等离子体电极普克尔盒电光开关单脉冲过程数值模拟

采用流体模型对等离子体电极普克尔盒(PEPC)电光开关单脉冲过程进行了数值模拟分析.模型包括带电粒子连续性方程、动量守恒方程、电子平均能量方程及空间电位泊松方程.分别采用隐式指数差分格式，超松弛迭代法(SOR)和经典四阶龙格-库塔法(R-K)对带电粒子连续性方程，泊松方程和电子平均能量方程进行数值求解.模拟分析了PEPC单脉冲过程中的带电粒子浓度、电子温度、空间电场、PEPC的放电电流、晶体两侧电压和开关效率的时间演化特性.模型得出了PEPC中气体放电等离子体的微观物理过程与PEPC宏观参量的关系，对设计 关键词： 等离子体电极普克尔盒 电光开关 数值模拟 气体放电     

Non-local model of hollow cathode and glow discharge

A general form of the non-local equation for an ionization source in glow discharge and hollow cathode 3D-simulation is formulated. It is a fundamental equation in hollow cathode theory, which allows formulation of a complete set of field equations for a self-consistent problem in a stationary glow discharge and hollow cathode. It enables us to describe the region of negative glow and the hollow cathode effect and compare calculation results of electrical dependencies (pressure-voltage) with experimental data, – under conditions of gradual appearance of the hollow cathode effect.     

Numerical investigation of a fast-axial-flow CW CO2 laser

This paper presents the results of the calculation of the parameters of the active medium of a fast-axial-flow CO₂ laser using numerical methods in the framework of a one-dimensional approximation of the set of continuity equations, Bernoulli equation, equation of gas state, energy equation and multi-temperature rate equations with regard to diffusion for the gas flow in the cylindrical discharge tube. The spatial distribution of the small-signal gain and gas temperature along the gas flow direction have been calculated for a given set of initial conditions, namely, gas flow velocity, gas pressure and the tube diameter. In addition, the dependence of small-signal gain, the asymmetric stretch vibrational temperature of CO₂ (T₃) and the gas temperature on the discharge current were studied.     

The space-time-averaging procedure and modeling of the RF dischargeII. Model of collisional low-pressure RF discharge

For pt.I see ibid., vol.19, p.130-40 (1991). A self-consistent equations system for the low-pressure RF discharge is formulated and qualitatively analyzed. If the plasma and sheath dimensions exceed the electron-energy relaxation length, a simple spatially averaged kinetic equation can be derived that resembles the conventional one for the local case. Since the energy-diffusion coefficient for the slow electrons that are trapped by the average electric field in the discharge center is small, the distribution function slope decreases significantly with the energy growth. Analytic estimates are derived and reasonable agreement with the experiments of Godyak (1976, 1979, 1986, 1990) is obtained     

Theory of the free full-circle arc

A theoretical investigation of the full-circle arc located between two planes is presented. The circular arc shape is due to an applied magnetic field. The basic equations for conservations of mass, momentum, energy, and charge, as well as Maxwell's equations and the equation of state lead to a coupled set of partial differential equations. By means of Green's formula, this set is transformed into a set of integral equations. Using the analytically known Green's function, the system may be solved by an iteration procedure. For a simplified arc model, the quantities of interest are computed: The temperature distribution, the mass flow field, and the external magnetic field necessary to maintain this arc configuration.     

Eigenschaften und Parameterabhängigkeit der Temperaturverteilung und der Charakteristik eines zylindersymmetrischen Stickstoffbogens

The purpose of this work is to examine the properties and dependence upon parameters of the temperature distribution, and to ascertain the characteristic of a stationary, cylindersymmetrical nitrogen arc with negligible convection. Proceeding from the local balance of energy (the Elenbaas-Heller differential equation), the article makes known a process designed to determine the axial field strength in the arc discharge tube explicity with the aid of the boundary conditions of the temperature and the material functions. To this end, the differential equation is converted to a nonlinear integral equation. This equation can then, provided that the material functions are known and the parameters — radius of discharge tube, axis temperature, wall temperature — are established, be solved either numerically or graphically by a method analogous with the Picard's method of successive approximations. The numerical results, parameter limitations, and assumptions concerning material functions, enable the graphic and analytical relationship between temperature distribution and characteristic to be ascertained within a predetermined range of parameters. Thus we are enabled to interpret and theoretically record a few empirical beginnings and laws.     

The fluid theory of steady-state magnetically confined electron clouds sustained by ionization and emission

Summary The fluid theory is applied to study the axisymmetrical steady-state magnetically confined electron clouds sustained by ionization or emission. These electron clouds can be obtained by means of low-pressure Penning discharge, thermoelectronic emission, ion beam ionization, etc. In the electron clouds the property of motion of electrons can be described by the fluid equations: the continuity equation, the momentum equation, the energy equation, the heat transfer equation and the electrostatic field equation. These equations are used to discuss the equilibrium between supplement and escape of electrons in the clouds and the distributions of the physical quantities of some long electron clouds. The authors of this paper have agreed to not receive the proofs for correction. The work is supported by National Natural Science Foundation of China.     

Anisotropic solutions of the Einstein-Boltzmann equations: I. General formalism

Given a choice of a timelike vector field, a particle distribution function in a general curved space-time can be analysed into spherical harmonics; the Liouville and Boltzmann equations can then be written as a set of equations relating these spherical harmonic components. We obtain these equations and the resulting equations for the spherical harmonic moments of the distribution function. An orthonormal tetrad formalism is used as an aid in our calculations; the set of moment equations used can be completed by giving Einstein's field equations as equations for the rotation coefficients of this tetrad. We discuss time and space reversal symmetry properties of the Boltzmann equation, but leave applications of the set of equations obtained to further papers.     

Anti-symmetrically fused model and non-linear integral equations in the three-state Uimin-Sutherland model

We derive the non-linear integral equations determining the free energy of the three-state pure bosonic Uimin-Sutherland model. In order to find a complete set of auxiliary functions, the anti-symmetric fusion procedure is utilized. We solve the non-linear integral equations numerically and see that the low-temperature behavior coincides with that predicted by conformal field theory. The magnetization and magnetic susceptibility are also calculated by means of the non-linear integral equation.     

Vague concept of “reversible cleavage” in the theory of the surface tension of solids

Numerous derivations of the well-known Shuttleworth equation have been based on the unclear concept of “reversible cleavage” leading to the decisive step in any derivation - equalization of the surface free energy and surface stress. This is the key concept in contemporary surface thermodynamics of solids. But “cleavage” is not a surface process and, in this field, it cannot be a reversible operation. Besides, the “reversible cleavage” has no formal definition in the domain of the surface tension of solids that is an abnormal for any exact science. Consequently, this concept and all its corollaries including the Shuttleworth and generalized Lippmann equations have to be recognized as incorrect.     

Superradiance and energy transfer within a system of atoms

We investigate cooperative effects in energy relaxation and energy transfer for N atoms in a thermal radiation field with superradiance master equations as well as a closed set of coupled moment equations. Both spatially large and spatially small systems are considered. For small systems nonlinear rate equations for the energy are related to the moment equations. Symmetry of the small system to interchanging atoms is used to incorporate off-diagonal solutions of the superradiance master equation in expressions for the probability of the transfer of energy from one group of atoms to another. The long time excitation probability for initially unexcited atoms is large and strongly correlated. Cooperative processes in a large system which fall off with the distance between a cooperating pair of atoms include energy loss and transfer terms in the master equation. The energy transfer is oscillatory in time. Energy relaxation is shown by numerical solution to become cooperative in a very sudden manner as the scale of the atomic system is decreased through the resonant wavelength.     

Three-dimensional modelling of inductively coupled plasma torches

A three-dimensional model has been developed for simulating the behaviour of inductively coupled plasma torches (ICPTs), using customized CFD commercial code FLUENT ^?. The helicoidal coil is taken into account in its actual 3-D shape, showing the effects of its non-axisymmetry on the plasma discharge. Steady state, continuity, momentum and energy equations are solved for argon optically thin plasmas under the assumptions of LTE and laminar flow. The electromagnetic field is obtained by solving the 3-D vector potential equation on a grid extending outside the torch region. In order to evaluate the importance of various 3-D effects on calculated plasma temperature and flow fields, comparisons of our new results with the ones obtainable from conventional 2-D models and from an improved 2-D model that includes 3-D coil effects are presented. The presence of wall temperature hot spots due to plasma discharge displacement from the torch axis is evidenced, while the use of the new 3-D code for optimization of induction coil geometry and plasma gas inlet features is foreseen. Received 5 September 2002 Published online 13 December 2002 RID="a" ID="a"e-mail: colombo@ciram.ing.unibo.it     

A relativistic field theory of the electron

A set of nonlinear partial differential equations covariant in a non-Euclidean space is reduced to the Dirac equation for the electron and the Maxwell-Lorentz equations of electromagnetic fields under certain assumptions. In the course of reduction, we have opportunities for understanding the relationship between the Dirac equation and the Maxwell-Lorentz equations, and also for visualizing conditions which limit feasible applications of those known equations in physics.     

Low pressure radio frequency and microwave discharges for d.c. sputtering of ferromagnetic materials

This paper describes a d.c. diode sputtering system in which the sputtering discharge is sustained by an r.f. or microwave plasma excited with a helix coil surrounded by eight SmCo magnets. The discharge is characterized in terms of the discharge d.c. current through the cathode. The microwave and r.f. excitation and two different configurations of the magnets are compared. The production of r.f. or microwave discharge in a magnetic field makes it possible to operate this system even at low pressures down to 0.01 Pa. This work was partly supported by the Grant Agency of the Czech Republic under Project No. 106/96/K245.     

Über die mögliche lineare Form von LORENTZ-kovarianten Gravitationstheorien

LORENTZ -covariant theories of gravitation which fulfil EINSTEIN 's weak principle of equivalence and which contain a pure Newtonian theory as an approximation are tensortheories with the linear approximative form for the field equations. In the case of EINSTEIN 's strong principle of equivalence the exact field equations must be the general relativistic EINSTEIN -equations (or the bimetrical EINSTEIN -ROSEN -equations). This follows from the dynamical equations and the BIANCHI identity according to JÁNOSSY and TREDER . However, from NEWTON 's axiom of reaction together with the weak principle of equivalence results that the strong principle of equivalence must be valid for the linear approximation of the field equations with sources. Therefore, the linear approximation of all physically meaningful Lorentz-covariant theories of gravitation is given by the linearized EINSTEIN -equations (with HILBERT -conditions): , that is by the ansatz α = 2. The main point of our arguments is LAUE 's postulate of the self-consistency of perfect static systems of isolated gravitational masses. In the lowest order of approximation this self-consistency is only possible if the gravitational matter-tensor is identical with the special-relativistic energy-momentum-tensor T_μv. LAUE 's postulate is fulfilled exactly for the general relativistic field equations according to the theorems of BIRKHOFF , TOLMAN and EINSTEIN and PAULI .     

One-dimensional fluid model of ECR discharge with inhomogeneityeffects of external magnetic field

A one-dimensional fluid model of the microwave electron cyclotron resonance (ECR) discharge, which includes the inhomogeneity effects of the external magnetic field, is developed. We use fluid equations which are obtained from the one-dimensional Bolzmann equation expressed in terms of magnetic moment and parallel velocity. We model the plasma and sheath separately, and appropriate plasma-sheath boundary conditions are utilized. Microwave is represented by an energy flow, and treated by a ray tracing technique. For the argon discharge, we obtain various quantities such as the axial profiles of plasma density, electron temperature, electrostatic potential, fluid velocity, and microwave power deposition. The results of simulation compare well with the experimental observation of the mirror field effects on the plasma parameters     

Stochastic electrodynamics. III. Statistics of the perturbed harmonic oscillator-zero-point field system

In this third paper in a series on stochastic electrodynamics (SED), the nonrelativistic dipole approximation harmonic oscillator-zero-point field system is subjected to an arbitrary classical electromagnetic radiation field. The ensemble-averaged phase-space distribution and the two independent ensemble-averaged Liouville or Fokker-Planck equations that it satisfies are derived in closed form without furtner approximation. One of these Liouville equations is shown to be exactly equivalent to the usual Schrödinger equation supplemented by small radiative corrections and an explicit radiation reaction (RR) vector potential that is similar to the Crisp-Jaynes semiclassical theory (SCT) RR potential. The wave function in this SED Schrödinger equation is shown to have thea priori significance of position probability amplitude. The other Liouville equation has no counterpart in ordinary quantum mechanics, and is shown to restrict initial conditions such that (i) The Wigner-type phase-space distribution is always positive, (ii) in the absence of an applied field, the only allowed solution of both equations is the quantum ground state, and (iii) if a previously applied field is suddenly turned off, then spontaneous transitions occur, with no need for a triggering perturbation as in SCT, until the system is in the ground state. It is also shown that the oscillator energy is a fluctuating quantity that must take on a continuum of values, with average value equal to the quantum ground-state energy plus a contribution due to the applied classical field.     

Wavelength of ionization waves and the electron energy losses in the d. c. discharge in rare gases

Changes in the wavelength expressed by the wave potential (the product of wavelength and the longitudinal electric field intensity) are investigated in the dependence on (similarity) parameters of the neon and argon d.c. discharge. The measured dependences show the influence of different state of the electron gas, which behaves hydrodynamically or kinetically (with spatial resonances) in dependence on the type of prevailing energy exchange by elastic, inelastic or Coulomb collisions.     

Local electron mean energy profile of positive primary streamer discharge with pin-plate electrodes in oxygen nitrogen mixtures

Local electron mean energy (LEME) has a direct effect on the rates of collisional ionization of molecules and atoms by electrons. Electron-impact ionization plays an important role and is the main process for the production of charged particles in a primary streamer discharge. Detailed research on the LEME profile in a primary streamer discharge is extremely important for a comprehensive understanding of the local physical mechanism of a streamer. In this study, the LEME profile of the primary streamer discharge in oxygen-nitrogen mixtures with a pin-plate gap of 0.5 cm under an impulse voltage is investigated using a fluid model. The fluid model includes the electron mean energy density equation, as well as continuity equations for electrons and ions and Poisson’s electric field equation. The study finds that, except in the initial stage of the primary streamer, the LEME in the primary streamer tip tends to increase as the oxygen-nitrogen mole ratio increases and the pressure decreases. When the primary streamer bridges the gap, the LEME in the primary streamer channel is smaller than the first ionization energies of oxygen and nitrogen. The LEME in the primary streamer channel then decreases as the oxygen-nitrogen mole ratio increases and the pressure increases. The LEME in the primary streamer tip is primarily dependent on the reduced electric field with mole ratios of oxygen-nitrogen given in the oxygen-nitrogen mixtures.