelization technique that ensures very good scaling of FFT-based solvers with an arbitrarily high number of guard cells. Our ’hybrid’ technique consists in performing distributed FFTs on local groups of processors with guard regions now appended to boundaries of each group of processors. It uses a dual domain decomposition method for the Maxwell solver and other parts of the PIC cycle to keep the simulation load-balanced. This ’hybrid’ technique was implemented in the open source exascale library PICSAR. Benchmarks show that for a large number of guard cells (>16), the ’hybrid’ technique offers up to ×3 speed-up and ×8 memory savings compared to the ’local’ one.

One of the main factors that limit the lifetime of the Hall effect Thrusters (HETs) is the erosion of the acceleration channel caused by the flux of energetic ions. The magnetic field that is curved and convex towards the anode has been widely used in HETs because of its role in reducing the divergence angle of the ion beam and the channel wall erosion. However, the mechanism of the influence of the magnetic field line curvature on the wall erosion is not clear. Therefore, in this paper, a 2D3V numerical model based on the immersed-finite-element and particle-in-cell (IFE-PIC) method is established to simulate the radial-azimuthal plane near the exit of the Hall thruster. The effect of the tilt angle of the magnetic field line on the wall sputtering erosion rate is analyzed. The results show that compared to the case with the electric field E perpendicular to the magnetic field B, the energy of the ions hitting the channel wall is smaller and the wall erosion is weaker when the magnetic field lines are convex to the anode. As the tilt angle of the magnetic field lines increases from 0° to 60°, the erosion rate is reduced by 90%. Conversely, when the magnetic field lines are convex to the exit plane of the channel, the wall erosion is much more serious compared to the case with the orthogonal electric field E and the magnetic field B. As the tilt angle of the magnetic field line changes from 0° to 60°, the erosion rate is enhanced by 171%. The results in this paper are instructive for the design and optimization of the magnetic field of the HETs. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new strategy for solving highly oscillatory two-dimensional Vlasov-Poisson systems by means of a specific version of the parareal algorithm. The novelty consists in using reduced models, obtained from the two-scale convergence theory, for the coarse solving. The reduced models are useful to approximate the original Vlasov-Poisson model at a low computational cost since they are free of high oscillations. Both models are numerically solved in a particle-in-cell framework. We illustrate this strategy with numerical experiments based on long time simulations of a charged beam in a focusing channel and under the influence of a rapidly oscillating external electric field. On the basis of computing times, we provide an analysis of the efficiency of the parareal algorithm in terms of speedup. [ABSTRACT FROM AUTHOR]

The domestic plasma modeling framework AZERAP is introduced and its capabilities in simulating the plasma based accelerators and intense beam-plasma interaction are discussed. The current first beta-release of AZERAP exploits the fully kinetic, electromagnetic relativistic PIC algorithm as its numerical engine. It is implemented in the object oriented language C++ and utilizes the Message Passing Interface (MPI) for parallelization. The main idea behind the development of AZERAP has been establishing a software platform for virtual plasma laboratory for plasma based particle beam sources and high power electromagnetic generators. Achieving this goal has implied attaining high functionality in introducing the input problem, supporting abstraction of the field and plasma structures/modules, and supporting high flexibility for future developments. The present first beta-release of AZERAP paws the way toward these objectives. Moreover, it offers a very comfortable user experience with code compile, debugging, execution, data accusation and data animation, simulating plasma based accelerators. [ABSTRACT FROM AUTHOR]

Five configurations of chamfered and sharp leading edge blocks are selected to study the heat load on leading edge at KSTAR central divertor using a 2D3V particle-in-cell (PIC) code PICS2, including ions and electrons with self-consistent electric fields. Results of the PIC simulations demonstrate that the height of the misalignment determines the peak heat flux and the sheath potential near the castellated tiles. Moreover, in the case of a negative misalignment, i.e., a block edge shadowed by the adjacent upstream block, the heat flux distribution is affected mainly by the spatial structure of the monoblock. When the monoblocks are chamfered to a depth of 2 mm in the toroidal direction, more electrons are attracted to the poloidal leading edge with little magnetic shadowing found in the calculation, bringing additional heat load to the beveled side. Therefore, applying a toroidal chamfer of 2 mm at the poloidal block edges turned out to be an ineffective way to reduce the peak heat load. The influence of gap geometries on the heat load and the relations among the ion Larmor radius, the misalignment height, and the gap width are discussed. These calculation results in KSTAR on different shapes of castellated tiles are helpful for understanding the physics of the heat load on the leading edge.

• Directly-irradiated high-temperature solid-gas flows laden with polydisperse particles are studied using a numerical model. • The model uses the multiphase particle-in-cell and Monte Carlo ray-tracing methods. • The number of the prescribed discrete particle components is the key parameter affecting the computational accuracy. • The particle vertical velocity increases up to 4 × for the particle diameter increasing from 43.4 µm to 202.8 µm. • Small and large particles are heated at noticeably different rates. Heat transfer in directly-irradiated high-temperature solid–gas flows laden with polydisperse particles is investigated using a novel transient three-dimensional computational fluid dynamics model. The model couples particle–gas hydrodynamics of solid–gas flows laden with polydisperse particles, radiative heat transfer in non-grey absorbing, emitting and anisotropically-scattering multi-component participating media, conduction heat transfer in the gas phase, and interfacial convection heat transfer. The multiphase particle-in-cell method is used to predict high-fidelity solid–gas flow characteristics, such as the local discrete particle size distribution, with increased computational efficiency by combining the advantages of both Eulerian and Lagrangian methods. The multi-component radiative transfer model is implemented using an advanced collision-based Monte Carlo ray-tracing method. The number of the prescribed discrete particle components is found to be the key parameter affecting the computational accuracy and efficiency, which primarily depends on the size distribution of the particles. For the model particle–gas flow featuring free-falling Gamma-distributed ceramic particles exposed to concentrated solar irradiation, the particle volume fraction, radiative, fluid flow and thermal characteristics appear to converge with the increasing number of the discrete particle components. Five particle components are sufficient to obtain physically meaningful results. A further increase in the number of the particle components only slightly increases the accuracy of the numerical predictions at the expense of a rapidly increasing computational time. For five particle components, the particle vertical velocity at the receiver exit for particles with the diameter of 43.4 μ m is 57% of that for the particles with the diameter of 202.8 μ m. The temperatures of these two particle components increase from the initial ambient values by factors of 2 and 1.2, respectively, during the simulation time. The model developed allows for increased fidelity of particle–gas flow simulations with significant radiative effects. [ABSTRACT FROM AUTHOR]

The generation of energy-efficient parallel scientific codes became very important in the time of carbon footprint reduction. In this paper, we briefly present our latest particle-in-cell code with the results of a numerical simulation of plasma dynamics in an open trap. This code can be auto-vectorized by the Fortran compiler for Intel Xeon processors with AVX-512 instructions such as Intel Xeon Phi and the highest series of all generations of Intel Xeon Scalable processors. Efficient use of processor architecture is the main feature of an energy-efficient solution. We present a step-by-step methodology of energy consumption calculation using Intel hardware features and Intel VTune software. We also give an estimated value of carbon footprint with the impact of high-performance water cooled hardware. The Power Usage Effectiveness (PUE) in the case of high-performance water cooled hardware is equal to 1.03–1.05, and is up to 1.3 in the case of air-cooled systems. This means that power consumption of liquid cooled systems is lower than that air-cooled ones by up to 25%. All these factors play an important role in the carbon footprint reduction problem. [ABSTRACT FROM AUTHOR]

The dielectric multipactor discharge in a vacuum has become one of the main factors limiting the power capacity of high-power microwave systems. In this paper, the particle-in-cell method is used to study the effects of microwave frequency on the single-surface multipactor discharge under the fixed ratio of microwave field to frequency. As the microwave frequency increases, the change in the amplitude of mean electron energy and secondary electron yield is very small, but the number of electrons in a steady state increases linearly. This results in an increase in the delay time for the number of electrons to reach a steady state. The thickness of normalized electron number density decreases with the increase of microwave frequency because the normal restoring electric field increases linearly with the microwave frequency. Finally, we confirm that the multipactor threshold increases linearly with the microwave frequency, which is consistent with the trend of the experimental results. [ABSTRACT FROM AUTHOR]

In current computer architectures, data movement (from die to network) is by far the most energy consuming part of an algorithm (≈20pJ/word on-die to ≈10,000 pJ/word on the network). To increase memory locality at the hardware level and reduce energy consumption related to data movement, future exascale computers tend to use many-core processors on each compute nodes that will have a reduced clock speed to allow for efficient cooling. To compensate for frequency decrease, machine vendors are making use of long SIMD instruction registers that are able to process multiple data with one arithmetic operator in one clock cycle. SIMD register length is expected to double every four years. As a consequence, Particle-In-Cell (PIC) codes will have to achieve good vectorization to fully take advantage of these upcoming architectures. In this paper, we present a new algorithm that allows for efficient and portable SIMD vectorization of current/charge deposition routines that are, along with the field gathering routines, among the most time consuming parts of the PIC algorithm. Our new algorithm uses a particular data structure that takes into account memory alignment constraints and avoids gather/scatter instructions that can significantly affect vectorization performances on current CPUs. The new algorithm was successfully implemented in the 3D skeleton PIC code PICSAR and tested on Haswell Xeon processors (AVX2-256 bits wide data registers). Results show a factor of ×2 to ×2.5 speed-up in double precision for particle shape factor of orders 1–3. The new algorithm can be applied as is on future KNL (Knights Landing) architectures that will include AVX-512 instruction sets with 512 bits register lengths (8 doubles/16 singles). Program summary Program Title: vec_deposition Program Files doi:http://dx.doi.org/10.17632/nh77fv9k8c.1 Licensing provisions: BSD 3-Clause Programming language: Fortran 90 External routines/libraries:  OpenMP>4.0 Nature of problem: Exascale architectures will have many-core processors per node with long vector data registers capable of performing one single instruction on multiple data during one clock cycle. Data register lengths are expected to double every four years and this pushes for new portable solutions for efficiently vectorizing Particle-In-Cell codes on these future many-core architectures. One of the main hotspot routines of the PIC algorithm is the current/charge deposition for which there is no efficient and portable vector algorithm. Solution method: Here we provide an efficient and portable vector algorithm of current/charge deposition routines that uses a new data structure, which significantly reduces gather/scatter operations. Vectorization is controlled using OpenMP 4.0 compiler directives for vectorization which ensures portability across different architectures. Restrictions: Here we do not provide the full PIC algorithm with an executable but only vector routines for current/charge deposition. These scalar/vector routines can be used as library routines in your 3D Particle-In-Cell code. However, to get the best performances out of vector routines you have to satisfy the two following requirements: (1) Your code should implement particle tiling (as explained in the manuscript) to allow for maximized cache reuse and reduce memory accesses that can hinder vector performances. The routines can be used directly on each particle tile. (2) You should compile your code with a Fortran 90 compiler (e.g Intel, gnu or cray) and provide proper alignment flags and compiler alignment directives (more details in README file).

A 2.5D PIC kinetic code is executed to simulate the excitation of electron whistlers and ion cyclotron whistler (L wave) during magnetic reconnection. Our simulation results suggest that quasi-parallel and anti-parallel whistler waves can be excited in the separatrix region near X-Line and in the outflow region, respectively. Electron whistlers play a crucial role in energy release and transfer, as the small mass of electrons allows them to move rapidly under the perturbation of a magnetic field during magnetic reconnection. The L wave excited near the separatrix region far from X-Line, it propagate obliquely to the local magnetic field. Velocity distribution functions (VDFs) indicate that these waves are associated with temperature anisotropy instabilities of electron-beams (ion-beam). The electron whistler in the separatrix region is excited by cyclotron resonance due to the electron beam. The electron whistler observed in the outflow region is generated by Landau resonance owing to beam-mode, where the v ∥ is close to the phase speed v p h of the wave. Regarding L wave, their excitation mechanism is attributed to significant perpendicular temperature anisotropy instability (T i ⊥ > T i ∥) of ion-beam, and satisfies cyclotron resonance condition. Meanwhile, our simulation results illustrate that the existence of energy conversion between particles and waves during the wave excitation by using the Wave-Particle Interaction Analyzer (WPIA). • The electron whistlers and ion cyclotron whistlers are excited in different regions of magnetic reconnection. • The excited waves exhibit interesting temperature anisotropy instabilities of electron-beam and ion-beam. • Wave-Particle Interaction Analyzer (WPIA) method confirms the efficient energy conversion between waves and particles. [ABSTRACT FROM AUTHOR]

One of the main factors that limit the lifetime of the Hall effect Thrusters (HETs) is the erosion of the acceleration channel caused by the flux of energetic ions. The magnetic field that is curved and convex towards the anode has been widely used in HETs because of its role in reducing the divergence angle of the ion beam and the channel wall erosion. However, the mechanism of the influence of the magnetic field line curvature on the wall erosion is not clear. Therefore, in this paper, a 2D3V numerical model based on the immersed-finite-element and particle-in-cell (IFE-PIC) method is established to simulate the radial-azimuthal plane near the exit of the Hall thruster. The effect of the tilt angle of the magnetic field line on the wall sputtering erosion rate is analyzed. The results show that compared to the case with the electric field E perpendicular to the magnetic field B, the energy of the ions hitting the channel wall is smaller and the wall erosion is weaker when the magnetic field lines are convex to the anode. As the tilt angle of the magnetic field lines increases from 0° to 60°, the erosion rate is reduced by 90%. Conversely, when the magnetic field lines are convex to the exit plane of the channel, the wall erosion is much more serious compared to the case with the orthogonal electric field E and the magnetic field B. As the tilt angle of the magnetic field line changes from 0° to 60°, the erosion rate is enhanced by 171%. The results in this paper are instructive for the design and optimization of the magnetic field of the HETs.

[Display omitted] • Developed a framework to implement gray and non-gray P1 model in MFiX. • Implemented different Weighted Sum of Gray Gases models. • Verified the implemented models for Eulerian-Eulerian and Eulerian-approaches approaches. • Studied the thermal radiation effects in chemically non-reacting and reacting gas-solid flows. Thermal radiation is a dominant mode of heat transfer in combustion/gasification, packed/circulating bed reactors, and energy storage/conversion devices. In hydrocarbon fuel combustion, the high absorption and emission of product gases like CO 2 and H 2 O significantly affect the heat transfer characteristics. It is essential to understand the radiative energy propagation in such applications. In the present study, we developed a framework to implement the P-1 radiation model in MFiX for Eulerian-Eulerian (Two fluid-TFM) and Eulerian-Lagrangian (Discrete element-DEM and Particle in cell-PIC) models. The P-1 is a simplification of the spherical harmonics method. The framework has been verified on various flue gas conditions. The verified solver results are validated against the benchmark results available in the literature. The verified and validated gray and non-gray weighted sum of gray gas models is evaluated for dry and wet flue gas conditions. They are also used to study gas-solid flows in a fluidized bed/riser. [ABSTRACT FROM AUTHOR]

The generation of energy-efficient parallel scientific codes became very important in the time of carbon footprint reduction. In this paper, we briefly present our latest particle-in-cell code with the results of a numerical simulation of plasma dynamics in an open trap. This code can be auto-vectorized by the Fortran compiler for Intel Xeon processors with AVX-512 instructions such as Intel Xeon Phi and the highest series of all generations of Intel Xeon Scalable processors. Efficient use of processor architecture is the main feature of an energy-efficient solution. We present a step-by-step methodology of energy consumption calculation using Intel hardware features and Intel VTune software. We also give an estimated value of carbon footprint with the impact of high-performance water cooled hardware. The Power Usage Effectiveness (PUE) in the case of high-performance water cooled hardware is equal to 1.03–1.05, and is up to 1.3 in the case of air-cooled systems. This means that power consumption of liquid cooled systems is lower than that air-cooled ones by up to 25%. All these factors play an important role in the carbon footprint reduction problem.

Linear gas stoppers are widely used to convert high-energy, rare-isotope beams and reaction products into low-energy beams with small transverse emittance and energy spread. Stopping of the high-energy ions is achieved through interaction with a buffer gas, typically helium, generating large quantities of He + /e − pairs. The Advanced Cryogenic Gas Stopper (ACGS) was designed for fast, efficient stopping and extraction of high-intensity, rare-isotope beams. As part of the design process, a comprehensive particle-in-cell code was developed to optimize the transport and extraction of rare isotopes from the ACGS in the presence of space charge, including He + /e − dynamics, buffer gas interactions including gas flow, radio-frequency carpets, and ion extraction through a nozzle or orifice. Details of the simulations are presented together with comparison to experiment when available. [Display omitted] • Particle-in-cell simulations were developed to study space charge in a gas cell. • Simulations were compared to experimental results of ion transport and extraction. • Sources of efficiency loss in ion transport up to 10 8 incident ions were studied. • Bottlenecks in operation at higher incident ion intensities were identified. [ABSTRACT FROM AUTHOR]

The initiating process of vacuum breakdown is still unknown despite the efforts of many researchers in the long history of vacuum insulation. This paper reports the results of Particle-In-Cell Monte Carlo Collision simulation of the electrons, positive ions, and neutrals in the vicinity of an emitter on the cathode. The radius of the emitter re, the temperature of the emitter T, product of macroscopic electric field and electric field enhancement factor β-Emac, and the electric field enhancement factor β itself are used as the parameters. In some combinations of the parameter values, the distort of electric field and the increase in current are observed as the result of the following positive feedback: field emission, positive ion generation, electric field enhancement by approach of positive ions, and increase in field emission electrons. All parameters affect whether the current increase or not. The radius of the emitter re is a key parameter that determines the occurrence of the current increase. This is because the density of the neutrals in the region where ionization occurs becomes larger with re. Necessary conditions to occur the current increase are the field emission current in the order of 0.1 µAormore and the line integral neutral density along z-direction at the center of the emitter in the order of 1017/m² or more. [ABSTRACT FROM AUTHOR]

In this paper, the generation of relativistic electron mirrors (REMs) and the reflection of an ultra-short laser off this mirrors are discussed, applying two-dimensional particle-in-cell (2D-PIC) simulations. REMs with ultra-high acceleration and expanding velocity can be produced from a solid nanofoil illuminated normally by an ultra-intense femtosecond laser pulse with a sharp rising edge. Chirped attosecond pulse can be produced through the reflection of a counter-propagating probe laser off the accelerating REM. In the electron moving frame, the plasma frequency of the REM keeps decreasing due to its rapidly expanding. The laser frequency, on the contrary, keeps increasing due to the acceleration of REM and the relativistic Doppler shift from the lab frame to the electron moving frame. Within an ultra-short time interval, the two frequencies will be equal in the electron moving frame, which leads the resonance between laser and REM. The reflected radiation near this interval and the corresponding spectra will be amplified due to the resonance. Through adjusting the arriving time of the probe laser, certain part of the reflected field could be selectively amplified or depressed, leading to the selectively adjusting of the corresponding spectra. [ABSTRACT FROM AUTHOR]

The large-angle scattered ions are generated in the plasma plume mainly due to the ion-atom collisions. These ions can induce thrust loss, backflow, or sputtering on the spacecraft. It is necessary, therefore, to give an accurate prediction of ion movement for the study on electric propulsions. In the present work, a particle simulation procedure, which includes (1) a Direct Simulation Monte Carlo method and (2) a particle-in-cell method with a Monte Carlo collisions technique coupled with an anisotropy scattering model, is applied to simulate the plume of a D55 anode-layer Hall thruster. The effective Xe+-Xe and Xe2+-Xe interaction potentials are employed to simulate the ion-atom scattering. The electron properties are obtained via a Boltzmann relation and a model that utilizes conservation-law-type equations, respectively. Comparisons are made between the experimental data together with the simulation results from the anisotropy model and those from an isotropic scattering model to analyze their disparities. Results show that, compared with the isotropic model, the electron number density from the anisotropy model matches better with the experimental data. However, the differences in ion current density, plasma potential, and electron temperature between the two scattering models are insignificant. The anisotropy model can give a more accurate prediction of the ion energy distribution, resulting from its more reasonable hypothesis than the isotropic model. For different electron models, the computed results from one using conservation-law-type equations are in better agreement with the measurements than a simple Boltzmann relation. • A newly proposed Xe+-Xe interaction potential is employed to simulate the elastic scattering. • Electron number density from the anisotropy scattering model is better than those from the isotropy one. • The anisotropy scattering model gives a more reasonable prediction of ion energy distribution. [ABSTRACT FROM AUTHOR]

Results are presented of the particle-in-cell numerical simulations by the KARAT code of the formation of a plasma–beam discharge in the absence of both the longitudinal magnetic field and the initial plasma. Oscillations of the electric field generated by the plasma–beam instability in the electron beam region almost do not affect the plasma at the periphery of the system. Simulation results are compared to the results obtained earlier by a simplified model and to the results of test experiments. The spatial distributions of the plasma density and electron temperature qualitatively agree with the experimental results. [ABSTRACT FROM AUTHOR]

The transverse electron current due to the crossed electric and magnetic fields results in the robust instability driven by the electron drift. In the regime of interest for electric propulsion applications, this instability leads to the excitation of quasicoherent nonlinear wave resulting in the anomalous electron transport. We investigate the nonlinear stage of the instability and resulting anomalous electron current using nonlinear Particle-in-Cell simulations. It is found that the anomalous current is proportional to the applied electric field thus demonstrating constant anomalous mobility. Moreover, the scaling of the current density follows the dependence of the dominant resonance wavelength on the electric and magnetic field strength thus clearly demonstrating the cyclotron nature of the instability. [ABSTRACT FROM AUTHOR]

The injection process is one of the most crucial attributes that determine the final properties of the electron bunch in laser wakefield accelerators. Here, a new injection method is proposed and studied via particle-in-cell simulations for the typical parameters of the bubble regime. The injection is triggered by the laser beam that reaches the super-Gaussian profile in the focus. Such a beam undergoes rapid variations in its intensity distribution during the diffraction process. If this diffraction occurs in underdense plasma, consequent changes in the bubble structure activate a localized transverse injection process. The generated electron bunch is characterized by the short duration (~2 fs) and low transverse emittance (≤1 mm mrad) while maintaining relatively high charge (~0.2 nC). [ABSTRACT FROM AUTHOR]

This paper presents a numerical study on the hydrodynamic performance of a vertical pile-restrained wave energy converter type floating breakwater. The aims are to further understand the characteristics of such integrated system in terms of both wave energy extraction and wave attenuation, and to provide guidance for optimising the shape of the floating breakwater for more energy absorption and less wave transmission at the same time. The numerical model solves the incompressible Navier-Stokes equations for free-surface flows using the particle-in-cell method and incorporates a Cartesian cut cell based strong coupling algorithm for fluid-structure interaction. The numerical model is first validated against an existing experiment, consisting of a rectangular box as the floating breakwater and a power take-off system installed above the breakwater, for the computation of the capture width ratio and wave transmission coefficients. Following that, an optimisation study based on the numerical model is conducted focusing on modifying the shape of the floating breakwater used in the experiment. The results indicate that by changing only the seaward side straight corner of the rectangular box to a small curve corner, the integrated system achieves significantly more wave energy extraction at the cost of only a slight increase in wave transmission. [ABSTRACT FROM AUTHOR]

In this paper, a selective discontinuous Galerkin (SDG) method and a polynomial preserving recovery (PPR) method are developed and integrated with the immersed-finite-element particle-in-cell (IFE-PIC) method, in order to carry out the plasma-material interaction simulation on adaptive Cartesian meshes (ACM). To significantly save the computational cost in practice, the PIC simulation often needs to use Cartesian meshes for the whole domain and the ACM for some focused regions in the plasma-material interaction problems. Therefore, we utilize the SDG method with immersed finite elements for the field solver of the IFE-PIC method, as the key technique to allow the local Cartesian mesh refinement which will generate hanging nodes. To minimize the degree of freedom of the SDG on the ACM and reduce the computational cost, a new selective technique of the discontinuous global basis functions is proposed for the SDG. Various types of nodes in the ACM are discussed for the implementation of this selective technique, including the hanging nodes. Meanwhile, the gathering and scattering steps of the PIC simulation also need to be appropriately performed on the ACM. The PPR method is a generic gradient recovery technique to be incorporated into the IFE-PIC method for more accurate force deposition on the ACM. In addition, two other algorithmic structures of the traditional IFE-PIC method have been modified to accommodate the ACM in the simulation, including a new mapping array structure for the particle positioning and a new charge deposition with some special particle positions in the ACM. As a result, the integrated immersed-selective-discontinuous-Galerkin particle-in-cell (ISDG-PIC) method can efficiently perform the plasma-material interactions simulation on the Cartesian meshes with local mesh refinement independent of the interface. Several numerical experiments are performed to demonstrate the convergence, efficiency, and applicability of the proposed ISDG-PIC method. • Immersed-selective-discontinuous-Galerkin particle-in-cell (ISDG-PIC) method. • Polynomial preserving recovery (PPR) method. • A new mapping array structure for the particle positioning. • A new charge deposition with some special particle positions in the adaptive Cartesian meshes. • A series of numerical examples for validation. [ABSTRACT FROM AUTHOR]

The Vlasov-Fokker-Planck equation (together with Maxwell's equations) provides the basis for plasma flow calculations. While the terms accounting for long range forces are established, different drift and diffusion terms are used to describe Coulomb collisions. Here, linear drift and a constant diffusion coefficient are considered and the electromagnetic fields are imposed, i.e., plasma frequency is not addressed. The solution algorithm is based on evolving computational particles of a large ensemble according to a Langevin equation, whereas the time step size is typically limited by plasma frequency, Coulomb collision frequency and cyclotron frequency. To overcome the latter two time step size constraints, a novel time integration scheme for the particle evolution is presented. It only requires that gradients of mean velocity, bath temperature, magnetic field and electric field have to be resolved along the trajectories. In fact, if these gradients are zero, then the new integration scheme is statistically exact; no matter how large the time step is chosen. Obviously, this is a computational advantage compared to classical integration schemes, which is demonstrated with numerical experiments of isolated charged particle trajectories under the influence of constant magnetic- and electric fields. Besides single ion trajectories, also plasma flow in spatially varying electromagnetic fields was investigated, that is, the influence of time step size and grid resolution on the final solution was studied. • The research highlight presented in this paper is an analytical solution of the coupled Langevin equations as they result from the Vlasov-Fokker-Planck equation for plasma flow with constant electromagnetic fields and constant friction coefficient. • This analytical solution involves a transformation into complex space and allows to take extremely large time steps when used in a solution algorithm. • This is demonstrated in the paper with numerical studies. [ABSTRACT FROM AUTHOR]

Abstract Floating structures are widely used for vessels, offshore platforms, and recently considered for deep water floating offshore wind system and wave energy devices. However, modelling complex wave interactions with floating structures, particularly under extreme conditions, remains an important challenge. Following the three-dimensional (3D) parallel particle-in-cell (PIC) model developed for simulating wave interaction with fixed bodies, this paper further extends the methodology and develops a new 3D parallel PIC model for applications to floating bodies. The PIC model uses both Lagrangian particles and Eulerian grid to solve the incompressible Navier-Stokes equations, attempting to combine both the Lagrangian flexibility for handling large free-surface deformations and Eulerian efficiency in terms of CPU cost. The wave-structure interaction is resolved via inclusion of a Cartesian cut cell method based two-way strong fluid-solid coupling algorithm that is both stable and efficient. The numerical model is validated against 3D experiments of focused wave interaction with a floating moored buoy. Good agreement between the numerical and experimental results has been achieved for the motion of the buoy and the mooring force. Additionally, the PIC model achieves a CPU efficiency of the same magnitude as that of the state-of-the-art OpenFOAM® model for an extreme wave-structure interaction scenario. [ABSTRACT FROM AUTHOR]

Nowadays, normal particle acceleration methods mostly used are chemical and conventional electric acceleration methods, whereas the chemical and traditional electric acceleration methods are limited by the chemical energy of the propellant and electrode erosion, respectively; so they are not suitable for the interplanetary travel. Ion cyclotron resonant heating (ICRH) is a mature plasma heating method that has been used in nuclear fusion for many years. It is realized by launching radio frequency waves into magnetoplasma and then accelerating it by increasing the rotational speed of the ions around the magnetic field lines. In this paper, we illustrate the principle of particle-in-cell (PIC) method first, and, then, simulate the plasma ICRH process with the software VSim using the PIC method. The acceleration of the plasma is studied from the three aspects of the incident velocity, ICRH electric field as well as background magnetic field, and the effect that different values of aforementioned parameters have on the ICRH acceleration is analyzed as well. The settings of these ICRH parameters are analyzed and summarized, which can lay the foundation for the optimal design of the experimental device for future work. [ABSTRACT FROM AUTHOR]

Acceleration of electrons in laser-driven plasma wakefields has been extended up to the ∼8 GeV energy within a distance of tens of centimeters. However, in applications, requiring small energy spread within the electron bunch, only a small portion of the bunch can be used and often the low-energy electrons represent undesired background in the spectrum. We present a compact and tunable scheme providing clean and mono-energetic electron bunches with less than one percent energy spread and with central energy on the GeV level. It is a two-step process consisting of ionization injection with attosecond pulses and acceleration in a capillary plasma wave-guide. Semi-analytical theory and particle-in-cell simulations are used to accurately model the injection and acceleration steps.

The development of ultra-intense laser-based sources of high energy ions is an important goal, with a variety of potential applications. One of the barriers to achieving this goal is the need to maximize the conversion efficiency from laser energy to ion energy. We apply a new approach to this problem, in which we use an evolutionary algorithm to optimize conversion efficiency by exploring variations of the target density profile with thousands of one-dimensional particle-in-cell (PIC) simulations. We then compare this ‘optimal’ target identified by the one-dimensional PIC simulations to more conventional choices, such as with an exponential scale length pre-plasma, with fully three-dimensional PIC simulations. The optimal target outperforms the conventional targets in terms of maximum ion energy by 20% and show a noticeable enhancement of conversion efficiency to >2 MeV ions. This target geometry enhances laser coupling to the electrons, while still allowing the laser to strongly reflect from an effectively thin target. These results underscore the potential for this statistics-driven approach to guide research into optimizing laser–plasma simulations and experiments.

The work is devoted to the problem of charged particle beam dynamics in self‐consistent electromagnetic fields in the modern colliders. The colliding beams move in vacuum with highly relativistic speeds (γ∼103 − 105). The achievement of the high luminosities for the high energy beams finds difficulties due to the beam disruption under the strong electromagnetic fields. We present our first results on the numerical simulations for the beams with the nonzero crossing angle with our parallel fully three‐dimensional algorithm. The results of the numerical modelling demonstrate qualitative and quantitative coincidence with theory for noncritical beam parameters. [ABSTRACT FROM AUTHOR]

The paper considers methods and algorithms providing the basis for a computer program implementing an axial-symmetric electrostatic version of the particle-in-cell method on unstructured triangular grids. In the presented implementation, the Poisson equation is approximated using the finite volume method. A discrete analog of the Poisson equation is solved by the multigrid method. Charged particle trajectories are calculated using the Boris method. Methods for interpolating electrostatic fields on unstructured grids and obtaining the charge density in the computational domain are considered. Special attention is paid to the specifics of implementing these methods in axisymmetric geometry. The developed computer code is tested on the problem of a flat diode operating in the space charge mode. [ABSTRACT FROM AUTHOR]

This article is devoted to the simulation of the processes of formation of dust clouds in the absence of gravitation, which is necessary for understanding the processes proceeding in dust clusters in outer space, upper planetary atmosphere, and on the surface of space objects, as well as for evaluating the possibilities of creating disperse structures with given properties. The chief aim of the simulation is to determine the general laws of the dynamics of the dust cloud at the initial stage of its formation. With the use of the original approach based on the particle-in-cell method that permits investigating the mechanics of large ensembles of particles on contemporary computational platforms, we consider the mechanics of a dusty medium in the process of its excitation in a closed container due to the vibration of the walls, and then in the process of particle scattering when the container opens in outer space. The main formation mechanisms of a dust formation have been elucidated, and the possibilities of mathematical simulation for predicting spatial and time characteristics of disperse structures have been shown. [ABSTRACT FROM AUTHOR]