From Field Emission to Vacuum Arc Ignition: A New Tool for Simulating Copper Vacuum Arcs

Understanding plasma initiation in vacuum arc discharges can help to bridge the gap between nano‐scale triggering phenomena and the macroscopic surface damage caused by vacuum arcs. We present a new twodimensional particle‐in‐cell tool to simulate plasma initiation in direct‐current (DC) copper vacuum arc discharges starting from a single, strong field emitter at the cathode. Our simulations describe in detail how a sub‐micron field emission site can evolve to a macroscopic vacuum arc discharge, and provide a possible explanation for why and how cathode spots can spread on the cathode surface. Furthermore, the model provides us with a prediction for the current and voltage characteristics, as well as for properties of the plasma like densities, fluxes and electric potentials in a simple DC discharge case, which are in agreement with the known experimental values. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Why Perform Code‐to‐Code Comparisons: A Vacuum Arc Discharge Simulation Case Study

Numerical modeling is increasingly becoming an indispensable tool for investigations in many fields of physics. Such modeling is especially useful in today's big science projects as a tool that can provide predictions and design parameters. The reliability of simulation results is thus essential. Code‐to‐code comparisons can help increase our confidence in simulation results, especially when other verification methods – such as comparison to theoretical models or experimental results – are limited or unavailable. In this paper, we describe a code‐to‐code comparison exercise wherein we compare one‐dimensional vacuum arc discharge simulation results from two independent particle‐in‐cell (PIC) codes. As part of our case study, we define a vacuum arc discharge test problem that can be used by other research groups for further comparison. Early disagreement between the two sets of our results motivated us to re‐examine the underlying methods in our codes. After remedying discrepancies, we observe good agreement in vacuum arc discharge time‐to‐breakdown, as well as in the time evolution of particle and current densities. This exercise demonstrates the usefulness of code‐to‐code comparisons and provides an example case study for the benefit of other research groups who may wish to carry out similar code‐to‐code comparisons (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Potential Formation in a Bounded Plasma System which is Terminated by an Electron Emitting Floating Collector Studied by a Particle‐in‐Cell Computer Simulation

Potential formation in one‐dimensional bounded plasma system terminated by a floating, electron emitting collector is studied by particle‐in‐cell (PIC) computer simulation. Attention is focused to the case of rather strong space charge limited emission. Formation of a potential well (virtual cathode) in front of the collector is observed. As emission increases the floating potential of the electrode and the potential of the bottom of the potential well both increase. The floating potential increases faster than the virtual cathode potential and consequently the depth of the potential well in front of the collector increases also. As long as the emission is not to large (up to approximately 40 times the critical emission) the relation between the depth of the potential well and the normalized emission follows a simple logarithmic formula. For larger emissions the depth of the potential well is larger than predicted by the model. It seems that at very large emission the floating potential of the collector might even exceed the zero reference potential of the source electrode. Such phenomenon has been reported by [A. Marek et al. Contrib. Plasma Phys., 48 , 491 (2008)], where it was observed that the floating potential of a strongly emissive probe exceeded the plasma potential determined from the knee of the current‐voltage characteristics when the same probe was used as a Langmuir probe. But before this actually happens the simulation breaks down. When positive ions start to be repelled by the positive collector back towards the source the system becomes unstable so that a steady state can not be reached and no results can be read from the output of the simulations. That electron emission may destabilize the sheath in front of it, was found also in Hall thrusters, see e.g. [Daren Yu et al. Phys. Plasmas, 15 , 104501, 2008] and [F. Taccogna et al Appl. Phys. Lett., 94 , 251502, 2009]. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigations of Droplet‐Plasma Interaction using Multi‐Dimensional Coupled Model

Recently developed multi‐dimensional coupled fluid‐droplet model is used to investigate the behavior of complex interaction between the liquid precursor droplets and atmospheric pressure plasma (APP). The significance of this droplet‐plasma interaction is not well understood under diverse realm of working conditions in two‐phase flow. In this study, we explain the implication of vaporization of liquid droplets in APP which are subsequently responsible to control major characteristics of surface coating depositions. Coalescence of water droplets is more dominant than Hexamethyldisiloxane (HMDSO) droplets because of its sluggish rate of evaporation. A disparity in the performance of evaporation is identified in two independent mediums, such as gas mixture and discharge plasma using HMDSO precursor. The length of evaporation of droplets is amplified by an increment of gas flow rate indicating with a reduction in the gas temperature and electron mean energy. In particular, the spatio‐temporal density distributions of charged particles show a clear pattern in which the typical nitrogen impurity ions are primarily effective as compared to other helium ionic species along the pulse of droplets in APP. Finally, we contrast the behavior of discharge species in the pure helium and He‐N2 gas mixtures revealing the importance of stepwise and Penning ionization processes. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Self‐Force in 1D Electrostatic Particle‐in‐Cell Codes for NonEquidistant Grids

Effects of non‐equidistant grids on momentum conservation is studied for simple test cases of an electrostatic 1D PIC code. The aim is to reduce the errors in energy and momentum conservation. Assuming an exact Poisson solver only numerical errors for the particle mover are analysed. For the standard electric field calculation using a central‐difference scheme, artificial electric fields at the particle position are generated in the case when the particle is situated next to a cell size change. This is sufficient to destroy momentum conservation. A modified electric field calculation scheme is derived to reduce this error. Independent of the calculation scheme additional fake forces in a two‐particle system are found which result in an error in the total kinetic energy of the system. This contribution is shown to be negligible for many particle systems. To test the accuracy of the two electric field calculation schemes numerical tests are done to compare with an equidistant grid set‐up. All tests show an improved momentum conservation and total kinetic energy for the modified calculation scheme of the electric field. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Particle‐in‐cell simulation of an optimized high‐efficiency multistage plasma thruster

Electric propulsion attracts increasing attention in contemporary space missions as an interesting alternative to chemical propulsion because of the high efficiency it offers. The High‐Efficiency Multistage Plasma thruster, a class of cusped field thruster, is able to operate at different anode voltages and operation points and thereby generate different levels of thrust in a stable and efficient way. Since experiments of such thrusters are inherently expensive, multi‐objective design optimization (MDO) is of great interest. Several optimized thruster designs have resulted from a MDO model based on a zero‐dimensional (0D) power balance model. However, the MDO solutions do not warrant self‐consistency due to their dependency on estimation from empirical modelling based on former experimental studies. In this study, one of the optimized thruster designs is investigated by means of particle‐in‐cell (PIC) analysis to examine the predicted performance characteristics with self‐consistent simulations. The 0D power balance model is used to develop additional diagnostics for the PIC simulations to improve the physics analysis. Using input parameters for the 0D power balance model from the PIC simulations allows further improvement for the design optimization.     

A Particle‐in‐Cell Simulation of the Breakdown Mechanism in Microdischarges with an Improved Secondary Emission Model

In this paper, the failure of the breakdown voltage from the Paschen's law at extremely small electrode separations is studied. The electrical breakdown in microgaps occurs at the voltages far below the Paschen curve minimum breakdown limit and the modified Paschen curve should be used. Offered explanation for the departure from the Paschen's law at small gap spacings is based on the increasing of the yield of the secondary electrons. The high electric fields existing in small gaps may enhance the secondary electron yield and this would lead to a lowering of the breakdown voltage and to the departure from the Paschen's law. Particlein‐cell/Monte‐Carlo (PIC/MCC) simulations with a new secondary emission model have been performed to estimate the importance of this mechanism in the discharge breakdown. Obtained simulation results suggest that deviations from the Paschen curve across the micron and submicorn gap spacing can be attributed to the ion‐enhanced field emissions. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

THz Radiation Generation via the Interaction of Ultra‐short Laser Pulses with the Molecular Hydrogen Plasma

In this paper, a two dimensional Particle In Cell‐Monte Carlo Collision simulation scheme is used to examine the THz generation via the interaction of high intensity ultra‐short laser pulses with an underdense molecular hydrogen plasma slab. The influences of plasma density, laser pulse duration and its intensity on the induced plasma current density and the subsequent effects on the generated THz signal characteristics are studied. It is observed that the induced current density in the plasma medium and THz spectral intensity are increased at the higher laser pulse intensities, laser pulse durations and plasma densities. Moreover, the generated THz electric field amplitude is reduced at the higher laser pulse durations. A wider frequency range for the generated THz signal is shown at the lower laser pulse durations and higher plasma densities. Additionally, it is found that the induced current density in hydrogen plasma medium is the dominant factor influencing the generation of THz pulse radiation. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Molecular Dynamics Simulations for the Shear Viscosity of the One‐Component Plasma

We discuss two methods for determining the shear viscosity of a fluid of particles with Yukawa interaction potential (a one‐component plasma). Both methods are based on computing the equilibrium dynamics using large‐scale molecular dynamics (MD) simulations. Our MD results illustrate that the hydrodynamic method for computing the shear viscosity is feasible and therefore complements the more widely used method based on the Green‐Kubo relation. We expect that in the future our shear viscosity calculations will be used to assist with the interpretation and analysis of x‐ray scattering experiments, which could in principle measure this fundamental dynamical quantity (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of a Planar Emissive Probe in a Mid‐Sized Tokamak Plasma

Planar emissive probe is studied for the first time using a massively parallel particle‐in‐cell code BIT1 [22]. The probe is immersed in a plasma similar to edge plasmas of mid‐sized tokamaks. Dependence of the floating potential on electron emission from the probe is studied. With increasing emission the floating potential increases, but then saturates ～2T_e below the actual plasma potential (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electrostatic simulations of the radio frequency heating of a non‐neutral plasma in an electron trap

The electrostatic simulations of the radio frequency (RF) heating mechanism, excitations, and ionization process of an electron plasma are carried out using a two‐dimensional (2D) particle‐in‐cell (PIC) code. RF drives with excitation frequencies of 1–15 MHz and amplitudes of 5 and 10 V were applied at two different axial positions, to the centre and to one end on the electrode stack of the ELTRAP device, at ultra‐high vacuum conditions. It is observed that the axial kinetic energy (eV) profile of the confined electrons increases with an increase of the RF excitation amplitudes, and densities from 5 × 10⁷ to 10¹² m^?3 for all cases under consideration. The simulation results indicate that with continuous RF excitations, the electron heating in the beginning is higher at the trap wall of the device and extends towards the central region of the trap over a simulation time of up to 100 µs. These results on the electron heating are in good agreement with the experimental findings (optical diagnostics of ELTRAP). The heating effect is larger when the RF power is applied from the position close to one end of the trap in comparison to the central position. Monte–Carlo PIC simulations with hydrogen as a background gas are also performed to evaluate the ionization process at pressures of 10^?8, 10^?7, and 10^?6 torr using the same electron plasma densities. The results show that at increasing pressures, the electron‐neutral collisions rate increases linearly with the background gas pressure. Increased collision frequency is obtained at higher RF drive amplitudes, which proportionally increases electron temperature, so that more ionization and secondary electrons are generated.     

Three Dimensional Angular Distributions of X‐Rays in a 4 kJ Plasma Focus Device for Different Anode Tips Using TLD‐100 Dosimeters

Time and energy integrated measurements of the 3‐D angular distribution of X‐rays emission within the chamber of a 4 kJ Mather‐type plasma focus is investigated employing four different anode shapes and using nitrogen as the filling gas by the TLD‐100 thermoluminescence dosimeters. The distributions of X‐ray radiation in the energy range of 5 keV to several hundred keV were bimodal for all of the anode tips, peaked approximately at ±15°. The intensity of X‐rays decreased abruptly along the central axis of the device where the quasi cylindrical plasma pinch was formed. High intensity of X‐ray was observed in the case of a tapered ?at‐end anode, whereas less was obtained with the cylindrical hollow‐end anode. The maximum nitrogen X‐rays were for the tapered flat‐end anode at 4.5 mbar and 13 kV. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A New Scheme for High‐Intensity Laser‐Driven Electron Acceleration in a Plasma

We propose a new approach to high‐intensity relativistic laser‐driven electron acceleration in a plasma. Here, we demonstrate that a plasma wave generated by a stimulated forward‐scattering of an incident laser pulse can be in the longest acceleration phase with injected relativistic beam electrons. This is why the plasma wave has the maximum amplification coefficient which is determined by the acceleration time and the breakdown (overturn) electric field in which the acceleration of the injected beam electrons occurs. We must note that for the longest acceleration phase the relativity of the injected beam electrons plays a crucial role in our scheme. We estimate qualitatively the acceleration parameters of relativistic electrons in the field of a plasma wave generated at the stimulated forward‐scattering of a high‐intensity laser pulse in a plasma. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Method of Separation of Polydisperse Particles in the Plasma of Radio‐Frequency Discharge

A method of separation of polydisperse dust particles in the plasma of radio‐frequency (RF) capacitive discharge is considered. Investigations of plasma equipotential field enabled us to determine conditions for separation of polydisperse dust particles. The simplicity of the technology made it possible to obtain small dispersed particles of different materials. Samples of small dispersed microparticles of silica and alumina were obtained. The size and chemical composition of samples were examined using a Quanta 3D 200i scanning electron microscope (SEM, FEI, USA). The average size of separated silica nanoparticles was 600 nm, that of silica and alumina microparticles was 5 μm. Two separation methods were developed: the first one used a special trap and shape of the bottom electrode of RF discharge (for separation of microparticles) and the second used an electrical trap (for separation of nanoparticles). The graphs of particle size distribution were constructed using graphical and mathematical calculations. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computational Model of Thermal‐Fluid Flow in a Radio‐Frequency Plasma Torch

The paper aims to clarify the modelling results concerning the heat transfer and fluid flow in a radio‐frequency plasma torch with argon at atmospheric pressure. Fluid numerical simulation requires the coupling of magnetohydrodynamics (MHD) and thermal phenomena. This model combines Navier–Stokes equations with the Maxwell's equations for compressible fluid and electromagnetic phenomena successively. A numerical formulation based on the finite element method is used. In this study, fluid flow and temperature equations are simultaneously solved (direct method, instead of using the indirect method) using a finite elements method (FEM) for optically thin argon plasmas under the assumptions of local thermodynamic equilibrium (LTE) and laminar flow. Appropriate boundary conditions are given, and nonlinear parameters such as the thermal and electrical conductivity of the gas and input power used in the simulation are detailed. We have found that the source of power is located on the torch wall in this type of inductive discharge. The center can be heated by conduction and convection via electromagnetic phenomena (power loss and Lorentz force). (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Filamentation Instability in a Current‐Carrying Plasma in the Presence of Quantum Effects

The filamentation instability of a current‐carrying plasma under the diffusion condition is investigated taking into account the Bohm potential and the Fermi electron pressure. Using quantum hydrodynamic equations, the dispersion relation and growth rate of the instability is obtained. It is found that the filamentation instability, in the presence of quantum effects, depends on various characteristic parameters such as: electron Fermi velocity, plasma number density, ion thermal velocity and electron drift velocity. Moreover, the wavelength region in which the instability occurs is more restricted and the minimum size of filaments is larger, in comparison with the classical case. It is also found that the growth rate of the instability is smaller in the presence of quantum effects. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Second Harmonic Generation of Self Focused Cosh‐Gaussian Laser Beam in Collisionless Plasma

This paper presents an investigation of self‐focusing of a Cosh‐Gaussian (ChG) laser beam and its effect on second harmonic generation in collisionless plasma. In the presence of ChG laser beam the carriers get redistributed from high field region to low field region on account of ponderomotive force as a result of which a transverse density gradient is produced in the plasma which in turn generates an electron‐plasma wave at pump frequency. Generated plasma wave interacts with the incident laser beam and hence generates its second harmonics. Moment theory has been used to derive differential equation governing the evolution of spot size of ChG laser beam propagating through collisionless plasma. The differential equation so obtained has been solved numerically. The effect of decentered parameter, intensity of ChG laser beam and density of plasma on self‐focusing of the laser beam and second harmonic yield has been investigated. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multidimensional Instability of Dust‐Acoustic Solitary Waves in a Magnetized Hot Dusty Plasma with Superthermal Electrons and Ions

Multidimensional instability of dust‐acoustic solitary wave (DASW) in magnetized dusty plasma with superthermal electrons and ions and micron size hot dust particles is investigated. The Zakharov‐Kuznetsov (ZK) equation, describing the small but finite amplitude DASW, was derived using the reductive perturbation method and its solitary answers was introduced. Effects of electrons and ions superthermality as well as the external magnetic field on the nature of DASW are discussed in detail. Dispersion relation, threshold condition, and growth rate of multidimensional instability of DASW were derived using small‐k (long wavelength plane wave) perturbation expansion method. We found that the direction and strength of external magnetic field extremely affect the growth rate and instability criterion. Results show that growth rate of instability decreases with increasing the number of superthermal electrons and increases with increasing the number of superthermal ions. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)