Particle-in-cell simulations of EUV-induced hydrogen plasma in the vicinity of a reflective mirror

Particle-In-Cell(PIC)simulations were performed in this work to study the dynamics of the EUVinduced hydrogen plasma.The Monte-Carlo Collision(MCC)model was employed to deal with the collisions between charged particles and background gas molecules.The dynamic evolution of the plasma sheath,as well as the flux and energy distribution of ions impacting on the mirror surface,was discussed.It was found that the emission of secondary electrons under the EUV irradiation on the ruthenium mirror coating creates a positively charged wall and then prevents the ions from impacting on the mirror and therefore changes the flux and energy distribution of ions reaching the mirror.Furthermore,gas pressure has a notable effect on the plasma sheath and the characteristics of the ions impinging on the mirrors.With greater gas pressure,the sheath potential decreases more rapidly.The flux of ions received by the mirror grows approximately linearly and at the same time the energy corresponding to the peak flux decreases slightly.However,the EUV source intensity barely changes the sheath potential,and its influence on the ion impact is mainly limited to the approximate linear increase in ion flux.

Particle-in-cell simulation for effect of anode temperature on discharge characteristics of a Hall effect thruster

Propellant gas flow has an important impact on the ionization and acceleration process of Hall effect thrusters （HETs）. In this paper, a particle-in-cell numerical method is used to study the effect of the anode temperature, i.e., the flow speed of the propellant gas, on the discharge characteristics of a HET. The simulation results show that, no matter the magnitude of the discharge voltage, the calculated variation trends of performance parameters with the anode temperature are in good agreement with the experimental ones presented in the literature. Further mechanism analysis indicates that the magnitude of the electron temperature is responsible for the two opposing variation laws found under different discharge voltages. When the discharge voltage is low, the electron temperature is low, and so is the intensity of the propellant ionization; the variation of the thruster performance with the anode temperature is thereby determined by the variation of the neutral density that affects the propellant utilization efficiency. When the discharge voltage is high, the electron temperature is large enough to guarantee a high degree of the propellant utilization no matter the magnitude of the anode temperature. The change of the thruster performance with the anode temperature is thus dominated by the change of the electron temperature and consequently the electron-neutral collisions as well as the electron cross-field mobility that affect the current utilization efficiency.

Spontaneous growth of the reconnection electric field during magnetic reconnection with a guide field:A theoretical model and particle-in-cell simulations

Reconnection electric field is a key element of magnetic reconnection.It quantifies the change of magnetic topology and the dissipation of magnetic energy.In this work,two-dimensional(2D)particle-in-cell(PIC)simulations are performed to study the growth of the reconnection electric field in the electron diffusion region(EDR)during magnetic reconnection with a guide field.At first,a seed electric field is produced due to the excitation of the tearing-mode instability.Then,the reconnection electric field in the EDR,which is dominated by the electron pressure tensor term,suffers a spontaneous growth stage and grows exponentially until it saturates.A theoretical model is also proposed to explain such a kind of growth.The reconnection electric field in the EDR is found to be directly proportional to the electron outflow speed.The time derivative of electron outflow speed is proportional to the reconnection electric field in the EDR because the outflow is formed after the inflow electrons are accelerated by the reconnection electric field in the EDR and then directed away along the outflow direction.This kind of reinforcing process at last leads to the exponential growth of the reconnection electric field in the EDR.

Electromagnetic Particle-in-Cell Simulations of Electron Holes Formed During the Electron Two-Stream Instability

Previous electrostatic particle-in-cell （PIC） simulations have pointed out that elec- tron phase-space holes （electron holes） can be formed during the nonlinear evolution of the electron two-stream instability. The parallel cuts of the parallel and perpendicular electric field have bipolar and unipolar structures in these electron holes, respectively. In this study, two-dimensional （2D） electromagnetic PIC simulations are performed in the x - y plane to investigate the evolution of the electron two-stream instability, with the emphasis on the magnetic structures associated with these electron holes in different plasma conditions. In the simulations, the background magnetic field （Bo = Boer） is along the x direction. In weakly magnetized plasma （Ωe 〈ωpe, where Ωe and ωpe are the electron gyrofrequency and electron plasma frequency, respectively）, several 2D electron holes are formed. In these 2D electron holes, the parallel cut of the fluctuating magnetic field δBx and δBz has unipolar structures, while the fluctuating magnetic field δBy has bipolar structures. In strongly magnetized plasma （Ωe 〉 ωpe）, several quasi-lD electron holes are formed. The electrostatic whistler waves with streaked structures of Ey are excited. The fluctuating mag- netic field δBx and δBz also have streaked structures. The fluctuating magnetic field δBx and δBy are produced by the current in the z direction due to the electric field drift of the trapped elec- trons, while the fluctuating magnetic field δBz can be explained by the Lorentz transformation of a moving quasielectrostatic structure. The influences of the initial temperature anisotropy on the magnetic structures of the electron holes are also analyzed. The electromagnetic whistler waves are found to be excited in weakly magnetized plasma. However, they do not have any significant effects on the electrostatic structures of the electron holes.

Particle-in-Cell Simulation of the Reflection of a Korteweg-de Vries Solitary Wave and an Envelope Solitary Wave at a Solid Boundary

Reflections of a Korteweg-de Vries （KdV） solitary wave and an envelope solitary wave are studied by using the particle-in-cell simulation method. Defining the phase shift of the reflected solitary wave, we notice that there is a phase shift of the reflected KdV solitary wave, while there is no phase shift for an envelope solitary wave. It is also noted that the reflection of a KdV solitary wave at a solid boundary is equivalent to the head-on collision between two identical amplitude solitary waves.

Particle-in-cell simulation of ion-acoustic solitary waves in a bounded plasma

We study some nonlinear waves in a viscous plasma which is confined in a finite cylinder.By averaging the physical quantities on the radial direction in some cases,we reduce this system to a simple one-dimensional model.It seems that the effects of the bounded geometry(the radius of the cylinder in this case)can be included in the damping coefficient.We notice that the amplitudes of both Korteweg–de Vries(KdV)solitary waves and dark envelope solitary waves decrease exponentially as time increases from the particle-in-cell(PIC)simulation.The dependence of damping coefficient on the cylinder radius and the viscosity coefficient is also obtained numerically and analytically.Both are in good agreement.By using a definition,we give a condition whether a solitary wave exists in a bounded plasma.Moreover,some of potential applications in laboratory experiments are suggested.

Effects of electron trapping on nonlinear electron-acoustic waves excited by an electron beam via particle-in-cell simulations

By performing one-dimensional particle-in-cell simulations, the nonlinear effects of electronacoustic(EA) waves are investigated in a multispecies plasma, whose constituents are hot electrons, cold electrons, and beam electrons with immobile neutralized positive ions. Numerical analyses have identified that EA waves with a sufficiently large amplitude tend to trap cold electrons. Because EA waves are dispersive, where the wave modes with different wavenumbers have different phase velocities, the trapping may lead to the mixing of cold electrons. The cold electrons finally get thermalized or heated. The investigation also shows that the excited EA waves give rise to a broad range of wave frequencies, which may be helpful for understanding the broadband-electrostatic-noise spectrum in the Earth’s auroral region.

Speeding-up direct implicit particle-in-cell simulations in bounded plasma by obtaining future electric field through explicitly propulsion of particles

The direct implicit particle-in-cell is a powerful kinetic method for researching plasma characteristics.However,it is time-consuming to obtain the future electromagnetic field in such a method since the field equations contain time-dependent matrix coefficients.In this work,we propose to explicitly push particles and obtain the future electromagnetic field based on the information about the particles in the future.The new method retains the form of implicit particle pusher,but the future field is obtained by solving the traditional explicit equation.Several numerical experiments,including the motion of charged particle in electromagnetic field,plasma sheath,and free diffusion of plasma into vacuum,are implemented to evaluate the performance of the method.The results demonstrate that the proposed method can suppress finite-grid-instability resulting from the coarse spatial resolution in electron Debye length through the strong damping of high-frequency plasma oscillation,while accurately describe low-frequency plasma phenomena,with the price of losing the numerical stability at large time-step.We believe that this work is helpful for people to research the bounded plasma by using particle-in-cell simulations.

Toward modeling of the scrape-off layer currents induced by electrode biasing using 2D particle-in-cell simulations

The property of scrape-off layer(SOL) currents induced by a biased electrode is investigated by fully kinetic collisionless two-dimensional particle-in-cell(PIC) simulations. A reduced Vlasov–Darwin model is employed, which is capable of describing the low-frequency kinetic behavior without electromagnetic vacuum modes(w^2=w_(pe)~2+ c^2k^2). A linear decay distribution of electron currents parallel to the background magnetic field is exhibited. Simulation analyses indicate that the cross field ion current is a key factor in sheath formation and global current balance. The influences of electrode area, biasing voltage and plasma source on the SOL current profile are studied, respectively.Characteristic plasma parameters in the far SOL region of the EAST tokamak are used in simulations to assess the current driving ability of the electrode biasing method. Due to the limitations of computational power, the geometrical size of the simulation domain is significantly smaller than the realistic SOL, which may lead to an absence of the quasi-neutral region in the upstream plasma.At last, a heuristic method is proposed to calculate the upper bound of the total current strength.

A Particle-in-Cell Simulation of Double Layers and Ion-Acoustic Waves

Double layers and ion-acoustic waves are investigated by using a one-dimensional electrostatic particle-in-cell simulation code. Our results show that double layers can be formed even when the drift velocity between electrons and ions is less than the electron thermal velocity. Electron and ion density depressions were clearly seen. Electrons gradually developed a distribu- tion comprising both background and beam components. In fact, as the initial electron-ion drift velocity was less than the electron thermal velocity, intense ion-acoustic waves could be found only at the places where the electron beam was located, suggesting that they are excited by the self-consistently developed electron beam. Besides the Langmuir waves and ion-acoustic waves, the beam mode excited by electron beams produced in our simulation has been clearly found.

Analysis of microwave propagation in a time-varying plasma slab with particle-in-cell simulations

Continuous microwave propagation through a time-varying plasma and frequency up-conversion has been demonstrated by particle-in-cell (PIC) simulation. In principle, it is possible to transform a 2.45 GHz source radiation to an arbitrary larger frequency radiation. The energy conversion is also obtained by the theoretical analysis and has been testified by PIC simulation. The source wave was propagating in a parallel plate waveguide locally filled with the ionized gas. In this paper we would discuss the effects of the rise time, the plasma length, the switching time and the collision frequency on the energy conversion, and the methods to improve the upshift wave energy are proposed. We also put forward the new concept of the critical values of the rise time and the source wave amplitude to provide a theoretical basis for the selection of parameters in the experiments.

Fully Kinetic, Electromagnetic Particle-in-Cell Simulations of Plasma Microturbulence

A novel numerical method,based on physical intuition,for particle-in-cell simulations of electromagnetic plasma microturbulence with fully kinetic ion and electron dynamics is presented.The method is based on the observation that,for lowfrequency modes of interest[ω/ω_(ci)≪1,ωis the typical mode frequency andωci is the ion cyclotron frequency]the impact of particles that have velocities larger than the resonant velocity,v^(r)∼ω/k_(||)(k_(||) is the typical parallel wavenumber)is negligibly small(this is especially true for the electrons).Therefore it is natural to analytically segregate the electron response into an adiabatic response and a nonadiabatic response and to numerically resolve only the latter:this approach is termed the splitting scheme.However,the exact separation between adiabatic and nonadiabatic responses implies that a set of coupled,nonlinear elliptic equations has to be solved;in this paper an iterative technique based on the multigrid method is used to resolve the apparent numerical difficulty.It is shown that the splitting scheme allows for clean,noise-free simulations of electromagnetic drift waves and ion temperature gradient(ITG)modes.It is also shown that the advantage of noise-free kinetic simulations translates into better energy conservation properties.

Molecular simulation study of the microstructures and properties of pyridinium ionic liquid[HPy][BF_(4)]mixed with acetonitrile

The microstructures and thermodynamic properties of mixed systems comprising pyridinium ionic liquid[HPy][BF_(4)]and acetonitrile at different mole fractions were studied using molecular dynamics simulation in this work.The following properties were determined:density,self-diffusion coefficient,excess molar volume,and radial distribution function.The results show that with an increase in the mole fraction of[HPy][BF_(4)],the self-diffusion coefficient decreases.Additionally,the excess molar volume initially decreases,reaches a minimum,and then increases.The rules of radial distribution functions(RDFs)of characteristic atoms are different.With increasing the mole fraction of[HPy][BF_(4)],the first peak of the RDFs of HA1-F decreases,while that of CT6-CT6 rises at first and then decreases.This indicates that the solvent molecules affect the polar and non-polar regions of[HPy][BF_(4)]differently.

On the energy conservation electrostatic particle-in-cell/Monte Carlo simulation: Benchmark and application to the radio frequency discharges

We benchmark and analyze the error of energy conservation （EC） scheme in particle-in-cell/Monte Carlo （PIC/MC） algorithms by simulating the radio frequency discharge. The plasma heating behaviors and electron distributing functions obtained by one-dimensional （1D） simulation are analyzed. Both explicit and implicit algorithms are checked. The results showed that the EC scheme can eliminated the self-heating with wide grid spacing in both cases with a small reduction of the accuracies. In typical parameters, the EC implicit scheme has higher precision than EC explicit scheme. Some ＂numerical cooling＂ behaviors are observed and analyzed. Some other errors are also analyzed. The analysis showed that the EC implicit scheme can be used to qualitative estimation of some discharge problems with much less computational resource cost without much loss of accuracies.

Implicit electrostatic particle-in-cell/Monte Carlo simulation for the magnetized plasma:Algorithms and application in gas-inductive breakdown

An implicit electrostatic particle-in-cell/Monte Carlo （PIC/MC） algorithm is developed for the magnetized discharging device simulation. The inductive driving force can be considered. The direct implicit PIC algorithm （DIPIC） and energy conservation scheme are applied together and the grid heating can be eliminated in most cases. A tensor-susceptibility Poisson equation is constructed. Its discrete form is made up by a hybrid scheme in one-dimensional （1D） and two- dimensional （2D） cylindrical systems. A semi-coarsening multigrid method is used to solve the discrete system. The algorithm is applied to simulate the cylindrical magnetized target fusion （MTF） pre-ionization process and get qualitatively correct results. The potential application of the algorithm is discussed briefly.

Particle-in-cell/Monte Carlo simulation of filamentary barrier discharges

The plasma behavior of filamentary barrier discharges in helium is simulated using a twodimensional（2D） particle-in-cell/Monte Carlo model. Four different phases have been suggested in terms of the development of the discharge： the Townsend phase; the space-charge dominated phase; the formation of the cathode layer, and the extinguishing phase. The spatialtemporal evolution of the particle densities, velocities of the charged particles, electric fields, and surface charges has been demonstrated. Our simulation provides insights into the underlying mechanism of the discharge and explains many dynamical behaviors of dielectric barrier discharge（DBD） filaments.

Explicit structure-preserving geometric particle-in-cell algorithm in curvilinear orthogonal coordinate systems and its applications to whole-device 6D kinetic simulations of tokamak physics

Explicit structure-preserving geometric particle-in-cell(PIC)algorithm in curvilinear orthogonal coordinate systems is developed.The work reported represents a further development of the structure-preserving geometric PIC algorithm achieving the goal of practical applications in magnetic fusion research.The algorithm is constructed by discretizing the field theory for the system of charged particles and electromagnetic field using Whitney forms,discrete exterior calculus,and explicit non-canonical symplectic integration.In addition to the truncated infinitely dimensional symplectic structure,the algorithm preserves exactly many important physical symmetries and conservation laws,such as local energy conservation,gauge symmetry and the corresponding local charge conservation.As a result,the algorithm possesses the long-term accuracy and fidelity required for first-principles-based simulations of the multiscale tokamak physics.The algorithm has been implemented in the Sym PIC code,which is designed for highefficiency massively-parallel PIC simulations in modern clusters.The code has been applied to carry out whole-device 6 D kinetic simulation studies of tokamak physics.A self-consistent kinetic steady state for fusion plasma in the tokamak geometry is numerically found with a predominately diagonal and anisotropic pressure tensor.The state also admits a steady-state subsonic ion flow in the range of 10 km s-1,agreeing with experimental observations and analytical calculations Kinetic ballooning instability in the self-consistent kinetic steady state is simulated.It is shown that high-n ballooning modes have larger growth rates than low-n global modes,and in the nonlinear phase the modes saturate approximately in 5 ion transit times at the 2%level by the E×B flow generated by the instability.These results are consistent with early and recent electromagnetic gyrokinetic simulations.

Parallelization of an Implicit Algorithm for Multi-Dimensional Particle-in-Cell Simulations

The implicit 2D3V particle-in-cell(PIC)code developed to study the interaction of ultrashort pulse lasers with matter[G.M.Petrov and J.Davis,Computer Phys.Comm.179,868(2008);Phys.Plasmas 18,073102(2011)]has been parallelized using MPI(Message Passing Interface).The parallelization strategy is optimized for a small number of computer cores,up to about 64.Details on the algorithm implementation are given with emphasis on code optimization by overlapping computations with communications.Performance evaluation for 1D domain decomposition has been made on a small Linux cluster with 64 computer cores for two typical regimes of PIC operation:”particle dominated”,for which the bulk of the computation time is spent on pushing particles,and”field dominated”,for which computing the fields is prevalent.For a small number of computer cores,less than 32,the MPI implementation offers a significant numerical speed-up.In the”particle dominated”regime it is close to the maximum theoretical one,while in the”field dominated”regime it is about 75-80%of the maximum speed-up.For a number of cores exceeding 32,performance degradation takes place as a result of the adopted 1D domain decomposition.The code parallelization will allow future implementation of atomic physics and extension to three dimensions.

Affine particle-in-cell method for two-phase liquid simulation

Background The interaction of gas and liquid can produce many interesting phenomena,such as bubbles rising from the bottom of the liquid.The simulation of two-phase fluids is a challenging topic in computer graphics.To animate the interaction of a gas and liquid,MultiFLIP samples the two types of particles,and a Euler grid is used to track the interface of the liquid and gas.However,MultiFLIP uses the fluid implicit particle(FLIP)method to interpolate the velocities of particles into the Euler grid,which suffer from additional noise and instability.Methods To solve the problem caused by fluid implicit particles(FLIP),we present a novel velocity transport technique for two individual particles based on the affine particle-in-cell(APIC)method.First,we design a weighed coupling method for interpolating the velocities of liquid and gas particles to the Euler grid such that we can apply the APIC method to the simulation of a two-phase fluid.Second,we introduce a narrowband method to our system because MultiFLIP is a time-consuming approach owing to the large number of particles.Results Experiments show that our method is well integrated with the APIC method and provides a visually credible two-phase fluid animation.Conclusions The proposed method can successfully handle the simulation of a two phase fluid.

CBETor:a hybrid-kinetic particle-in-cell code for cross-beam energy transfer simulation

The parametric instability related to ion motion and the resulting cross-beam energy transfer are important aspects in the physics of inertial confinement fusion.The numerical simulation of the above physical problems still faces great technical challenges.This paper introduces a 2D hybrid-kinetic particle-in-cell(PIC)code,CBETor.In this code,the motion of ions is described by the kinetic method,the motion of electrons is described by the simplified fluid method and the propagation of laser in plasma is described by solving the wave equation.We use CBETor and the popular fully kinetic PIC code EPOCH to simulate the stimulated Brillouin scattering and cross-beam energy transfer process,respectively.The physical images are in good agreement,but CBETor can significantly reduce the amount of calculation.With the premise of correctly simulating the ion dynamics,our hybrid-kinetic code can effectively suppress the noise of numerical simulation and significantly expand the simulation scale of physical problems.CBETor is very suitable for simulating the physical process dominated by ion motion in the interaction of medium intensity laser and underdense plasma.