Modelling of electron stream discharge

Particle-in-cell Monte Carlo code is used to simulate gas discharge initiated by a high current (I _e10kA) middle energy ( _e10keV) hot ( _e1 keV) electron stream. The generation of such an overthermal electron stream has been clearly demonstrated at the experimental REBEX facility during the relativistic electron beam-plasma interaction. When the electron beam (represented by1000 macroparticles) is injected into the drift tube filled by neutral gas (hydrogen,p=13.3–133 Pa) two different stages are observed. During the initial stage the arising Virtual Cathode (VC) is filled by hydrogen ions. The VC disappears when the quasineutrality of ionized gas is achieved. Then the severe exponential growth of electron and ion component of ionized gas is observed.List of symbols x distance from the left electrode [m] - t time [s] - v _x ,v _y velocity components [m/s] - g4(x) potential [Volt] - g4 _1/2(t) middle potential [Volt] - E(x) electric field [Volt/m] - Q _wall wall charge [C/m.m] - I current [C/s] - _tot total energy [J] - N number of macroparticles - f() energy distribution of electron macroparticles at the left electrode, is kinetic energy of macroparticle [eV]. Presented at 17^th Symposium Plasma Physics and Technology, Prague, June 13–16, 1995.     

Efficient optically pumped NH3 amplifiers in the 10–12 μm region

A pulsed transversely excited CO₂ laser operating on the 9R(30) transition is used to optically pump mixtures of NH₃ in buffer gas. A simple oscillator/amplifier system characterizes the performance of the NH₃ amplifier in the 11 m region. Small-signal gain coefficients of >10%/cm measured on the aQ(3,3) transition at 10.7 m, while pump conversion efficiencies of 50% are shown to occur under saturation conditions. The NH₃ laser system is described by a rate-equation model, which is validated by comparison with experiment over a wide range of operating conditions. Measurements are made for NH₃ concentrations ranging from 0.05 to 0.2%, with Ar, N₂, and He buffer gas pressures from 170 to 700 Torr, and for gas temperatures from 200 to 300 K. Optically pumped NH₃ is shown to be a versatile and efficient system for the amplification of mid-infrared radiation.     

Removal of NOx from NO2∶NO∶N2 mixture by a pulsed and dc streamer corona in a needle-to-plate reactor

The results of laboratory experiments on reduction of NO _x in the oxygen free gas mixture NO₂NON₂ simulating exhaust gas, by means of pulsed and dc streamer corona discharges generated in a needle-to-plate reactor have been presented. The results show that the dc corona discharge is more efficient in De-NO _x process than the pulsed corona discharge. This is in contrast to the results obtained in the wire-to-cylinder reactors where the pulsed corona discharge removes NO _x more efficiently. The results also lead to the conclusion that in the dc streamer corona discharge the short pulses and long interelectrode distances are recommended in order to increase the NO _x conversion rate.Presented at 17^th Symposium Plasma Physics and Technology, Prague, June 13–16, 1995.This work was financially supported by the Polish Academy of Sciences (projects IMP 3.1 and 3.3) and by the Polish Committee for Scientific Research (KBN Grant No. P40103304).     

Microscopic theory of gas-surface interaction

A kinetic theory for inelastic scattering, trapping and desorption of gas molecules by surfaces is described. The theory is valid if the time scale _l = 1/r introduced by the relaxation ratesr in the kinetic equations (which is of the order of the life time of vibrational states of adsorbates) is sufficiently large compared to the vibrational period ₀. For sufficiently large activation energies of the adsorbates another time constant _res, the residence time of adsorbed particles, can be determined from the theory. One thus may distinguish four different partly overlapping regimes defined by the time scalest _{I l} , ₀t_II, _l t_III and _rest_IV. Regime I is governed by the Schrödinger equation regime II by the kinetic equations. In the region where both regimes overlap the kinetic coefficients can be expressed in terms of microscopic quantities which have been calculated previously. The relevant quantities in the other regimes are introduced and discussed from a unified point of view thus providing a link between the regimes I and IV which have been treated in detail before.     

Gas‐Kinetic Temperature of Planar High‐Frequency Capacitive Discharge Plasma in N2/CO2/He Gas Mixtures

Using methods of emission spectroscopy, we have determined the gaskinetic temperature fields of planar highfrequency capacitive discharge plasma in N₂/CO₂/He gas mixtures depending on the excitation frequency, discharge current, pressure, and chemical composition of the mixture. It is shown that the dominant contribution to the neutral component heating in the center of the discharge chamber is made by the processes of V–T relaxation of vibrationally excited molecules N₂(X ¹, V) and CO₂(X ¹, V), whereas in the zones near the electrodes an important role in the heating is played, along with the V–T relaxation of the N₂(X ¹, V) and CO₂(X ¹, V) molecules, by the processes of deactivation of the metastable states A ³ of the N₂ molecule.     

Proof of the existence of the cluster free energy

LetZ _p be the partition function over internal configurational degrees of freedom of ap-particle cluster. The existence of the limit, asp, of (p)^–1 logZ _p is demonstrated for the square, triangle, hexagon, simple cubic, face-centered cubic, and body-centered cubic lattice gas models, and for continuous space models with potentials satisfying stability and tempering conditions. Pairwise, finite-range bonding is assumed throughout.Supported in part by the Robert A. Welch Foundation.     

Exact Solution of a Charge-Asymmetric Two-Dimensional Coulomb Gas

The model under consideration is an asymmetric two-dimensional Coulomb gas of positively (q ₁=+1) and negatively (q ₂=–1/2) charged pointlike particles, interacting via a logarithmic potential. This continuous system is stable against collapse of positive-negative pairs of charges for the dimensionless coupling constant (inverse temperature) <4. The mapping of the Coulomb gas is made onto the complex Bullough–Dodd model, and recent results about that integrable 2D field theory are used. The mapping provides the full thermodynamics (the free energy, the internal energy, the specific heat) and the large-distance asymptotics of the particle correlation functions, in the whole stability regime of the plasma. The results are checked by a small- expansion and close to the collapse =4 point. The comparison is made with the exactly solvable symmetric version of the model (q ₁=+1,q ₂=–1), and some fundamental changes in statistics caused by the charge asymmetry are pointed out.     

Hydrogen sulphide doping of GaAs and AlxGa1−xAs grown by molecular beam epitaxy (MBE)

H₂S gas has been used during molecular beam epitaxy (MBE) growth of GaAs and Al _x Ga_1–x As as sulphur vector forn-type doping. Doping efficiencies are less than 10^–3 at usual growth temperatures, and are limited by an incorporation competitive surface process, probably 2Ga+H₂SGa₂S+H₂. In Al_xGa_1–x As forx0.2 the doping efficiency is further reduced by carrier freeze-out at deep levels. Measured thermal activation energies depend on growth conditions and remain relatively low even up to the direct-indirect bandgap crossover for substrate temperatures in the 585–645 C range.     

Computer simulation of some dynamical properties of the Lorentz gas

We carried out molecular dynamics simulations of a Lorentz gas, consisting of a lone hydrogen molecule moving in a sea of stationary argon atoms. A Lennard-Jones form was assumed for the H₂-Ar potential. The calculations were performed at a reduced temperatureK ^* =kT/_{H 2–Ar} = 4.64 and at reduced densities ^*= _{Ar Ar} ³ in the range 0.074–0.414. The placement of Ar atoms was assumed to be random rather than dictated by equilibrium considerations. We followed the trajectories of many H₂ molecules, each of which is assigned in turn a velocity given by the Maxwell-Boltzmann distribution at the temperature of the simulation. Solving the equations of motion classically, we obtained the translational part of the incoherent dynamic structure factor for the H₂ molecule,S _tr(q, ). This was convoluted with the rotational structure factorS _rot(q, ) calculated assuming unhindered rotation to obtain the total structure factorS(q, ). Our results agree well with experimental data on this function obtained by Egelstaffet al. At the highest density ( ^*=0.414) we studied the dependence ofS(q, ) on system size (number of Ar atoms), number of H₂ molecules for which trajectories are generated, and the length of time over which these trajectories are followed.     

Clusters,metastability, and nucleation: Kinetics of first-order phase transitions

We describe and interpret computer simulations of the time evolution of a binary alloy on a cubic lattice, with nearest neighbor interactions favoring like pairs of atoms. Initially the atoms are arranged at random; the time evolution proceeds by random interchanges of nearest neighbor pairs, using probabilities compatible with the equilibrium Gibbs distribution at temperatureT. For temperatures 0.59T_c, 0.81 T_c, and 0.89T _c, with density of A atoms equal to that in the B-rich phase at coexistence, the density C₁ of clusters ofl A atoms approximately satisfies the following empirical formulas: C₁ w(1 –)³ andC ₁, (1 –)⁴Q₁w¹ (2 l 10). Herew is a parameter and we defineQ _l = _K e ^–E(K) , where the sum goes over all translationally nonequivalentl-particle clusters andE(K) is the energy of formation of the clusterK. Forl > 10,Q ₁ is not known exactly; so we use an extrapolation formulaQ _l Aw _s ^–l l ^– exp(–bl ), wherew _s is the value ofw at coexistence. The same formula (withw > w _s) also fits the observed values of C, (for small values ofl) at densities greater than the coexistence density (forT=0.59T_c): When the supersaturation is small, the simulations show apparently metastable states, a theoretical estimate of whose lifetime is compatible with the observations. For higher supersaturation the system is observed to undergo a slow process of segregation into two coexisting phases (andw therefore changes slowly with time). These results may be interpreted as a more quantitative formulation (and confirmation) of ideas used in standard nucleation theory. No evidence for a spinodal transition is found.Supported by AFOSR Grant No. 73-2430D and by ERDA Contract No. EY-76-C-02-3077*000.     

CW and pulsed FIR-CO2 hybrid laser with improved efficiency and amplitude stability at short FIR wavelengths

For the first time stable cw output of a FIR-CO₂ hybrid laser has been achieved at wavelengths shorter than 300 m. Due to the saturable absorber characteristic of the FIR laser gas, cw or pulsed emission is observed on both, the CO₂ and the FIR laser output, depending on the operating conditions. Results are reported on different resonant lines in CH₃OH and the 67 m Raman line in NH₃. The good efficiency of this laser is also demonstrated by the excitation of two new emission lines in CH₃OH, namely 49 and 56 m, pumped by 9R(22) and 9R(24), respectively.On leave from the Institute of Physics, University of Beograd YU-11000, Beograd, Yugoslavia     

Ergodic properties of infinite-dimensional stochastic systems

The ergodic properties of two stochastic models _I and _II are investigated. Each model is described by a fieldx(t),t > 0, on the lattice =Z ^d,d < . For _I,x(t) evolves according to the equations wherex _s (t) R for eachs eF. Here the {w_s(t): s } are independent, one-dimensional Wiener processes, ₂ is a bounded interaction between adjacent lattice sites, and the potentials ₁ and ₂ satisfy appropriate regularity conditions. It is shown that for each model,x(t) is a Markov process on an infinite-dimensional phase spaceX. The probability measures onX that satisfy the Dobrushin-Lanford-Ruelle (DLR) conditions are stationary for this process and have a mixing property. Moreover, for _I any stationary, time-reversal-invariant probability measure that has certain regularity properties must satisfy the DLR conditions.This paper is based on a portion of the author's Ph.D. thesis.⁽²⁾     

Analytic study of power spectra of the tent maps near band-splitting transitions

Successive band-splitting transitions occur in the one-dimensional map x_i+1=g(x_i),i=0, 1, 2,... withg(x)=x, (0 x 1/2) –x +, (1/2 <x 1) as the parameter is changed from 2 to 1. The transition point fromN (=2ⁿ) bands to 2Nbands is given by=(2)^1/N (n=0, 1,2,...). The time-correlation function _i=x_ix₀/(x₀)²,x_i x_i–x_i is studied in terms of the eigenvalues and eigenfunctions of the Frobenius-Perron operator of the map. It is shown that, near the transition point=2, _i–[(10–42)/17] _i,0-[(102-8)/51]_i,1 + [(7 + 42)/17](–1)ⁱe^–yi, where2(–2) is the damping constant and vanishes at=2, representing the critical slowing-down. This critical phenomenon is in strong contrast to the topologically invariant quantities, such as the Lyapunov exponent, which do not exhibit any anomaly at=2. The asymptotic expression for _i has been obtained by deriving an analytic form of _i for a sequence of which accumulates to 2 from the above. Near the transition point=(2)^1/N, the damping constant of _i fori N is given by _N=2(^N-2)/N. Numerical calculation is also carried out for arbitrary a and is shown to be consistent with the analytic results.     

Growth of correlation in the Hopfield model

Introducing a finite correlation ₀ between any two learned patterns (others remaining uncorrelated), we observe in a numerical simulation that the Hopfield model stores these two patterns with correlation _f such that _f0 for any loading capacity. The patterns are memorized perfectly (with _f= ₀) up to -0.05 for finite correlations ₀ not exceeding a value _c(), where _c() decreases continuously to zero at -0.05.     

The coherent K L 0 C → K S 0 C regeneration at high energies

New experimental results on the coherentK _L ⁰ C K _S ⁰ C regeneration in the momentum range 10p30 GeV/c are presented. For the quantity (f ₀–¯f ₀/k (where f₀ and¯f ₀ are theKC and¯K ⁰C forward scattering amplitudes andk is the wave number) we have obtained: arg (f ₀–¯f ₀)/k=–126±14 and ¦(f ₀–¯f ₀/k¦ p ^{–0.62±0.14} These results are well described by a simple Regge pole model including only the (-trajectory exchange in thet-channel with the intercept (0) close to 0.4.Presented at the IV International Symposium on High Energy and Elementary Particle Physics, Warszaw, September 1975.     

Diffraction Spectrum of Lattice Gas Models above T c

The diffraction spectra of lattice gas models on ^d with finite-range ferromagnetic two-body interactions above T _c or with certain rates of decay of the potential are considered. We show that these diffraction spectra almost surely exist, are ^d-periodic and consist of a pure point part and an absolutely continuous part with continuous density.     

Static and stationary axially symmetric gravitational fields of bounded sources II. solutions obtainable from Weyl's class

This paper shows that a new class of axially symmetric static electrovacuum/magnetovacuum solutions is obtainable from Weyl's class of static vacuum solutions. The new class contains an infinite set of asymptotically flat solutions (in closed form) each of which involves an arbitrary set (d, _i) of parameters. These parameters have to be interpreted as functions of massm, chargee, and higher electric/magnetic multipole moments _i of the particle. The cased = 0, _i =0 leads to the Darmois solution and the cased = 0, _i 0 leads to the results of [1]. The case d=0, e=_i=0 leads to the Schwarzschild solution, the cased 0, _i =0,e 0 leads to the Reissner-Nordström solution. To get more general examples is a lengthy but straightforward exercise.     

First-order phase transitions in finite-size strips with interfaces

Finite-size rounding of the magnetization discontinuity at the magnetic phase transition atH=0 (T<T _c ) in 2d Ising-type strips of sizeL ×L , with ± boundary conditions alongL inducing an interface of lengthL , is studied by phenomenological considerations and transfer matrix techniques. Scaling expressions are derived forL =O(L ) and also in the infinite strip limitL . Most of the results can be extended to the 3d case.     

Estimate of foil thickness by stereomicroscopy technique

The determination of foil thickness by stereomicroscopy technique is discussed. The calculation of the foil thickness is performed in a general position of the foil in an electron microscope for a general choice of the marker position. In this case the crystallographic orientation of the foil normal has to be known. But there exists a special case (markers lie in the diffraction plane) where it is not necessary to know the orientation of the foil normal. The relative error in determining the foil thickness is about 10%.List of symbols B direction in the foil parallel with the primary beam in the first micrograph - d vector describing a common straight line of and ₁ ( ₁) - F direction in the foil parallel with the primary beam in the second micrograph - g diffraction vector - M magnification - n foil normal - o vector defined byn ×B - p ₁ first coordinate ofX in the first micrograph - p ₂ first coordinate ofX in the second micrograph - p _1i ,P _2i quantitiesP ₁,P ₂ corresponding to thei-th markers on the top surface - t _B foil thickness measured in theB direction - auxiliary quantity - corresponding to thei-th markers on the top surface - t _d foil thickness measured in thed direction - t _F foil thickness in general - t _n foil thickness measured in then direction - X ₁ point in _B characterizing one of the markers - X ₂ point in _T characterizing one of the markers - X _2i X ₂ corresponding to thei-th markers on the top surface - X _g magnitude ofX _g - X _gi magnitude ofX _gi - X magnitude ofX - X vector connecting pointX ₁ withX ₂ (X X ₂–X ₁ - X _g component ofX perpendicular to the plane ₁ - X _gi X _gi corresponding to thei-th markers on the top surface - X component ofX lying in the plane ₁ - z distance between _{1 T} and the end point ofX divided by cos Greek symbols angle between ₁ and _{1 B} - angle betweeng and _T - ₁, ₂ reflection planes - plane containingn andg - m measure error - p difference betweenp ₂ andp ₁ (p=p ₂–p ₁) - P accuracy of length measurement - (t _B )_max maximum error oft _B - maximum error of - accuracy of angle measurement - angle characterizing the deviation from the foil position when symmetrical tilting is achieved - angle of tilt betweenB andF (between stereomicrographs) - _T plane describing approximately the top surface of the foil - _b plane describing approximately the bottom surface of the foil - screen plane - angle between ₁ andX - plane containingn andB - angle of tilting from starting (after inserting the foil into the microscope) to working position (position during image observation) Special symbol intersection of two planes (common straight line)     

Thes-f model with Coulomb repulsion: Thermodynamics of two atomic cluster. Spin 1/2

A cluster of two atoms described by thes-f model with Coulomb repulsion has been considered. The interaction between localized 4f electrons (S=1/2) is taken in the molecular field approximation. The thermodynamic quantities like magnetization, specific heat and correlation functions n , n , S ^z n , S ^z n , S ^z (n –n ), n n and S ⁺ a ⁺ a as functions of temperature are presented for different band fillingN=0, 0.5, 1, 1.5, 2. The dependence of Curie temperature onN is calculated. The phase diagram forN=1 (T=0K) shows the possibility of existence of two phases: paramagnetic and ferromagnetic.The Curie temperature and the specific heat as functions ofN exhibit similar trends as found in experiments on doped magnetic semiconductors.