A One‐Dimensional Particle‐in‐Cell Model of Plasma Build‐Up in Vacuum Arcs

Understanding the mechanism of plasma build‐up in vacuum arcs is essential in many fields of physics. A one‐dimensional particle‐in‐cell computer simulation model is presented, which models the plasma developing from a field emitter tip under electrical breakdown conditions, taking into account the relevant physical phenomena. As a starting point, only an external electric field and an initial enhancement factor of the tip are assumed. General requirements for plasma formation have been identified and formulated in terms of the initial local field and a critical neutral density. The dependence of plasma build‐up on tip melting current, the evaporation rate of neutrals and external circuit time constant has been investigated for copper and simulations imply that arcing involves melting currents around 0.5–1 A/μm², evaporation of neutrals to electron field emission ratios in the regime 0.01 – 0.05, plasma build‐up timescales in the order of ～ 1 – 10 ns and two different regimes depending on initial conditions, one producing an arc plasma, the other one not. Also the influence of the initial field enhancement factor and the external electric field required for ignition has been explored, and results are consistent with the experimentally measured local field value of ～ 10 GV/m for copper (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

Influence of bias magnetic field on the vacuum arc in double‐break vacuum circuit breakers

When double‐break vacuum circuit breakers (VCBs) interrupt the fault current, the series arc will generate their individual magnetic fields in different breaks. The magnetic field in one break will influence the arc in another break if the magnetic field is strong enough or the two breaks are very close. In this case, an interactive magnetic field effect happens. This field is also called the bias magnetic field (BMF). BMF can cause anode erosion and affect the performance at current zero. The distribution of BMF and the optimal configuration of the double‐break VCBs were obtained by the electromagnetic field simulation using the Ansoft Maxwell software. Based on the simulated magnetic field data, in the experiments, the interaction between the series vacuum arcs in double‐break VCBs was equivalent to the interaction between a single vacuum arc and the magnetic field generated by a Helmholtz coil. A high‐speed CMOS camera was used to record the trajectory of the vacuum arc plasma under different BMFs with different types of contacts. The results show the BMF can increase the arc voltage, and the arc becomes unstable. When the BMF becomes stronger, the arc voltage increases, and the arc becomes more unstable. In addition, for different types of contacts, the development process of the arc and the influence level are different under the same BMF. For a Wan‐type transverse magnetic field (TMF) contact or strong BMF, metal sputtering is evident and anode erosion becomes serious. For a cup‐type axial magnetic field (AMF) contact, the influence of BMF on the series arc plasma in double‐break VCBs is less than that of the Wan‐type TMF contact. The results of this work may be helpful for the design of compact double‐break VCBs.     

SN方法粒子输运计算程序自动建模关键技术问题研究

在充分调研和分析SN方法粒子输运计算程序自动建模方法的基础上，对建模过程中的模型文件格式识别、属性编辑、空腔处理及自动划分离散网格等关键技术问题进行了研究，并提出了合理可行的解决方法。通过对SNAM程序建模部分功能测试，验证了这些方法的正确性和有效性。This paper presents two approaches to enhance the geometry modeling ability of SN particle transport simulation codes and focus on the key issues that lie in the processing from CAD model to SN code geometry model, e.g. CAD file format support, void modeling, mesh generation and model-editing. SNAM （SN Automatic Modeling system） has been developed as an interface code between commercial CAD software and SN particle transport simmulation codes. The testing results have shown that the algorithm and implementation used in SNAM are efficient and capable of all the necessary processing from CAD model to SN geometry model.     

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.     

Particle‐in‐Cell Simulations for Ion Thrusters

The Particle‐in‐Cell (PIC) method was used to study two different ion thruster concepts: Hall Effect Thrusters (HETs) and High Efficiency Multistage Plasma Thrusters (HEMPs), in particular the plasma properties in the discharge chamber due to the different magnetic field configurations. Special attention was paid to the simulation of plasma particles fluxes on the thrusters inner surfaces. In both cases PIC proved itself as a powerful tool, delivering important insight into the basic physics of the different thruster concepts.The simulations demonstrated that the new HEMP thruster concept allows for a high thermal efficiency due to both minimal energy dissipation and high acceleration efficiency. In the HEMP thruster the plasma contact to the wall is limited only to very small areas of the magnetic field cusps, which results in much smaller ion flux to the thruster channel surface as compared to HET. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic behaviour of alternating current arc discharge in a multi‐arc generator at atmospheric pressure

In this letter, a multi‐arc generator with three high‐voltage electrodes and a common grounded one was developed for the purpose of obtaining large area and steady arc plasma at atmospheric pressure. Three typical discharge states were found in the multi‐arc generator: independent movement of three arc columns, confluence of two arc columns, and confluence of three arc columns. The three discharge states cyclically occur on the evolution of the arc discharge and their duration is influenced by the power dissipation and plasma working gas flow rate. With an increase of discharge power and a decrease of the gas flow rate, the duration of multiple arc confluence increases, which contributes to the suppression of the fluctuation amplitude of each arc. Frequency domain analysis of the arc voltage envelope shows that the frequency of arc fluctuation increases in the multi‐arc mode in the multi‐arc generator compared to that in the single arc mode.     

Synergia: An accelerator modeling tool with 3-D space charge

High precision modeling of space-charge effects, together with accurate treatment of single-particle dynamics, is essential for designing future accelerators as well as optimizing the performance of existing machines. We describe Synergia, a high-fidelity parallel beam dynamics simulation package with fully three-dimensional space-charge capabilities and a higher order optics implementation. We describe the computational techniques, the advanced human interface, and the parallel performance obtained using large numbers of macroparticles. We also perform code benchmarks comparing to semi-analytic results and other codes. Finally, we present initial results on particle tune spread, beam halo creation, and emittance growth in the Fermilab Booster accelerator.     

Atmospheric‐Pressure Plasmas for Solar Cell Manufacturing

Innovative plasma technologies operating at atmospheric pressure are especially advantageous concerning continuous processing capability. They are characterized by low costs, easy integration in existing production lines, low processing temperatures and high throughput. These economic and technological benefits are especially interesting for the manufacturing of crystalline silicon solar cells. Potential applications include PECVD as well as plasma‐chemical etching. In this work two principles of a large area plasma activation are presented: a linearly extended DC arc discharge (LARGE) and a microwave plasma (CYRANNUS). The atmosphericpressure reactors are designed for the continuous air‐to‐air processing of flat or slightly curved substrates. Gas purge systems enable the control of the atmosphere in the deposition zone and prevent the leakage of toxic gases. Extensive fluid‐dynamic modeling is used for optimization of plasma sources and reactors. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Merocyanines based on 1,3‐indanedione: electronic structure and solvatochromism

A series of merocyanines derived from 1,3‐indanedione and heterocycles of various electron‐donating properties was studied in detail. Their solvatochromic properties were explored in a wide range of solvent polarities to reveal the dependences of their chromacity and electronic structure on the key structural parameters – the properties of a donor heterocycle and the polymethine chain length. Also the dyes were studied by NMR spectroscopy and by quantum chemical calculations, both with the semiempirical AM1 and the non‐empirical density functional theory/B3LYP method. The solvatochromic properties of the explored dyes are rather close to those of merocyanines derived from malononitrile as acceptor group. Appreciable distinctions were observed only in protic ethanol; obviously, they are connected with the formation of solvent–solute H‐bonds in the case of 1,3‐indanedione derivatives. The electron‐acceptor properties of 1,3‐indanedione were found to be somewhat stronger in comparison with those of malononitrile even in aprotic solvents, contrary to the known literature data. Analysis of the merocyanines' molecular orbitals and simulation of their electronic spectra were carried out both in vacuum and in the solvent matrix, and the absorption electronic transitions were analyzed. Static nonlinear optical properties were calculated for both the new merocyanines and the corresponding cationic and anionic cyanine dyes. Copyright © 2010 John Wiley & Sons, Ltd.     

Opacity Calculations for Dense Plasmas

A code has been developed for calculating opacities of hot dense plasmas. This uses the average atom model to calculate the frequency dependent opacities with contributions from bound‐bound, bound‐free, free‐free and scattering processes. In this paper, we report work in three areas. Firstly, we present the enhanced absorption found in certain photon energy regions with the use of screening coefficients with l‐splitting in comparison to those obtained without l‐splitting. Secondly, we have generalized the code to allow mixture of elements, albeit without molecular effects. Thirdly, we compare our code results with other codes and experimental data.     

Equation‐of‐state studies of high‐energy‐density matter using intense ion beams at the Facility for Antiprotons and Ion Research

This paper describes an experiment design based on numerical simulations to measure the equation‐of‐state properties of high‐energy‐density (HED) matter using intense particle beams. The simulations are performed using a 2D hydrodynamic computer code, BIG2, while the beam parameters are considered to match the Facility for Antiprotons and Ion Research beam. This study has shown that in such experiments one can generate different phases of HED lead. Similar calculations are planned for other materials.     

Modeling of Nanoplasmas Created from Finite Systems by Ultrafast Intense X‐ray Pulses

In this review we discuss various simulation methods for modeling nanoplasmas created from finite‐size samples after their irradiation with femtosecond, intense X‐ray pulses. Depending on the sample composition and its size, either a particle method or a transport method can be applied. Also, the observables of interest influence the choice of the simulation method. The current status of dedicated methods developed by the CFEL Theory Division at DESY in Hamburg and their possible extensions are presented together with some application examples. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Laser‐Triggered Proton Acceleration From Micro‐Structured thin Targets

By using relativistic massively parallel PIC code MANDOR, which features arbitrary target design including 3D micro‐structuring, a study of ion acceleration in short laser pulse interaction with different thin targets has been performed. Based on 3D simulation results it has been shown that micro‐structures on the front surface of thin plane targets increase a number and energy of hot electrons in comparison with that for the case of pure plain foils of optimal thickness. As a result, the energy of accelerated ions also increases up to 50%. However, the efficiency of ion acceleration from structured target reduces with laser pulse intensity increase, so that for laser pulses of ultra‐relativistic intensity a positive role of surface micro‐structuring diminishes. We have also studied to which extent a sub‐ps imperfection of the laser pulse shape, which smoothes the surface micro‐structures suppresses high‐energy ion generation. (© 2013 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)     

Minimizing correlation effect using zero cross correlation code in spectral amplitude coding optical code division multiple access

The use of minimal multiple access interference (MAI) in code design is investigated. Applying a projection and mapping techniques, a code that has a zero cross correlation (ZCC) between users in optical code division multiple access (OCDMA) is presented in this paper. The system is based on an incoherent light source—LED, spectral amplitude coding (SAC), and direct detection techniques at the receiver. Using power spectral density (PSD) function and Gaussian approximation, we obtain the signal-to-noise ratio (SNR) and the bit-error rate (BER) to measure the code performance. Making a comparison with other existing codes, e.g., Hadamard, MFH and MDW codes, we show that our code performs better at BER 10⁻⁹ in terms of number of simultaneous users. We also demonstrate the comparison between the theoretical and simulation analyses, where the results are close to one another.     

Intensity‐Enhanced Apodization Effect on an Axially Illuminated Circular‐Column Particle‐Lens

A particle can function as a refractive lens to focus a plane wave, generating a narrow, high intensive, weak‐diverging beam within a sub‐wavelength volume, known as the ‘photonic nanojet’. It is known that apodization method, in the form of an amplitude pupil‐mask centrally situated on a particle‐lens, can further reduce the waist of a photonic nanojet, however, it usually lowers the intensity at the focus due to blocking the incident light. In this paper, the anomalously intensity‐enhanced apodization effect was discovered for the first time via numerical simulation of focusing of the axially illuminated circular‐column particle‐lenses, and a greater than 100% peak intensity increase was realised for the produced photonic nanojets.     

Plasma Diagnostics Using K‐Line Emission Profiles of Silicon

Modifications of K‐line profiles due to a warm dense plasma environment are a suitable tool for plasma diagnostics. We focus on Si K_α emissions due to an electron transfer from 2P to 1S shell. Besides 2P fine structure effects we also consider the influence of excited and higher ionized emitters. Generally spoken, a plasma of medium temperature and high density (warm dense matter) is created from bulk Si the greater part of atoms is ionized. The high energy of K_α x‐rays is necessary to penetrate and investigate the Si sample. The plasma effect influences the many‐particle system resulting in an energy shift due to electron‐ion and electron‐electron interaction. In our work we focus on pure Si using LS coupling. Non‐perturbative wave functions are calculated as well as ionization energies, binding energies and relevant emission energies using the chemical ab initio code Gaussian 03. The plasma effect is considered within a perturbative approach to the Hamiltonian. Using Roothaan‐Hartree‐Fock wave functions we calculate the screening effect within an ion‐sphere model. The different excitation and ionization probabilities of the electronic L‐shell and M‐shell lead to a charge state distribution. Using this distribution and a Lorentz profile convolution with a Gaussian instrument function we calculate spectral line profiles depending on the plasma parameters. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)