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This article discusses the characteristics of an Ar/CF4 capacitively coupled plasma (CCP) excited using 40 MHz sinusoidal and 800 kHz rectangular voltage waveforms. The simulations focus on the effect of the low frequency (LF) rectangular wave duty cycle (defined as the period at negative voltage) on the plasma properties and uniformity for constant 100 W power at 40 MHz and 20 mTorr gas pressure. Given the importance of kinetic effects in low pressure CCPs, a hybrid plasma model is used. This model treats electrons as particles using the particle-in-cell formalism while ions and neutral species are represented as fluids. By incorporating electron kinetic effects, this approach allows for the accurate modeling of low-pressure CCPs with complex plasma chemistries. Results show that, at 80% duty cycle, the peak in the density of all species is near the edge of the electrodes. As the LF rectangular wave duty cycle is decreased while keeping the 40 MHz power fixed, the species' densities increase, the 40 MHz radio-frequency voltage decreases, and the peak in species' densities shifts towards the chamber center. These trends can be explained based on how the LF voltage modulates the coupling of 40 MHz power to the electrons. Under the conditions considered, the plasma is mostly produced through electron stochastic heating at the sheath edge by the 40 MHz voltage. The 40 MHz couples to the electrons more efficiently when the LF voltage at the powered electrode sheath is small and the sheath is thin. The plasma is produced relatively uniformly in the inter-electrode region during this phase. Therefore, at small duty cycles when the powered electrode sheath is thin for a long time, the plasma is uniform and requires a smaller 40 MHz voltage to deposit 100 W at 40 MHz in the plasma. When the LF voltage in the powered electrode sheath is large and negative, plasma production is weak and occurs at the edge of the powered electrode where the sheath is thinner. At large duty cycles, the plasma is efficiently produced for only a short period, necessitating a larger 40 MHz voltage. The plasma density also peaks near the electrode edge at large duty cycles. [ABSTRACT FROM AUTHOR]

In a previous paper Christlieb et al. (A particle-in-cell method for plasmas with a generalized momentum formulation, part I: Model formulation, 2024), we developed a new particle-in-cell (PIC) method for the relativistic Vlasov–Maxwell system in which the electromagnetic fields and the equations of motion for the particles were cast in terms of scalar and vector potentials through a Hamiltonian formulation. This new method evolved the potentials under the Lorenz gauge using integral equation methods. New methods to construct spatial derivatives of the potentials that converge at the same rates as the fields were also presented. The new particle method was compared against standard explicit discretizations, including the well-known FDTD-PIC method, for a range of applications involving sheaths and particle beams. This paper extends this new class of methods by focusing on the enforcement the Lorenz gauge condition in both exact and approximate forms using co-located meshes. A time-consistency property of the proposed field solver for the vector potential form of Maxwell’s equations is established, which is shown to preserve the equivalence between the semi-discrete Lorenz gauge condition and the analogous semi-discrete continuity equation. Using this property, we present three methods to enforce a semi-discrete gauge condition. The first method introduces an update for the continuity equation that is consistent with the discretization of the Lorenz gauge condition. Both the finite difference and spectral implementations satisfy this discrete gauge condition to machine precision. The second approach we propose enforces a semi-discrete continuity equation using the boundary integral solution to the field equations. The potential benefit of this approach is that it eliminates spatial derivatives that appear on the particle data, namely the current density, which is often calculated by linear combinations of low-order spline basis functions. This method is ideally suited to boundary integral equation methods that invert multi-dimensional operators without dimensional splitting techniques and will be the subject of future work. The third approach introduces a gauge correcting method that makes direct use of the gauge condition to modify the scalar potential and uses local maps for both the charge and current densities. This results in a gauge error, as the maps do not enforce the continuity equation. The vector potential coming from the current density is taken to be exact, and using the Lorenz gauge, we compute a correction to the scalar potential that makes the two potentials satisfy the gauge condition. This method also enforces the gauge condition to machine precision. We demonstrate two of the proposed methods in the context of periodic domains. Problems defined on bounded domains, including those with complex geometric features remain an ongoing effort. However, this work shows that it is possible to design computationally efficient methods that can effectively enforce the Lorenz gauge condition in a non-staggered PIC formulation. [ABSTRACT FROM AUTHOR]

The spatiotemporal evolution of plasma plumes is accompanied by various phenomena such as chemical reactions, sheath layer formation, and secondary electron emission, which have a crucial impact on the working characteristics and performance improvement of plasma devices. This study uses a direct simulation Monte Carlo/particle‐in‐cell (DSMC/PIC) parallel coupling algorithm for numerical simulations, with the PIC method using full particle simulations. The main focus of the study is to explore, through numerical simulations, the effects of the initial injection density, electron temperature, and charge exchange reactions. Two energy spectrum models are used for secondary electron emission, namely, the Furman model and the vertical model. The modified Mozorov coefficient model simulates two types of insulation wall materials: boron nitride and silicon carbide. The spatiotemporal evolution of H2, H, X, H2+, H+, and e in the flow field is demonstrated by simulating a double cylindrical axisymmetric calculation example. This paper provides a detailed analysis of the structural characteristics of number‐density cloud images under different initial conditions. Increasing the injection density enhances the radial electric field and results in a low‐density region of ion distributions. Furthermore, the electron temperature increases the deposition of wall charges. Lastly, the charge exchange reaction has a weak effect on the specific distribution of particles in the convection field. [ABSTRACT FROM AUTHOR]

Fast blue optical transients (FBOTs) represent a new class of highly energetic sources observed from radio to X-rays. High luminosity, light curves and spectra of the sources can be understood if they are associated with supernova-like or tidal disruption events. Radio observations of the transient sources revealed a mildly relativistic expansion of some of the remnants. The high power and mildly relativistic shock velocities are providing favorable conditions for very high energy particle acceleration. In this paper we present a model of particle acceleration in mildly relativistic magnetohydrodynamic (MHD) outflow of the transient source. To construct the non-thermal radiation and cosmic ray spectra in a broad range of energies we combined the microscopic particle-in-cell simulations of electron and proton injection at mildly relativistic shock with Monte Carlo technique for high energy particle transport and acceleration. The model allows describing the observed non-thermal radio and X-ray emission of CSS161010, and predicts that such sources can accelerate cosmic rays to energies above 10 PeV, and possible upper limit of maximum energy is 100 PeV. With the expected event rate of FBOTs they can contribute to the very high energy cosmic rays population in galaxies. [ABSTRACT FROM AUTHOR]

Accelerated particles have multiple applications in materials research, medicine, and the space industry. In contrast to classical particle accelerators, laser-driven acceleration at intensities greater than 1018 W/cm2, currently achieved at TW and PW laser facilities, allow for much larger electric field gradients at the laser focus point, several orders of magnitude higher than those found in conventional kilometer-sized accelerators. It has been demonstrated that target design becomes an important factor to consider in ultra-intense laser experiments. The energetic and spatial distribution of the accelerated particles strongly depends on the target configuration. Therefore, target engineering is one of the key approaches to optimizing energy transfer from the laser to the accelerated particles. This paper provides an overview of recent progress in 2D and 3D micro-structured solid targets, with an emphasis on fabrication procedures based on laser material processing. Recently, 3D laser lithography, which involves Two-Photon Absorption (TPA) effects in photopolymers, has been proposed as a technique for the high-resolution fabrication of 3D micro-structured targets. Additionally, laser surface nano-patterning followed by the replication of the patterns through molding, has been proposed and could become a cost-effective and reliable solution for intense laser experiments at high repetition rates. Recent works on numerical simulations have also been presented. Using particle-in-cell (PIC) simulation software, the importance of structured micro-target design in the energy absorption process of intense laser pulses—producing localized extreme temperatures and pressures—was demonstrated. Besides PIC simulations, the Finite-Difference Time-Domain (FDTD) numerical method offers the possibility to generate the specific data necessary for defining solid target material properties and designing their optical geometries with high accuracy. The prospects for the design and technological fabrication of 3D targets for ultra-intense laser facilities are also highlighted. [ABSTRACT FROM AUTHOR]

Ambipolar plasma thrusters are an appealing technology due to multiple system-related advantages, including propellant flexibility and the absence of electrodes or neutralizer. Understanding the plasma generation and acceleration mechanisms is key to improving the performance and capabilities of these thrusters. However, the source and plume regions inside are often simulated separately, and no self-consistent strategy exists which can couple these different simulations together. This paper introduces the MUlti-regime Plasma Equilibrium Transport Solver (MUPETS), a self-consistent coupled model integrating a fluid solver for the plasma dynamics in the source, which are collision-driven, with a kinetic Particle-In-Cell (PIC) code for the plasma dynamics in the magnetic nozzle, which involve expansion across a diverging magnetic field. The methodology begins by solving the plasma source with the classical Bohm condition at the thruster's throat. The resulting plasma profiles (density, temperature, speed) are input into the PIC code for the magnetic nozzle. The PIC code calculates the plasma plume expansion and determines the electric field at the thruster's throat. This electric field is then used as a boundary condition in the fluid code, where it replaces the Bohm assumption, and the fluid simulation is repeated. This iterative process continues until convergence. In comparing the MUPETS results with those for an experimental thruster, the plasma densities at the thruster's throat differed by less than 2–5% between the fluid and PIC regions. The thrust predictions agreed with the experimental trend, and were kept well within the measurement's uncertainty band. These results validate the effectiveness of the coupling strategy for enhancing plasma thruster simulation accuracy. [ABSTRACT FROM AUTHOR]

ABSTRACT The present study investigates the interaction between a proton‐electron plasma beam and an arched magnetic trap using the particle‐in‐cell (PIC) simulation method. The results show that when the magnetic field is sufficiently weak, the beam disrupts the arched magnetic field configuration, causing the breaking and reconnection of magnetic field lines. The relationships between the coil current threshold (the coil current at which the disruption of the magnetic induction just happens) and initial plasma velocity, and between the critical beam velocity (the plasma is just enough to reach the arched magnetic field) and coil current, are quantified. Additionally, the interaction between the beam and the arched magnetic field is observed to induce microwave excitation. These findings lay the foundation for theoretically simulating the dynamic behavior of space plasma in a unique magnetic field environment within a laboratory setting. [ABSTRACT FROM AUTHOR]

ProPIC is a fully kinetic particle-in-cell (PIC) solver developed for space electric propulsion. This work has extended its capabilities to simulate satellite surface charging and wake generation in low Earth orbit (LEO). A novel scaling approach has been implemented, decreasing computational cost by more than one order of magnitude. The methodology and scaling approach have been verified against the revised orbital-motion-limited theory. The surface charging and wake generation in LEO have been examined for a satellite that is more complex and larger than what is typically handled with a fully kinetic PIC approach in LEO, particularly due to the presence of large solar panels. Notably, the simulated wake can be used to identify the optimal position for the plasma diagnostic sensor that minimizes interference with the wake. Moreover, despite not being a failure risk, the attitude greatly influences the surface charging of a satellite with large solar arrays installed parallel to the satellite speed vector. The study suggests that, for high positive pitch angles (> 45 ∘), the surface charging of the solar panels can increase by as much as 75% compared to low negative pitching cases. Additionally, the study highlights that the pitch angle and satellite envelope along the motion direction significantly influence the potential gradients on the solar panels. [Display omitted] • Fully kinetic particle-in-cell simulation feasible for low Earth orbit satellites. • First such computations on surface charging of a medium, complex satellite design. • Tractable simulations with novel numerical scaling that lowers compute time tenfold. • Charging on complex geometries is not just determined by the area-facing freestream. • Two distinct potential gradients due to edge effect and freestream plasma arise. [ABSTRACT FROM AUTHOR]

This article presents a kinetic study of fusion burn waves in compressed deuterium-tritium and proton-boron plasmas. The study uses particle-in-cell simulations with Monte Carlo collisions to analyze the energy balance in the expansion of a hot-spot, capturing alpha particle heating and radiative losses. The simulations show that the energy radiated by the hot-spot is recaptured by the surrounding high-density fuel, resulting in a net fusion energy production that is twice the initial hot-spot energy. The study provides insights into the feasibility of proton-boron fusion as an alternative fusion fuel. The given text describes a simulation model for studying Coulomb collisions, fusion reactions, and bremsstrahlung radiation in high-density, highly-collisional systems. The model uses a binary Monte Carlo collision method to simulate these interactions between particles. The text explains the implementation of bremsstrahlung emission and inverse bremsstrahlung absorption in the simulation model. The model is verified through simulations of bremsstrahlung emission from an electron beam incident on solid boron, laser heating of a hydrogen plasma, and photon emission and absorption in a p-11B plasma. The given text discusses the results of simulations on various plasma scenarios. The simulations include laser heating of a hydrogen plasma, fusion burn waves in compressed DT and p-11B plasmas, and the measurement of radiation and fusion power density in a fully ionized p-11B plasma. The results show close agreement between the simulations and other [Extracted from the article]

Laser propagation in an electron-positron-ion (EPI) plasma medium having a constant density gradient is studied for the soliton evolution in the presence of a parallelly applied strong magnetic field. In a nonlinear regime, laser-plasma interaction forms an electron density hill that moves backward due to the density gradient. This hill localizes laser energy by the mechanism of resonance absorption (ωl = ωpe) and remains stable for a longer period, qualifying for the evolution of electromagnetic soliton. The position of the soliton from where it starts moving backward depends on the slope of the linear density variation. If the slope increases, then the position of the soliton is closer to the plasma boundary (x = 0). Another interesting property of the soliton is that its height decreases, and width increases as the temperature of plasma species rises. We simulate this phenomenon of electromagnetic soliton evolution in 1-D and 2-D by using Particle-In-Cell (PIC) simulation using the EPOCH-4.17.10. [ABSTRACT FROM AUTHOR]

Geometric particle-in-cell discretizations have been derived based on a discretization of the fields that is conforming with the de Rham structure of the Maxwell's equations and a standard particle-in-cell ansatz for the fields by deriving the equations of motion from a discrete action principle. While earlier work has focused on finite-element discretization of the fields based on the theory of finite-element exterior calculus, we propose in this article an alternative formulation of the field equations that is based on the ideas conveyed by mimetic finite differences, the needed duality being expressed by the use of staggered grids. We construct a finite-difference formulation based on degrees of freedom defined as point values, edge, face, and volume integrals on a primal and its dual grid. Compared to the finite-element formulation, no mass matrix inversion is involved in the formulation of the Maxwell solver. In numerical experiments, we verify the conservation properties of the novel method and study the influence of the various parameters in the discretization. [ABSTRACT FROM AUTHOR]

Direct laser acceleration has proven to be an efficient source of high-charge electron bunches and high brilliance x-rays. However, an analytical description of the acceleration in the interaction with varying plasma density targets is still missing. Here, we provide an analytical estimate of the maximum energies that electrons can achieve in such a case. We demonstrate that the maximum energy depends on the local electron properties at the moment when the electron fulfills the resonant condition at the beginning of the acceleration. This knowledge enables density shaping for various purposes. One application is to decrease the required acceleration distance needed to achieve the maximum electron energy. Another use for density tailoring is to achieve acceleration beyond the radiation reaction limit. We derive the energy scaling law that is valid for arbitrary density profile that varies slowly compared with the betatron period. Our results can be applied to electron heating in exponential preplasma of thin foils, ablating plasma plumes, or gas jets with long-scale ramp-up. [ABSTRACT FROM AUTHOR]

During magnetospheric substorms, plasma from magnetic reconnection in the magnetotail is thought to reach the inner magnetosphere and form a partial ring current. We simulate this process using a fully kinetic 3D particle‐in‐cell (PIC) numerical code along with a global magnetohydrodynamics (MHD) model. The PIC simulation extends from the solar wind outside the bow shock to beyond the reconnection region in the tail, while the MHD code extends much further and is run for nominal solar wind parameters and a southward interplanetary magnetic field. By the end of the PIC calculation, ions and electrons from the tail reconnection reach the inner magnetosphere and form a partial ring current and diamagnetic current. The primary source of particles to the inner magnetosphere is bursty bulk flows (BBFs) that originate from a complex pattern of reconnection in the near‐Earth magnetotail at xGSM=−18RE ${x}_{\text{GSM}}=-18{R}_{\mathrm{E}}$ to −30RE ${-}30{R}_{\mathrm{E}}$. Most ion acceleration occurs in this region, gaining from 10 to 50 keV as they traverse the sites of active reconnection. Electrons jet away from the reconnection region much faster than the ions, setting up an ambipolar electric field allowing the ions to catch up after approximately 10 ion inertial lengths. The initial energy flux in the BBFs is mainly kinetic energy flux from the ions, but as they move earthward, the energy flux changes to enthalpy flux at the ring current. The power delivered from the tail reconnection in the simulation to the inner magnetosphere is >2×1011 ${ >} 2\times 1{0}^{11}$ W, which is consistent with observations. Plain Language Summary: During intervals of increased solar activity, the magnetic field in Earth's stretched night‐side tail undergoes intense reconfiguration that can energize particles. This process is called magnetic reconnection. Ions and electrons from reconnection can reach the inner magnetosphere. In this paper, we simulate this process using a novel model that includes Earth's global magnetic field configuration and self‐consistently models particle physics for both electrons and ions. We find that the particles are accelerated significantly near the sites of magnetic field reconfiguration with ions gaining 10 s of keV energy. As they propagate earthward, they end up contributing energetically to the formation of a ring current system partially encircling Earth. Key Points: Ions and electrons accelerated by 10–50 keV near the magnetotail reconnection can reach the inner magnetosphereA partial ring current is formed during the simulation, with highest energy flux between midnight and duskThe ion and electron energy fluxes are mostly kinetic in the reconnection region but change to enthalpy flux earthward [ABSTRACT FROM AUTHOR]

To study the symmetry of electrical potential, we model plasma transport in the edge region of a toroidal device with two spatial dimensions (2D) and three coordinates for velocities (3V) using a Particle-In-Cell (PIC) code. A twodimensional magnetic field is applied, including poloidal and toroidal components, which are periodic in the poloidal direction. We discover relationships between the magnetic gradient drift and potential formation using PIC simulation, which has not been captured in other numerical models. We find that the inverse aspect ratio influences the asymmetry of the potential in an axisymmetric magnetic configuration. [ABSTRACT FROM AUTHOR]

A study of multi‐ion species plasmas in divertor region through kinetic simulation helps us understand particle transports and wall interactions. We analyzed plasma sheath behavior without collisions involving electrons, hydrogen isotopes, and helium ions using a one‐dimensional spatial space and three‐dimensional velocity space (1D3V) Particle‐In‐Cell (PIC) simulation. The PIC simulation model follows Maxwellian velocity distributions with the pre‐sheath acceleration for each particle species in the plasma source, and the plasmas move to the absorption wall with equal and constant flux. This revealed spatial potential variations due to differences in masses and charges of multi‐ion species plasmas, including independent sound velocities of each ion species. Increasing ion masses result in a more negative wall potential. The electrostatic force repels electrons and accelerates multi‐ions to reach the absorption wall. This information is found in the phase spaces of velocity in the sheath. [ABSTRACT FROM AUTHOR]

Owing to their large accelerating gradients, plasma-based accelerators have attracted considerable interest as potential drivers for future, compact electron-positron colliders. Despite great progress achieved in plasma-based electron acceleration, positron acceleration still remains a challenging task, with an efficient positron source being the prerequisite for such acceleration. Here a concept for a compact, two-stage plasma-based positron source is discussed. In the first stage the positrons are created by a multi GeV electron beam produced by a laser-plasma accelerator interacting with a solid density foil. In the second stage the positrons are captured and accelerated in a plasma wave driven by either an electron beam or a laser pulse. Three potential configurations of such a source are considered: (i) a single electron beam is used for both the creation of positrons in the foil and for driving the wakefield in the second stage; (ii) a train of two electron beams is used: the positrons produced by the trailing beam in the foil are captured and accelerated in the second stage by the plasma wave generated by the leading beam; and (iii) a single electron beam is used to produce positrons in the foil and an independent laser pulse is coupled to the second stage to drive the plasma wave. These three configurations show different degrees of effectiveness with positron capture efficiency, varying from less than a percent to almost half of all produced positrons.

We present a method for creating spacecraft‐like data which can be used to train Machine Learning (ML) models to detect and classify structures in in situ spacecraft data. First, we use the Grad‐Shafranov equation to numerically solve for several magnetohydrostatic equilibria which are variations on a known analytic equilibrium. These equilibria are then used as the initial conditions for Particle‐In‐Cell simulations in which the structures of interest are observed and labeled. We then take one‐dimensional slices through the simulations to replicate what a spacecraft collecting data from the simulation would observe. This sliced data then can be used as training data for the initial training of ML models intended for use on spacecraft data. We demonstrate the method applied to the problem of detecting small‐scale plasmoids in the magnetotail, which is important for understanding complex magnetotail reconnection dynamics. The simple 1D classifier we train is able to detect more than 70% of the plasmoid points in the data set but also produces a large number of false positives. Our further work on this example problem is detailed, and further potential uses of the method are discussed. Key Points: We present a method to use analytic magnetohydrostatic equilibria to develop perturbed numerical equilibria to initialize simulationsWe present a method to use Particle‐In‐Cell simulation data to simulate in situ spacecraft data, for use in training Machine Learning modelsThe above techniques are demonstrated by training a 1D Convolutional Neural Network to detect small‐scale plasmoids in the magnetotail [ABSTRACT FROM AUTHOR]

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Terrestrial gamma ray flashes (TGFs) are short bursts of gamma rays occurring during thunderstorms. They are believed to be produced by relativistic runaway electron avalanches (RREAs). It is usually admitted that the number of high‐energy electrons produced in the brightest TGFs remains mostly confined within a range from 1017 to 1019. To understand the constraints in the development of RREAs, we perform self‐consistent simulations using a newly developed model with a finite acceleration region and various injection rates. We find that RREAs should naturally self‐quench for a fixed total number of runaway electrons, and hence a fixed number of bremsstrahlung photons. From the idea that TGF sources quench themselves, we derive a simple equation controlling the total number of runaway electrons. In this framework, the existence of a saturation in the electron density discovered in a previous work places a lower limit on TGF durations. Plain Language Summary: Terrestrial gamma ray flashes (TGFs) are short bursts of high‐energy photons occurring during thunderstorms. They are believed to be produced by energetic electrons accelerating due to the intense electric field, forming a Relativistic Runaway Electron Avalanche (RREA). Discovered fairly recently, many of the TGF features remain unexplained. In this article, we aim to understand the constraint on the number of high‐energy electrons produced during TGFs, that always remains confined between 1017 and 1019. Using a newly developed simulation model, we find that RREAs naturally quench themselves when the number of high‐energy electrons and photons reach the range previously mentioned. Based on a limited number of fundamental processes, we were able to derive a simple equation controlling the total number of runaway electrons and deduce a lower limit for TGF durations. Key Points: There is a maximum low‐energy electron density reachable in Terrestrial Gamma Ray Flashe (TGF) sources when relativistic runaway electron avalanches (RREAs) reach saturation: nesat∼1015 ${n}_{e}^{\mathit{sat}}\sim 1{0}^{15}$ m−3There exists a minimum TGF timescale equal to the RREA timescale: τmin ∼ 1 μsThe self‐quenching of the TGF sources implies a maximum number of electrons Ne ∼ 1017 [ABSTRACT FROM AUTHOR]

This paper presents a recently developed full kinetic particle simulation code package, which is a two-dimensional highly integrated and universal framework for low-temperature plasma simulation on both Cartesian and axisymmetric coordinate systems. This code package is named CFIRM, since it is designed based on the continuous Galerkin immersed-finite-element (IFE) particle-in-cell (PIC) model with the polynomial-preserving-recovery (PPR) technique and the Monte-Carlo-collision (MCC) method. Both the traditional and implicit PIC methods were implemented in the package. Incorporating the advantages of all these methods together, the CFIRM code can adopt explicit or implicit PIC schemes to track the motion trajectory of charged particles and deal with the collisions between plasma and neutral gas. Additionally, it can conveniently handle complex interface problems on structured grids. The CFRIM code has excellent versatility in low-temperature plasma simulation and can easily extend to various particle processing modules, such as the variable weights and adaptive particle management algorithms which were incorporated into this code to reduce the memory utilization rate. The implementation for the main algorithms and the overall simulation framework of the CFIRM code package are rigorously described in details. Several simulations of the benchmark cases are carried out to validate the reliability and accuracy of the CFIRM code. Moreover, two typical low-temperature plasma engineering problems are simulated, including a hall thruster and a capacitively coupled plasma reactor, which demonstrates the applicability of this code package. [ABSTRACT FROM AUTHOR]

Terrestrial Gamma Ray Flashes (TGFs) are short bursts of gamma rays occurring during thunderstorms. They are believed to be produced by Relativistic Runaway Electron Avalanches (RREAs). In this paper, we present a new numerical model based on the Particle‐In‐Cell (PIC) method to simulate the interactions between the electromagnetic fields and the electron avalanche self‐consistently. The code uses a cylindrical Yee lattice to numerically solve the electromagnetic fields, a Monte Carlo approach to simulate collisions with air molecules, and a plasma fluid model to calculate the effects of low‐energy electrons and ions. The model is first tested through the reproduction of dispersion relations in a hot plasma. RREAs propagating under a homogeneous background electric field are then simulated. Owing to the self‐consistent nature of this description, we report here new physical properties such as saturation processes in the electron density and in the number of high‐energy electrons, detailed dynamical screening of the electric field in the ion trail of the avalanche, and the associated electric currents. We find that the saturation of RREAs is obtained when the numbers of high‐energy electrons and photons is consistent with those believed to be representative of TGF sources. Key Points: Development of a self‐consistent model coupling a Monte Carlo code with an electromagnetic particle‐in‐cell code to simulate Relativistic Runaway Electron Avalanches (RREAs)We identify a saturation phenomenon of the RREA, constraining the maximum number of high‐energy electrons and photons in terrestrial gamma‐ray flashesOnce saturation is reached, the electric field is partially screened, preventing the subsequently injected electrons from accelerating [ABSTRACT FROM AUTHOR]

We present particle-in-cell simulations with Monte Carlo collisions of fusion burn waves in compressed deuterium–tritium and proton–boron plasmas. We study the energy balance in the one-dimensional expansion of a hot-spot by simulating Coulomb collisions, fusion reactions, and bremsstrahlung emission with a Monte Carlo model and inverse bremsstrahlung absorption using a new PIC model. This allows us to self-consistently capture the alpha particle heating and radiative losses in the expanding hot-spot and surrounding cold fuel. After verifying our model in a code-to-code comparison with both kinetic and fluid codes for the case of a deuterium–tritium hot-spot, we simulate the expansion of a proton–boron hot-spot initialized at 200 keV and 1,000 g/cm3. Our model predicts that energy radiated by the hot-spot is recaptured by the surrounding high-density opaque fuel reducing the expansion work done by the propagating burn wave. As a result, we find the net fusion energy produced over the course of $20$∼ps is twice the initial hot-spot energy independent of whether radiation physics is included.

To study the symmetry of electrical potential, we model plasma transport in the edge region of a toroidal device with two spatial dimensions (2D) and three coordinates for velocities (3V) using a Particle-In-Cell (PIC) code. A two-dimensional magnetic field is applied, including poloidal and toroidal components, which are periodic in the poloidal direction. We discover relationships between the magnetic gradient drift and potential formation using PIC simulation, which has not been captured in other numerical models. We find that the inverse aspect ratio influences the asymmetry of the potential in an axisymmetric magnetic configuration.

Electromagnetic particle-in-cell (PIC) codes are widely used to perform computer simulations of a variety of physical systems, including fusion plasmas, astrophysical plasmas, plasma wakefield particle accelerators, and secondary photon sources driven by ultra-intense lasers. In a PIC code, Maxwell's equations are solved on a grid with a numerical method of choice. This article focuses on pseudo-spectral analytical time-domain (PSATD) algorithms and presents a novel hybrid PSATD PIC scheme that combines the respective advantages of standard nodal and staggered methods. The novelty of the hybrid scheme consists in using finite-order centering of grid quantities between nodal and staggered grids, in order to combine the solution of Maxwell's equations on a staggered grid with the deposition of charges and currents and the gathering of electromagnetic forces on a nodal grid. The correctness and performance of the novel hybrid scheme are assessed by means of numerical tests that employ different classes of PSATD equations in a variety of physical scenarios, ranging from the modeling of electron-positron pair creation in vacuum to the simulation of laser-driven and particle beam-driven plasma wakefield acceleration. It is shown that the novel hybrid scheme offers significant numerical and computational advantages, compared to purely nodal or staggered methods, for all the test cases presented.

Ambipolar plasma thrusters are an appealing technology due to multiple system-related advantages, including propellant flexibility and the absence of electrodes or neutralizer. Understanding the plasma generation and acceleration mechanisms is key to improving the performance and capabilities of these thrusters. However, the source and plume regions inside are often simulated separately, and no self-consistent strategy exists which can couple these different simulations together. This paper introduces the MUlti-regime Plasma Equilibrium Transport Solver (MUPETS), a self-consistent coupled model integrating a fluid solver for the plasma dynamics in the source, which are collision-driven, with a kinetic Particle-In-Cell (PIC) code for the plasma dynamics in the magnetic nozzle, which involve expansion across a diverging magnetic field. The methodology begins by solving the plasma source with the classical Bohm condition at the thruster’s throat. The resulting plasma profiles (density, temperature, speed) are input into the PIC code for the magnetic nozzle. The PIC code calculates the plasma plume expansion and determines the electric field at the thruster’s throat. This electric field is then used as a boundary condition in the fluid code, where it replaces the Bohm assumption, and the fluid simulation is repeated. This iterative process continues until convergence. In comparing the MUPETS results with those for an experimental thruster, the plasma densities at the thruster’s throat differed by less than 2–5% between the fluid and PIC regions. The thrust predictions agreed with the experimental trend, and were kept well within the measurement’s uncertainty band. These results validate the effectiveness of the coupling strategy for enhancing plasma thruster simulation accuracy.

Accelerated particles have multiple applications in materials research, medicine, and the space industry. In contrast to classical particle accelerators, laser-driven acceleration at intensities greater than 1018 W/cm2, currently achieved at TW and PW laser facilities, allow for much larger electric field gradients at the laser focus point, several orders of magnitude higher than those found in conventional kilometer-sized accelerators. It has been demonstrated that target design becomes an important factor to consider in ultra-intense laser experiments. The energetic and spatial distribution of the accelerated particles strongly depends on the target configuration. Therefore, target engineering is one of the key approaches to optimizing energy transfer from the laser to the accelerated particles. This paper provides an overview of recent progress in 2D and 3D micro-structured solid targets, with an emphasis on fabrication procedures based on laser material processing. Recently, 3D laser lithography, which involves Two-Photon Absorption (TPA) effects in photopolymers, has been proposed as a technique for the high-resolution fabrication of 3D micro-structured targets. Additionally, laser surface nano-patterning followed by the replication of the patterns through molding, has been proposed and could become a cost-effective and reliable solution for intense laser experiments at high repetition rates. Recent works on numerical simulations have also been presented. Using particle-in-cell (PIC) simulation software, the importance of structured micro-target design in the energy absorption process of intense laser pulses—producing localized extreme temperatures and pressures—was demonstrated. Besides PIC simulations, the Finite-Difference Time-Domain (FDTD) numerical method offers the possibility to generate the specific data necessary for defining solid target material properties and designing their optical geometries with high accuracy. The prospects for the design and technological fabrication of 3D targets for ultra-intense laser facilities are also highlighted.

Modeling plasma accelerators is a computationally challenging task and the quasi-static particle-in-cell algorithm is a method of choice in a wide range of situations. In this work, we present the first performance-portable, quasi-static, three-dimensional particle-in-cell code HiPACE++. By decomposing all the computation of a 3D domain in successive 2D transverse operations and choosing appropriate memory management, HiPACE++ demonstrates orders-of-magnitude speedups on modern scientific GPUs over CPU-only implementations. The 2D transverse operations are performed on a single GPU, avoiding time-consuming communications. The longitudinal parallelization is done through temporal domain decomposition, enabling near-optimal strong scaling from 1 to 512 GPUs. HiPACE++ is a modular, open-source code enabling efficient modeling of plasma accelerators from laptops to state-of-the-art supercomputers. Program summary: Program Title: HiPACE++ CPC Library link to program files: https://doi.org/10.17632/zh3rc7hvrm.1 Developer's repository link: HiPACE++ GitHub repository Licensing provisions: BSD 3-clause Programming language: C++ Nature of problem: Modeling plasma accelerators is a computationally challenging task requiring nanometer-scale resolutions over meter-scale propagation distances. The quasi-static particle-in-cell method enables high-fidelity simulations of this strongly non-linear process, but these simulations can be very expensive. Solution method: The quasi-static particle-in-cell algorithm is modified to enable efficient utilization of accelerated hardware, in particular with GPU computing, reducing the cost of simulations by orders of magnitude. A novel longitudinal parallelization enables excellent strong scaling of this method up to hundreds of GPUs. Reference: 10.5281/zenodo.5358483

A parallel, relativistic, three-dimensional particle-in-cell code SPACE has been developed for the simulation of electromagnetic fields, relativistic particle beams, and plasmas. In addition to the standard second-order Particle-in-Cell (PIC) algorithm, SPACE includes efficient novel algorithms to resolve atomic physics processes such as multi-level ionization of plasma atoms, recombination, and electron attachment to dopants in dense neutral gases. SPACE also contains a highly adaptive particle-based method, called Adaptive Particle-in-Cloud (AP-Cloud), for solving the Vlasov-Poisson problems. It eliminates the traditional Cartesian mesh of PIC and replaces it with an adaptive octree data structure. The code's algorithms, structure, capabilities, parallelization strategy, and performance have been discussed. Typical examples of SPACE applications to accelerator science and engineering problems are described.

A fully kinetic 2D axisymmetric Particle-in-Cell (PIC) model is used to examine the effects of background facility pressure on the plasma transport and propulsive efficiency of magnetic nozzles. Simulations are performed for a low-power (150 W class) cathode-less radio-frequency (RF) plasma thruster, operating with xenon, between background pressures up to 1 0 − 2 Pa and average electron discharge temperatures of 4–16 eV. When the electron temperature within the near-plume region reaches 8 eV, a decisive reduction in performance occurs: at 1 0 − 2 Pa, in-plume power losses surpass 25% of the discharge energy flux. Given that the ionisation energy for Xe is 12 eV, the 8 eV threshold indicates that a consistent percentage of electrons has energy enough to trigger ionisation. On the other hand, when the temperature is below such threshold, the primary collisions are charge-exchange and inelastic ion scattering, and the power loss remains less than 10%. It is established that losses in the considered thruster are significant if the facility pressure is greater than 1 0 − 3 Pa, at absorbed powers larger than 130 W. At the nominal 150 W, this results in a 15% thrust reduction. When facility pressure is taken into consideration over ideal vacuum simulations, numerical error is reduced to < 30% when compared to experimental thrust measurements at 1 0 − 3 Pa. • Investigation of facility effects on cathode-less RF thruster performance. • Particle-in-Cell (PIC) simulation of magnetic nozzle expansion into background gas. • Up to 15% thrust reduction at 150 W beyond 1 0 − 3 Pa. • Electron inelastic collisions can cause up to 70% of total in-plume power losses. • Experimental results/setup should therefore take into account facility pressure. [ABSTRACT FROM AUTHOR]

Abstract We present a method for creating spacecraft‐like data which can be used to train Machine Learning (ML) models to detect and classify structures in in situ spacecraft data. First, we use the Grad‐Shafranov equation to numerically solve for several magnetohydrostatic equilibria which are variations on a known analytic equilibrium. These equilibria are then used as the initial conditions for Particle‐In‐Cell simulations in which the structures of interest are observed and labeled. We then take one‐dimensional slices through the simulations to replicate what a spacecraft collecting data from the simulation would observe. This sliced data then can be used as training data for the initial training of ML models intended for use on spacecraft data. We demonstrate the method applied to the problem of detecting small‐scale plasmoids in the magnetotail, which is important for understanding complex magnetotail reconnection dynamics. The simple 1D classifier we train is able to detect more than 70% of the plasmoid points in the data set but also produces a large number of false positives. Our further work on this example problem is detailed, and further potential uses of the method are discussed.

Abstract Terrestrial gamma ray flashes (TGFs) are short bursts of gamma rays occurring during thunderstorms. They are believed to be produced by relativistic runaway electron avalanches (RREAs). It is usually admitted that the number of high‐energy electrons produced in the brightest TGFs remains mostly confined within a range from 1017 to 1019. To understand the constraints in the development of RREAs, we perform self‐consistent simulations using a newly developed model with a finite acceleration region and various injection rates. We find that RREAs should naturally self‐quench for a fixed total number of runaway electrons, and hence a fixed number of bremsstrahlung photons. From the idea that TGF sources quench themselves, we derive a simple equation controlling the total number of runaway electrons. In this framework, the existence of a saturation in the electron density discovered in a previous work places a lower limit on TGF durations.

This study investigates the propagation dynamics of plasma streamers in a packed-bed dielectric barrier discharge using a 2D particle-in-cell/Monte Carlo collision model. To accurately simulate the high-intensity discharge and streamer propagation mechanism at atmospheric pressure, additional algorithms for particle merging and a new electron mechanism are incorporated into the traditional particle-in-cell/Monte Carlo collision model. To validate the accuracy of this improved model, qualitative comparisons are made with experimental measurements from the existing literature. The results show that the speed of streamer propagation and the distribution of plasma are strongly influenced by the dielectric constant of the packed pellet, which is commonly used as a catalyst. In cases with a moderate dielectric constant, the presence of a strong electric field between the pellet and dielectric layer on the electrode significantly enhances the discharge. This enables the streamer to propagate swiftly along the pellet surface and results in a wider spread of plasma. Conversely, a very high dielectric constant impedes streamer propagation and leads to localized discharge with high intensity. The improved model algorithms derived from this research offer valuable insights for simulating high-density plasma discharge and optimizing plasma processing applications.

For the Isotope Decay At Rest (IsoDAR) experiment in neutrino physics (searching for sterile neutrinos), we have developed a novel compact isochronous cyclotron with direct injection through an axially embedded RFQ. For IsoDAR to be decisive within five years of running, 10 mA of protons, cw at 80% duty factor are needed on a neutrino production target. To alleviate space charge in the cyclotron driver, we accelerate 5 mA of H 2 + , to be broken up into 10 mA of protons after extraction from the cyclotron. An open question that we are answering with this paper is whether the beam losses from gas-stripping (the removal of electrons from H 2 + through the interaction of the beam ions with the residual gas in the accelerator) are going to be a significant challenge. Using a newly added feature to the well-established Object-Oriented Parallel Accelerator Library code, we calculate gas-stripping losses in the IsoDAR cyclotron using realistic beam distributions, magnetic fields, gas composition, and pressure. We show that to maintain losses due to dissociation below 1% over the entire acceleration region, a vacuum of at least 6 × 10−7 mbar is required. [ABSTRACT FROM AUTHOR]

A hybrid Fluid-Kinetic model based on a polymorphic Particle-in-Cell method is developed for the simulation of plasmas in ion thruster. The numerical scheme is suited for scenarios in which thermal ions or electrons undergo strong acceleration. The polymorphic PIC model is tested for the extraction region of an ion thruster. In this paper, we report the results achieved by implementing the scheme on a single extraction orifice and compare our results with the simulation from known IGUN software for ion extraction. [ABSTRACT FROM AUTHOR]

The supersonic ion jet generated in vacuum arc plasma has numerous applications, but the ion acceleration mechanism is incompletely understood. In this paper, a one-dimensional spherical vacuum arc discharge model is established, and the ion acceleration from vacuum breakdown to steady arc stage is investigated using particle-in-cell direct simulation Monte Carlo method. The results show that a potential hump exists and locates about 1 μ m far away from the cathode, but the potential drop provides a small contribution to the ion acceleration. A potential valley forms near the plasma–vacuum boundary and propagates towards the anode as the plasma expands during the vacuum breakdown stage. The ion mounting this valley experiences continuous acceleration by the dynamic electric field of the potential valley. As the plasma reaches the anode, a steady arc stage is gradually build-up, and the potential valley disappears. Consequently, the maximum mean ion velocity decreases. The source dominating the ion acceleration in this stage is turned into the electron–ion Coulomb collision. [ABSTRACT FROM AUTHOR]

The plume deflection of an applied-field magnetoplasmadynamic thruster is demonstrated using an asymmetrical magnetic nozzle. The two-dimensional plume diagnoses are performed downstream the deflected plume, where the plasma density, electron temperature, plasma potential, ion current density and the external current are measured by the Langmuir single probe, Faraday probe and a water-cooled Hall probe. A maximum plume deflecting angle of 12°is achieved. And a high-electric-potential region named the deflection arm is found on the anti-deflection side of the thruster axis. To obtain more kinetic insights, a fully-kinetic planar particle-in-cell simulation is also conducted under similar operating conditions, and the general distributions of the properties are reproduced qualitatively. Related closely to the deflection arm region, the E × B -induced Lorentz force is found to be one of the dominant deflecting force under ion non-magnetization condition, besides the Lorentz force induced by the diamagnetic current. As for the other contributors, the inertia-induced and the stress-induced Lorentz forces are rather insignificant. • First experiment of MPDT plume deflection by asymmetric magnetic nozzle. • An asymmetric high potential is found to facilitate the deflection. • A 2D PIC simulation is conducted to analyze the deflection kinetically. • The ExB-induced Lorentz force is found to dominate the deflection. [ABSTRACT FROM AUTHOR]

Laser-ion acceleration with ultra-short pulse, petawatt-class lasers is dominated by non-thermal, intra-pulse plasma dynamics. The presence of multiple ion species or multiple charge states in targets leads to characteristic modulations and even mono-energetic features, depending on the choice of target material. As spectral signatures of generated ion beams are frequently used to characterize underlying acceleration mechanisms, thermal, multi-fluid descriptions require revision for predictive capabilities and control in next-generation particle beam sources. We present an analytical model with explicit inter-species interactions, supported by extensive ab initio simulations. This enables us to derive important ensemble properties from the spectral distribution resulting from these multi-species effects for arbitrary mixtures. We further propose a potential experimental implementation with a novel cryogenic target, delivering jets with variable mixtures of hydrogen and deuterium. Free from contaminants and without strong influence of hardly controllable processes such as ionization dynamics, this would allow a systematic realization of our predictions for the multi-species effect.

In this study, experiments were performed to measure the inception and breakdown voltages of SF6/CO2 mixed gases with varying mixing ratios at two different pressures (1 and 2 bar). Using the preliminary data obtained from the experiments, a 3D particle model was used to investigate positive streamer initiation in SF6/CO2 with field ionization. Field ionization using Zener’s model was assumed to be similar to the electron detachment in air. The experimental results showed that at $P=1$ bar, the discharge inception voltage increased for CO2 concentrations lower than 50% and decreased for CO2 concentrations higher than 50%. The inception voltage of 80%CO2/20%SF6 was close to the inception voltage of pure SF6. A similar trend of the inception and breakdown voltages was observed at $P=2$ bar. The simulation results show the evolution of the thin filaments of the streamer into three distinct stages. The streamer morphology was similar irrespective of the type and concentration of the mixed gas. Other parameters such as the electric field, electron density, and streamer length increased with increasing CO2 concentration in SF6 at both pressures. Zener’s field ionization could be considered a primary ionization mechanism for SF6/CO2 in the case of very high non-uniform electric fields; however, finding the experimental validation of Zener’s field ionization for electronegative gases is still a challenging task.

The energy-conserving semi-implicit (ECsim) method presented by the author in 2017, is a particle-in-cell (PIC) algorithm for the simulation of plasmas. Energy conservation is achieved within a semi-implicit formulation that does not require any non-linear solver. A mass matrix is introduced to linearly express the particle-field coupling. With the mass matrix, the algorithm preserves energy conservation to machine precision. The construction of the mass matrix is the central nature of the method and also the main cost of the computational cycle. Here, three methods that modify the construction of the mass matrix are analyzed. First, the paper considers how the sub-cycling of the particle motion modifies the mass matrix. Second, a form of smoothing that reduces the noise while retaining exact energy conservation is introduced. Finally, an approximation of the mass matrix is discussed that transforms the ECsim scheme to the implicit moment method.

In recent years, the increasing demand for simple and low-cost propulsion for small satellites has given rise to a growing interest in low-power cathode-less plasma thrusters. Plasma is produced within a source tube using radiofrequency (RF) ionisation, enhanced by a magnetic field which also accelerates the discharge via the magnetic nozzle effect. A key advantage of cathode-less thrusters is that they can operate on a wider range of propellants, more easily stored, and often inexpensive (e.g., iodine) compared to traditional xenon. Despite simple hardware, plasma dynamics in this kind of device are highly complex. This work presents a numerical suite developed for cathode-less plasma thruster design and analysis. First, a 0D Global Source Model provides the plasma production in the source. A fully kinetic Particle-in-Cell model (2D and 3D) then handles plasma expansion in the magnetic nozzle. The capabilities of the suite are presented by-way-of investigation into the behaviour of alternative propellants iodine and krypton within the 50 and 150 W class REGULUS thrusters. The performance of each propellant is assessed in terms of plasma source and magnetic nozzle efficiencies. The results are then benchmarked against experimental measurements, obtaining agreement of < 30%. At absorbed powers < 20 W, iodine exhibits comparable performance to xenon but produces about 50% less thrust as the power is increased above 40 W. This occurs because of the molecular reaction processes seen by iodine, and associated inelastic energy thresholds which result in higher collisional energy losses. The high ionisation energy of krypton results in a low source efficiency. Instead, in the magnetic nozzle, krypton was found to perform best, facilitating the most thermal-to-kinetic conversion. But, the final thrust is < 20% of xenon; instead iodine performs within 43% of the thrust provided by xenon. Finally, iodine contamination of spacecraft surfaces is found to be comparable to estimates found in other electric propulsion devices. • Multiscale numerical model for cathode-less plasma thruster design and characterisation. • 0D Global Source Model for inductive RF plasma production. • Fully kinetic Particle-in-Cell model for the magnetic nozzle and expansion cone. • Iodine performs within 43% of the thrust provided by xenon. • Experimental agreement to REGULUS-50 and REGULUS-150 thrusters within 30%. [ABSTRACT FROM AUTHOR]

Laser-plasma interaction is a fascinating subject in view of its various applications in wave generation, particle acceleration, radiation generation, etc. The laser beam gets reflected at the vacuum-plasma interface if the plasma density is equal or larger than the critical density. However, in the presence of strong magnetic field in the order of kilo Tesla, the beam can travel some distance through over-dense plasma. Here E×B heating and pondermotive force play role for the laser beams to propagate through the over-dense plasma. In the present article, taking the external magnetic field along the propagation direction of the laser beam we have observed the R- and L- waves to be excited. The applied magnetic field is chosen in such way that the laser frequency -l falls between the electron cyclotron frequency ωce and ion cyclotron frequency ωci. Under this situation, it generates only an R-wave. If the laser frequency is considered to be less than the ion cyclotron frequency (ωlaser < ωci) then an L-wave is additionally generated. In both the cases, an electrostatic disturbance is also formed with different but significant electric field amplitudes. We simulate these R- and L-waves in 1-D by using Particle-in-Cell (PIC) simulation using the EPOCH-4.17.10. Specifically, the electric and magnetic fields are studied that are associated with these waves, and the waves are verified based on the dispersion relation and the polarization studies. [ABSTRACT FROM AUTHOR]