Velocity distribution of plasma electrons in the negative H2- and He-glow with superimposed longitudinal magnetic field

The negative glow plasma has been found nearly field free in axial direction. Therefore plasma electrons in the stationary glow can thermalize down to the temperature of the neutral gas, whenever their diffusion—and recombination—lifetime is high enough. Applying Boltzmann's equation to this problem, the conditions of thermalization of plasma electrons are derived as a function of the outer parameters of the plasma: vessel diameter 2R, neutral gas pressurep and longitudinal magnetic fieldB. — If plasma electrons have a too short diffusion—and recombination—lifetime to be in thermal equilibrium with the neutral gas, the electron energy increases. For this case the distribution function of plasma electrons is derived using Boltzmann's equation. Approximating the calculated energy distribution by a Maxwellian distribution function, the electron temperature in the glow is obtained as a function of the parameters:R, p, B. OurT _e -measurements carried out in the H₂- and He-glows of different tube diameters, neutral gas pressures and magnetic fields agree closely with the theoretical results. TheT _e -measurements have been performed with Langmuir probes and by the method of reversal of the radial ambipolar electric field in a longitudinal magnetic field.     

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.     

Development of ionization in nonequilibrium inert-gas plasmas in magnetogasdynamic channels

Effects accompanying the interaction of a flow of preionized inert gas with a magnetic field are studied: selective electron heating, the development of nonequilibrium ionization, and the onset of the ionization instability. Local and average densities and temperatures of the electrons are measured and the average ionization rate is determined. It is found that the average electron density increases as the magnetic induction is raised, in both stable and ionization unstable plasmas. The difference in the rates at which ionization develops in these two states is revealed. The mechanism for the coupling between the average ionization rate in an ionization unstable plasma and the spatial-temporal characteristics of the plasma inhomogeneities is established. Zh. Tekh. Fiz. 69, 56–61 (November 1999)     

Imaginary-time method in quantum mechanics and field theory

An imaginary-time method was developed for calculating the probability of particle transmission through smooth barriers variable with time. Within the imaginary-time method, the tunneling process is described by using classical equations of motion written in terms of an imaginary time (t → it), while the probability of tunneling is determined by the imaginary part of the action functional, this imaginary part being calculated along the subbarrier particle trajectory. The fundamentals of the imaginary-time method are surveyed, and its applications in the theory of atomic-state ionization under the effect of constant electric and magnetic fields that have various configurations, in the field of intense monochromatic laser radiation and of an ultrashort electromagnetic pulse, in the process of Lorentz ionization of atoms and ions during their motion in a strong magnetic field, etc., are outlined. The applications of the imaginary-time method in relativistic cases—for example, in the theory of ionization of levels of multiply charged ions whose binding energy is commensurate with the electron rest energy—and in quantum field theory (Schwinger effect, which consists in the production of electron-positron pairs from a vacuum by a superstrong external field) are briefly described. Particular attention is given to methodological issues and details of the imaginary-time method that are of importance in solving specific physics problems, but which are usually skipped in original publications.     

Stationary collisionless shock waves in an initial plasma with high ion temperature

Stationary collisonless shock waves propagating perpendicularly to an initial magnetic field are produced by the fast-rising magnetic field \((\dot B = 7 \cdot 10^{10} G/sec)\) of a theta pinch (coil diameter 16 cm, coil length 60 cm). The initial plasma is produced by a fast theta pinch discharge (810 kHz). At filling pressures between 5 and 15 mtorr H₂ or D₂ the degree of ionization is about 50%. By choosing the filling pressure properly it is possible to trap a homogeneous magnetic field. The ions of this plasma have a temperature of a few 10 eV. This value is much higher than the electron temperature and results in a local plasmaβ between 0.3 and 5. In this initial plasma stationary collisionless shock waves with Mach numbers between 1.5 and 5 are observed. The snow-plough model is used to derive conditions for the stationary state, attainable Mach number, and velocity of the front which relate the external magnetic field and the parameters of the initial plasma. Strong collisionless dissipation can be demonstrated by measuring the profiles of magnetic field, density, and electron temperature of the shock waves. For the electrons this dissipation mechanism can be described by an effective collison frequency. This phenomenologically introduced frequency determines the width of the shock front at least for subcritical shock waves. It exceeds the classical electron-ion collision frequency by 1–2 orders of magnitude and is roughly equal to one-third of the ion plasma frequency. The ion temperature can be estimated from the steady state conservation relations. The ions are heated in the two degrees of freedom perpendicular to the magnetic field. For shock waves with Mach numbers below the critical one the ions seem to be heated merely adiabatically. In strong shock waves this heating is considerably exceeded, and for high Mach numbers it yields ion temperatures up to about 500 eV. Finally, semi-empirical formulas are derived to estimate the possible temperatures of electrons and ions behind the shock front.     

Entstehung und Eigenschaften des Halo bei Pinch-Plasmen

In pinch discharges a second plasma regime called halo^1,2 outside the central plasma column^1-4 has been observed. This surrounding plasma was investigated in the experiments with the 5.4 m long compression coil in the ISARI linear theta pinch because there it appears highly pronounced. The development of the discharge was observed side-on (stereoscopic) with image converters and a streak camera. It appears possible to resolve the space-time behaviour of the plasma, especially in the dynamic phase of the discharge where the halo shows a filament like structure, by using high-speed color reversal film (streak camera). Furthermore, the smear pictures show that after 6–8 μsec the halo region is frozen into the external magnetic field, that is from this time the halo is characterized by a high electrical conductivity. The boundary layer of the halo follows a magnetic flux tube. The parameters of the halo, such as electron densityn _e (< 10¹⁵ cm^?3), atomic temperatureT _a , and ion temperatureT _i (< 15 eV), were determined spectroscopically as a function of time and location from the broadening of the deuterium Balmer lines. The absolutely measured line intensities do not allow direct calculation of the electron temperature since the excited levels of the investigated Balmer lines are mainly populated from the ground level. By numerical solution of a system of rate equations describing the change of the levels a region for the electron temperature 5<T _e <10eV can be specified. Different mechanisms, such as photoionization, ionization by electron impact in a time varying magnetic field, ionizing collisions of high velocity neutral atoms with neutral gas at rest, transport processes in the plasma across the magnetic field, instabilities which may cause the development of the halo, are discussed by means of the experimental results. It is concluded that the halo region is caused by flute instabilities.     

Measuring magnetic fields in plasmas by means of light scattering

The theory of light scattering in plasmas containing a magnetic field yields the special case of modulated scattering spectra. The modulation frequency is governed by the field in the plasma and is equal to the electron cyclotron frequency. In this investigation magnetic fields in a plasma were determined by a laser scattering experiment. The experimental data were: electron densityn _e=10¹⁶cm^?3, electron temperatureT _e=3.2 eV, scattering angle θ=90 °, scattering parameter α=0.6, and a maximum field in the plasma of 125 kG. The spectrum measured at the maximum magnetic field was modulated with 3.6 × 10¹¹ Hz. In scattering experiments with a field reduced by about 20% the observed modulation frequency was 2.8 × 10¹¹ Hz. A thermal spectrum with a smooth profile was found when no field was present in the plasma. Applying the theory of cyclotron modulated spectra one obtains from the scattering experiment magnetic fields of 128, 100, and 0 kG. Within the experimental accuracy these values agree well with the fields determined by means of magnetic probes. Other possible interpretations of the measured deviations from thermal spectra (modulation with the plasma frequency or additional cold electron components in the plasma) are discussed, but they afford no explanation. This experiment has domonstrated that magnetic fields in plasmas can be measured locally and almost without disturbance by means of light scattering.     

电子回旋共振等离子体密度均匀性的数值研究

基于漂移扩散近似,在轴对称假设下,对电子回旋共振等离子体源腔室内的等离子体建立了二维流体模型.采用有限差分法对所建立的模型进行了自洽数值模拟,得到了等离子体密度均匀性随时间演化的数值结果.通过对数值结果的分析,研究了背景气体压强、微波功率和磁场线圈电流对等离子体密度均匀性的影响.研究表明,在电离初期,电子密度的均匀性好于离子密度的均匀性.在电离后期,离子密度的均匀性好于电子密度的均匀性.随着背景气体压强的增大,电子密度和离子密度的均匀性都在增加,且离子密度的均匀性增加的更快.随着微波功率的增大,电子密度和 关键词： 等离子体密度均匀性 背景气体压强 微波功率 磁场线圈电流     

Microwave spectroscopy of the Zeeman effect in Rydberg atoms of sodium

Experimental results of studying the spectrum of the microwave 37P-37S transition of Rydberg sodium atoms in a weak magnetic field (≤7 G) are reported. The populations of the Rydberg states were measured using the method of selective ionization with a pulsed electric field. When the magnetic field was parallel to the ionizing electric field, a good agreement between the calculated and experimental spectral shapes was observed, making it possible to determine the unknown polarization of the microwave radiation. In the case of the orthogonal configuration of the fields, the resonance structure was suppressed in the field ionization signals due to the strong influence of the magnetic field on the electron trajectories in the detection system.     

Electron distribution function and recombination coefficient in ultracold plasma in a magnetic field

The electron distribution function and diffusion coefficient in energy space have been calculated for the first time for a weakly coupled ultracold plasma in a magnetic field in the range of magnetic fields B = 100?50000 G for various temperatures. The dependence of these characteristics on the magnetic field is analyzed and the distribution function is shown to depend on the electron energy shift in a magnetic field. The position of the “bottleneck” of the distribution function has been found to be shifted toward negative energies with increasing magnetic field. The electron velocity autocorrelators as a function of the magnetic field have been calculated; their behavior suggests that the frequency of collisions between charged particles decreases significantly with increasing magnetic field. The collisional recombination coefficient α _B has been calculated in the diffusion approximation for a weakly coupled ultracold plasma in a magnetic field. An increase in magnetic field is shown to lead to a decrease in α _B and this decrease can be several orders of magnitude.     

Theoretical investigation of tunable polarized broadband terahertz radiation from magnetized gas plasma

The mechanism of terahertz(THz) pulse generation with a static magnetic field imposed on a gas plasma is theoretically investigated. The investigation demonstrates that the static magnetic field alters the electron motion during the optical field ionization of gas, leading to a two-dimensional asymmetric acceleration process of the ionized electrons. Simulation results reveal that elliptically or circularly polarized broadband THz radiation can be generated with an external static magnetic field imposed along the propagation direction of the two-color laser. The polarization of the THz radiation can be tuned by the strength of the external static magnetic field.     

Ionization formation of plasma inhomogeneity by the near-zone field of a magnetic-type source in a magnetized plasma

An investigations is made of the steady-state structure of a plasma inhomogeneity arising as a result of high-frequency heating and additional ionization of a background magnetized plasma by the near-zone field of a magnetic-type source (ring electric current). It is assumed that the source axis is parallel to an external magnetic field; the source frequency belongs in the low hybrid band. The main attention is focused on the particular case (important for possible applications) when the characteristic longitudinal and transverse scales of density distribution considerably exceed the corresponding scales of distribution of the electron temperature and of the source field. Simplified equations for the near-zone field of the source, the electron temperature, and the plasma density are written for this particular case. Based on the numerical solution of these equations, steady-state distributions of plasma parameters in the formed plasma inhomogeneity are found. It is demonstrated that a plasma inhomogeneity proves to be markedly extended along the external magnetic field. It is found that, for the values of the source current that are attainable under the conditions of active ionospheric and model laboratory experiments, the maximum plasma density in a nonuniform plasma may appreciably exceed the background value.     

Mikrowellenabsorption in der Nähe der 2. Harmonischen der Elektronenzyklotronfrequenz

In plasmas produced by microwave power the electron density displays a dependence on the magnetic field strength obviously asymmetric with respect to the harmonics of the electron cyclotron frequency. In regions of the magnetic field strength just above the harmonics there are extremely high values of electron density, the density values dropping sharply off towards the other wing of the harmonics. Absorption experiments near the second harmonic at low microwave power — the plasma being produced by different means — reveal a resonant absorption structure in the magnetic field region above the harmonic. This can be attributed to excitation of geometrical eigenmodes of electrostatic. waves propagating perpendicular to the magnetic field (Bernstein waves).     

Calculation of cross sections of simultaneous ionization in ion-atom collisions by the generalized geometrical model

The geometrical model (GM) of ionization in ion—atom collisions [8, 9] was generalized to describe ionization of both colliding particles (simultaneous ionization) due to electron—electron interaction. The generalized GM (GGM) allows calculation of the cross sections for electron loss by an incident particle with simultaneous target ionization at collision velocities higher than characteristic electron velocities, accurate within a factor of two with respect to the Born or impulse approximation. An advantage of the GGM, except for its simplicity, is easy calculation of p(b) (p is the ionization probability and b is the impact parameter), which makes it possible to include the contribution of simultaneous ionization into more general approximate schemes for calculating cross sections of multielectron ionization of atoms or ions.     

Observation of collisionless plasma heating by strong shock waves

The heating of a plasma by collisionless shock waves is investigated by measuring the variation of magnetic field (with magnetic probes), density and electron temperature (from Thomson scattering of laser light) in the shock waves. The compression waves are produced in a tube of 14 cm diameter by the fast rising magnetic field (12 kG in 0.5Μsec) of a theta pinch. For shocks with Mach numbers between 2 and 3 propagating into a hydrogen or deuterium plasma with a localΒ of about 1 (Β=ratio of particle pressure to magnetic pressure) the measured jump in density and magnetic field across the front is 2 to 4, and the electron temperature increases in the front from 3 to 50 eV with a further rise to between 100 and 250 eV in the piston region. Only about 20% of the measured electron heating can be explained by adiabatic heating and resistive heating based on binary collisions, indicating a high turbulent plasma resistance. Both the observed electron heating and the width of the shock front, which is about 0.6 ·c/Ω _p, can be accounted for using an effective collision frequency close to the ion plasma frequencyΩ _p. The ion heating in the almost stationary shock fronts can be inferred indirectly from the steady state conservation relations. For shock waves with Mach numbersM<M _crit it seems to be consistent with an adiabatic heating process, whereas forM>M _crit the calculated ion temperatures exceed those one would except for a merely adiabatic heating.     

Structure of an extended plasma jet in a vacuum arc in an axial magnetic field

The motion, heating, and ionization of a plasma in a ring anode vacuum arc in an axial magnetic field are studied using a quasi-one-dimensional MHD model. The region between the cathode and anode (a current-carrying plasma jet), as well as the region behind the anode (a current-free plasma jet), is considered. It is shown that, over a long portion of a current-free plasma jet, the electron density and temperature remain high and the ion charge increases substantially due to electron-impact ionization.     

Combined breakdown in bismuth—Antimony semiconductor alloys

S-shaped current-voltage characteristics for Bi_1?xSb_x alloys are studied theoretically and experimentally. The phenomenon is shown to occur due to the combined interband breakdown, the impact ionization being caused both by the external electric field and the Hall field. The latter is governed by the proper magnetic field of the plasma current. The negative differential resistance (NDR) occurs for the range of currents where the impact ionization is growing intensively but the pinch effect is not yet developed to full extent. The phenomenon is enhanced if the impact ionization rate in the Hall field is greater than in the applied one.     

Excited atoms in argon gas discharge plasma

General principles are discussed for a gas discharge plasma involving excited atoms where electron-atom collision processes dominate. It is shown that an optimal kinetic model of this plasma at not large electric field strengths can be based on the rate constants of quenching excited atom states by electron impact. The self-consistent character of atom excitation in gas discharge plasma is important and results in the tail of the energy distribution function of electrons being affected by the excitation process, which in turn influences the excitation rate. These principles are applied to an argon gas discharge plasma where excitation and ionization processes have a stepwise character and proceed via formation of argon atom states with the electron shell 3p ⁵4s.     

Z-pinch dynamics under the combined breakdown in bismuth-antimony alloys

Time scans of the electric field in n-Bi_0.9Sb_0.1 samples are calculated under the impact ionization for various field orientations with respect to the crystal axes (the conditions of current given). The strong anisotropy of the pinch characteristics in the electron-hole plasma of such alloys is shown to be caused by the joint effect of the hole mobility anisotropy in the T-valley and the combined breakdown, the impact ionization being produced both by the external electric field and the Hall field. The magnitude of the latter is governed by the proper magnetic field of the current. The results explain the experimental data of Brandt et al. [1] who have observed the dynamical characteristics of the pinch in the above mentioned alloys to be strongly anisotropic.     

Instabilities of electron-hole plasma under impact ionization and microwave emission

The nonlinear stage of the evolution of electron—hole plasma instabilities in semiconductors under impact ionization (static differential conductivity σ_d > 0) is considered for the case of spatially uniform pertubations of density and electric field. If the differential mobility of carriers μ _d > 0, the instability arises only with allowance for the retardation of the process of impact ionization (linear theory of this effect was developed by M. Toda [4]). When μ _d < 0, the instability may appear in the absence of the retardation. Both these instabilities exhibit oscillating form and are due to h.f. negative dynamic differential conductivity. We determine time sweeps of the electric field under condition of fixed current for the case n-InSb at T = 77 K. The amplitude and the frequency (f>10¹⁰Hz) of the oscillations are evaluated and the conditions, when the shape of E(t)-oscillations is essentially non-harmonic, are determined. Microwave emission observed in semiconductors under impact ionization may have resulted from the instabilities at hand.