Anfachung und Dämpfung von Ionisationswellen in MHD-Kanälen und ihr Einfluß auf die effektive elektrische Leitfähigkeit,den effektiven Hall-Parameter und die mittlere Elektronentemperatur

The phase velocity, the amplification rate and the critical Hall parameter are theoretically determined for ionization waves in a weakly ionized plasma streaming across a strong external magnetic field and bearing a current flowing perpendicular to both the magnetic field and the stream velocity. The investigations hold for seeded rare gases at any degree of seed ionization. The critical Hall parameter β_c depends on the degree of ionization, the ionization energy and the temperatures of electron gas T₀ and neutral gas T_g · β_c is always greater than one, if 0 < T₀ — T_g ? T₀ holds. The three-dimensional treatment indicates the existence of waves with a nonvanishing wave vector component in the direction of the magnetic field. The influence of ionization waves on mean current density, mean Hall field intensity and mean electron temperature is determined up to second order terms in the relative fluctuations of the electron temperature. The amplification of ionization waves reduces the effective electric conductivity, the effective Hall parameter and the mean electron temperature compared to the undisturbed state. Similar results are also obtained for steady state homogeneous isotropic turbulence and a special case of axially symmetric turbulence. Furthermore, a component of the electric field in direction or in opposite direction to the magnetic field vector may be generated by non isotropic and non homogeneous turbulence.     

随机磁场对静电波驱动的速度扩散的影响

随机磁场改变了波与粒子之间的耦合关系。因而使波驱动的速度扩散受到影响。其结果是:波电场的横向分量可以对纵向速度扩散有贡献;∈<<1情形,扩散系数的共振峰被展宽;∈>>1情形,扩散系数的振荡效应被削弱。当随机磁场的关联时间与波的特征时间之间相对大小不同时,随机磁场产生影响的具体机制不完全相同,所造成的后果也有差别。对于接近于在垂直方向传播的波,随机磁场对速度扩散的影响一般是重要的。     

Dispersion relation for space-charge waves in a warm plasma-filled elliptical waveguide in an infinite axial magnetic field

A perfectly conducting elliptical cylinder filled with a warm plasma and immersed in an infinite axial magnetic field is considered. Using Maxwell’s equations and dielectric tensor, a Mathieu differential equation for axial component of electric field is obtained. Considering the boundary conditions, dispersion relation for waves in a plasma of warm electrons and immobile ions, which fills an elliptical waveguide and it is under the action of infinite axial magnetic field are calculated. Furthermore, dispersion relation and scalar potential in the quasi-static approximation in a cold magnetized plasma elliptical waveguide is calculated. The obtained results are graphically presented.     

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     

Magnetic field-aligned plasma expansion in critical ionizationvelocity space experiments

The temporal evolution of a plasma cloud released in an ambient plasma is studied. Time-dependent Vlasov equations for both electrons and ions, as well as the self-consistent electric field parallel to the ambient magnetic field, are solved. The initial cloud is considered to consist of cold, warm, and hot electrons with temperatures of approximately 0.2 eV, 2 eV, and 10 eV, respectively. It is found that the minor hot electrons escape the cloud; their velocity distribution function shows the typical time-of-flight dispersion feature, i.e. the average drift velocity of the escaping electrons is proportional to the distance from the cloud. The major warm electrons expand along the magnetic field lines with the corresponding ion-acoustic speed. The combined effect of the escaping hot electrons and the expanding warm ones sets up an electric potential structure that accelerates the ambient electrons into the cloud. Thus, the energy loss due to the electron escape is partly replenished. The electric field distribution in the potential structure depends on the stage of the evolution; before the rarefaction waves propagating from the edges of the cloud reach its center, the electric fields point into the cloud. After this stage the cloud divides into two subclouds, each having its own bipolar electric field. The effects of collisions on the evolution of plasma clouds are also discussed. The relevance of the results seen from the calculations are discussed in the context of space experiments on critical ionization velocity     

Modeling of stochastic forces in turbulent space plasmas

A model of a Langevin equation for electrons in turbulent, almost collisionfree magnetoactive plasmas is developed, which can form the starting point for particle simulations, especially in regions with reconnection of magnetic-field lines. The mean wave force is expressed by a friction force and a velocity derivative of the intensity of the stochastic force. The obtained expression for the Langevin force is consistent with the kinetic theory in a polarization approximation. The intensity of the stochastic force corresponds to the velocity diffusion tensor of the electrons, which is estimated for plasmas with ionacoustic turbulence using two different methods. One method is based on direct calculation of the space-time spectral density of the wave energy. The second method uses approximations of quasi-linear plasma theory. The estimates for the intensities of the stochastic forces found by the two methods differ by orders. A table of parameters of ion-acoustic waves, electron-wave collision frequencies, and intensities of stochastic-wave forces on electrons in solar flares, in the solar wind, as well as in different regions of the earth's magnetosphere is presented. Results are given for the entire ranges of available experimental data for the mean magnetic induction, mean plasma temperatures, and mean particle densities.Published from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 1, pp. 93–107, January, 1996.     

Anfachung und Dämpfung magneto-akustischer Wellen in MHD-Kanälen und ihr Einfluß auf die mittlere Stromdichte und die mittlere Hall-Feldstärke

Magneto-acoustic waves generated by fluctuations in the Hall parameter, the electric conductivity and the stream velocity are theoretically investigated in a weakly ionized plasma streaming across a strong external magnetic field and bearing a current flowing perpendicular to both magnetic field and stream velocity. The investigations hold for seeded rare gas plasmas at any degree of seed ionization but are resticted to waves propagating in parallel or antiparallel direction to the current density vector and in parallel or antiparallel direction to the stream velocity vector and to wave lengths which are small in comparsion to the interaction length which occurs as a characteristic wave length. The influence of these waves on the mean current density and the mean Hall field intensity is calculated in case of small amplitudes and low degree of seed ionization up to second order terms. Omitting Ohmic heating the dispersion equation can be solved exactly. A phase shift exists between the fluctuations in gas density and gas velocity. The phase velocity and the amplification rate depend on the wave length. Typical results are represented in a diagram. For both types of waves the phase velocity slightly rises with increasing wave length, while the amplification rate decreases. Waves propagating in opposite direction to the current density vector are amplified, if the electron velocity exceeds a critical value. They reduce the mean current density and the mean Hall field intensity. Waves propagating in opposite direction to the stream velocity vector are also amplified except for very high degrees of seed ionization. The threshold current density is greater than that for the waves of the first type approximately by the Hall parameter as factor. At extremely high degree of seed ionization the phase velocity is directed opposite to the direction occuring at weakly ionized seed. Waves of the second type decrease the mean current density, but increase the mean Hall field intensity.     

Allgemeine Berechnung der Elektronenverteilungsfunktion von schwach ionisierten Plasmen in beliebig zeitabhängigen elektromagnetischen Feldern

The behaviour of a weakly ionized plasma in external, arbitrarily time-dependent, electromagnetic fields is treated within the framework of kinetic theory. The Boltzmann kinetic equation is solved using the Lorentz ansatz, taking into account elastic collisions between electrons and neutral particles and assuming that the collision frequency is independent of the electron velocity. The drift velocity of electrons enters into the isotropic part f₀ and into the direction-dependent part f₁ of the electron distribution function. A method is given for the calculation of the drift velocity, which is calculated explicitly for the important but difficult case of a sinusoidal electric field in the presence of a magnetic switching field. f₀ and f₁ are calculated; f₀ is investigated generally. f₀ consists of an expansion in generalized Laguerre polynomials. The influence of the electromagnetic fields on the distribution function and its time variation is discussed and the relaxation behaviour is shown. The following two special cases are calculated explicitly: a linear rising electric field and a sinusoidal electric field, both in the presence of a constant magnetic field.     

Mikrophysikalische Bestimmung elektronenkinetischer Kenngrößen im binären Molekül-Mischplasma von Stickstoff und Wasserstoff I. Geschwindigkeitsverteilungsfunktion,Transportgrößen und Stoß-frequenzen für Dissoziation und Direktionisation im Mischplasma

For the low ionized anisothermal plasma in a mixture of moleculare nitrogen and molecular hydrogen the isotropic part of the velocity distribution function of the electrons is calculated and compared with the experimentally determined velocity distribution. the calculation of this distribution is performed by the help of the homogeneous and stationary electron Boltzmann-equation and takes into consideration all essential collision processes between the electrons and the N₂ and H₂ molecules. Furthermore, the calculated results of the mean energy, of the transport coefficients, of the collision frequencies for dissociation and direct ionization of the molecules, of the first Townsend coefficient of the molecules and of the collision rates for the direct ionization of the N- and H-atoms in the mixture are represented for the range 6–100 V/(cm Torr) of the reduced electric field strength and for any composition of the N₂-H₂ mixture.     

A confident source of hard X‐rays: radiation from a tokamak applicable for runaway electrons diagnosis

In a tokamak with a toroidal electric field, electrons that exceed the critical velocity are freely accelerated and can reach very high energies. These so‐called `runaway electrons' can cause severe damage to the vacuum vessel and are a dangerous source of hard X‐rays. Here the effect of toroidal electric and magnetic field changes on the characteristics of runaway electrons is reported. A possible technique for runaways diagnosis is the detection of hard X‐ray radiation; for this purpose, a scintillator (NaI) was used. Because of the high loop voltage at the beginning of a plasma, this investigation was carried out on toroidal electric field changes in the first 5 ms interval from the beginning of the plasma. In addition, the toroidal magnetic field was monitored for the whole discharge time. The results indicate that with increasing toroidal electric field the mean energy of runaway electrons rises, and also an increase in the toroidal magnetic field can result in a decrease in intensity of magnetohydrodynamic oscillations which means that for both conditions more of these high‐energy electrons will be generated.     

Driftgeschwindigkeit von Elektronen in Argon

Drift velocities of electrons in pure argon are derived from measurements of transit times in a homogeneous electric field. The electron avalanches are initiated by the light pulse of a spark, and the current of electrons is observed. The influence of the diffusion on the drift velocity measurements is taken into account.     

The nonlinear interaction of waves generated by the stimulated Raman scattering with plasma in the PALS experiment

This paper is devoted to the study of the nonlinear interaction of the waves generated by stimulated Raman scattering in plasma. The influence of nonlinear interaction of plasma wave with plasma electrons on the sum of action densities of waves generated by the laser wave is solved. The electron acceleration in the forward and backward wave fields is described. The change of the electric field of the quasimode of forward and backward plasma waves of Raman scattering given by trapping of plasma particles is calculated. Numerical results are calculated for typical parameters of the PALS experiment.     

Operatorenmethode zur Lösung der Vlasov-Gleichung mit BGK-Stoßglied und äußerem elektrischem Feld

Irreversible processes in a classical electron plasma are treated on the basis of a linearized Vlasov equation supplemented by Bhatnagar-Gross-Krook terms describing electron-electron and electron-ion collisions correctly. The infinitely extended plasma is under the action of a space- and time-dependent external electric field. A general method of solution with projection operator techniques is given which results in a system of two coupled Volterra integral equations of the convolution type for the internal electric field and the current density. From there follows the electron distribution function, the electric field in the plasma, the electrical conductivity and a very general dispersion relation including Landau and collision damping. The method given can be generalized f. i. for multicomponent plasmas and for strong external electric fields.     

平行速度剪切驱动湍流引起的粒子输运

通过离子温度梯度及平行速度剪切的准线性湍流理论，得到了由杂质离子及抵频E×B湍流所驱动的径向离子流及相应的输运系数．理论分析表明，主要离子和杂质离子的径向离子流具有相反的方向，并随着平衡流速剪切以及杂质离子的密度梯度的变化而改变．增强平行速度剪切对主要离子的约束可产生有利影响 关键词：     

Zur Theorie der Bewegung geladener Teilchen in richtungskonstanten Magnetfeldern exponentieller Zeitabhängigkeit. I. Allgemeine Theorie und Einschaltvorgang

The general solution of the equations of motion for a charged particle in a magnetic field is given for the following case: the spatially homogeneous magnetic field having a constant direction is a superposition of a field constant in time and one decreasing exponentially in time; taken into account is the influence of the electric field induced by the time dependent magnetic field and a friction force proportional to the particle velocity. The higher transcendental functions appearing in the exact solution are approximated in various ways in dependence on the values of the argument and parameters. The important case of a switching process without a friction force is investigated in detail. The higher transcendential functions can be approximated by simplier functions in such a way, that the solutions for the switching process, valid for all times, differ from the solutions in the case of a linear increasing magnetic field only by factors consisting of elementary functions. Approximated formulae of a very simple form are obtained for position, velocity, kinetic energy and magnetic moment of the particle. The particle orbits are classified and their dependence on the initial values and parameters of the magnetic fields is studied. A comparison between our results and a rectangular variation of the field shows that the latter is not a good approximation for a really exponential increasing field. Finally a detailed investigation shows that the electric field induced by the time dependent magnetic field has an important influence on the particle motion.     

Finiteness conditions for plane axisymmetric self-consistent motions of charged plasma electrons in a magnetic field

The plane axisymmetric self-consistent motions of electrons constituting a cylindrical beam is studied. The electrons move under the action of the electric field of uncompensated space self-charge against the background of plasma ions in the presence of a magnetic field. Conditions of electron movement finiteness for the given configuration of the electron beam are found.     

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.     

Electron acceleration and type II radio emission at quasi-parallel shock waves

Solar type II radio bursts are interpreted as the radio signature of shock waves travelling through the solar corona. Some of these shock waves are able to enter into the interplanetary medium and are observed as interplanetary type II bursts. The nonthermal radio emission of these bursts indicates that electrons are accelerated up to superthermal and/or relativistic velocities at the corresponding shocks. Plasma wave measurements at interplanetary shock waves support the assumption that the fundamental type II radio emission is generated by wave-wave interactions of electron plasma waves and ion acoustic waves and that the source region is located near the transition region of the shock. Therefore, the instantaneous bandwidth of type II bursts should reflect the density jump across the shock. Comparing the theoretically predicted density jump of coronal shock waves (Rankine-Hugoniot relations) and the measured instantaneous bandwidth of solar type II radio bursts it is appropriate to assume that these bursts are generated by weak supercritical quasi-parallel shock waves. Two different mechanisms for the accelaration of electrons at this kind of shock waves are investigated in the form of test particle calculations in given magnetic and electric fields. These fields have been extracted from in-situ measurements at the quasi-parallel region at Earth’s bow shock, which showed large amplitude magnetic field fluctuations (so-called SLAMS: Short Large Amplitude Magnetic Field Structures) as constituent parts. The first mechanism treats these structures as strong magnetic mirrors, at which charged particles are reflected and accelerated. Thus, thermal electrons gain energy due to multiple reflections between two approaching SLAMS. The second mechanism shows that it is possible to accelerate electrons inside a single SLAMS due to a noncoplanar component of the magnetic field in these structures. Both mechanism are described in the form of test particle calculations, which are supplemented by calculations according to adiabatic theory. The results are discussed for circumstances in the solar corona and in interplanetary space.