Monte Carlo Collision Method Research Articles

Analysis of application range of simplified models for field to thermo-field to thermionic emission processes from the cathode

Electron emission plays a dominant role in plasma–cathode interactions and is a key factor in many plasma phenomena and industrial applications. It is necessary to illustrate the various electron emission mechanisms and the corresponding applicable description models to evaluate their impacts on discharge properties. In this study, detailed expressions of the simplified formulas valid for field emission to thermo-field emission to thermionic emission typically used in the numerical simulation are proposed, and the corresponding application ranges are determined in the framework of the Murphy–Good theory, which is commonly regarded as the general model and to be accurate in the full range of conditions of the validity of the theory. Dimensionless parameterization was used to evaluate the emission current density of the Murphy–Good formula, and a deviation factor was defined to obtain the application ranges for different work functions (2.5‒5 eV), cathode temperatures (300‒6000 K), and emitted electric fields (105 to 1010 V·m−1). The deviation factor was shown to be a nonmonotonic function of the three parameters. A comparative study of particle number densities in atmospheric gas discharge with a tungsten cathode was performed based on the one-dimensional implicit particle-in-cell (PIC) with the Monte Carlo collision (MCC) method according to the aforementioned application ranges. It was found that small differences in emission current density can lead to variations in the distributions of particle number density due to changes in the collisional environment. This study provides a theoretical basis for selecting emission models for subsequent numerical simulations.

Numerical Investigation of Electrodeless Plasma Thruster with Rotating Electric Field

Two-dimensional simulations of various cross-sections under different magnetic field strengths in an electrodeless plasma thruster acceleration part using rotating electric field were conducted. The Particle-In-Cell and Monte Carlo Collision method was used to better understand plasma movement and find the ideal condition for the azimuthal current formation. The findings suggest that raising the voltage amplitude can improve the electric field’s penetration into the plasma, diminish the disparity between the azimuthal current’s maximum and minimum values, and consequently generate a more uniform size and distribution. Peak azimuthal current values are directly proportional to the ac frequency at frequencies above 100 MHz and inversely proportional to the frequency below 100 MHz. A rotating electric field that matches the background magnetic field could be produced by adjusting the phase difference among the two sets of antennas. And then the plasma is accelerated by the effect of E×B to achieve a more favorable azimuthal current. The results also demonstrate that an appropriately sized and distributed azimuthal current benefits more from a magnetic field with a strength between 200 and 1000 G and a value that declines from the cross-section center to its periphery.

Multi-hole grid thruster plume simulation model based on single grid aperture analytical model

This paper presents a plume divergence angle prediction model for ion thruster. Firstly, an analytical model using Gaussian distribution for single grid hole plume is proposed. The parameters of this single hole model are obtained from the particle simulation results of ion optics which utilizes the immersed finite element Particle-in-cell Monte Carlo collision (IFE-PIC-MCC) method. Then, by the extension of the single hole model, a three-dimensional plume model for the whole ion optics is proposed. This plume model can be used to predict the divergence angle of ion thruster plume. Finally, a numerical example with the simulation of a 217-hole ion optics is provided to demonstrate the features of the proposed method.

Energy and mass transport properties in the near-cathode region of atmospheric thermal plasma

As the main region where charged particles are accelerated by the electric field and accumulated near the cathode, the near-cathode region has significant non-local equilibrium characteristics and plays a crucial role in exploring the energy and mass transport properties of the thermal plasma from the arc column region to the hot cathode surface. However, there is a lack of universally adopted models and accepted theories for the study of the near-cathode region due to the complexity of the physical mechanisms involved in the sheath. According to the physical characteristics of the arc discharge, an external circuit is usually used to regulate the total current applied to the electrodes to maintain stable discharge. Therefore, the energy and mass transport properties of atmospheric thermal plasma driven by a current source coupled to an external circuit are investigated in this work to explore the transport mechanism of charged particles in the near-cathode region based on an implicit particle-in-cell Monte Carlo collision method. Firstly, the current-driven model in this work is compared with the present voltage-driven model and fluid model to verify the correctness of this model. Then, the collisions between charged particles and gas atoms inside the sheath are analyzed, and the spatial distributions of particle current density and particle heating rate inside the sheath are also studied. Finally, the variations of typical parameters of thermal particles under different current densities (106–107 A m−2) are analyzed, including maximum particle number density, maximum particle spatially-averaged temperature, sheath thickness, charge density and electric field strength in the cathode.

Effects of Magnetic Field Gradient on the Performance of a Magnetically Shielded Hall Thruster

The objective of this study is to investigate the effects of a magnetic field gradient on the performance of a magnetically shielded Hall thruster. The Particle-in-cell with Monte Carlo collision method (PIC-MCC) is used to simulate the discharge process of the thruster. The performance and plasma characteristics are obtained in conditions with different magnetic field gradients by numerical simulations. As the maximum of the gradient is increased from 1.2 to 3.33 T/m, the electron number density near the channel exit decreases, which leads to less ionization and a weaker radial electric field. As a result, the thrust and specific impulse are decreased, while the plume divergence angle is reduced.

Study on the influence of discharge voltage on the performance of Hall propulsion system

The discharge characteristics of the Hall thruster are numerically studied at different discharge voltages when the magnetic field does not change based on the particle in cell plus Monte Carlo collision methods. The distributions of electrons and Ar+ ions densities at different discharge voltages show that the change of the discharge voltage significantly influences the distribution of electrons and Ar+ ions. The electron density is relatively large when the discharge voltage is 100 V, up to 6.01 × 1018 m−3. At a discharge voltage of 400 V, the high-density region formed by electrons is significantly smaller than in other cases. The ion density rises less when reaching a steady state with increasing discharge voltage. The Ar+ ions density decreases after the discharge voltage reaches 400 V, up to 4.42 × 1018 m−3. After calculation, it was found that under a specific mass flow, the discharge voltage significantly impacts the thrust of the Hall thruster. The results have reference values for the performance testing and application of Hall thrusters.

Simulation study of the influences of beryllium on the tokamak start-up process

Tokamak start-up is strongly dependent on the state of the initial plasma formed during plasma breakdown. To acquire a better understanding of the process and to estimate the influence of the impurity of beryllium on the ohmic heating tokamak start-up process, one-dimensional particle-in-cell coupled with a Monte Carlo collision method has been developed. The main aim is to investigate the plasma performance under various amounts of beryllium with different discharge parameters. Tokamak breakdown with the impurity of beryllium in the ohmic heating strategy has been simulated. The simulation results show that with the impurity of beryllium, the increase of plasma density is suppressed compared with the case without beryllium. The breakdown time is delayed by the impurity. Moreover, the successful breakdown has a much higher requirement on discharge parameters with a low electric field operational scenario, since in the low electric field discharge the influence of beryllium impurity is greater. As the plasma density increases, the effect of beryllium impurity on plasma becomes more critical. It indicates that impurities cannot be neglected in the high plasma density.

Investigation of air breakdown and plasma evolution on microstrip antenna surface using the particle-in-cell method

This paper investigates the breakdown of two microstrip antennas through experiments and particle-in-cell simulations. The breakdown thresholds of a microstrip dipole antenna and a double-layer patch microstrip antenna are investigated experimentally and found to be 15.6 and 30.8 kW, respectively. Ablation is observed on the surface of the antennas, indicating that the local electric field is particularly intense. To further understand the breakdown process, the particle-in-cell and Monte Carlo collision methods are combined to investigate the inception and development of partial discharge on the surface of the antennas. Under the criterion of continuous electron density growth, the breakdown thresholds of the dipole and double-layer patch antennas are estimated to be 19.4 and 52.9 kW in our simulations. The simulation results are in reasonable agreement with the experimental measurements. In the microstrip dipole antenna, the plasma evolution of the partial discharge is initiated near the tip, while the electric field close to the tip is distorted and a positive streamer directed toward the tip is observed. In the double-layer patch microstrip antenna, a more uniform discharge is observed at the edge of the circular patch in the simulations.

Three-dimensional analysis of RF-biased ion optics with misalignments of apertures

Accelerator grid hole shift is a critical reason for erosion failure of optic systems in ion thrusters, which may also cause an unexpected roll torque about the ion beam axis. A three-dimensional (3D) model of ion optics is developed based on a particle-in-cell Monte Carlo collision method to investigate the plasma dynamics and performance of radio frequency (RF) grid systems with misalignments of apertures, which are compared with those in the direct current (DC) grid system. For the benchmark case, the 3D model gives a better agreement with the experiments in the ion energy distribution function (IEDF) compared with the two-dimensional model from a previous publication, with 36.4% and 47.9% relative error reduction of the peak position and full width at half maximum (FWHM), respectively, indicating the effectiveness of the developed 3D model. Simulations show that in the RF grid system the ion beamlet is deflected in the direction opposite to the shift of the accelerator grid hole, while electrons move first in the hole shift direction, and then deflect in the opposite direction. The average ion beamlet deflection angle calculated is consistent with the predictions from linear optical theory in both the RF and DC grid system. The amplitude of beamlet deflection angle fluctuation with time decreases with the increase of RF frequency. When the grid holes shift, the ion beamlet will deflect with the divergence angle almost unchanged in the DC grid system, while the beamlet divergence angle increases in the RF grid system. When RF frequency is low, the big vortex-like structure in the electron velocity phase diagram breaks into small vortices, showing a reduced oscillation intensity. The hole shift also causes high-frequency oscillation in the shift direction. In terms of performance, the RF grid system is more sensitive to grid hole shift than the DC grid system.

Plasma transport simulation under different conditions and optimization analysis of dual-stage grid ion thruster

In order to study the extraction and acceleration mechanism of the dual-stage grid, a three-dimensional model based on the Particle-In-Cell/ Monte Carlo Collision (PIC/MCC) method is performed. Dual-stage grid ion thruster is a new type of electrostatic ion thruster, which can break through the limitations of traditional gridded ion thrusters, and greatly improve the specific impulse. The high performance also makes the grid sensitive to operating parameters. In this paper, the influence of grid parameters on xenon ion thruster’s performance in a wide range is systematically simulated, and the optimal operating condition is given. Both the over-focusing of the plume, and the transparency of the screen grid are improved, and the grid corrosion is reduced through simulation optimization. The specific impulse under the given working conditions is 9877.24 s and the thrust is 7.28 mN. Based on the simulation optimization, the limitation of the dual-stage grid is discussed. The grid performs well under high voltage conditions (>3000 V) but not well under low voltage conditions (<2000 V). Finally, since argon is cheaper and more advantageous in future engineering applications, the plasma distribution and grid extraction ability under xenon and argon are analyzed and compared to study the flexibility of the dual-stage grid ion thruster. The simulation results show that a set of optimal parameters is only applicable to the corresponding propellant, which needs to be optimized for different propellant types.

Optimized design of the ion optics based on the over-perveance characteristics of the beam current

To illustrate the erosion mechanism of the edge aperture by high-energy ions, a three-dimension simulation model was established, and a particle-in-cell method was applied in tracking the hitting processes as well as a Monte Carlo collision method was used to deal with the particles’ collision. Numerical results showed that the potentials interacted among the sheaths of adjacent holes and the beam ions were over-focused in the accelerator gap, causing some ions to be intercepted on the downstream wall of the decelerator grid. This was a typical under-perveance characteristic of the beam current, operating at significantly less than the optimal perveance and corresponding to lower beam currents than optimal combination, which pushed the sheath to the left farther into the plasma. The farther the grid was, the more serious erosion patterns developed. In addition, the charge exchange ions were attracted and bombarded on the decelerator and the accelerator grids, respectively. The ion optics of the 30 cm ion thruster was optimized from four-zone to three-zone, where the plasma density upstream of the screen grid was increased by 1.5% and the perveance characteristics of the beam ions were improved such that many ions struck the edge hole. The background pressure was reduced from 3.0 × 10−3 to 8.0 × 10−4 Pa to decrease the erosion depths of the grids caused by the charge exchange ions, about 9.09% and two orders of magnitude, respectively, for the accelerator and decelerator grids.

Studies on plasma transport processes in the cathode sheath of atmospheric direct-current arc discharge with particle-in-cell and Monte Carlo collision simulation

A voltage-driven cathode sheath model in an atmospheric-pressure argon arc discharge is developed in the framework of an implicit particle-in-cell Monte Carlo collision (PIC–MCC) method. Plasma transport processes are solved numerically in one dimension without any local-equilibrium hypotheses, in particular, without explicitly dividing sheath and a quasi-neutral plasma region. The right boundary of the computational domain located at the pre-sheath is determined first by observing the variation in typical parameters. A comparison of results is given with different positions of the right boundary to study the plasma transport processes in the cathode sheath. Number densities, spatially averaged energies, electric field and potential, collision frequency, heating rate of electrons, as well as the spatially averaged electron energy probability function inside the sheath, are predicted self-consistently based on this newly developed kinetic model. It is shown that both excitation collisions and ionization collisions occur inside the sheath, and collision frequency of the former is larger than the latter. The collision frequency of charge exchange is higher than that of elastic collision for ions. In addition, the effects of different electron emission processes are described. It is indicated that the thermionic emission on the hot cathode surface is not the only significant emission mechanism to sustain the arc discharges.

Influence of neutral gas supply position on wall erosion of Hall thruster studied by particle-in-cell simulation

In this work, we have carried out a simulation study on the discharge process of Hall thrusters under the conditions of different neutral gas radial supply positions based on the particle-in-cell (PIC) and Monte Carlo collision (MCC) methods. This paper compares the two-dimensional (2D) distributions of neutral gas, plasma and wall erosion-related parameters under different neutral gas supply positions. The comparison results show that the change of the neutral gas supply position affects the radial distribution uniformity of the neutral gas and plasma in the channel. From the comparison of the density peaks, it can be found that the neutral gas density and the plasma density peak under the upper gas supply condition are relatively low, and the plasma density peak is 22.49% lower than the density peak under the middle gas supply condition. Meanwhile, as the radial position of the gas supply moves from the lower gas supply to the upper gas supply, the position of the ionization zone also gradually moves toward the anode. The results of erosion-related parameter distribution comparison show that the change of gas supply location has an obvious influence on erosion rate and erosion range. In terms of erosion rate, the wall erosion rate is relatively low under the upper gas supply condition, and the peak erosion rates of the inner and outer walls are 33.3% and 29.9% lower than those under the other two conditions. In terms of erosion range, as the gas supply position moves from the lower gas supply position to the upper gas supply position, the erosion range gradually increases from 5 to 7.5 mm.

Understanding of deposition mechanism of vanadium on LiF with large mismatch by facing target sputtering (FTS)

V/LiF is a significant window material for investigation of phase transition of materials at ultra-high pressure which is a fundamental issue in condensed matter physics. However, the large mismatch of lattice and thermal makes vanadium growth on LiF as big challenge. In this current study, over 1.5 μm thick vanadium films were grown on LiF via facing target sputtering (FTS). The transmission electron microscopy (TEM) observation showed the grown vanadium films feature vertically well-aligned columnar crystals with numerous micro-sized gaps. For understanding the deposition mechanism, the behaviors of plasma discharge, transport of sputtered atoms and growth of films were simulated by particle-in-cell Monte Carlo collision (PIC-MCC) and Kinetic Monte Carlo (KMC) methods, respectively. The growth model of vanadium film was established based on the experimental and simulation results. And the micro-sized gaps of columnar crystals contribute to release residual stresses generated by large mismatch, which can be explained by the grain boundary relaxation model.

Particle simulation of the strong magnetic field effect on dust particle charging process

A particle-in-cell simulation is modeled and run on a dusty plasma to determine the effect of the magnetic field on the process of dust-particle charging through electron–ion plasma. The electric field is solved through the Poisson equation, and the electron-neutral elastic scattering, excitation, and ionization processes are modeled through Monte Carlo collision method. The effects observed from the initial density of the plasma, the initial temperature of the electrons, and the changing magnetic field are included in this simulation model. In the dust particle charging process, saturation time and saturation charge are compared. An increase in the magnetic field does not reduce time to reach the saturation state. Determining the magnetic field boundaries which depend on the physical properties of the plasma, can be contributive in some areas of dusty(complex) plasma. The applications of the results obtained here for fusion plasma conditions and space and laboratory plasmas are discussed. The results here can be applied in future simulation models with a focus on the dust particle movement and their effect on plasma, leading to the modeling of different astrophysical plasmas thorough laboratory experiments.

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Study on the effect of discharge chamber length on the performance of electron cyclotron resonance ion thruster

Discharge chamber length is one of the factors in optimizing the electron cyclotron resonance ion thruster performance. It adjusts the distance between bulk plasma and grid system to change the plasma density upstream of the screen grid, which will affect the ion beam current and focusing state to achieve optimization purpose. However, new evidence shows the discharge chamber length plays an important role in ionization during ion beam extraction, which means that the effect of discharge chamber length on the performance of electron cyclotron resonance ion thruster should be reexamined. After applying grid voltages, another high electron temperature region located upstream of the screen grid is observed in the integrated simulation using particle-in-cell with Monte Carlo collision method, but it is not observed in the traditional discharge chamber simulation. It is believed in the paper that the high electron temperature region exists objectively, because the Child-Langmuir sheath will repel electrons moving towards screen grid back to magnetic mirrors again. Those electrons will gain energy from microwave, and finally form a high electron temperature region along the Child-Langmuir sheath. This phenomenon implies that discharge chamber length can adjust the high electron temperature distribution upstream of screen grid to affect the plasma generation. Therefore, in this work, the effect of discharge chamber length on discharge and ion beam performance is systematically studied by adopting the integrated simulation. In this paper, three ion thrusters with different discharge chamber lengths are simulated. Under the conditions of same magnetic field and operation parameters, the comparisons of electron energy gain, plasma parameter distributions and ion beam current among the three ion thrusters are conducted. The results show that shorter discharge chamber length has higher electron energy gain, plasma density and voltage, but smaller ion beam current. This abnormal phenomenon can also be seen experimentally. By analyzing the ionization rate inside the chamber, it can be seen that high-temperature electrons upstream of the screen grid have a significant contribution to ionization. And thus, a little bit longer discharge chamber length with lower plasma density inside the chamber has bigger ion beam current for having higher plasma density upstream of the screen grid. According to this phenomenon, an electron heating mode is proposed: electrons gain energy by reciprocating through the electron cyclotron resonance layer between the Child-Langmuir sheath and magnetic mirrors. This heating mode can be used as a supplement to the electronic constraints outside the magnetic mirrors to improve the energy utilization efficiency of the thruster, which can provide a new insight into the electron cyclotron resonance ion thruster design in the future.

Hybrid plasma modeling of the interaction between the vacuum arc jet and the hot metallic particle near the current zero

In this paper, the interaction between the vacuum arc plasma jet and the hot metallic particle near current zero was investigated by numerical simulation. A vacuum arc plasma jet model was developed using the hybrid simulation method, in which electrons were considered as a massless fluid, while heavy particles such as atoms and ions were modeled as particles. In this model, the effect of the evaporation of metal atoms from the metallic particle was considered. Additionally, the Monte Carlo collision method was used to model inelastic collisions between electrons and heavy particles. The simulation results demonstrate that the metallic particle blocks the plasma jet, causing an asymmetric and nonuniform distribution in the plasma jet. Furthermore, some of the evaporated atoms from the hot metallic particle are converted into Cu1+ ions by ionization collisions with electrons. The drift velocity of Cu1+ ions coming from the ionization of metal vapor is much lower than that of highly energetic ions emitted from the cathode spot, making it difficult for them to be completely dissipated as soon as possible during the extinguishing phase. Moreover, the presence of a hot metallic particle causes an increase in the density of plasma in its surroundings, which increases the probability of arc reignition in the post-arc phase.

Development of a Noninvasive Real-Time Ion Energy Distribution Monitoring System Applicable to Collisional Plasma Sheath.

As the importance of ion-assisted surface processing based on low-temperature plasma increases, the monitoring of ion energy impinging into wafer surfaces becomes important. Monitoring methods that are noninvasive, real-time, and comprise ion collision in the sheath have received much research attention. However, in spite of this fact, most research was performed in invasive, not real-time, and collisionless ion sheath conditions. In this paper, we develop a noninvasive real-time IED monitoring system based on an ion trajectory simulation where the Monte Carlo collision method and an electrical model are adopted to describe collisions in sheaths. We technically, theoretically, and experimentally investigate the IED measurement with the proposed method, and compared it with the result of IEDs measured via a quadrupole mass spectrometer under various conditions. The comparison results show that there was no major change in the IEDs as radio-frequency power increased or the IED gradually became broad as gas pressure increased, which was in a good agreement with the results of the mass spectrometer.

Unified modeling and kinetic analysis of the near-cathode region and hot cathode in atmospheric-pressure arc discharges

The near-cathode region plays a crucial role in exploring the transport characteristics of the transition from arc column to the hot cathode in atmospheric-pressure arc discharges because of the existing non-equilibrium phenomena. A one-dimensional unified model, including the near-cathode region and the cathode body, is developed for an argon arc discharge with the tungsten cathode at atmospheric pressure in this paper. The electrostatic model coupled with an external circuit in the near-cathode region is solved based on the implicit particle-in-cell coupled Monte Carlo collision method without any assumptions of thermal or ionization equilibrium or quasi-neutrality. A detailed description of the arc plasma–cathode and cathode–gas interactions is obtained by calculating the nonlinear heat conduction equation in the cathode. It is shown that the space-charge sheath strongly affects particle transport in the near-cathode region and energy transport from arc plasma to the thermionic cathode. The total current density has significant effects on the kinetic characteristics of arc plasma by feedback-like mechanisms. The Joule heating by the external circuit and charged particles deposited into the cathode are dominating mechanisms of energy transfer from the near-cathode region to the cathode, while energy loss by radiation is more significant compared with natural convection.