Calculation of the equation of state of a dense hydrogen plasma by the Feynman path integral method

A method is developed for calculating the equation of state of a system of quantum particles at a finite temperature, based on the Feynman formulation of quantum statistics. A general analytical expression is found for the virial estimator for the kinetic energy of a system with rigid boundaries at a finite pressure. An effective method is developed for eliminating the unphysical singularity in the electrostatic potential between a discretized Feynman path of an electron and a proton. It is shown that the “refinement” of an expansion of a quantum-mechanical propagator by addition of high powers of time exacerbates, rather than eliminates, the divergence of a Feynman path integral. A brief summary of the current status of the problem is presented. The proposed new approaches are presented in relation to progress made in this field. Path integral Monte Carlo simulations are performed for nonideal hydrogen plasmas in which both indistinguishability and spin of electrons are taken into account under conditions preceding the formation of the electron shells of atoms. The electron permutation symmetry is represented in terms of Young operators. It is shown that, owing to the singularity of the Coulomb potential, quantum effects on the behavior of the electron component cannot be reduced to small corrections even if the system must be treated as a classical system according to the formal de Broglie criterion. Quantum-mechanical delocalization of electrons substantially weakens the repulsion between electrons as compared to protons. In relatively cold plasmas, many-body correlations lead to complex behavior of the potential of the average force between particles and give rise to repulsive forces acting between protons and electrons at distances of about 5 angstroms. Plasma pressure drops with decreasing plasma temperature as the electron shells of atoms begin to form, and the electron kinetic energy reaches a minimum at a temperature of about 31000 K. The minimum point weakly depends on plasma density. Owing to quantum effects, the electron component is “heated” well before electrons are completely bound in the field of protons.     

Ion surface cyclotron waves at plasma-metal interfaces

The dispersion properties of slow electromagnetic surface waves propagating across a constant external magnetic field and along a plane plasma-metal interface at harmonics of the ion cyclotron frequency are studied. The motion of the plasma particles is described by a Vlasov-Boltzmann kinetic equation. The effects of the plasma size, the dielectric permittivity of the transition region between the plasma and metal, and the magnitude of the constant external magnetic field on the dispersion characteristics of ion surface cyclotron waves are studied. Zh. Tekh. Fiz. 69, 83–89 (October 1999)     

大气压氩气/空气针-环式介质阻挡放电发射光谱诊断

为了更加深入地了解氩气/空气等离子体射流内的电子输运过程及化学反应过程,通过针-环式介质阻挡等离子体发生器在放电频率10 kHz,一个大气压条件下对氩气/空气混合气进行电离并产生了稳定的等离子体射流。通过发射光谱法对不同峰值电压下氩气/空气等离子体射流的活性粒子种类、电子激发温度及振动温度进行了诊断。结果表明,射流中的主要活性粒子为N₂的第二正带系、Ar Ⅰ原子以及少量的氧原子,其中N₂的第二正带系的相对光谱强度最强、最清晰,在本试验的发射光谱中没有发现N+₂的第一负带系谱线,这说明在氩气/空气等离子体射流中几乎没有电子能量高于18.76 eV的自由电子。利用Ar Ⅰ原子激发能差较大的5条谱线做最小二乘线性拟合对等离子体射流的电子激发温度进行了计算,得到大气压氩气/空气等离子体射流的电子激发温度在7 000~11 000 K之间。随峰值电压的增大,电子激发温度表现出先增大后减小的变化趋势,这说明电子激发温度并不总是随峰值电压的增长单调变化的。通过N₂的第二正带系对等离子体振动温度进行了诊断,发现大气压氩气/空气等离子体射流振动温度在3 000~4 500 K之间,其随峰值电压的增大而减小,这意味着虽然峰值电压的提高可有效提高自由电子的动能,但当电子动能较大时自由电子与氮分子之间的相互作用时间将会缩短,进而二者之间的碰撞能量转移截面将会减小,从而导致等离子体振动温度的降低。     

Brownian particles with long- and short-range interactions

We develop the kinetic theory of Brownian particles with long- and short-range interactions. Since the particles are in contact with a thermal bath fixing the temperature T, they are described by the canonical ensemble. We consider both overdamped and inertial models. In the overdamped limit, the evolution of the spatial density is governed by the generalized mean field Smoluchowski equation including a mean field potential due to long-range interactions and a generically nonlinear barotropic pressure due to short-range interactions. This equation describes various physical systems such as self-gravitating Brownian particles (Smoluchowski-Poisson system), bacterial populations experiencing chemotaxis (Keller-Segel model) and colloidal particles with capillary interactions. We also take into account the inertia of the particles and derive corresponding kinetic and hydrodynamic equations generalizing the usual Kramers, Jeans, Euler and Cattaneo equations. For each model, we provide the corresponding form of free energy and establish the H-theorem and the virial theorem. Finally, we show that the same hydrodynamic equations are obtained in the context of nonlinear mean field Fokker-Planck equations associated with generalized thermodynamics. However, in that case, the nonlinear pressure is due to the bias in the transition probabilities from one state to the other leading to non-Boltzmannian distributions while in the former case the distribution is Boltzmannian but the nonlinear pressure arises from the two-body correlation function induced by the short-range potential of interaction. As a whole, our paper develops connections between the topics of long-range interactions, short-range interactions, nonlinear mean field Fokker-Planck equations and generalized thermodynamics. It also justifies from a kinetic theory based on microscopic processes, the basic equations that were introduced phenomenologically to describe self-gravitating Brownian particles, chemotaxis and colloidal suspensions with attractive interactions.     

激光惯性约束聚变动理学效应研究进展

动理学效应的研究是近年来激光惯性约束聚变领域的研究热点,有助于理解实验结果和传统流体模拟之间的偏差。间接驱动黑腔中等离子体的温度、密度跨越多个量级且靶丸组分复杂,在局域的高温低密度区域,粒子的非平衡效应开始变得显著,可能会间接影响内爆性能。对ICF领域动理学效应的概念和部分进展做了简要综述。     

Increase of Kinetic Energy of Dusty Cluster Particles Due to Parametric Instability Caused by Nanosecond Electric Pulses

Experimental investigations of high voltage nanosecond pulses influence on charged dust particles in low pressure rf–plasma were carried out. Application of repetitive pulses leads to the vertical oscillations of the mi‐croparticles. Evolution of the total kinetic energy for the cluster consisting of 14 particles is investigated. Flat clusters exhibit parametric instabilities of horizontal modes. In the initial phase the kinetic energy oscillates around a certain value and its amplitude grows very slowly. At a certain moment during the instability it goes into the exponential growth phase and then saturates under the effect of repetitive pulses. It is possible if the eigenfrequency is the function of height and the dust particle oscillates vertically in the non uniform electric field (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dusty plasma structures in magnetic fields in a dc discharge

The formation of dusty plasma structures has been experimentally investigated in a cylindrical dc discharge in axial magnetic fields up to 2500 G. The rotation of the dusty plasma structures about the discharge symmetry axis with a frequency depending on the magnetic field has been observed. When the field increases to 700 G, the displacement of dust particles from the axial region of the discharge to the periphery, along with the continuation of the rotation, has been observed. The kinetic temperatures of the dust particles, the diffusion coefficients, and the effective nonideality parameter have been determined for various magnetic fields. The explanation of the features in the behavior of the dust particles in the discharge in the magnetic field has been proposed on the basis of the analysis of ambipolar diffusion in the magnetized plasma. The maximum magnetic field at which the levitation of the dust particles in the discharge is possible has been estimated.     

Motions of particles in an oscillating plasma

An alternative consideration of oscillations and waves in plasma is suggested based on equations for small deflections of particles from their equilibrium trajectories instead of equations for perturbations of distribution functions and fields, so that average values are calculated with equilibrium distribution functions. Instead of the Maxwell equations for an electromagnetic field their solutions in the Lienard-Wiechert form are used. All the known results of the linear kinetic theory of plasma oscillations are shown to be derivable in this way, and small correlations for dispersion relations of the first order in the plasma parameter due to the Debye screening have been obtained. A simplified consideration of a rarefield plasma in a strong magnetic field is given showing a non-cyclotron character of the motion of the particles. Such a combination of statistical and dynamical approaches may be useful in many problems of plasma physics.     

Micro‐Disperse Particles in Plasmas: From Disturbing Side Effects to New Applications

The research effort in the area of dusty plasmas initially aimed at avoiding particle formation and controlling the contamination level in industrial reactors. Nowadays, dusty plasmas have grown into a vast field and new applications of plasma‐processed dust particles are emerging. There is demand for particles with special properties, and for particle‐seeded composite materials. Low‐pressure plasmas offer a unique possibility of confinement, control and fine tailoring of particle properties. The role of plasma technology in treatment and surface modification of powder grains is reviewed and illustrated with examples. The interaction between plasma and injected micro‐disperse powder particles can also be used as a diagnostic tool for the study of plasma surface processes.     

Interaction between glow discharge plasma and dust particles

The effect of dust particle concentration on gas discharge plasma parameters was studied through development of a self-consistent kinetic model which is based on solving the Boltzmann equation for the electron distribution function. It was shown that an increase in the Havnes parameter causes an increase in the average electric field and ion density, as well as a decrease in the charge of dust particles and electron density in a dust particle cloud. Self-consistent simulations for a wide range of plasma and dust particle parameters produced several scaling laws: these are laws for dust particle potential and electric field as a function of dust particle concentration and radius, and the discharge current density. The simulation results demonstrate that the process of self-consistent accommodation of parameters of dust particles and plasma in condition of particle concentration growth causes a growth in the number of high-energy electrons in plasma, but not to depletion of electron distribution function.     

Parametrical Instability of Surface Type X-modes Immersed into a Nonmonochromatic Pumping Electric Field

Parametrical excitation of surface type X-modes (STXM) at the second harmonic of electron cyclotron frequency by nonmonochromatic external alternating electric field is under consideration. STXM are the eigenmodes of a planar magnetoactive plasma waveguide structure consisting of a metal wall with dielectric coating and uniform plasma filling. An external steady magnetic field is applied along the plasma interface, so it is perpendicular to the group velocity of the considered extraordinarily polarized waves. Influence of the plasma waveguide parameters on the parametrical instability of the STXM is studied. External alternating electric field is assumed to consist of two fields with different amplitudes and frequencies. A theoretical investigation is carried out using kinetic equation for plasma particles under the conditions of weak plasma spatial dispersion and small amplitudes of external electric fields. The obtained results can be useful for research in branch of edge plasma physics.     

Influence of inert gas pressure on deposition rate during pulsed laser deposition

The deposition rates of permalloy and Ag are monitored during pulsed laser deposition in different inert gas atmospheres. Under ultrahigh vacuum conditions, resputtering from the film surface occurs due to the presence of energetic particles in the plasma plume. With increasing gas pressure, a reduction of the particle energy is accompanied with a decrease of resputtering and a rise in the deposition rate for materials with high sputtering yield. In contrast, at higher gas pressures, scattering of ablated material out of the deposition path between target and substrate is observed, leading to a decrease in the deposition rate. While in the case of Xe and Ar these processes strongly overlap, they are best separated in He. A He pressure of about 0.4 mbar should be used to reduce the kinetic energy of the deposited particles, to reach the maximum deposition rate and to avoid implantation of the particles. This is helpful for the preparation of stoichiometric metallic alloy films and multilayers with sharp interfaces. Received: 27 March 2002 / Accepted: 3 April 2002 / Published online: 5 July 2002     

量子等离子体中波的色散关系以及朗道阻尼

利用动理学理论研究量子等离子体中波的色散关系和电子朗道阻尼.从电子的量子流体动力学方程和动理学描述下的光子运动方程出发,研究量子效应对光子朗道阻尼的修正.研究发现量子效应只对纵波模式,即电子等离子体波的色散关系有修正,对横向电磁波的色散关系没有影响.量子效应减小了朗道阻尼,起着朗道增长的作用. 关键词： 量子等离子体 朗道阻尼 电子等离子体波 色散关系     

Effect of the size of nanoparticles on the properties of a capacitive high-frequency discharge

The properties of a capacitive HF discharge with growing nanoparticles are studied with the use of kinetic PIC-MCC simulation. At the initial stage of growth, the nanoparticles are shown to be localized at the interface between the near-electrode layer and quasi-neutral plasma, where the rate of ionization by electron impact has the maximum value. At the beginning of formation of particles, plasma parameters change rapidly and a transition between the capacitive and spatial discharge burning modes is observed for a certain critical size of the particles. If the growth of the dust particles continues, their distribution over the discharge becomes more uniform and the steady-state parameters of the gas-discharge plasma hardly change.     

Runaway-Ströme hoher Intensität in einer toroidalen Entladung

Intensive currents of runaway electrons with energies of 50 keV or more have been observed at high pressures in a plasma betatron in addition to betatron accelerated electrons at lower pressures. The measurements agree with the assumption that these electrons are accelerated in the external field while they are guided by the self magnetic field of the plasma current. Macroscopic instabilities and plasma waves can be excluded as accelerating mechanisms. The strong dependence of the runaway flux upon the gas pressure and the electric field can be explained by collisions between electrons and the other plasma particles. Furthermore the influence of the external magnetic field on the movement of the plasma current to the torus wall was investigated. A maximum circulating runaway current of more than 2000 A (Xenon) appeared when the plasma current was kept approximately in balance by the external magnetic field.