Two-dimensional Particle-in-cell Research Articles

Magnetic nozzle performance in a cluster of helicon plasma thrusters

A numerical study of the plasma dynamics in a Helicon Plasma Thrusters’ (HPT) cluster is presented. For the first time in the literature, the three-dimensional (3D) plasma dynamics occurring in the plume of a HPTs’ cluster is analyzed. The physical investigation relies on ProPic, a 3D particle-in-cell (PIC) code specifically designed to simulate the plasma dynamics in magnetic nozzles and in a non-axi-symmetric domain. The code has been validated against experiments reported in the literature and cross-validated with Starfish, an open-source two-dimensional PIC software. The physical investigation has revealed an interesting mutual influence between the thrusters that constitute the cluster. Three significant phenomena that affect the cluster’s performance have been identified. The first phenomenon is related to the effect that clustering has on the shape of the magnetic field lines and, in turn, on the divergence angle of the plume. The second phenomenon is related to electron currents flowing among different thrusters, which affect the potential drop across the plume. The third phenomenon is related to the effect that neighboring thrusters have on the plasma potential map and, in turn, on the expansion of the ions.

Control of the ion flux and energy distribution of dual-frequency capacitive RF plasmas by the variation of the driving voltages

Due to its advantages of spatial uniformity and ion energy control, a dual-frequency (DF) capacitive-coupled plasma is widely used in semiconductor etching and deposition processes. In low-pressure discharges, the mean free path of ions is longer than the sheath width, and the ion energy distribution function is sensitive to the driving voltage waveform. In this respect, it is necessary to use a particle-in-cell (PIC) simulation to observe ion movement according to the time-varying electric field in the sheath. This study uses a two-dimensional PIC simulation parallelized with a graphics processing unit to monitor the ion energy distribution and flux according to the DF voltage waveform. We suggested a method to control the ion energy through a phase-resolved ion energy distribution in the region, where the ion transit time is longer than the high-frequency period and shorter than the low-frequency period.

Surface plasma wave excited by laser pulse obliquely incident on a double-layer plasma target and ts application

Surface plasma wave (SPW) will significantly affect the subsequent mutual coupling between laser and plasma, so there are many important applications such as particle acceleration driven by laser pulses and transmission enhancement. In this work, the properties of the SPW produced by an ultra-short and ultra-intensity laser pulse incident on a double-layer plasma target are studied by using the all-electromagnetic large-scale two-dimensional particle in cell (PIC) simulations. It is shown that the high-intensity laser incident with a large angle, <i>θ</i> =75°, can drive the electrons of the low-density layer to form a transportable periodic structure with the propagation speed close to light speed, and excite electrostatic wave whose wavelength is similar to that of the incident laser and is numerically close to the theoretical result according to previous theory. In order to excite the SPW, the laser intensity needs to reach a certain threshold. Besides, the ratio of the surface wave intensity to the incident laser intensity in the double-layer target case obviously deviates from the theoretical result of the single-layer target case, showing a nonlinear relationship. In the second part of the simulation, it is found that the SPW can significantly enhance the transmission of subsequent laser pulse, allowing the subsequent laser to break through the "black barrier" due to the dense plasma. A pre-laser irradiates the double-layer plasma target at <i>θ</i> = 75°, and then the subsequent laser is normally incident after a delay of Δ<i>t</i> = 23<i>T</i>. As a result, an obvious electromagnetic wave with the same direction as the sub-laser can be observed behind the target, which indicates that the sub-laser absolutely transmits the dense plasma. In comparison, when a single laser is normally incident on the target without pre-laser while other conditions keep unchanged, no obvious wave can be distinguished behind the target, that is, the field is nearly zero. Another simulation where a single-layer target is injected by pre-laser and sub-laser in order but the wave behind the target is also unobservable, proves that it is SPW that plays the main role in transmission enhancement instead of accelerated hot electrons on the target which can also transport the laser energy.

Simulation of the plume of a magnetically enhanced plasma thruster with SPIS

A three-dimensional fully kinetic particle-in-cell (PIC) simulation strategy has been implemented to simulate the acceleration stage of a magnetically enhanced plasma thruster (MEPT). The study has been performed with the open-source code Spacecraft Plasma Interaction Software (SPIS). The tool has been copiously modified to simulate properly the dynamics of a magnetized plasma plume. A cross-validation of the methodology has been done with Starfish, a two-dimensional open-source PIC software. Two configurations have been compared: (i) in the absence of a magnetic field and (ii) in the presence of a magnetic field generated by a coil with maximum intensity of 300 G at the thruster outlet. The results show a reduction of the plume divergence angle, an increase of ion speed and an increase of the specific impulse in the presence of the magnetic nozzle. The simulations presented in this study are representative of the operative conditions of a 50 W MEPT. Nonetheless, the methodology adopted can be extended to handle the magnetized plasma plume of several other types of thrusters such as electron cyclotron resonance and applied field magnetoplasmadynamic thrusters.

Investigation of dual-frequency effect on the ion energy and flux in Torr-regime plasma by a two-dimensional GPU-PIC simulation

Dual frequency (DF) capacitively coupled plasma (CCP) equipment has been widely used in semiconductor processing and requires particle-in-cell (PIC) simulations to investigate the nonlinear particle dynamics. It is believed that DF driving controls the electron density and ion energy separately, but a strong coupling exists between the two frequencies in reality. The two-dimensional (2D) PIC simulation of DF CCPs under deposition process conditions has not yet been reported due to the heavy computational load that can be resolved with a graphics processing unit (GPU) computation. This study quantitatively investigates the Torr-regime DF CCP using a 2D GPU-PIC simulation. The increase of the low-frequency (LF) power enhances ion transport, which results in the rise of plasma potential, the increase of sheath thickness, and the reduction of the electron density. The ions exhibit the Maxwellian distribution due to the frequent charge-exchange collisions. The ion flux keeps uniformity while electron density becomes abruptly nonuniform with the increase of the LF power, which is suitable to maintain the quality of deposited films.

Mach number dependence of ion-scale kinetic instability at collisionless perpendicular shock: Condition for Weibel-dominated shock

We investigate ion-scale kinetic plasma instabilities at the collisionless shock using linear theory and nonlinear particle-in-cell (PIC) simulations. We focus on the Alfvén ion cyclotron (AIC), mirror, and Weibel instabilities, which are all driven unstable by the effective temperature anisotropy induced by the shock-reflected ions within the transition layer of a strictly perpendicular shock. We conduct linear dispersion analysis with a homogeneous plasma model to mimic the shock transition layer by adopting a ring distribution with finite thermal spread to represent the velocity distribution of the reflected ions. We find that, for wave propagation parallel to the ambient magnetic field, the AIC instability at lower Alfvén Mach numbers tends to transition to the Weibel instability at higher Alfvén Mach numbers. The instability property is, however, also strongly affected by the sound Mach number. We conclude that the instability at a strong shock with Alfvén and sound Mach numbers both in excess of ∼20–40 may be considered as Weibel-like in the sense that the reflected ions behave essentially unmagnetized. Two-dimensional PIC simulations confirm the linear theory and find that, with typical parameters of young supernova remnant shocks, the ring distribution model produces magnetic fluctuations of the order of the background magnetic field, which is smaller than those observed in previous PIC simulations for Weibel-dominated shocks. This indicates that the assumption of the gyrotropic reflected ion distribution may not be adequate to quantitatively predict nonlinear behaviors of the dynamics in high Mach number shocks.

The formation mechanism of nonuniformity from 2D nonlocal particle-dynamics in capacitive RF discharges

Kinetic effects and nonlinear characteristics caused by multi-dimensional effects in capacitively coupled plasma (CCP) devices are reported using particle-in-cell (PIC) Monte-Carlo collision simulations. Many PIC simulations so far are limited to one-dimensional (1D) dynamics due to computational load, and the nonuniformity occurring in a direction parallel to the electrode cannot be reflected consequently. A two-dimensional (2D) PIC–MCC simulation based on a graphics processing unit is utilized to observe the variations in the spatial distribution that cannot be dealt with by 1D simulations. This simulation considers the pressure regime of the nonlocal electron kinetics. Contrary to the expectation that motions in the vertical direction to the electrode in a CCP dominate most of the particle dynamics, it was observed that electron heating in the horizontal direction around the electrode edge plays an important role. Accordingly, the change in the spatial distribution between the center of the CCP equipment and the peripheral region of the electrode edge has been analyzed by phase-resolved electron flux and power deposition to understand the principle of the formation of spatial nonuniformity.

Plasma inhomogeneity effects on particles energization by high-power laser pulse in a finite-size plasma

In this paper, the plasma inhomogeneity effects on the nonlinear laser energy absorption in a finite-size plasma have been studied in details, using two-dimensional relativistic electromagnetic PIC (Particle-In-Cell) simulation code. To this end, the effects of inhomogeneity characteristics on the nonlinear phenomena involved in the nonlinear laser absorption such as phase-mixing, wave-breaking, and parametric instabilities have been investigated. The simulation results show that the inhomogeneity causes the phase-mixing time to be reduced, in agreement with the results of recent theoretical works. As a more significant result, it is illustrated that although the plasma inhomogeneity increases the nonlinear absorption of laser in a finite-size plasma at the early time due to the phase-mixing/wave-breaking phenomenon, it eventually reduces the absorption rate because of the growth of parametric instabilities, in contrast to the interaction of laser with an infinite plasma where the laser scattering enhances the laser energy absorption. The results of the present investigation can greatly contribute to the further progression of knowledge in the experiments on the interaction of high-power lasers with inhomogeneous finite-size plasmas where the laser energy absorption is of crucial importance.

Plasma expansion accompanying superthermal electrons in over-picosecond relativistic laser-foil interactions

We study the plasma expansion dynamics in over-picosecond relativistic laser-foil interactions using one-dimensional particle-in-cell (PIC) simulations. A new expansion mode ‘isofield expansion’ appears after the well-known isothermal expansion due to the continuous energy input from the laser light to the plasma. The blowout of the heated plasma at the front surface triggers the transition from the isothermal mode to the new mode. In the new expansion mode, electrons and ions expand quasi-neutrally with a constant sheath electric field, and a large scale low density plasma is formed where superthermal electrons are produced efficiently. A two-dimensional PIC simulation confirms the appearance of the isofield expansion mode after the plasma blowout for a large focal spot laser.

High-Frequency Wave Generation in Magnetotail Reconnection: Nonlinear Harmonics of Upper Hybrid Waves.

MMS3 spacecraft passed the vicinity of the electron diffusion region of magnetotail reconnection on 3 July 2017, observing discrepancies between perpendicular electron bulk velocities and E→×B→ drift, and agyrotropic electron crescent distributions. Analyzing linear wave dispersions, Burch et al. (2019, https://doi.org/10.1029/2019GL082471) showed the electron crescent generates high‐frequency waves. We investigate harmonics of upper‐hybrid (UH) waves using both observation and particle‐in‐cell (PIC) simulation, and the generation of electromagnetic radiation from PIC simulation. Harmonics of UH are linearly polarized and propagate along the perpendicular direction to the ambient magnetic field. Compared with two‐dimensional PIC simulation and nonlinear kinetic theory, we show that the nonlinear beam‐plasma interaction between the agyrotropic electrons and the core electrons generates harmonics of UH. Moreover, PIC simulation shows that agyrotropic electron beam can lead to electromagnetic (EM) radiation at the plasma frequency and harmonics.

Model description of a two-dimensional electrostatic particle-in-cell simulation parallelized with a graphics processing unit for plasma discharges

Many key aspects of low-temperature plasmas include nonlinear, transient, and kinetic effects related to the spatio-temporal variation of electron energy distribution function (EEDF) which cannot be treated in a fluid simulation model. The particle-in-cell (PIC) simulation calculates kinetic effects through the statistical representation of the EEDF using many particles and thus gives accurate results. However, the computational cost is very expensive to resolve all aspects in a plasma discharge with millions of computational particles as well as hundreds of thousands of grids during millions of time steps. Additionally, the simulation of discharge plasmas should handle the collision processes and the rapid increase in the total number of simulation particles. In this presentation, details of a two-dimensional PIC simulation parallelized with graphics processing units (GPUs) are explained for the improvement of computation speed. The resulting GPU-PIC code executes aggregate time steps in two-dimensional geometry from 80 to 140 times faster than a conventional single CPU-PIC code with the same numerical scheme modelling a standard capacitively coupled plasma (CCP) reactor.

Particle-in-cell and Weak Turbulence Simulations of Plasma Emission

Abstract The plasma emission process, which is the mechanism for solar type II and type III radio burst phenomena, is studied by means of particle-in-cell (PIC) and weak turbulence (WT) simulation methods. “Plasma emission” is meant as a loose description of a series of processes, starting from the solar flare-associated electron beam exciting Langmuir and ion-acoustic turbulence, and subsequent partial conversion of beam energy into radiation energy by nonlinear processes. PIC simulation is rigorous but the method is computationally intense, and it is difficult to diagnose the results. The numerical solution of equations of WT theory, known as WT simulation, on the other hand, is efficient and naturally lends itself to diagnostics because various terms in the equation can be turned on or off. Nevertheless, WT theory is based upon a number of assumptions. It is therefore desirable to compare the two methods, which we do for the first time with numerical solutions of the complete set of equations of WT theory and a two-dimensional electromagnetic PIC simulation. Upon making quantitative comparisons, it is found that WT theory is largely valid, although some discrepancies are also found. The present study also indicates that large computational resources are required in order to accurately simulate the radiation emission processes, especially for low electron beam speeds, such that it may be more advantageous to employ the WT method in order to describe the radiation emission itself. Findings from the present paper thus imply that both methods may be useful for the study of solar radio emissions, as they are complementary.

Efficient laser acceleration of deuteron ions through optimization of pre-plasma formation for neutron source development

With the objective to develop a compact neutron source with laser accelerated ions, optimization of pre-formed plasmas for efficient target normal sheath acceleration (TNSA) of deuteron ions is investigated using two-dimensional radiation hydrodynamic and particle in cell (PIC) simulation codes. The plasma profile of a foil target irradiated with a pre-pulse of ns duration at the intensity of 1011–1013 W cm−2 is obtained with the radiation hydrodynamic simulation code. In addition to the formation of a long scale length pre-formed plasma at the front of the target foil, decrease of the plasma scale length at rear side is observed during temporal evolution of the preformed plasma. The two-dimensional PIC simulation on ultra-high intensity laser irradiation shows that the pre-formed plasma profiles at both sides of the target can be optimized for efficient TNSA acceleration, leading to generation of deuteron ions, collimated in the forward direction, with a larger amount and higher energy. The number of neutrons generated by deuteron-beryllium reaction increases by an order of magnitude in comparison to the laser irradiation without a pre-pulse.

Dominance of hole-boring radiation pressure acceleration regime with thin ribbon of ionized solid hydrogen

Laser-driven proton acceleration from novel cryogenic hydrogen target of the thickness of tens of microns irradiated by multiPW laser pulse is investigated here for relevant laser parameters accessible in near future. It is demonstrated that the efficiency of proton acceleration from relatively thick hydrogen solid ribbon largely exceeds the acceleration efficiency for a thinner ionized plastic foil, which can be explained by enhanced hole boring (HB) driven by laser ponderomotive force in the case of light ions and lower target density. Three-dimensional particle-in-cell (PIC) simulations of laser pulse interaction with relatively thick hydrogen target show larger energies of protons accelerated in the target interior during the HB phase and reduced energies of protons accelerated from the rear side of the target by quasistatic electric field compared with the results obtained from two-dimensional PIC calculations. Linearly and circularly polarized multiPW laser pulses of duration exceeding 100 fs show similar performance in terms of proton acceleration from both the target interior as well as from the rear side of the target. When ultrashort pulse (∼30 fs) is assumed, the number of accelerated protons from the target interior is substantially reduced.

TNSA proton maximum energy laws for 2D and 3D PIC simulations

Numerical simulations are a prominent tool in laser-plasma experiments. Their role, as a guide in new regime explorations and as a support for understanding laboratory results, is undisputed. But as the experiments themselves are growing in costs, setup time and complexity, so are the numerical counterparts. Nowadays it is often necessary to investigate, with great accuracy, a huge set of parameters, in order to explore interesting features.In literature, it is well known that two-dimensional particle in cell (2D PIC) simulations can only give a qualitative estimation of experimental results, often through a great layer of arbitrariness. On the other hand, three-dimensional (3D) PIC simulations, for the same setup, can typically require two orders of magnitude more of computational resources, to deliver results that, while being similar to laboratory results, are still far from being a real match, due to the many uncertainties, in the parameters and in the model, included in the physical engine.Following our recent published work, we discuss here a couple of empirical laws that we proposed, that can help giving quantitative insight into 2D PIC simulations and determining when 3D simulations should be stopped, if it is not really necessary to do a detailed exploration of the numerical results at long times.

Generation of high quality ion beams through the stable radiation pressure acceleration of the near critical density target**Project supported by the National Natural Science Foundation of China (Grant Nos. 11365020, 11475026, 11565022, and 11547304), the Science and Technology Program of Gansu Province of China (Grant No. 1606RJZA090), the Fundamental Research Funds for the Higher Education Institutions of Gansu Province of

In order to generate high quality ion beams through the stable radiation pressure acceleration (RPA) of the near critical density (NCD) target, we propose a new type of target where an ultra-thin high density (HD) layer is attached to the front surface of an NCD target, which has a preferable self-supporting property in the RPA experiments than the ultra-thin foil target. It is found that in one-dimensional particle-in-cell (PIC) simulation, by the block of the HD layer in the new target, there emerges the hole-boring process rather than propagation in the NCD layer when the intense laser pulse impinges on this target. As a result, a typical RPA structure that the compressed electron layer overlaps the ion layer as a whole is formed and a high quality ion beam is obtained, e.g., a circularly polarized laser pulse with normalized amplitude impinges on this new target and a 1.2 GeV monoenergetic ion beam is generated through the RPA of the NCD layer. Similar results are also found in the two-dimensional PIC simulation.

Electrostatic Structure of the Electron Phase-space Holes Generated by the Electron Two-stream Instability with a Finite Width

Space satellite observations in an electron phase-space hole (electron hole) have shown that bipolar structures are discovered at the parallel cut of parallel electric field, while unipolar structures spring from the parallel cut of perpendicular electric field. Particle-in-cell (PIC) simulations have demonstrated that the electron bi-stream instability induces several electron holes during its nonlinear evolution. However, how the unipolar structure of the parallel cut of the perpendicular electric field formed in these electron holes is still an unsolved problem, especially in a strongly magnetized plasma (<i>Ω</i>_e &gt; <i>ω</i>_pe, where <i>Ω</i>_e is defined as electron gyrofrequency and <i>ω</i>_pe is defined as plasma frequency, respectively). In this paper, with two-dimensional (2D) electrostatic PIC simulations, the evolution of the electron two-stream instability with a finite width in strongly magnetized plasma is investigated. Initially, those conditions lead to monochromatic electrostatic waves, and these waves coalesce with each other during their nonlinear evolution. At last, a solitary electrostatic structure is formed. In such an electron hole, a bipolar structure is formed in the parallel cut of parallel electric field, while a unipolar structure presents in the parallel cut of perpendicular electric field.

Direct heating of compressed core by ultra-intense laser

We propose a new scheme for heating an imploded core in the fast-ignition scheme. In this method, a heating laser irradiates an imploded core plasma directly. The accelerated fast-ions as well as fast-electrons heat the core. Two-dimensional particle in cell (PIC) simulation confirmed that carbon C6+ and deuteron D+ ions were accelerated as well as fast electrons when ultra-intense laser irradiates the CD plasma. In order to estimate the temperature scaling of the heated core in this scheme, we conducted transport simulations in the one-dimensional conical geometry. Our results show that 5 keV of ignition temperature can be achieved at the intensity of 1021 W/cm2, and 1.5 ps pulse for the compressed CD plasma with 10g/cm3 density.

Numerical studies of petawatt laser-driven proton generation from two-species targets using a two-dimensional particle-in-cell code

Laser-driven generation of high-energy ion beams has recently attracted considerable interest due to a variety of potential applications including proton radiography, ICF fast ignition, nuclear physics or hadron therapy. The ion beam parameters depend on both laser pulse and target parameters, and in order to produce the ion beam of properties required for a particular application the laser and target parameters must be carefully selected, and the mechanism of the ion beam generation should be well understood and controlled. Convenient and commonly used tools for studies of the ion acceleration process are particle-in-cell (PIC) codes. Using two-dimensional PIC simulations, the properties of a proton beam generated from a thin erbium hydride (ErH3) target irradiated by a 25fs laser pulse of linear or circular polarization and of intensity ranging from 1020 to 1021 W/cm2 are investigated and compared with the features of a proton beam produced from a hydrocarbon (CH) target. It has been found that using erbium hydride targets instead of hydrocarbon ones creates an opportunity to generate more compact proton beams of higher mean energy, intensity and of better collimation. This is especially true for the linear polarization of the laser beam, for which the mean proton energy, the amount of high energy protons and the intensity of the proton beam generated from the hydride target is by an order of magnitude higher than for the hydrocarbon target. For the circular polarization, the proton beam parameters are lower than those for the linear one, and the effect of target composition on the acceleration process is weaker.

Quasimonoenergetic proton beam acceleration from intense laser interaction with a double cone target

A new double cone target for accelerating quasimonoenergetic proton beam is proposed in this paper. Using two-dimensional PIC (particle-in-cell) simulation, the physical process of accelerating protons and the quality of proton beam from interaction of intense laser with the double cone target are investigated. In the case of same laser parameters, the peak energy and divergence angle of proton beams accelerated by the double cone target are superior to those by the single cone or planar target. Especially, compared to the planar target, the peak proton energy in the double cone target is increased by more than five times and quasimonoenergy can be well maintained. The critical density of the inner cone of the double cone target can increase the laser absorption efficiency. Moreover, the larger quasistatic magnetic field inside the double cone target can confine and guide more fast electrons to transport through the cone tip, which may enhance the sheath field for proton acceleration.