Numerical calculation of the current specific action integral at the electrical explosion of wires

The electrical explosion of aluminum wires is numerically simulated in the magnetohydrodynamic approximation for the current density ranging from 10⁷ to 10¹⁰ A/cm² and times to explosion varying from 10^?10 to 10^?6 s. It is shown that, at current densities of 10⁸?10⁹ A/cm², low-temperature explosion conditions change to high-temperature ones, when inertial forces preventing the wire dispersion play a decisive role. This transition is accompanied by a sharp change in the thermodynamic parameters (the temperature and the energy deposited into the wire by the instant of explosion increase by several times), and the action integral for this transition increases smoothly approximately threefold as the explosion characteristics (current density and time to explosion) change by two orders of magnitude. The instant of transition from the low-temperature explosion to the high-temperature one depends on the radial dimensions of an exploding wire and does not depend on the properties of the environment.     

丝电爆过程的电流导入机理

丝电爆制备纳米粉时, 电流从电极导入金属丝的过程直接影响电极烧损和粉末中微米级大颗粒产生. 分别通过接触和气体放电两种方式导入电流进行电爆试验. 结果表明, 光测量装置检测到的丝端部光电流几乎与回路放电电流同时产生, 而中间位置的光电流则要滞后一段时间; 由探针收集的产物确定, 金属丝端部主要形成熔融粒子, 中间部分主要形成气相粒子. 分析可知, 接触方式导入电流时, 丝端部也存在气体放电现象, 大电流主要通过气体放电形成的等离子体导入. 等离子体对电流的旁路作用会阻碍能量向金属丝沉积, 这是产生微米级大颗粒和"积瘤"主要原因. 通过气体放电方式导入电流时, 电极烧损明显减轻, 并可以避免"积瘤"产生.     

介观金属双环系统中的持续电流和量子能谱

基于电荷的不连续性,对处于外磁场中的介观双环系统进行量子化.假设系统在电荷表象中具有变换的对称性,通过求解电流和Hamilton算符的本征值方程,给出介观金属环互感系统中的量子电流和能谱关系;分析和研究了介观金属环中量子电流和能谱的性质.结果表明,持续电流和量子能谱不仅与外磁场、介观双环参数有关,而且还明显地依赖于电荷的量子化性质.     

The effects of normal current density and the plasma spatial structuring in argon DBDs

This paper presents the results of theoretical studies of high-pressure dielectric barrier discharges (DBD) in argon. Two different DBDs at the megahertz and the kilohertz power frequency range were simulated. The effect of normal current density was obtained in the numerical model for both types of the discharge. The discharge of megahertz range was uniform over the radius. The increase in the discharge current is accompanied by increase in the discharge area. The discharge of kilohertz range is not uniform over the radius. The concentric ring formation was observed during calculations. The increase in the discharge current occurs due to increase in the number of rings and as a result in the discharge area. The developed 2D model is able to describe only the first stage of the filament formation – the formation of concentric plasma rings. The filament formation starts at the edge of the current channel and spreads to its centre. Both the effect of normal current density and the filaments formation are caused by the nonstationarity at the current channel boundary.     

电流密度场叠加原理及其应用

电流密度矢量场也满足叠加原理,给出了一些应用电流密度场叠加原理的例子.     

The effect of the plasma density gradient on current filamentation instability

The filamentation instability is one of the basic beam-plasma instabilities that play a significant role in the energy deposition mechanism of the relativistic electrons generated by the laser-plasma interaction in the fast ignition scenario. In this paper, the effect of the density gradient into plasma on the filamentation instability was investigated in the Weibel unstable plasma, where the plasma temperature anisotropy can play an important role. Results indicated that the density gradient enhances the instability growth rate so that decreasing the density gradient from the critical surface to the core of fuel leads to instability for longer regions in k space. Also, investigations in the region close to the critical surface showed that for decreasing the beam number density n_b ≤ 0.01n₀, the instability occurs for while this can be different for higher values. Increasing the beam relativistic factor causes a decreasing peak of instability growth rate because of a reduction in beam current, whereas the initial thermal spread of plasma amplifies the filamentation instability.     

The negative energy density for a three-single-electron state in the Dirac field

We examine the energy density produced by a state vector which is the superposition of three single electron states in the Dirac field in the four-dimensional Minkowski spacetime. We derive the conditions on which the energy density can be negative. We then show that the energy density satisfies two quantum inequalities in the ultrarelativistic limit.     

也谈概率密度和概率流密度算符

针对<大学物理>2008年第8期上关于粒子概率密度算符和概率流密度算符的讨论一文进行了补充,对一般空间(如动量空间)中的概率和概率流进行了较系统的阐述,并纠正了该文中的有关错误论断.     

The dependence of current density on the electric field strength in homopolar semi-conductors

The distribution function is derived for conduction electrons in a semi-conductor under the effect of a homogeneous electric field, on the basis of which one can explain the deviations from the validity of Ohm's law in strong electric fields or at low temperatures in homopolar semiconductors as well as the temperature dependence of the mobility.     

几类粒子密度算符和粒子流密度算符的讨论

从粒子密度和粒子流密度出发,分析了几类相关的算符,讨论了它们的性质与相互关系;从具体的物理意义出发,明确了合适的粒子密度算符和粒子流密度算符的表达形式.     

The axial dependence of the cathode current density in the longitudinal hollow cathode discharge

In the present paper the axial dependence of the cathode current distribution in the longitudinal hollow cathode discharge is investigated. On the basis of experimental results the model of the longitudinal hollow cathode discharge is developed and axial distribution of the cathode current is discussed.This work has been done in the frame of the Association for Education, Research and Application in Plasma-Chemical Processes and has been partially financially supported by Nos. 202/93/0659 and 202/95/1222 grants of Grant Agency of the Czech Republic. The main results have been presented as a poster on 10th Symposium on Elementary Processes and Chemical Reaction in Low Temperature Plasma, Stará Lesná (Slovakia), 1994.     

The density matrix picture of laser coherent control current

The photocurrent has been widely investigated for a long time. Conventionally the current results from the directional motion of the photo-electrons accelerated by dc bias. In recent years, the development of the optical information science calls for the Tbit per second transport speed, so the related devices must work on a time scale of picosecond even femtosecond. But this requirement is limited by the lifetime of the conventional photo-electrons. With the development of ultrafast laser pul…     

Coulomb energies and nuclear radii in the energy density formalism

The relation between Coulomb displacement energies,ΔE _c , andΔr=r _n -r _p , the difference between the rms radii of neutrons and protons in nuclei, is investigated within the energy density formalism (EDF). The variational equation, obtained by minimizing the Coulomb plus symmetry energies, is solved assuming the symmetry interaction is a simple functional of the local nuclear matter density. Varying parameters of the model, rather unique relation betweenΔE _c andΔr is obtained (within ±50 keV).ΔE _c isindependent ofr _ex, the rms radius of the excess neutrons distribution. Using the experimental values ofr _p and adjusting the model to reproduce the recent data onΔr (Δr∽~0.05 fm for⁴⁸Ca and²⁰⁸Pb), which are significantly smaller than those obtained from current Hartree-Fock calculations, the calculatedΔE _c agree with the experimental results. Using the value ofΔr～0.05 fm and the experimental values ofr _ex, a small compression (<0.02 fm) of the proton core in the analogue state relative to its parent state emerges, thus contributing an additional electrostatic term to the Coulomb displacement energy. The size of this relative core-compression effect depends on the values assumed forΔr andr _ex, it increases with the decreasing ofΔr and the increasing ofr _ex. IfΔr～0.05 fm the effect is large enough to remove the long standing Coulomb energy anomaly. The main result of the present work is the correlation betweenΔE _c andΔr, suggesting that the difficulties of current Hartree-Fock calculations in reproducing isotope shifts ofr _p , the small value ofr _n ?r _p and the values ofΔE _c may all be different manifestations of some missing residualp n effective interaction.     

The role of energy density and acoustic cavitation in shock wave lithotripsy

Today a high percentage of urinary stones are successfully treated by extracorporeal shockwave lithotripsy (SWL); however, misconceptions regarding fragmentation mechanisms, as well as treatment parameters like dose, applied energy and focal area are still common. A main stone comminution mechanism during SWL is acoustic cavitation. The objective of this study was to analyze the influence of cavitation and energy density on stone fragmentation. A research lithotripter was used to expose a large set of artificial kidney stones to shock waves varying different parameters. Hundreds of pressure records were used to calculate the energy density of the lithotripter at different settings. Results indicate that energy density is a crucial parameter and that better SWL treatment outcomes could be obtained placing the calculus at a prefocal position.     

Numerical simulation of the initial plasma formation and current transfer in single-wire electrical explosion in vacuum

In this paper, a computational model is constructed to investigate the phenomenon of the initial plasma formation and current transfer in the single-wire electrical explosion in a vacuum. The process of the single-wire electrical explosion is divided into four stages. Stage Ⅰ: the wire is in solid state. Stage Ⅱ: the melting stage. Stage Ⅲ: the wire melts completely and the initial plasma forms. Stage IV: the core and corona expand separately. The thermodynamic calculation is applied before the wire melts completely in stages Ⅰ and Ⅱ. In stage Ⅲ, a one-dimensional magnetohydrodynamics model comes into play until the instant when the voltage collapse occurs. The temperature, density, and velocity, which are derived from the magnetohydrodynamics calculation, are averaged over the distribution area. The averaged parameters are taken as the initial conditions for stage Ⅳ in which a simplified magnetohydrodynamics model is applied. A wide-range semi-empirical equation of state, which is established based on the Thomas-Fermi-Kirzhnits model, is constructed to describe the phase transition from solid state to plasma state. The initial plasma formation and the phenomenon of current transfer in the electrical explosion of aluminum wire are investigated using the computational model. Experiments of electrical explosion of aluminum wires are carried out to verify this model. Simulation results are also compared with experimental results of the electrical explosion of copper wire.