Effective-viscosity approach for nonlocal electron kinetics in inductively coupled plasmas

In inductively coupled plasmas, nonlocal electron kinetics lead to the anomalous skin effect. We show that this can be approximately described through a fluid equation for electron momentum including a viscosity term with an effective-viscosity coefficient. The solution of this momentum equation coupled with the Maxwell equations is in good agreement with results from a particle-in-cell simulation over a wide range of conditions, reproducing the nonmonotonic structure of the anomalous skin with sometimes local negative power absorption.     

Twisted shear Alfvén waves with orbital angular momentum

It is shown that a dispersive shear Alfvén wave (DSAW) in a magnetized plasma can propagate as a twisted Alfvén vortex beam carrying orbital angular momentum (OAM). We obtain a wave equation from the generalized ion vorticity equation and the magnetic field-aligned electron momentum equation that couple the scalar and vector potentials of the DSAW. A twisted shear Alfvén vortex beam can trap and transport plasma particles and energy in magnetoplasmas, such as those in the Earth?s auroral zone, in the solar atmosphere, and in Large Plasma Device (LAPD) at University of California, Los Angeles.     

Der Drehimpulssatz in der Thermodynamik der irreversiblen Prozesse

The conservation law of the angular momentum has not been given sufficient attention in thermodynamics of irreversible processes. It plays an important part, however, when irreversible processes in the presence of electromagnetic fields are examined and the intrinsic angular momentum, due to spins of electrons and nuclei and electron orbits in atoms and molecules, is taken account of. Then the thermodynamic properties of matter with the macroscopic intrinsic angular momentum as an additional extensive parameter can be developed. Thermodynamics of irreversible processes is completed by the fact that a characteristic irreversible process is now associated also with the conservation law of angular momentum and Bloch's equation of nuclear induction is thus obtained in a straightforward way as one of the phenomenological equations.     

Moment equations and the dynamic equilibrium condition for a relativistic electron beam propagating along an external magnetic field in dense and rarefied gas-plasma media

Equations of transfer of mass, momentum, and energy for a transverse segment of a paraxial relativistic electron beam propagating in dense and rarefied gas-plasma media along an external magnetic field are derived from the kinetic equation. A virial equation is obtained, and the dynamic equilibrium condition that generalizes the wellknown Bennet equation for the cases under study is found.     

Viscous effects on motion and heating of electrons in inductivelycoupled plasma reactors

A transport model is developed for nonlocal effects on motion and heating of electrons in inductively coupled plasma reactors. The model is based on the electron momentum equation derived from the Boltzmann equation, retaining anisotropic stress components which in fact are viscous stresses. The resulting model consists of transport equations for the magnitude of electron velocity oscillation and terms representing energy dissipation due to viscous stresses in the electron energy equation. In this model, electrical current is obtained in a nonlocal manner due to viscous effects, instead of Ohm's law or the electron momentum equation without viscous effects, while nonlocal heating of electrons is represented by the viscous dissipation. Computational results obtained by two-dimensional numerical simulations show that nonlocal determination of electrical current indeed is important, and viscous dissipation becomes an important electron heating mechanism at low pressures. It is suspected that viscous dissipation in inductively coupled plasma reactors in fact represents stochastic heating of electrons, and this possibility is exploited by discussing physical similarities between stochastic heating and energy dissipation due to the stress tensor     

紧聚焦飞秒脉冲与石英玻璃相互作用过程中的电子动量弛豫时间研究

本文通过数值模拟(3+1)维扩展的广义非线性薛定谔方程,研究了紧聚焦飞秒激光脉冲在诱导石英玻璃的非线性电离过程中电子动量弛豫时间对于该电离过程的影响.计算结果证明电子动量弛豫时间会直接影响入射脉冲在焦点区域所形成的峰值场强、自由电子态密度和能流等参量的分布态势,因此在与实验结果相比较后发现适合于相互作用过程的电子动量弛豫时间的理论值约为1.27 fs.进一步的研究表明,电子动量弛豫时间与逆韧致吸收效应、雪崩电离的概率、等离子体密度、等离子体的自散焦效果以及间接引起的焦平面位置的移动都有着密切的联系.当前的研究结果表明电子动量弛豫时间在飞秒激光脉冲与物质相互作用的过程中发挥着重要作用.     

Formation of the distribution function for runaway electrons in strong fields of pulsed gas discharges

A simplified Boltzmann equation describing the escape of electrons in a weakly ionized gas is constructed. The electric fields are assumed to be so strong that all electrons are runaway electrons and the electron distribution function is strongly anisotropic. The equation is solved analytically, and it is shown that the electron density in relatively weak fields exponentially increases with time, while the momentum dependence of the distribution function exponentially decreases. In strong fields, the electron density increases with time logarithmically and the momentum dependence of the electron distribution function is nonmonotonic. The characteristic scales of time and energy, which determine different scenarios, are obtained.     

Path of Momentum Integral in the Skorniakov-Ter-Martirosian Equation

The Skorniakov-Ter-Martirosian (STM) integral equation is widely used for the quantum three-body problems of low-energy particles (e.g., ultracold atom gases). With this equation these three-body problems can be efficiently solved in the momentum space. In this approach the boundary condition for the case that all the three particles are gathered together is described by the upper limit of the momentum integral, i.e., the momentum cutoff. On the other hand, in realistic systems, the three-body recombination (TBR) process can occur when all these three particles are close to each other. In this process two particles form a deep dimer and the other particle can gain high kinetic energy and then escape from the low-energy system. In the presence of the TBR process, the momentum-cutoff in the STM equation would include a non-zero imaginary part. As a result, the momentum integral in the STM equation should be done in the complex-momentum plane. In this case the result of the integral depends on the choice of the integral path. Obviously, only one integral path can lead to the correct result. In this paper we consider how to correctly choose the integral path for the STM equation. We take the atom-dimer scattering problem in a specific ultracold atom gas as an example, and show the results given by different integral paths. Based on the result for this case we explore the reasonable integral paths for general case.     

Two-dimensional photoelectron momentum distribution of hydrogen in intense laser field

Two-dimensional (2D) electron momentum distributions and energy spectra of a hydrogen in an intense laser field are calculated by solving the time-dependent Schrödinger equation combined with the window-operator technique. Compared with the standard projection technique, the window-operator technique has the advantage that the continuum states of atoms can be avoided in the calculation. We show that the 2D electron momentum distributions and the energy spectra from those two techniques accord quite well with each other if an appropriate energy width is used in the window operator.     

Momentum transfer in crystal lattices with vibrating atoms

A momentum transfer equation previously used to describe non-elastic deformation in crystalline solids represented by point masses at fixed lattice positions is extended to take into account the existence of intrinsic (e.g. thermal) small amplitude vibrations of the masses about their mean positions in a lattice. Use of the time-dependent Schroedinger equation to describe momentum transfer and deformation is also discussed in terms of this vibrating point-mass lattice model. The result is that a modified and identical differential equation for momentum transfer is obtained from each approach; some solutions to this equation are presented. The previous particle momentum wave frequency dependence on wave vector and resulting applications to non-elastic deformation are unchanged, but these particle momentum waves can now be considered as modulating the usual high-frequency waves associated with the elastic modes of a crystalline solid.     

A hybrid fluid–kinetic neutral model based on a micro–macro decomposition in the SOLPS-ITER plasma edge code suite

We present a hybrid fluid–kinetic model for the hydrogenic atoms in the plasma edge that is implemented in SOLPS-ITER. A micro–macro decomposition of the kinetic equation leads to a fluid model with a continuity and parallel momentum equation (implemented in B2.5) coupled to a kinetic correction equation (implemented in EIRENE). We assess the hybrid model for a high recycling fixed background plasma. The hybrid approach leads to a reduction of the Central Processing Unit(CPU) time required to obtain the same statistical error as the full kinetic Monte Carlo (MC) simulation with approximate factors of 1.7, 4.9, and 1.9 for the particle, parallel momentum, and electron energy source, respectively. However, there is an increase in CPU time for the ion energy source. By comparing the results with our in-house plasma edge code, we conclude that the hybrid performance can be improved by adapting some default MC features in EIRENE.     

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.     

THE FLUID THEORY OF SELF-SUSTAINING MAGNETICALLY CONFINED ELECTRON CLOUDS (Ⅰ) FLUID EQUATIONS

In this paper the axisymmetrical self-sustaining magnetically confined electron clouds are studied by means of the fluid theory.In the electron clouds which supported by the Penning discharge the property of motion of electrons can be described by the fluid equations:continuity equation,momentum equation,energy equation,Poisson equation and heat transfer equation.The problems of the diffusion and escape of electrons and the energy transport in the electron clouds are discussed.     

Strong field electron emission from fixed in space H(2)(+) ions

We have studied electron emission from the H(2)(+) ion by a circularly polarized laser pulse (800 nm, 6×10(14) W/cm(2)). The electron momentum distribution in the body fixed frame of the molecule is experimentally obtained by a coincident detection of electrons and protons. The data are compared to a solution of the time-dependent Schr?dinger equation in two dimensions. We find radial and angular distributions which are at odds with the quasistatic enhanced ionization model. The unexpected momentum distribution is traced back to a complex laser-driven electron dynamics inside the molecule influencing the instant of ionization and the initial momentum of the electron.     

X波段准周期加载微波腔研究

 准周期加载微波腔的基本结构是周期结构，在强引导磁场作用下，强流电子束同微波强作用产生高功率微波；作用过程分为三个阶段：电子俘获、群聚和换能；而周期结构的作用主要在于电子俘获。适当设计的结构，不仅束波转换效率高，而且对电子束质量（如能散）的要求也不高。从微波场对电子运动的影响，研究了电子束在微波腔中的俘获、群聚和换能的束波互作用过程。基于760kV，7kA的环形电子束，采用准周期加载微波腔结构，在模拟上获得了X波段（9.3GHz）峰值功率为1.3GW的微波输出，效率接近24%。     

托卡马克等离子体边缘梯度和杂质辐射驱动的湍流理论

本文考虑了托卡马克等离子体边缘的物理性质，由电子连续性方程和离子动量平衡方程导出了电子密度演变方程。分析了各种驱动源在线性和非线性发展过程中的作用。电子密度梯度直接影响密度涨落，并通过杂质辐射与温度涨落相互耦合，进而影响静电势涨落。理论结果能够分别与高、低密度装置上的实验较好地相符合。     

Monte Carlo method for the Schrödinger equation with an asymmetric periodic potential

A new numerical method is proposed for solving the Cauchy problem for the Schrödinger equation with an asymmetric periodic potential superimposed by a constant electric field. The solution to the Cauchy problem is used to determine the electron’s mean momentum as a function of time, initial conditions, and the applied field. Given an initial state, the mean momentum characterizes the mean current and the conductivity of an asymmetric periodic structure known as the ratchet potential.     

Measurement of the temperature and flow fields of the magnetically stabilized cross-flow N2 arc

A straight, steady-state cross-flow arc is burning in an N₂ wind tunnel. The arc is held in position by the balance of the Lorentz forces produced by an external magnetic field perpendicular to the arc axis and by the viscous forces of the gas flow acting on the arc column. The temperature field in the discharge is determined spectroscopically using the radiation of N I lines. Because of the lack of rotational symmetry an inversion method developed by Maldonado was used to determine the local emission coefficient from the measured integrated spectral intensity distributions across the arc in various directions. For known local temperature the mass flow field inside the arc may be evaluated from the convective term of the energy equation and the continuity equation. This is done by expanding the terms of these two equations around the point of the temperature maximum into Fourier-Taylor series and determining coefficients of the same order and power. The solution of the resulting set of algebraic equations yields the unknown coefficients of the mass flow. The flow field obtained by these calculations shows a relatively strong counterflow through the arc core. In the region for which the series expansion holds a partial structure pertaining to a closed double vortex can be recognized. The terms of the momentum equation are calculated on the basis of these results. In order to obtain a better understanding of the importance attributed to the individual local forces acting on the plasma, a simple model was devised which separates the momentum equation into gradient and curl terms. The discussion shows that the gradient part of the Lorentz force causes mainly the pressure gradient, while the much smaller rotational part of thej×B forces is responsible for propelling the mass flow. The momentum transport inside the arc as well as in its neighbourhood is due to the viscous forces and to the pressure gradient. By contrast, at larger distances from the arc it is essentially the inertial force that determines the momentum transport. It is shown that viscosity as a damping mechanism is necessary for the existence of stationary flow fields as investigated in this work.     

Generation of zonal magnetic fields by drift waves in a current carrying nonuniform magnetoplasma

It is shown that zonal magnetic fields (ZMFs) can be nonlinearly excited by incoherent drift waves (DWs) in a current carrying nonuniform magnetoplasma. The dynamics of incoherent DWs in the presence of ZMFs is governed by a wave-kinetic equation. The governing equation for ZMFs in the presence of nonlinear advection force of the DWs is obtained from the parallel component of the electron momentum equation and the Faraday law. Standard techniques are used to derive a nonlinear dispersion relation, which depicts instability via which ZMFs are excited in plasmas. ZMFs may inhibit the turbulent cross-field particle and energy transport in a nonuniform magnetoplasma.