Monte Carlo Collision Research Articles

Experimental study on the performance characteristics of a miniature microwave discharge cathode

This study experimentally examined several magnetic field topologies for the miniature microwave discharge cathode driven by water, which is indispensable for realizing water ion thrusters. The electron emission currents were measured for various operating conditions; microwave power, mass flow rate, and microwave frequency. The magnetic field topology with the magnetic field lines passing through the orifice hole without intersecting the cathode increased the electron emission current. This result agreed with the prediction derived from the 3D-Particle-in-Cell simulations with Monte Carlo collisions. The measured performance was 11.1 mA electron emission current at 2.0 W microwave forward power and 20μg/s water mass flow rate. On the other hand, the dependency of electron emission current on magnetic field topology became smaller as the mass flow rate or microwave power decreased. Additionally, the performance dependency on mass flow rate was remarkably different by the magnetic field topology. We explained those newly found trends by the difference in electron temperature dependency for the electron transport against the magnetic field lines.

The Limitation Analysis of Two Dimensional Magnetic Field Configuration in Annular Ion Thruster

In this paper, the limitations of two-dimensional magnetic field configuration for an annular ion thruster are analyzed theoretically and numerically. The two-dimensional magnetic field, which is commonly used in traditional ion thrusters, has been proved to be a very effective way for the confinement of primary electrons and ions. Hence, the confinement characteristics of primary electrons and ions in an annular ion thruster with the two-dimensional magnetic field configuration are first analyzed theoretically. Then, according to the analysis, a two-dimensional magnetic field for an annular ion thruster is designed. On this basis, the limitations of the two-dimensional magnetic field configuration are analyzed and discussed by a three-dimensional (3D) Particle-in-cell Monte Carlo collision (PIC-MCC) model. The results show that if the collision process is not considered, a uniform distribution of primary electrons can be achieved theoretically. However, when considering the collision process, the atom forms a significant impedance to the circumferential motion of primary electrons, thus greatly increasing the loss rate of primary electrons. Finally, it is found that, since primary electrons are not guided and constrained in the circumferential direction under the two-dimensional magnetic field, the discharge uniformity cannot be improved only by increasing the magnetic field intensity.

Qualification of uniform large area multidipolar ECR hydrogen plasma

The design and characterization of a multi-dipolar microwave electron cyclotron resonance (ECR) hydrogen plasma reactor are presented. In this configuration, 16 ECR sources are disposed uniformly along the azimuthal direction at a constant distance from the center of a cylindrical reactor. Several plasma diagnostics have been used to determine key parameters such as neutral species temperature; electron density and temperature; and H+, H2+, and H3+ ion energy distributions. The experimental characterization is supported by electromagnetic and magnetostatic field simulations as well as Particle In-Cell Monte Carlo Collisions simulations to analyze the observed ion energy distribution functions. Especially, we show that both electron density and temperature are spatially uniform, i.e., 1011 cm−3 and 3 eV, respectively. This plasma enables generating ion flux and energy in the ranges 1019–1022 ions m−2 s−1 and few keVs, respectively. The H2+ ion distribution function shows two populations which were attributed to surface effects. These features make this reactor particularly suitable for studying hydrogen plasma surface interaction under controlled conditions.

On the use of ultra-high resolution PIC methods to unveil microscale effects of plasma kinetic instabilities: electron trapping and release by electrostatic tidal effect

Abstract Ultra-high resolution particle-in-cell coupled to Monte-Carlo collisions modelling unveils microscale instabilities in non-equilibrium plasmas fulfilling Penrose’s instability criterion. The spontaneous development of ion turbulence in the phase-space generated by charge exchange collisions leads to finite amplitude modulations of the local electric field. The latter are responsible for the trapping of low energy electrons and their transport from the plasma volume to the sheath vicinity. Electrostatic tidal effect occurring near the sheath is responsible for the release of the trapped electrons as a monochromatic bunch, accelerated back towards the source. This instability provides an additional theoretical ground for the anomalous enrichment of low-energy electrons observed by Langmuir probes in similar conditions. The present results demonstrate that marginally fulfilling PIC criteria is insufficient to study the microscale instabilities effects on the electrons dynamics in non-equilibrium low temperature plasmas.

Enhancement of the Nonresonant Streaming Instability by Particle Collisions.

Streaming cosmic rays can power the exponential growth of a seed magnetic field by exciting a nonresonant instability that feeds on their bulk kinetic energy. By generating the necessary turbulent magnetic field, it is thought to play a key role in the confinement and acceleration of cosmic rays at shocks. In this Letter we present hybrid-particle-in-cell simulations of the nonresonant mode including MonteCarlo collisions, and investigate the interplay between the pressure anisotropies produced by the instability and particle collisions in the background plasma. Simulations of poorly ionized plasmas confirm the rapid damping of the instability by proton-neutral collisions predicted by linear fluid theory calculations. In contrast we find that Coulomb collisions in fully ionized plasmas do not oppose the growth of the magnetic field, but under certain conditions suppress the pressure anisotropies and actually enhance the magnetic field amplification.

Particle-in-cell simulation of vacuum arc breakdown process of tip-to-plate electrode configuration

The breakdown of a vacuum arc under high applied voltage conditions usually occurs on very short time and space scales, and a deep understanding of these processes is essential to extend the application of vacuum arc devices. To study the time and spatial evolution of plasma parameters during vacuum breakdown, a two-dimensional axial-symmetric particle-in-cell code with Monte Carlo collisions is used in the numerical simulation of tip-to-plate electrode configuration. In this simulation, in addition to considering the primary and secondary ionization of copper atoms, the excitation and de-excitation processes of copper atoms are also introduced so that the evolution of the light intensity of the vacuum arc in the different stages of breakdown processes can be obtained by tracking the de-excitation process of the atoms, which can be considered a virtual camera. In this way, the cathode radiance, anode light expansion, arc channel establishment, and arc quenching processes can be visually observed, and the trends are consistent with the images taken by Intensified Charge-Coupled Device (ICCD) and streak cameras reported in the literature. The analysis of the sputtering amount of the anode material due to the impact of the cathode plasma to the anode surface shows that the contribution of atoms, singly, and doubly ionized ions to the sputtering of the anode material varies at different stages of the discharge.

Electron–neutral collisions effects on Langmuir probe in the lower E-region ionosphere

We present the first set of particle-in-cell simulations including Monte Carlo collisions between charged and neutral particles used to simulate a cylindrical Langmuir probe in the electron saturation regime with a collisional electron sheath. We use a setup focused on the E-region ionosphere; however, the results of these simulations are analyzed in a general sense using dimensionless values. We find that the electron currents get enhanced as the collision frequency for electrons increases and the values of λe/λD→1, where λe is the electron mean free path and λD is the electron Debye length. In addition, we apply the simulation results to a sounding rocket experiment and show how we can correct the currents for the Investigation of Cusp Irregularities-4 sounding rocket due to collisions while it flies through the E-region.

Radio-frequency biasing of ion acceleration grids with different propellants

In order to ensure the space charge compensation of the plume, conventional ion thrusters need an additional neutralizer to release electrons. When a radio-frequency (RF) voltage is applied across the grid system instead of a direct-current voltage, the simultaneous extraction of ions and electrons is achieved, thereby a neutralizer is not required. In this paper, based on the non-uniform distribution of neutral gas density calculated using the angular coefficient method, the particle-in-cell Monte Carlo collision method is used to thoroughly investigate the spatial and temporal dynamics of particles and the grid system performance for different propellants (argon, krypton and xenon) in such an RF grid system. RPA and E × B probe are employed to measure the ion flux distribution functions (IFDFs) of RF ion thruster with RF biasing, which are used to compare with the simulations. The simulated linear relationship between the self-bias voltage and the RF voltage amplitude and the multi-peak behavior of IFDF under low RF frequency conditions are comparable with the experimental data. The simulated IFDFs compare well with the experiments with the deviation of energy peak position less than 7% and 10% from those by RPA and E × B probe respectively, indicating the effectiveness of the used model. Simulations show the RF grid system is able to realize the extraction of electrons for all three propellants, so as to achieve the plume neutralization without an external neutralizer through the spatial and temporal oscillations of the beams. Electrons pass through the grid twice (extracted from the upstream, and backflow from the downstream), bringing two peaks of electron current to the accelerator grid in one period. The thrust-RF voltage curves for all three propellants show obvious slope transition, when the perveance limit is reached. The low-energy ions in the plume are mainly generated by the electron impact ionization processes for Xe while by CEX collisions for Ar. A larger ion current density of Xe on the downstream surface of the accelerator grid, which may lead to possibly more serious erosions of grids, is found compared with those of Kr and Ar. This is mainly contributed by the larger density of electron impact ionization generated ions of Xe in the downstream because Xe propellant has a larger electron density and ionization cross-section.

Ionization waves (striations) in a low-current plasma column revisited with kinetic and fluid models

A one-dimensional particle-in-cell Monte Carlo collisions method has been used to model the development and propagation of ionization waves in neon and argon positive columns. Low-current conditions are considered, that is, conditions where stepwise ionization or Coulomb collisions are negligible (linear ionization rate). This self-consistent model describes the development of self-excited moving striations, reproduces many of the well-known experimental characteristics (wavelength, spatial resonances, potential drop over one striation, and electron “bunching” effect) of the ionization waves called p, r, and s waves in the literature, and sheds light on their physical properties and on the mechanisms responsible for their existence. These are the first fully kinetic self-consistent simulations over a large range of conditions reproducing the development of p, r, and s ionization waves. Although the spatial resonances and the detailed properties of the striations in the nonlinear regime are of kinetic nature, the conditions of existence of the instability can be obtained and understood from a linear stability analysis of a three-moment set of quasi-neutral fluid equations where the electron transport coefficients are expressed as a function of electron temperature and are obtained from solutions of a 0D Boltzmann equation. An essential aspect of the instability leading to the development of these striations is the non-Maxwellian nature of the electron energy distribution function in the uniform electric field prior to the instability onset, resulting in an electron diffusion coefficient in space much larger than the energy diffusion coefficient.

Influence of temporal variations in plasma conditions on the electric potential near self-organized dust chains

Self-organization of dust grains into stable filamentary dust structures (or “chains”) largely depends on dynamic interactions between individual charged dust grains and complex electric potential arising from the distribution of charges within a local plasma environment. Recent studies have shown that the positive column of the gas discharge plasma in the Plasmakristall-4 (PK-4) experiment at the International Space Station supports the presence of fast-moving ionization waves, which lead to variations of plasma parameters by up to an order of magnitude from the average background values. The highly variable environment resulting from ionization waves may have interesting implications for the dynamics and self-organization of dust particles, particularly concerning the formation and stability of dust chains. Here, we investigate the electric potential surrounding dust chains in the PK-4 experiment by employing a molecular dynamics model of the dust and ions with boundary conditions supplied by a particle-in-cell with Monte Carlo collision simulation of the ionization waves. The model is used to examine the effects of the plasma conditions within different regions of the ionization wave and compare the resulting dust structure to that obtained by employing the time-averaged plasma conditions. The comparison between simulated dust chains and experimental data from the PK-4 experiment shows that the time-averaged plasma conditions do not accurately reproduce observed results for dust behavior, indicating that more careful treatment of plasma conditions in the presence of ionization waves is required. It is further shown that commonly used analytic forms of the electric potential do not accurately describe the electric potential near charged dust grains under these plasma conditions.

Ion-focused propagation of a relativistic electron beam in the self-generated plasma in atmosphere

It is known that ion-focused regime (IFR) can effectively suppress expansion of a relativistic electron beam (REB). Using the particle-in-cell Monte Carlo collision (PIC-MCC) method, we numerically investigate the propagation of an REB in neutral gas. The results demonstrate that the beam body is charge neutralization and a stable IFR can be established. As a result, the beam transverse dimensions and longitudinal velocities keep close to the initial parameters. We also calculate the charge and current neutralization factors of the REB. Combined with envelope equations, we obtain the variations of beam envelopes, which agree well with the PIC simulations. However, both the energy loss and instabilities of the REB may lead to a low transport efficiency during long-range propagation. It is proved that decreasing the initial pulse length of the REB can avoid the influence of electron avalanche. Using parts of REB pulses to build a long-distance IFR in advance can improve the beam quality of subsequent pulses. Further, a long-distance IFR may contribute to the implementation of long-range propagation of the REB in space environment.

Numerical simulation of electron extraction from micro electron cyclotron resonance neutralizer under different magnetic circuits

The electron cyclotron resonance (ECR) neutralizer is an important part of the micro ECR ion thruster. The electrons extracted from the neutralizer are used to neutralize the ions extracted from the ECR ion source, thereby avoiding the surface charges accumulating on the spacecraft, and the behaviour of electron extraction affects the overall performance of the thruster. In order to investigate the electron extraction through the orifices of the micro ECR neutralizer, a two-dimensional particle-in-cell with Monte Carlo collision (PIC/MCC) model is established in this work. The effects of different magnetic circuits on the electron extraction of the neutralizer and the influence of different cavity lengths on the wall current loss are studied through numerical simulation. The effects of different magnetic circuit structures on the electron extraction and wall current loss of the neutralizer are studied. The calculation results show that the position of the ECR layer and the magnetic flux lines near the extraction orifices are very important for the electron extraction performance of the neutralizer. When the ECR layer is located upstream of the antenna, electrons are easily lost in migration and diffusion motion, and the energy required for the electrons to cross the potential well before the extraction hole is higher. If more magnetic flux lines pass parallelly through the extraction orifices, the neutralizer requires a small voltage to extract the same electron current. When the ECR layer is cut by the antenna or is located downstream of antenna, more electrons may migrate along the magnetic flux lines to the vicinity of the extraction orifices, thereby reducing the voltage of collector plate. The effects of different cavity lengths on the extraction of electrons under the same magnetic circuit structure are studied. It is found that increasing the length of the cavity allows more parallel-axis magnetic flux lines to pass through the extraction holes to avoid electron loss on the surface of the extraction plate, and thus increasing the extraction electron current. The research results conduce to designing a reasonable neutralizer magnetic circuit and cavity size.

Characterization of plasma discharge channel in EDM using photography and spectroscopy

The plasma discharge channel of electrical discharge machining (EDM) brings a temperature of several thousands of degrees Celsius into the gap between the anode and cathode, resulting in the material removal by means of melting and evaporating. To investigate the characteristics of the plasma discharge channel, high-speed imaging technology is adopted to observe the dimension of the plasma. A spectrometer is used to calibrate the temperature of the plasma as well. Then the particle-in-cell with Monte Carlo collision (PIC-MCC) simulation is conducted to analyze the variation and distribution of the plasma and heat flux. The experimental results demonstrate that the discharge channels’ morphology obtained is stable after a few microseconds of expansion after breakdown, and the diameter of discharge channel and the current density increases with the increase of discharge current. Besides, the emission intensity of plasma increases with the increase of electrical parameters. However, the temperature of plasma decreases after high current, which means debris particles make machining condition deteriorated. Finally, the simulation results demonstrate that despite the current density increases, the maximum heat flux at the center of electrode reduces rapidly with the expansion of the discharge channel. The distribution of heat flux upon electrode evolves towards "wider and flatter", leading to larger debris particles than exceptional size.

Working principle and layout logic of closed magnetic field in sputtering

Closed magnetic field constructed by unbalanced magnetron sputtering (MS) cathodes has been a general means of developing the MS coating system. However, owing to the difficulties in characterizing the complex plasma behaviors, there are still no quantitative criteria or design bases for some critical points, such as the effective object, the working mechanism, the closure condition, the layout logic and the effectivity of the closed magnetic field. Here in this work, out of the movements of charged particles in magnetic field, the motion behaviors of electrons and ions in the vacuum chamber are studied and it is also revealed that the closed magnetic field can affect mainly the electrons and further control the distributions of ions. A Monte-Carlo collision (MCC) model of the closed magnetic field MS coating system is established by test-electron to characterize the plasma transport characteristics, and the electron constraint and coating deposition efficiency are studied by different layouts of the magnetron cathodes and the ion sources. The simulation results show that the cathode numbers and vacuum chamber size determine the constraint effect on electrons in closed magnetic field. By 8 MS cathodes and the chamber radius of 0.5 m, the proportion of the overflow electrons can decrease to 1.77%. To increase the proportion of the electrons in the coating region, four coupled magnetic fields are introduced in the center of vacuum chamber. The studies of cathode type, rotation angle and magnetic field direction reveal that the proportion of the overflow electrons is less than 3%. A local dense plasma distribution and a continuous uniform plasma distribution can be observed in the vacuum chamber, corresponding to the same and opposite layout in magnetic poles of the MS cathodes and the ion sources, and the proportion of the electrons in the coating region significantly increases to 53.41% and 42.25%, respectively.

A comparison of particle and fluid models for positive streamer discharges in air

Both fluid and particle models are commonly used to simulate streamer discharges. In this paper, we quantitatively study the agreement between these approaches for axisymmetric and 3D simulations of positive streamers in air. We use a drift–diffusion–reaction fluid model with the local field approximation and a particle-in-cell, Monte Carlo collision particle model. The simulations are performed at 300 K and 1 bar in a 10 mm plate–plate gap with a 2 mm needle electrode. Applied voltages between 11.7 and 15.6 kV are used, which correspond to background fields of about 15–20 kV cm−1. Streamer properties like maximal electric field, head position and velocity are compared as a function of time or space. Our results show good agreement between the particle and fluid simulations, in contrast to some earlier comparisons that were carried out in 1D or for negative streamers. To quantify discrepancies between the models, we mainly look at streamer velocities as a function of streamer length. For the test cases considered here, the mean deviation in streamer velocity between the particle and fluid simulations is less than 4%. We study the effect of different types of transport data for the fluid model, and find that flux coefficients lead to good agreement whereas bulk coefficients do not. Furthermore, we find that with a two-term Boltzmann solver, data should be computed using a temporal growth model for the best agreement. The numerical convergence of the particle and fluid models is also studied. In fluid simulations the streamer velocity increases somewhat using finer grids, whereas the particle simulations are less sensitive to the grid. Photoionization is the dominant source of stochastic fluctuations in our simulations. When the same stochastic photoionization model is used, particle and fluid simulations exhibit similar fluctuations.

Hybrid modelling of cavity system generated electromagnetic pulse in low pressure air

The surface of metal system exposed to ionizing radiation (X-ray and γ-ray) will emit high-energy electrons through the photoelectric effect and other processes. The transient electromagnetic field generated by the high-speed electron flow is called system generated electromagnetic pulse (SGEMP), which is difficult to shield effectively. An ongoing effort has been made to investigate the SGEMP response in vacuum by numerical simulation. However, the systems are usually operated in a gaseous environment. The objective of this paper is to investigate the effect of low-pressure air on the SGEMP. A three-dimensional hybrid simulation model is developed to calculate the characteristics of the electron beam induced air plasma and its interaction with the electromagnetic field. In the hybrid model, the high-energy photoelectrons are modelled as macroparticles, and secondary electrons are treaed as fluid for a balance between efficiency and accuracy. A cylindrical cavity with an inner diameter of 100 mm and a length of 50 mm is used. The photoelectrons are emitted from one end of the cavity and are assumed to be monoenergetic (20 keV). The photoelectron pulse follows a sine-squared distribution with a peak current density of 10 A/cm<sup>2</sup>, and its full width at half maximum is 2 ns. The results show that the number density of the secondary electrons near the photoelectron emission surface and its axial gradient increase as air pressure increases. The electron number density in the middle of the cavity shows a peak value at 20 Torr (1 Torr = 133 Pa). The electron temperature decreases monotonically with the increase in pressure. The low-pressure air plasma in the cavity prevents the space charge layer from being generated. The peak value of the electric field is an order of magnitude lower than that in vacuum, and the pulse width is also significantly reduced. The emission characteristic of the photoelectrons determines the peak value of the current response. The current reaching the end of the cavity surface first increases and then decreases with pressure increasing. The plasma return current can suppress the rising rate of the total current and extend the duration of current responses. Finally, to validate the established hybrid simulation model, the calculated magnetic field is compared with that from the benchmark experiments. This paper helps to achieve a better prediction of the SGEMP response in a gaseous environment. Compared with the particle-in-cell Monte Carlo collision method, the hybrid model adopted can greatly reduce the computational cost.

Higher harmonics in complex plasmas with alternating screening

We report how higher harmonics of collective excitations emerge in a two-dimensional layer of strongly correlated charged microparticles in a complex plasma with a periodically alternating screening. The simulation results of the radio frequency discharge and the charged microparticles are obtained using a highly accurate multiscale and multiphysics approach based on the particle-in-cell technique, Monte Carlo collision calculations, and molecular dynamics simulations. We also devise a simple phenomenological expression for the dispersion relation of higher harmonics. Furthermore, our analysis reveals that the periodically alternating screening causes a self-conjugate state with negative refraction. In doing so, we demonstrate how complex plasmas can serve as a test bed for studying the fundamental physics of a self-conjugate state in strongly correlated systems.

Study on the Electromagnetic Radiation Effect of a Thermal Control Layer

To study the electromagnetic radiation effect of a thermal control layer (TCL) on the surface of general spacecraft in a space environment, a model of thermal control material irradiated with microwaves was established, a particle-in-cell (PIC)-Monte Carlo collisions (MCC) simulation was used, and the processes of field emission, multipacting, outgassing, and impact ionization on the surface of thermal control materials were simulated. By comparing the primary electrons, secondary electrons, and impact ionization electrons produced under different field intensities and frequencies of electromagnetic waves, different compositions of outgassing, and different thermal control materials, the influencing factors and critical thresholds of avalanche ionization were obtained. The simulation results show that whether avalanche ionization occurs in outgassing on the surface of the TCL is affected by the electromagnetic wave amplitude, electromagnetic wave frequency, outgassing composition, and the material of the TCL. This provides a theoretical reference for the safe operation of spacecraft.

Transition from ballistic to thermalized transport of metal-sputtered species in a DC magnetron

Tunable diode-laser induced fluorescence technique has been optimized to accurately measure the titanium (Ti)-sputtered atom velocity distribution functions (AVDFs) in a magnetron discharge operating in DC mode. The high spatial and spectral resolution achieved reveals some features of the transport of the metal-sputtered atoms and their thermalization. The two groups of thermalized and energetic atoms have been very well separated compared to previous works. Hence, the fitting of the energetic atom group shows dumping from modified Thompson to Gauss distribution when the product pressure-distance from the target increases. In parallel, sputtered metal transport from the target has been simulated using the Monte Carlo collision (MCC) approach. Direct comparison between numerical and experimental results led to an improved cross-section for Ti–Ar momentum transfer, based on the ab initio formulas of the interaction potential derived from noble gas interaction. The accuracy of the experimental data enabled the numerical parametric study of the angular distribution and cut-off energy for the initial distribution of sputtered atoms to reveal the precise characterization of the initial conditions. A very good overall agreement is obtained for measured and calculated AVDFs. Comparison between the measured and modeling results emphasized the major role played by the argon (Ar) ions, not only in the sputtering process, but in the neutral metal transport by the gas rarefaction near the target. The microscopic description provided by the MCC model clearly reveals different transport regimes: ballistic, diffusive and back-scattering, which provide new insight into the thermalization of sputtered species in the intermediate pressure range.

Charged particles density distribution in the cathode fall region of the glow discharge in helium

In the present work, the mechanism of formation and propagation of the group of high energy electrons in the cathode regions of a glow discharge in helium is discussed. Using the method of the Monte Carlo collisions simulation, the beam electron energy distribution function in the cathode fall region of a glow discharge has been determined in the gas pressure range of 30−70 Pa. It is shown that the electron distribution function at the end of the cathode fall region contains a lot of electrons which have no any collisions and have energies close to the cathode fall potential. On the basis of the obtained results the distribution of the ion density was simulated using the Poisson equation. It is shown that the ion density distribution stays almost constant in the cathode fall region. The beam and ion density increased with the pressure growth.