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

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

PIC/MCC Simulation of Radio Frequency Hollow Cathode Discharge in Nitrogen

A two-dimensional PIC/MCC model is developed to simulate the nitrogen radio frequency hollow cathode discharge（rf-HCD）.It is found that both the sheath oscillation heating and the secondary electron heating together play a role to maintain the rf-HCD under the simulated conditions.The mean energy of ions（N＋_2,N＋）in the negative glow region is greater than the thermal kinetic energy of the molecular gas（N2）,which is an important characteristic of rf-HCD.During the negative portion of the hollow electrode voltage cycle,electrons mainly follow pendulum movement and produce a large number of ionization collisions in the plasma region.During the positive voltage of the rf cycle,the axial electric field becomes stronger and its direction is pointing to the anode（substrate）,therefore the ions move toward the anode（substrate）via the axial electric field acceleration.Compared with dc-HCD,rf-HCD is more suitable for serving as a plasma jet nozzle at low pressure.

Characteristics of temporal evolution of particle density and electron temperature in helicon discharge

On the basis of considering electrochemical reactions and collision relations in detail, a direct numerical simulation model of a helicon plasma discharge with three-dimensional two-fluid equations was employed to study the characteristics of the temporal evolution of particle density and electron temperature. With the assumption of weak ionization, the Maxwell equations coupled with the plasma parameters were directly solved in the whole computational domain. All of the partial differential equations were solved by the finite element solver in COMSOL Multiphysics^（TM） with a fully coupled method. In this work, the numerical cases were calculated with an Ar working medium and a Shoji-type antenna. The numerical results indicate that there exist two distinct modes of temporal evolution of the electron and ground atom density, which can be explained by the ion pumping effect. The evolution of the electron temperature is controlled by two schemes： electromagnetic wave heating and particle collision cooling. The high RF power results in a high peak electron temperature while the high gas pressure leads to a low steady temperature. In addition, an OES experiment using nine Ar I lines was conducted using a modified CR model to verify the validity of the results by simulation, showing that the trends of temporal evolution of electron density and temperature are well consistent with the numerically simulated ones.

Kinetic effects of nanosecond discharge on ignition delay time

The effects of nanosecond discharge on ignition characteristics of a stoichiometric methane–air mixture without inert diluent gas were studied by numerical simulation at 0.1 MPa and an initial temperature of 1300 K. A modified non-equilibrium plasma kinetic model was developed to simulate the temporal evolution of particles produced during nanosecond discharge and its afterglow. As important roles in ignition, path fluxes of O and H radicals were analyzed in detail. Different strength of E/N and different discharge duration were applied to the discharge process in this study. And the results presented that a deposited energy of 1–30 m J·cm^(-3) could dramatically reduce the ignition delay time. Furthermore, temperature and radicals analysis was conducted to investigate the effect of non-equilibrium plasma on production of intermediate radicals. Finally, sensitivity analysis was employed to have further understanding on ignition chemistries of the mixture under nanosecond discharge.

Preliminary Analysis of Advanced Equilibrium Configuration for the Fusion-Driven Subcritical System

The Fusion-Driven Subcritical System(FDS)is a subcritical nuclear energy systemdrived by fusion neutron source.In this paper,an advanced plasma configuration for FDS systemhas been proposed,which aims at high beta,high bootstrap current and good confinement.Afixed-boundary equilibrium code has been used to obtain ideal equilibrium configuration.In order

Plasma Shape and Current Control Simulation of HT-7U Tokamak

This paper describes the discharge simulation of HT-7U tokamak plasma equilibrium and plasma current by solving MHD equations and surface average transport equations using an equilibrium evolution code. The simulated result shows the evolution of plasma parameter versus time.The simulated result can play an important role in the design of the plasma equilibrium and control system of a tokamak.

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

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

Modeling and Simulations in Symmetrical Supercapacitors Using Time Domain Mathematical Expressions

This study presents the deduction of time domain mathematical equations to simulate the curve of the charging process of a symmetrical electrochemical supercapacitor with activated carbon electrodes fed by a source of constant electric potential in time ε and the curve of the discharge process through two fixed resistors. The first resistor RCo is a control that aims to prevent sudden variations in the intensity of the electric current i1(t) present at the terminals of the electrochemical supercapacitor at the beginning of the charging process. The second resistor is the internal resistance RA of the ammeter used in the calculation of the intensity of the electric current i1(t) over time in the charging and discharging processes. The mathematical equations generated were based on a 2R(C + kUC(t)) electrical circuit model and allowed to simulate the effects of the potential-dependent capacitance (kUC(t)) on the charge and discharge curves and hence on the calculated values of the fixed capacitance C, the equivalent series resistance (ESR), the equivalent parallel resistance (EPR) and the electrical potential dependent capacitance index k.

Numerical analysis of flow separation zone in a confluent meander bend channel

The flow pattern in the confluent meander bend channel under the conditions of different discharge ratios and junction angles is numerically simulated by means of the large eddy simulation（LES）, and the characteristics of the flow separation zone are analyzed. Numerical results are well validated by experimental data with a good agreement. Analysis of the vertical confinement shows that the turbulence within the separation zone can be characterized as quasi-2-D. Details of the separation zone characteristics are revealed as shown by mean velocity isolines. According to the analysis of numerical results, the length and the width of the separation zone generally increase with the increase of the discharge ratio and the junction angle. However, the width of the separation zone keeps substantially constant when the junction angle increases from 60 o to90o. The dimensionless shape of the separation zone is nearly the same for three discharge ratios and three junction angles. The formulas of the relative width and the relative length of the separation zone are obtained by means of the polynomial fit method.