The paraxial approximation for a dense electron beam

Approximate equations are derived for a narrow (paraxial) electron beam with a three-dimensional axis; these equations generalize the familiar equations [1] to the case in which the field of the charge in the beam is important. A class of beams is distinguished for which the problem reduces to ordinary differential equations. The paraxial approximation for a narrow beam of electron trajectories in a given field is well known for the case in which the characteristic dimension L_* of the irregularities is much greater than a_*, the characteristic width of the beam. The field of a three-dimensional beam can be included in the equations [1] if the beam density ρ is nonuniform over lengths L_*. The self-field of the beam was not actually taken into account in[1]. In this paper we attempt to remedy this deficiency, with partial success for an axisymmetric beam with a rectilinear axis [2]. Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 9, No. 5, pp. 3–10, 1968.     

Electric characteristics of a probe in a subsonic plasma flow

Lam [1] and Su [2] have formulated and given some results of the solution to the problem of the concentration distributions of the charged particles and electric field in a weakly ionized plasma that flows past a conducting body (an electric probe) under the condition that the Reynolds number of the oncoming flow is high. In the present paper, this problem is solved by the method of exterior and interior asymptotic expansions with respect to a small parameter [3]. The form of the current-voltage characteristics of the probe is found as a function of the determining parameters of the problem. Data of an experimental verification of the obtained results for the case of a cold probe in a flowing air plasma containing added potassium are given.     

In situ calibration of hot wire probes in turbulent flows

A method for in situ calibration of hot-wires in a turbulent flow is presented. The method is particularly convenient (even necessary) for calibrating large probe arrays, like the 143-wire boundary layer rake of the WALLTURB experiment. It is based on polynomial expansion of the velocity statistics in terms of voltage statistics as originally described by George et al. [Exp Ther Fluid Sci 2(2):230–235, 1989]. Application of the method requires knowing reference mean velocity and higher order central moments (with the array in place) of the turbulent velocity at the probe location at only one freestream velocity. These were obtained in our experiment by a stereo PIV plane just upstream of the probe array. Both the procedure for implementing the method and sample results are presented in the article.     

Motion of a two-temperature plasma in the channel of a disc-type magnetohydrodynamic generator

A study was made of the fully developed homogeneous flow of a two-temperature partially ionized plasma in the channel of a disc-type Hall generator. Experiments with a disc-type generator are described in [1, 2]. In a simplified statement, the problem is analogous to that considered in [3]. The present article takes the chemical reactions of ionization and recombination into account. The energy equation for an electron gas is brought down to a differential form which permits clarification of the question of the applicability of the Kerrebrock [4] formula for the difference in the temperatures of the electrons and the heavy particles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 18–25, November–December, 1970.In conclusion, the author thanks V. V. Gogosov for his interest in the work and for his valuable observations.     

Investigation of a dense,chemically reacting plasma by the high-frequency probe potential modulation method

A method is proposed for investigating a chemically reacting plasma by means of an electric probe whose potential is modulated by a high-frequency sinusoidal voltage. The method is based on the use of a numerical solution of the problem of an electric probe introduced under negative potential into a steady-state low-temperature plasma formed in a mixture of chemically reacting molecular gases. The conditions under which the charged particle concentration in the region undisturbed by the probe is constant as a result of equilibrium between the ionization and recombination rates are examined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 114–119, November–December, 1987.     

Contraction of a highly nonequilibrium current-bearing plasma

Contracted is the term applied to that inhomogeneous state of a plasma in which it withdraws from the enclosing walls and concentrates in a more or less thin layer through which a current passes. Contraction is the result of instability developed in the original homogeneous state and may be related to the existence of a volt-ampere characteristic segment with negative differential conductivity. This phenomenon is known in semiconductor physics, and various instability mechanisms leading to contraction have been studied [1], Well known in a low-temperature plasma is thermal contraction connected with superheating instability of the electron gas [2–4]. In the present study we will consider a highly nonequilibrium plasma in which contraction may develop as a result of disproportion in the number of electrons, i.e., contraction of a recombination-ionization character. We consider below the homogeneous state of a nonequilibrium weakly ionized plasma with charged-particle concentration n_e- 10¹¹-10¹³ cm^–3 (electron temperature T of the order of thousands of degrees, with gas cold). Disequilibrium is produced by the departure of radiation beyond the limits of the plasma volume. Such a state will be considered with respect to the instability noted, but not studied, in [5]. As a consequence of this instability the plasma may transform to an inhomogeneous (contracted) state, which is considered under conditions such that Joulean electron heating is compensated by losses due to elastic collisions with atoms of the gas. Charge diffusion plays the basic role in establishing the boundaries dividing the currentbearing region from that without current. More complex is the situation where radiation losses of energy are also significant and superheating, as well as ionization instability, is possible. This case is evaluated briefly at the close of the study.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 45–54, January–February, 1975.     

Stability of a high-frequency glow discharge in the normal combustion regime

A high frequency glow discharge in its high current form differs from a dc discharge in that there is a significant decrease in the role of the pre-anode region in plasma generation [1], thus leading to greater stability [2]. In a dc discharge the pre-anode current-voltage characteristic (CVC) is falling [3], which causes electrodynamic instability of the plasma column and leads to its contraction over times much shorter than the thermal times [4]. It is characteristic that conductivity in the volume of a dc discharge at moderate pressures is caused by drift of ions from the pre-anode region. In an hf discharge the plasma distribution is symmetric about the midpoint of the interelectrode gap and the space charge zones near the electrodes are separated from the volume by narrow zones with high conductivity. Under such conditions, together with volume ionization processes a noticeable contribution to maintenance of conductivity can be produced by ambipolar diffusion and plasma drift due to disruption of quasineutrality [5, 6]. In order to study the stability of an hf discharge plasma column it is of interest to find the current-voltage characteristic of this part of the discharge under conditions of high longitudinal inhomogeneity and low values of E/p. In connection with the experimentally observed weak current form of the discharge [1, 2], which is characterized by a unique value of the normal current density and lacks a proper theoretical explanation, there has been increased interest in the properties of the hf discharge which are produced by phenomena in the pre-electrode regions. In particular, it is necessary to theoretically confirm the similar properties of the dc discharge and the hf discharge in the normal current density regime. The present study will present results of a numerical calculation of an hf discharge in nitrogen with consideration of space charge effects within the framework of a two-dimensional model and calculated the CVC of a plasma column with the diffusion-drift mechanism for maintenance of conductivity.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 16–26, November–December, 1986.The authors express their gratitude to N. A. Yatsenko for information provided during the course of the study, and to L. G. Gryukanov for performing the numerical calculations and assistance in formulating the results.     

Kinetics of electron recombination in a molecular gas expanding into a cavity

The kinetics of recombination in a diatomic or polyatomic gas dispersing into a cavity is investigated in a model gas with one ionization potential and one electron affinity. In addition to the recombination reaction in triple collisions, which play the most important role in the case of a monatomic gas [1], dissociative recombination, ion-atom charge transfer, and reactions involving negative ions are considered. The qualitative differences in the kinetics of recombination of a molecular gas (in comparison with a monatomic gas) are due to the smallness of the relative electron concentrations at the instant of disturbance of ionization equilibrium and to the important contribution of dissociative recombination reactions and the kinetics of formation and recombination of negative ions.In addition, owing to the greater specific heat of a polyatomic gas and the corresponding lower rate of cooling on dispersion, recombination due to collision of three charged particles is not, as distinct from the case of a monatomic gas, decisive for the asymptotic values of the adiabatic exponent and residual ionization. For this reason the values of the adiabatic exponent can be assigned irrespective of a in the solution of the equations of the kinetics of recombination of diatomic and polyatomic gases. Expressions for the instant of failure of the equilibrium relationship between electrons and, respectively, positive and negative ions are obtained.The relationship between the charged-particle concentration in a gas in ionization nonequilibrium and the time for known values of the reaction rate constants is expressed by quadratures. The values of the rate constants of some ionization processes are known only in order of magnitude. However, available data on rate constants indicate that for practically any initial data for dispersion of the products of explosion or combustion of chemical compounds ionization equilibrium is upset at a time when there is still an equilibrium ratio of concentrations of electrons and negative ions.     

Test of a new tip material for Langmuir probe diagnostic

The objective of the work is to test a nickel–chrome alloy as a probe tip material for characterization of discharge plasmas. In order to meet the objective, a symmetric triple Langmuir probe diagnostic system and an associated driving circuit are designed and tested in an inductively coupled plasma generated by a 13.56-MHz radio frequency source coupled with an automated impedance match network. This probe is used to measure the electron temperature, electron number density, and ion saturation current as functions of the input power of the radio frequency source and the filling gas pressure. An increasing trend is noticed in the electron temperature and electron number density with an increase in the input power, whilst a decreasing trend is evident in these parameters with an increase in the nitrogen gas pressure. The overall inaccuracies in electron temperature and electron number density measurements are 5–12% and 3–13%, respectively.     

Development of a local continuous sampling probe for the equivalence air–fuel ratio measurement. Application to spark ignition engine

This paper is a contribution to the development of an original technique for measuring the in-cylinder equivalence air–fuel ratio. The main objective was to construct an instrument able to furnish instantaneous values of hydrocarbon concentration for many consecutive cycles at a definite location, especially at the spark plug location. The probe is based on a hot-wire-like apparatus, but involves catalytic oxidation on the wire surface in order to be sensitive to the hydrocarbon concentration. In this paper, we present the different steps needed to develop and validate the probe. The first step focuses on the geometric configuration to simplify as much as possible the mass transfer phenomena on the wire. The second step is a parametric study to evaluate the sensitivity, confidence and lifetime of the wire. By physical analysis, we propose a relationship between the electrical signal and the air–fuel equivalence ratio of the sampled gases. The third step is the application of the probe to in-cylinder motored engine measurements, which confirms the ability of the technique to characterise, quantitatively, the homogeneity of the air–fuel mixture, especially during the compression stroke. This work points out that the global sensitivity is estimated at 4 V per unit of equivalence air–fuel ratio and the response time is estimated at about 400 μs. The equivalence air–fuel ratio range is from pure air to 1.2. Experiments show that it is necessary to calibrate the system before use because of the existence of multiple catalysis states. The probe presents advantages associated with its simplicity, its low cost and its direct engine application without any modifications. Received: 1 November 2000 / Accepted: 30 May 2001     

Numerical investigation of the expansion dynamics and generation of magnetic fields in plasma jets

The processes of interaction between concentrated energy fluxes and solid targets have been investigated in a number of studies. The generation of magnetic fields in erosional plasma formations has been experimentally observed [1–4]. However, the evolution of magnetic fields in plasma jets has not yet been studied in sufficient detail. This paper is devoted to a numerical investigation of unsteady three-dimensional erosion plasma flows and the generation in those flows of magnetic fields resulting from the action of laser radiation on solid targets. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 135–140, November–December, 1986. The authors are grateful to I. V. Nemchinov and B. T. Fedyushin for useful discussion of their results.     

High-resolution (∼0.05%) red shift of a ∼ 60 keV Kβ line upon ionization

A recent measurement [1] demonstrates that iridium's Kα₂-line, centered at ?63286.96 eV for a cold atom, increases ?+10 eV in energy when it is emitted by a modestly (～17×) ionized plasma. This measurement, enabled by a near-coincident lutetium K-edge filter, agrees well with atomic physics computations. Not understood at the time was a similar measurement with a thulium filter at the ?59370 eV energy of ytterbium's Kβ₁ line, which indicated that its photon energy decreases with ionization. The computation reported here shows that the ionization energy shift for Yb's Kβ lines is indeed negative and agrees qualitatively with the measurements. For the K-lines the ionization energy shift may be most interesting in atomic physics, while for the L-lines the ionization energy shift is a promising plasma diagnostic [2].     

Hydrodynamical Modeling of Charge Carrier Transport in Semiconductors

Enhanced functional integration in modern electron devices requires an accurate modeling of energy transport in semiconductors in order to describe high-field phenomena such as hot electron propagation, impact ionization and heat generation in the bulk material. The standard drift-diffusion models cannot cope with high-field phenomena because they do not comprise energy as a dynamical variable. Furthermore for many applications in optoelectronics one needs to describe the transient interaction of electromagnetic radiation with carriers in complex semiconductor materials and since the characteristic times are of order of the electron momentum or energy flux relaxation times, some higher moments of the distribution function must be necessarily involved. Therefore these phenomena cannot be described within the framework of the drift-diffusion equations (which are valid only in the quasi-stationary limit). Therefore generalizations of the drift-diffusion equations have been sought which would incorporate energy as a dynamical variable and also would not be restricted to quasi-stationary situations. These models are loosely speaking called hydrodynamical models. One of the earliest hydrodynamical models currently used in applications was originally put forward by Blotekjaer [1] and subsequently investigated by Baccarani and Wordeman [2] and by other authors [3]. Eventually other models have also been investigated, some including also non-parabolic effects [4–6, 8–20]. Most of the implemented hydrodynamical models suffer from serious theoretical drawbacks due to the ad hoc treatment of the closure problem (lacking a physically convincing motivation) and the modeling of the production terms (usually assumed to be of the relaxation type and this, as we shall see, leads to serious inconsistencies with the Onsager reciprocity relations). In these lectures we present a general overview of the theory underlying hydrodynamical models. In particular we investigate in depth both the closure problem and the modeling of the production terms and present a recently introduced approach based on the maximum entropy principle (physically set in the framework of extended thermodynamics [21, 22]). The considerations and the results reported in the paper are exclusively concerned with silicon.     

Use of Tikhonov’s regularization method for solving identification problem for elastic systems

We present a method for solving nonlinear inverse problems, which also include identification problems for elastic systems. The problems whose initial data contain an error are usually solved by regularization methods [1–5]. In the present paper, we give preference to Tikhonov’s regularization method, which has been widely used in the recent years in practice to increase the stability of computational algorithms for solving problems in various areas of mechanics [6–9].     

Gas flow activated in an electron-beam plasma

Probe measurements of electron temperature and density, electron energy distribution functions, and plasma potential in a free gas jet activated in an electron-beam plasma and in a planar reactor are presented. The measurements are performed by single, double, and triple electrostatic probes in jets of helium-argon and helium-argon-monosilane gas mixtures. The latter mixture is used to deposit films of microcrystalline and epitaxial silicon. Microcrystalline silicon films of higher quality are obtained in a dense (n_e ≈ 10¹⁷ m⁻³) and cold (T_e ≈ 1.0–0.5 eV) plasma with a low potential (U_sp ≈ 10 V), whereas the growth of monocrystalline silicon films requires a hotter plasma (T_e ≈ 3–5 eV) with a potential U_sp ≈ 15 V. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 3–10, January–February, 2007.     

Performance of a 12-sensor vorticity probe in the near field of a rectangular turbulent jet

The design and operational characteristics of a 12-sensor hot wire probe for three-dimensional velocity–vorticity measurements in turbulent flow fields is described and discussed. The performance of the probe is investigated in comparison with X-sensor probe measurements in the near field of a rectangular turbulent jet with aspect ratio 6. Measurements have been conducted at Reynolds number Re _D = 21,000 at nozzle distances of x/D = 1, 3, 6 and 11, where D is the width of the nozzle. The results obtained with the 12-sensor probe compare well to the results of the X-sensor probe. Distributions of mean and fluctuating velocity–vorticity fields are presented and discussed. Among the results the most prominent is the experimental confirmation of the high levels of fluctuating vorticity in the shear layers.     

Simultaneous measurement of velocity and temperature in high-temperature turbulent flows: a combination of LDV and a three-wire temperature probe

This paper deals with a simple and reliable technique for simultaneous measurement of velocity and temperature in high-temperature turbulent flows, including combustion. The technique is based on the combination of laser Doppler velocimetry and a digitally compensated fine-wire thermocouple. For temperature measurement, a two-thermocouple probe with a fine cold wire [Tagawa et al. (1998) Rev Sci Instrum 69: 3370–3378] is used, which enables in situ measurement of thermocouple time constants and accurate compensation of the thermocouple response. When tested in a turbulent wake behind a heated cylinder, the technique proves to be highly reliable and effective for investigating heat transport processes in various non-isothermal turbulent flows. Received: 24 June 1999/Accepted: 10 March 2000     

The method of geometrical optics for differential equations of the fourth order as applied to low-frequency plasma oscillations

The theory of osculations of a spatially inhomogeneous plasma [1] draws substantially on the theory of geometrical optics as applied to differential equations of the second order. The theory of asymptotic solutions for equations of the second order has now been thoroughly developed [2]. The quasi-classical quantization rules determining the spectrum of eigenvalues of such equations are written in the form of the well-known Bohr -Sommerfeld integrals [3]. However, in analyzing the spectrum of oscillations of an inhomogeneous plasma it is insufficient in many cases to confine oneself to equations of the second order. For example, in an inhomogeneous magnetoactive plasma, even when the thermal motion of the particles is neglected, the field equations, generally speaking, reduce to a differential equation of the fourth order. Equations of the fourth order also arise in investigating the stability of the hydrodynamical flow of a viscous fluid [4].Certain special forms of fourth-order equations were studied in [4–6]. The authors of [6] obtained a quasi-classical quantization rule for equations of the fourth order with a small parameter associated with the leading derivative. The present paper investigates the general fourth-order equation with real coefficients. Asymptotic solutions of such an equation are obtained with an accuracy to terms of the first order in the approximation of geometrical optics, and quasi-classical quantization rules are established for various concrete cases. Using the theory thus developed, a new spectrum of oscillations is determined, characteristic only for an inhomogeneous plasma in a magnetic field.In conclusion, the authors express their gratitude to V. P. Silin who suggested the idea of matching the quasi-classical solutions, and also to Yu. N. Dnestrovskii and D. P. Kostomarova for discussing the paper and offering valuable criticism.