Temporal relaxation of plasma electrons acted upon by directcurrent electric and magnetic fields

On the basis of the time-dependent electron Boltzmann equation the temporal relaxation of the electrons in the presence of electric and magnetic fields in weakly ionized, collision dominated plasmas has been studied. The relaxation process is treated by using a strict time-dependent two-term approximation of the velocity distribution function expansion in spherical harmonics. A new technique for solving the time-dependent electron kinetic equation in this two-term approximation for arbitrary angles between the electric and magnetic fields has been developed and the main aspects of the efficient solution method are presented. Using this new approach and starting from steady-state plasmas under the action of time-independent electric fields only, the impact of superimposed DC magnetic fields on the electron relaxation is analyzed with regard to the control of a neon plasma. The investigations reveal an important effect of the magnetic field on the temporal relaxation process. In particular, it has been found that the relaxation time of the electron component with respect to the establishment of steady-state can be enlarged by some orders of magnitude when increasing the magnetic field strength     

The Electron Relaxation to Stationary States in Collision Dominated Plasmas in Molecular Gases

The temporal collision dominated relaxation of electrons to new stationary states, starting from initial stationary states and due to jump-like changes of the electric field, was studied in the plasmas of the molecular gases N₂ and CO. Numerical solving of the time dependent Boltzmann equation for the electrons yields the temporal evolution of their energy distribution function and of resulting macroscopic quantities. The varying relaxation due to different values of the field strength in the final stationary state has been investigated considering the molecules of the plasma only as vibrationally non-excited and, in another case, including the additional impact of collisions with vibrationally excited molecules. The results obtained are discussed and, in particular, the relaxation times found for the transitions to the new stationary states are analysed on the basis of the energy transfer effectiveness by the collision processes. An approximative microphysical basis for the understanding of the main features of the relaxation in such complex molecular gas plasmas could be obtained.     

Response of the Electron Kinetics on Spatial Disturbances of the Electric Field in Nonisothermal Plasmas

An efficient method for solving the inhomogeneous electron Boltzmann equation for a weakly ionized collision dominated plasma is represented. As a first application this method is used to investigate in a helium plasma the response of the electron velocity distribution function and of the relevant macroscopic quantities to the impact of spatially limited disturbances in the electric field. In addition to the field action elastic and (conservative) inelastic collisions of electrons with gas atoms are taken into account in the kinetic treatment. In this way the spatial relaxation behaviour of the electrons and their establishment into homogeneous plasma states could be studied on a strict kinetic basis. Unexpectedly large relaxation lengths in electron acceleration direction have been found at medium electric fields.     

On the Relaxation of Energetic Electrons in Plasmas

The impact of individual collision processes on the relaxation of the velocity distribution function of a group of electrons, initially localized in a narrow region at relatively high energies, has been studied. By having recourse to solutions of the non-stationary Boltzmann equation and to corresponding Monte-Carlo simulations, the temporal behaviour of electrons in CO₂ plasmas, both in the absence and the presence of an external dc field, has been investigated. A microphysical interpretation of observed relaxation phenomena, based on the data relevant to the individual collision processes, is also given.     

The development and investigation of a strongly non-equilibrium model of heat transfer in fluid with allowance for the spatial and temporal non-locality and energy dissipation

The differential equation of heat transfer with allowance for energy dissipation and spatial and temporal nonlocality has been derived by the relaxation of heat flux and temperature gradient in the Fourier law formula for the heat flux at the use of the heat balance equation. An investigation of the numerical solution of the heat-transfer problem at a laminar fluid flow in a plane duct has shown the impossibility of an instantaneous acceptance of the boundary condition of the first kind — the process of its settling at small values of relaxation coefficients takes a finite time interval the duration of which is determined by the thermophysical and relaxation properties of the fluid. At large values of relaxation coefficients, the use of the boundary condition of the first kind is possible only at Fo → ∞. The friction heat consideration leads to the alteration of temperature profiles, which is due to the rise of the intervals of elevated temperatures in the zone of the maximal velocity gradients. With increasing relaxation coefficients, the smoothing of temperature profiles occurs, and at their certain high values, the fluid cooling occurs at a gradientless temperature variation along the transverse spatial variable and, consequently, the temperature proves to be dependent only on time and on longitudinal coordinate.     

Die Berücksichtigung der Ionisation durch Elektronenstoß in der Elektronenkinetik des schwachionisierten anisothermen Plasmas III. Das instationäre Verhalten bei großer impulsförmiger Feldstörung

The Influence of Ionization by Electron Collisions on the Electron Kinetics of the Low Ionized Anisothermal Plasmas The time behaviour of the electron component was calculated during the additional application of a single pulse to the electric field in the plasma. The investigations were performed for the weakly ionized Ne-plasma as a typical example taking into account supplementarily the direct ionization due to electron collisions and an electron loss term with a constant life time besides elastic and exciting collisions. Using the instationary Boltzmann equation we determined the time behaviour of the essential macroscopic quantities. Besides the caluclation of the marked temporal development of such quantities as the electron concentration, the electron collision frequencies for excitation and ionization and the different energy transfer rates especially the relaxation of the electron component was analysed after switch on and switch off the additional rectangular pulse.     

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为了准确计算稠密等离子体电离平衡,在理想Saha方程的基础上,加入了压致电离理论和德拜理论相结合的修正。此电离模型可以描述稠密等离子体内电离机制随着密度的增加由热电离转变为压致电离的现象。压致电离理论结合德拜理论修正的 Saha 方程的计算结果与其它电离模型结果作了对比和分析。电离气体区域采用完全电离等离子体模型计算电子弛豫时间,而在凝聚态区域采用电子平均自由程计算电子弛豫时间。提出了将两个区域平滑连接起来的公式,从而建立了一种可以计算从理想等离子体态到凝聚态物质的半经验电导率模型,半经验模型计算结果与实验数据作了对比。     

一种计算稠密等离子体电导率的半经验模型

为了准确计算稠密等离子体电离平衡,在理想Saha 方程的基础上,加入了压致电离理论和德拜理论相结合的修正。此电离模型可以描述稠密等离子体内电离机制随着密度的增加由热电离转变为压致电离的现象。压致电离理论结合德拜理论修正的Saha 方程的计算结果与其它电离模型结果作了对比和分析。电离气体区域采用完全电离等离子体模型计算电子弛豫时间,而在凝聚态区域采用电子平均自由程计算电子弛豫时间。提出了将两个区域平滑连接起来的公式,从而建立了一种可以计算从理想等离子体态到凝聚态物质的半经验电导率模型,半经验模型计算结果与实验数据作了对比。     

[Russian Text Ignored]

The plasmon turbulence parametrically excited by two strong external waves with a frequency difference close to twice the electron plasma frequency is investigated in underdense plasmas. The nonlinear stabilization of the growing plasmons due to scattering by ions is described by a nonlinear integro-differential equation for the spectral plasmon energy density. The dependence of the turbulent relaxation of the plasmon energy and its stationary level on the parameters of the plasma and the pump waves is given by analytical and numerical solutions of this equation.     

Results of investigation of the langmuir and upper-hybrid plasma turbulence evolution by means of stimulated ionospheric emission

The results of investigations of the temporal evolution of high-frequency plasma turbulence obtained by measurements of stimulated ionospheric emission (SIE) features for different stages of interaction of powerful radio emission, with an ionospheric F region plasma are presented. It is found that the relaxation time decreased up to 2–4 times with increase in the pump duration and pumping power under the conditions of striction parametric instability (excitation of Langmuir plasma turbulence) over times t≤2.00 ms. A similar decrease of the SIE relaxation time was also observed under the conditions of thermal parametric instability (excitation of upper-hybrid plasma turbulence) in long-term quasicontinuous heating of ionospheric plasma. The possible mechanisms of collisionless dissipation of plasma turbulence energy are discussed to explain the observed dependence of the plasma wave damping rate on the temperal stage of development and intensity of plasma turbulence. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 3, pp. 313–347, March, 1998.     

Numerical approach to non-equilibrium carrier relaxation in picosecond and subpicosecond physics

We present a numerical resolution of the time-dependent Boltzmann equation which describes the electron relaxation kinetics in direct gap semiconductors under subpicosecond optical excitation. The calculation is specialized to GaAs. We investigate, around the Mott density, the conditions of internal thermalization and energy relaxation of electrons, which depend strongly on the plasma concentration.     

Modeling the pulse shape of Q-switched lasers to account for terminal-level relaxation

To account for the effect of lower-level relaxation,we have derived a characteristic equation for describing the laser pulse from the modified rate equations for Q-switched lasers.The pulse temporal profile is related to the ratio of the lower-level lifetime to the cavity lifetime and the number of times the population inversion density is above the threshold.By solving the coupled rate equations numerically,the effect of terminal-level lifetime on pulse temporal behaviour is analysed.The mode is applied to the case of a diode-pumped Nd:YAG laser that is passively Q-switched by a Cr 4+:YAG absorber.Theoretical results show good agreement with the experiments.     

自由边界等离子体平衡方程的直接解法

本文介绍了外维持场随时间变化条件下等离子体平衡方程(非线性椭圆型偏微分方程)的数值求解方法。文中着重叙述了差分方程组为直接解法,并与通常采用的松弛迭代法进行了比较,结果表明直接法比松弛法精度高且节省机时。     

Relaxation of fast electrons in laser fusion targets

Collisional relaxation of a low density beam of non-thermal electrons injected into a high density Maxwellian plasma is investigated by computational treatment of Fokker-Planck type equation, with respect to the fast electron energy deposition and geometry configuration effects.     

Response signal in a femtosecond pump-probe experiment in a condensed medium with account of the memory induced by the relaxation medium

For a model molecular system with one vibrational degree of freedom and three electronic states coupled by pump and probe laser pulses in a condensed medium, the response signal in a femtosecond pump-probe experiment is calculated. The potential curves of all three states are described by the Morse potential. Calculations are performed using two qualitatively different approaches to describing the medium-induced relaxation: with memory of the relaxation process and without memory (Markovian approximation). The temporal evolution of the vibrational wave packet in the intermediate electronically excited state is described using a master equation for the density matrix of the molecular system, which is derived within the framework of the Nakajima-Zwanzig formalism. It is demonstrated that, at short delay times, when the proposed approach is applicable, taking into account memory effects can substantially change the form of the pump-probe experiment signal in comparison with the signal calculated in the Markovian approximation.     

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.     

Transport coefficients of quark-gluon plasma

Transport coefficients of quark-gluon plasma are discussed in the framework of relativistic kinetic theory with the relaxation time approximation of Boltzmann transport equation. The expressions for the coefficients of shear and volume viscosities and heat conductivity are derived assuming quark-gluon plasma to be a non-reactive mixture of quarks, anti-quarks and gluons. A lowest order in deviations from local thermal equilibrium and in plasma phase, lowest order in coupling constant are assumed. Entropy production due to irreversible processes is discussed.     

Stochastic generalization for a hyperbolic model of spinodal decomposition

A model for diffusion and phase separation which takes into account exponential relaxation of the solute diffusion flux and its fluctuations is developed. The model describes a system undergoing phase separation governed by a partial differential equation of hyperbolic type. The analysis is done for the evolution of patterns in spinodal decomposition for the system supercooled below critical temperature. Analytical results show that relaxation processes of the solute diffusion flux lead to the selection of patterns with different wavenumbers. Considering spatial-temporal correlations of the flux fluctuations, we have found that the temporal correlations promote selecting large-period patterns, whereas the corresponding spatial correlations accelerate such processes.     

The asymptotic dynamics of processes with multiplicative quadratic noise

The mean value of a non-Markovian stochastic process modelled by the rate equation with a multiplicative Ornstein-Uhlenbeck noise is investigated. The stability properties are discussed and the temporal evolution of the mean value and fluctuations of the process are presented. The effective relaxation time of the system is analysed.The research reported in this paper is supported in part by the Polish Academy of Sciences under the contract CPBP 1.1.4. The authors acknowledge the referee for valuable remarks.