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     

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.     

DC column plasma kinetics in a longitudinal magnetic field

The cylindrical column plasma of a neon dc glow discharge under the influence of a weak longitudinal magnetic field is studied. An extended, fully self-consistent model of the column plasma has been used to determine the kinetic quantities of electrons, ions and excited atoms, the radial space charge field, and the axial electric field for given discharge conditions. The model includes a nonlocal kinetic treatment of the electrons by solving their spatially inhomogeneous kinetic equation, taking into account the radial space charge field and the axial magnetic field. The treatment is based on the two-term expansion of the velocity distribution and comprises the determination of its isotropic and anisotropic components in the axial, radial, and azimuthal direction. A transition from a distinctly nonlocal kinetic behavior of the electrons in the magnetic-field-free case to an almost local kinetic behavior has been found by increasing the magnetic field. The establishment of the electron cyclotron motion around the column axis increasingly restricts the radial electron energy transport and reduces the radial ambipolar current. The complex interaction of these transport phenomena with the alterations in the charge carrier production leads finally to a specific variation of the electric field components. The axial field increases by applying weak magnetic fields, however, decreases with increasingly higher magnetic fields. At higher magnetic fields, the radial space-charge field is considerably reduced     

On the electron energy distribution in the gas discharge positive column: Langmuir paradox

The results of calculations of electron drift characteristics in a dc spatially inhomogeneous periodic electric field are presented. It is shown that the effect of field inhomogeneities on the drift velocity and the average electron energy is insignificant under typical conditions of experiments with gas-discharge plasma at low gas pressures. However, the intensity of the processes of excitation, ionization, and plasma spatial distribution are strongly affected by the inhomogeneity (variance) and field variation behavior. It is shown that the electric field inhomogeneity in the gas discharge positive column leads to maxwellization of the electron energy distribution function.     

On the Interaction of an Alternating Electrical Field with an Inhomogeneous Magnetized Plasma

It is found out the form of the vectorial and isotropic cartesian component for the distribution function for electrons in an inhomogeneous plasma interacting with an alternative electric field, without being done any previous supposition on the temporal dependence of these quantities. For this purpose it is applied a method of succesive approximations for solving an integro-differential equation for the isotropic component of the distribution function. The scalar and vector components of the plasma spherical harmonic expansion are calculated including transient and secular terms. Some particular quantities as time-independent part of vectorial component of distribution function and of nonlinear conductivity were also obtained. Also corrected expressions for the transport coefficients in a electrical field, are obtained.     

Laser-Plasma Interaction in Presence of an Obliquely External Magnetic Field: Application to Laser Fusion without Radioactivity

In this paper, the nonlinear interaction of ultra-high power laser beam with fusion plasma at relativistic regime in the presence of obliquely external magnetic field has been studied. Imposing an external magnetic field on plasma can modify the density profile of the plasma so that the thermal conductivity of electrons reduces which is considered to be the decrease of the threshold energy for ignition. To achieve the fusion of Hydrogen-Boron (HB) fuel, the block acceleration model of plasma is employed. Energy production by HB isotopes can be of interest, since its reaction does not generate radioactive tritium. By using the inhibit factor in the block model acceleration of plasma and Maxwell's as well as the momentum transfer equations, the electron density distribution and dielectric permittivity of the plasma medium are obtained. Numerical results indicate that with increasing the intensity of the external magnetic field, the oscillation of the laser magnetic field decreases, while the dielectric permittivity increases. Moreover, the amplitude of the electron density becomes highly peaked and the plasma electrons are strongly bunched with increasing the intensity of external magnetic field. Therefore, the magnetized plasma can act as a positive focusing lens to enhance the fusion process. Besides, we find that with increasing θ-angle (from oblique external magnetic field) between 0 and 90°, the dielectric permittivity increases, while for θ between 90° and 180°, the dielectric permittivity decreases with increasing θ.     

Momentum spread in a relativistic electron beam in an undulator

The motion of the relativistic electron beam in the spatially periodic magnetic field of an undulator has been considered taking into account the effect of the incoherent field of the spontaneous undulator radiation on the motion of the electrons. An expression for the rms momentum of the electrons has been obtained. It has been shown that the momentum spread in the ultrarelativistic electron beam increases in the spontaneous incoherent emission mode. Conditions for the self-amplification of the spontaneous undulator radiation in ultrashort-wavelength free-electron lasers have been discussed.     

General Formulation for the Ponderomotive Force in a Warm Two Fluid Magnetized Plasma

A general expression for the ponderomotive force in a warm, inhomogeneous, nonstationary, magnetized and collisionless two fluid plasma in the presence of electromagnetic field is obtained. We start with two fluid equations viz. continuity, momentum equations and Maxwell's equation. Expanding the physical quantities in terms of a high frequency part and a slowly varying part and averaging the quantities over one period of the high frequency, we have obtained the expression for the ponderomotive force. The results are compared with the results of earlier workers under different approximations.     

Enhancement of electron density in the interaction of high-power electromagnetic waves with inhomogeneous magnetized plasma

Propagation characteristics of a high-power electromagnetic wave through an inhomogeneous magnetized plasma is investigated. Considering the momentum transfer equations for electrons and ions and taking into account the ponderomotive force, the distribution of electron density and dielectric permittivity are obtained. Using non-linear dielectric permittivity and Maxwell's equations in the absence of external current and charge densities, non-linear wave equations are achieved. The results indicate that the external static magnetic field can modify the profiles of both the electric and magnetic fields. It is also shown that the external static magnetic field enhances the amplitude of the electron density and the non-linear dielectric permittivity.     

Spectral measurements of local parameters of plasmas using CCD matrices

The possibility of obtaining local contours of spectral lines of strongly inhomogeneous doubly ionized nitrogen plasma with the help of a system that involves a spectrograph and a megapixel CCD matrix is shown. An automated measuring system based on a CCD matrix is described, and a procedure for processing matrix spectra is presented. The results of the Abel transform of the chord distributions of spectral line intensities of ions with different degrees of ionization are presented. Determined local contours of spectral lines can be used for estimating local temperatures and electron concentrations in strongly ionized spatially inhomogeneous plasmas.     

Dissipation in the Klein-Gordon Field

The formalism of (±)-frequency parts , previously applied to solution of the D'Alembert equation in the case of the electromagnetic field, is applied to solution of the Klein-Gordon equation for the K-G field in the presence of sources. Retarded and advanced field operators are obtained as solutions, whose frequency parts satisfy a complex inhomogeneous K-G equation. Fourier transforms of these frequency parts are solutions of the central equation, which determines the time dependence of the destruction/creation operators of the field. The retarded field operator is resolved into kinetic and dissipative components. Correspondingly, the energy/stress tensor is resolved into three components; the power/force density, into two—a kinetic and a dissipative component. As in the analogous electromagnetic case the dissipation theorem is derived according to which work done by the dissipative power/force is negative: energy/momentum is dissipated from the sources to the K-G field. Boson quantization conditions are satisfied by the kinetic component but not by the dissipative component of the retarded K-G field.     

Arc spot ignition caused by sheath instability

The transition from the stationary and homogeneous state of the collision-free space charge sheath between plasma and wall to a strongly inhomogeneous and instationary state with are spots is initiated by local enhancement of power supply from the plasma, connected with increasing electron emission. The general relations between surface emissivity, net current density, sheath potential, and power density in such “active” boundary layers are derived, taking the feedback of emitted electrons on the plasma parameters into account, as far as necessary. Joule heat generation is taken into account. The decisive effect of the transition is the rapidly increasing yield of thermo-field electron emission. Conditions and possible paths to sheath instability and arc spot formation are discussed     

The parallel permittivity of magnetized toroidal plasmas with elliptic magnetic surfaces

The asymptotic solution of the Vlasov equation under the drift approximation, for an axially symmetric toroidal plasma configuration with an elliptic cross section of magnetic surfaces, is presented. The analytical expressions for the parallel component of the dielectric permittivity tensor are obtained. These expressions are used for theoretical analyses of the trapped and untrapped electron influence on the collisionless wave dissipation. The evaluated dielectric tensor components can be used for computer calculations of the radio frequency field structure and the collisionless dissipated power related to trapped and untrapped electrons in tokamak plasmas.This work was supported by the State University of Rio de Janeiro (UERJ), Rio de Janeiro Research Foundation (FAPERJ) and Brazilian National Council of Research (CNPq).     

Self-sustained oscillations in a plasma-wall system with strongly inhomogeneous diffusion of charged particles

A simple system with a hydrogen plasma confined by a magnetic field parallel to the bounding material wall is considered. The charged particles diffuse out of the plasma, recombine on the wall and return into the plasma volume as neutrals, which are ionized by electrons. It is demonstrated that macroscopic self-sustained oscillations are an intrinsic feature of such a system if the diffusion coefficient of charged particles is strongly inhomogeneous in the plasma.     

Electron acceleration via collisions with ions in plasma under the action of a relativistically strong laser field

Electron-ion collisions in plasma in a strong electromagnetic field are considered in the ultrarelativistic limit (in which the vector potential A is such that a = eA/mc ² ? 1). Expressions relating the electron drift coordinates and momentum to those in the laboratory frame are obtained using exact canonical transformations with allowance for adiabatic effects. The appearance of ultrafast particles with a maximum energy proportional to the third power of the laser pulse vector potential is predicted. Expressions for the energy (and number) distribution function of such high-energy (hot) electrons appearing as a result of electron-ion collisions are obtained. These distribution functions obey a power law, which agrees with the results recently obtained by Mangles et al. [1] in experiments with a petawatt laser.     

脉冲射频容性耦合氩等离子体的发射探针诊断

利用工作在浮点模式下的发射探针,对500 Hz脉冲调制的27.12 MHz容性耦合氩气等离子体的空间电位和电子温度的时变特性进行了诊断.等离子体空间电位是通过测量强热状态下的发射探针电位获得的,而电子温度则是由发射探针在冷、热状态下的电位差来估算得到.测量结果表明:脉冲开启时,空间电位会快速上升并在300μs内趋于饱和;当脉冲关断后,空间电位经历了快速下降后趋于稳定的过程.电子温度在脉冲开启时存在过冲并趋于稳定的特征;而在脉冲关断期间,电子温度在300μs内则快速下降到0.45 e V后略有上升.无论在脉冲开启或关断期间,空间电位基本上都随功率和气压的变化存在有线性的依赖关系;而放电功率对脉冲开启期间过冲电子温度与稳态电子温度差异的影响较大.针对空间电位和电子温度在各阶段及不同放电条件下的时变特性,给出了相应的解释.     

Stoßbestimmte Relaxation des Elektronenensembles im Plasma bei zusätzlicher Aufheizung durch ein elektrisches Feld. III. Das periodische Verhalten der Elektronenkomponente im elektrischen Feld großen Modulationsgrades

Collision Dominated Relaxation of the Electron Ensemble in a Plasma with Additional Heating by an Electric Field. III. The Periodic Behaviour of the Electron Component in an Electric Field with a Large Modulation Amplitude With the aid of the non-stationary Boltzmann-equation the periodic behaviour of the isotropic part of the velocity distribution of electrons and thereby determined macroscopic quantities is calculated for periodic electric fields with large modulation amplitude. The investigations concern a weakly ionized column plasma in neon under typical low and medium pressure conditions. Based on the numerical results for typical ranges of field strength and cycle times of the electric field a qualitative physical interpretation for the periodic behaviour of the electron component is obtained. The introduction of special field-dependent adjustment times allows the formalution of conditions which characterize the case of quasi-stationary behaviour and also the case of small amplitudes of modulation in the macroscopic quantities determined by the isotropic distribution function. The periodic states between these two limiting cases can be interpreted as due to two competing processes. The first one is the energy input controlled by the electric field and the second one is the energy loss in binary collisions of the electrons with the atoms.     

时空非均匀等离子体鞘套中太赫兹波的传播特性

高超声速飞行器再入地面的过程中,其周围等离子体的电子密度是非均匀且随时间变化的.对于不同的再入高度,飞行器周围的温度和压强也会发生改变.因此,研究电磁波在时空非均匀等离子体鞘套中的传播特性意义重大.首先建立了时变非均匀的等离子体鞘套模型,然后通过经验公式得到温度、压强与碰撞频率三者的关系.采用时域有限差分方法计算了太赫兹波段中不同电子密度弛豫时间、温度、压强时的反射系数、透射系数和吸收率.研究结果表明:在太赫兹波段中,电子密度的弛豫时间越长,温度越高,压强越大,电磁波越容易穿透等离子体;弛豫时间越短,温度越低,压强越小,等离子体对电磁波吸收率的变化越明显.这些结果为解决"黑障"问题提供了理论依据.