The theory of moving striations in a D-C discharge plasma II. High current approximation

The integrodifferential equation of striations, found in the preceding part [1] of this theory, is simplified for the case when the Debye lengthl _D is vanishingly small in comparison with the wave-length of the striations. It then takes the form (51b). The still non-zero space charge field then influences the motion of the charge carriers in such a way that it takes on the character of ambipolar diffusion in the axial direction. This is expressed by the first term on the right-hand side of Eq. (51b). The second and third terms describe the influence of the space charge field on the ionization rate through the changes in the electron temperature. Thus the third (integral) term causes the oscillatory behaviour of the transient process excited by a pulse disturbance, while the second term can lead to growth of the amplitude (i.e. to amplification) of the transient wave.The transient solution of Eq. (51b) is given by the formula (73). It is in full qualitative agreement with the experiment and the quantitative agreement is also sufficient. This shows that processes found to be decisive for the very nature of moving striations [11] and for their amplification [16] do determine with sufficient accuracy even other finer properties of striations. The choice of optimum wave-length, in the conditions studied in this paper, is fulfilled by the ambipolar diffusion in the axial direction, which damps the short wave-length striations, and by the final value of the relaxation length of the electron temperature [1/a ₁, see Eq. (4)] which limits the long-distance effect of the electric space charge field on the ionization rate.In conclusion, the authors thank F. Kroupa and M. Novák for carefully reading the paper and for valuable remarks, and S. Vepek for help in the calculations.     

A contribution to the theory of the space-charge region in thin semiconductor monocrystalline films

The potential distribution in films the thickness of which is equal to or smaller than the Debye length is derived from Poisson's equation under general boundary conditions. It is shown that there exist three basic forms of this distribution depending on the densities and character of charges on both surfaces, on the geometrical thickness of the thin film and on the Debye length of the semiconductor.Notation E _S 1,E _S 2 dimensionless surface field intensities - F ₁ F ₂ space-charge functions - L _D Debye length - k Boltzmann's constant - n _b bulk electron density - N _S 1,N _S 2 concentration of surface charges - p _b bulk hole density - q electron charge - T absolute temperature - thickness of thin film measured in Debye lengths - coordinate perpendicular to the surface measured in Debye lengths - ₀ permittivity of free space - _s relative permittivity of semiconductor - dimensionless potential (multiples of kT/q) - E _cb energy of bulk conduction-band edge - E _c energy of conduction-band edge - E _i energy line that runs parallel to band edges and coincides in the bulk (assumed homogeneous) withE _ib , the intrinsic Fermi level - E _v energy of valence-band edge - E _vd energy of bulk valence-band edge - V potential     

Charge screening in a plasma with an external ionization source

An asymptotic theory for the screening of the electric field of a dust particle or a spherical probe in a plasma with an external steady and/or internal (proportional to the electron density) gas ionization source has been developed for the first time. It has been established that the screening of the charge of a spherical body adsorbing the charge of the incident plasma particles is described by a superposition of two exponentials with different screening constants. The two exponentials are retained even in the absence of nonequilibrium fluxes on the macroparticle and only in the special case of an isothermal plasma does the screening become Debye one. The screening length is determined by the ratio of the electron-ion, β_ei, and Langevin, β_L = 4πeμ_i (where μ_i is the ion mobility), recombination coefficients. If β_L ? β_ei, then it is much larger than the electron Debye length. The ions in an isothermal plasma have been found to give the same contribution to the screening as the electrons if the electron-ion recombination coefficient exceeds the Langevin ion recombination coefficient by a factor of 2 or more, β_ei ≥ 2β_L. The Vlasov equation is used to analyze the asymptotic behavior of the macroparticle potential in a collisionless plasma.     

Non-LTE Argon-plasma Composition

In this paper theory of calculation of non-LTE plasma composition is presented. The calculations are conducted for argon plasma for temperature ranges from 500 K to 30, 000 K and T _e/T _h ratios from 1 to 10. The effect of different versions of the Saha equation, Debye length, lowering of ionisation energy and pressure correction on the argon-plasma composition is evaluated. It was concluded that the modified Saha equation could not be used for calculation of non-LTE plasma composition. Application of various Debye lengths can change the electron number density by 8%. The lowering of the ionisation energy decreases the electron number density by 18%. For LTE-plasma pressure correction has a negligible effect on the electron number density.     

Electron spin relaxation of copper(II) ions in diamagnetic crystals

The electron spin-lattice and spin-spin phase relaxation measurements of Cu²⁺ ions in various crystals are reviewed and discussed. Examples of the Debye temperature determination from a wide temperature range measurements of the spin-lattice relaxation time T₁ are shown. An influence of the Jahn-Teller dynamics on T₁ is presented. The phase relaxation described by the phase memory time T_M is affected by temperature due to the spin packet width modulation by molecular motions. The T_M is anisotropic in crystals and can be different for different hyperfine lines of an EPR spectrum.     

Fractal representation of the Debye theory for studying the heat capacity of macro-and nanostructures

The traditional theory of Debye heat capacity with a single free parameter (characteristic temperature θ_D) is extended to fractal spaces taking into account two more “latent” parameters contained in it, viz., the phonon spectrum dimension d _f and dimension d determining the geometry of the skeleton of the structure under investigation. In the classical version of the Debye theory, d _f = d = 3. In the case under investigation, these parameters can assume arbitrary (including fractional) values, which is typical of materials such as polymers, colloid aggregates, and various porous structures and nanostructures, as well as materials with a complex chemical composition. The application of a fractal approach makes it possible to substantially extend the class of materials with a heat capacity described by the continual Debye approximation.     

Peak in the magnetic-field dependence of diffusion-induced thermopower for n-Bi-Sb semiconducting alloys

A peak is detected on the dependence of the diffusion-induced thermopower on transverse magnetic field in degenerate semiconducting alloys n-Bi_1?x Sb_x (0.07≤x≤0.15) doped with tellurium donor impurity. The temperature gradient is directed along the bisector axis C ₁ of the monocrystalline sample and the magnetic field is along the triad axis C ₃. The electron spectrum of the Bi-Sb alloys under investigation consists of three equivalent ellipsoids with distinctly different effective masses along the axes of the ellipsoid (m _∥/m _⊥). A simple kinetic theory shows that the presence of the peak on the diffusion thermopower is a manifestation of this strong anisotropy in the electron spectrum and of the additive contribution of all three ellipsoids to electron transport. The nonmonotonic dependence of thermopower on the transverse magnetic field makes it possible to determine the electron relaxation time, while the temperature dependence of this relaxation time can be used to separate the relaxation time for electrons scattered from ionized impurities and from acoustic phonons.     

Sondenmessung der Plasmaparameter und deren Fluktuation in Argon-Niederdruck-Schwachstrom-Säulen im transversalen Magnetfeld

This paper reports on measurements of probe noise and double probe characteristics in argon-low-pressure low-current discharges under the influence of a local transversal magnetic field. Above a critical value of magnetic field intensity B_c there are no moving striations but partially correlated fluctuations. The space distribution of probe noise (ion saturation current and floating potential) and the measured values of electron temperature and density are discussed. At B_c a characteristic value of electron temperature T_e,c ≈ 1,4 eV independent of filling pressure has been found. A first opinion on the character of the fluctuations is given.     

Dielectric relaxation in Bi12SiO20 crystals

Anomalies of the dielectric properties of undoped and aluminum-and gallium-doped crystals of Bi₁₂SiO₂₀ are investigated in the frequency and temperature range ν=10²–10⁸ Hz and T=300–800 K. They are shown to be due to Debye relaxation processes and determined by the relaxor parameters. The mechanism of electron thermal polarization is discussed. Fiz. Tverd. Tela (St. Petersburg) 39, 1223–1229 (July 1997)     

Proton magnetic relaxation in solutions of E. coli ribosomal RNA containing Mn2+ ions

A study has been made over a range of temperatures and magnetic field strengths of the spin relaxation of water protons in aqueous solutions of E. coli ribosomal RNA containing Mn²⁺ ions. The effects of the paramagnetic ions are enhanced in the presence of the RNA. As the temperature falls T ₁ passes through a minimum value, the magnitude of which is field dependent, and this is attributed to a change in dipolar relaxation mechanism from rotation of the aquocomplex to electron spin relaxation. The relevance of this work is assessed in relation to other work on proton relaxation enhancement in Mn²⁺-containing solutions of biopolymers.     

Structural relaxation investigations of glassy polystyrene by radial distribution functions

The structural relaxation of an atactic polystyrene under sub-T _g annealing at 50°C and at 70°C was investigated by the radial distribution function (RDF) derived from its wide-angle x-ray scattering (WAXS). By recording the changes in RDF (i.e., ΔH(r), where r is the radial distance from an arbitrary reference atom) after it had been annealed for a certain period of days, and taking the integration of ΔAH(r) ²dr, we found that the atom density within structural domains in a size below 15 Å was changed dramatically, but that the tendency leveled off as annealing proceeded. However, the atom density outside the domains is barely changed by sub-T _g annealing. The size of the domain is similar to the statistical segment length reported in the literature. The behavior of the domains—that the segmental relaxation inside the domains in the initial sub-T _g annealing is unconstrained by their neighbors outside the domains—is also similar to the behavior of the statistical segments. The domains are believed to be composed of a statistical segment across the center, which has about 6 styrene repeat units, and 6 equal-distanced parallel segments tangent to the edge of the domain. On the other hand, as the annealing temperature is closer to the glass transition temperature, the frozen unstable chain segments reach equilibrium sooner and with less disturbance in their conformation.     

Saturation recovery electron spin–lattice relaxation studies on benzene anion radical and its derivatives: application of Kivelson–Orbach mechanism of electron spin relaxation

The role of low-lying excited states on the spin–lattice relaxation times (T₁) of organic radicals has been investigated. To test the applicability of Kivelson's electric field fluctuation model (D. Kivelson, J. Chem. Phys. 45, 1324 (1966)), based on the Orbach mechanism of spin relaxation, the T₁s of the anion radicals of benzene, benzene-1-d, toluene, ethyl benzene, isopropyl benzene, t-butyl benzene, p-xylene, 1,2,4-trimethyl benzene and 1,3,5-trimethyl benzene in liquid solutions, with potassium cation as the counter ion, have been measured by the pulse saturation recovery technique. The energy gap between the ground and the first excited electronic states changed with the substitutions to different extent. The spin–lattice relaxation rates showed correlation with this energy gap. Anion radicals of benzene and benzene-1-d showed the shortest T₁ among the radicals studied here. A small but measurable energy splitting due to the deuterium substitution in benzene-1-d radical was obtained from the temperature dependence of T₁. Spin–lattice relaxation times of benzene anion measured here decreased monotonically in the range of ?60 to ?125 °C, in contrast to some reported claims of very unusual temperature dependence, based on the continuous wave microwave power saturation studies. Our results also showed that the ion pairing between benzene anion and potassium cation did not significantly influence the spin–lattice relaxation times.     

Experimental Evidence of Parametric Instabilities in an Unmagnetized Plasma Subjected to a Strong H.F. Electric Field

Experimental evidence of parametric excitation, by an intense external H.F. field, of an electron surface mode and an ion wave is presented. The pumping electromagnetic energy density is equal to or slightly larger than the thermal energy density of the electrons. The value of f_pc/f₀ (electron plasma frequency/external field frequency) is that for an electron surface wave. Depending on the pressure and field intensity, this decay instability can lead to three types of low frequency oscillations, with frequencies close to the ion plasma frequency. Two of these are described by Aliev and Silin's intense field theory: one is the volume ion plasma oscillation and the other a surface ion plasma oscillation. The third corresponds to no known ion eigenmode. Several other features of the theory by Aliev and co-workers are also confirmed experimentally, such as the harmonic excitation of the instability (nf₀ ≈ f_pe/√2, where n is an integer), the instability amplitude as a function of f_pe/f₀ (above threshold conditions), the value of the mismatch parameter as a function of field strength and ion mass, and the existence of a fine structure corresponding to the symmetric and antisymmetric electron surface oscillations. Even at high pump field strengths, the decay products are nearly monochromatic i.e. the plasma does not become turbulent.     

Analytical investigation into the mechanism of dielectric losses due to interlayer polarization

The theory of dielectric space-charge polarization losses describes well both the model of an inhomogeneous dielectric [1] and the polarization resulting from mosaic blocks of alkali-halide crystals [2]. The Debye frequency dependences ε*(ω) and tan δ(ω) with non-Arrhenius relaxation time are calculated in the first approximation of perturbation theory [3, 4] with the use of a nonlinear system of the Fokker-Planck and Poisson equations for the interlayer polarization with allowance for tunnel transitions of relaxation oscillators. For the Maxwell mechanism of space-charge relaxation, tan δ(ω) also has the Debye form [5]. It should be noted that in studies cited above the electric field was considered uniform, and the nonlinearity of the initial system of equations was not investigated. This paper removes these restrictions and elaborates a theory of relaxation mechanism. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 28–34, November, 2006.     

Collective Grain Interactions II. Non‐linear Collective Drag Force

It is found that the collective effects operating at large distances from the grain surface can produce substantial scattering of the ion flux and create an additional collective drag force dominant for large grain densities. The consideration is restricted to large grain charges β = Z_de ²a /T_iλ_Di ? 1 and T_i /T_e ? 1 (–eZ_d being the grain charge in units of electron charge, a being the grain size, λ_Di being the ion Debye radius and T_e,i being electron and ion temperatures, respectively). For present dusty plasma experiments β ≈ 10–50, the large charges of grains are screened non‐linearly and the ion scattering creates non‐linear drag force. The present investigation considers effects of scattering by collective grain fields at large distances from the grains. It is found that the physical reason of the importance of collective drag force, calculated in this paper, is related to presence of weakly screened collective field of grains outside the non‐linear screening distance depending on grain densities. The amplitude of this collective fields of the grains is determined by non‐linear screening at non‐linear screening radius. It is shown that for dust densities of present experiments the collective drag force related to this scattering can be of the order of the non‐linear drag force caused by scattering inside the non‐linear screening radius or even larger. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Knudsen Ion Layer Problem in the Theory of the Collisionless Sheath

The interaction of a partially ionized continuum gas with a negatively charged electrode is investigated theoretically. It is supposed that l_d ? 1, where l_d is the Debye length, l is the mean-free-path. The self-consistent solution is given for two cases: l_I ? l and l_I ～ l, l_I is the effective ionisation length. The matched asymptotic expansions method is used. The Bohm sheath criterion is shown to be satisfied automatically in the considered cases.     

Study of dipole dynamics and pre-transitional effects at isotropic to nematic phase transition by low-frequency dielectric relaxation measurements

Thermal microscopy (TM) as well as low-frequency (LF) dielectric relaxation studies are carried out on a nematic liquid crystal (NLC), viz E7 (Merck Ltd, UK). The isotropic to nematic (IN) transition temperatureT _IN determined by TM and LF-dielectric permittivity measurements agrees with the available data. Dielectric loss studies in the frequency region of 5–10?MHz indicate a relaxation (in the kHz region) akin to Debye type off-centered dispersion. The observed nematic relaxation is found to correspond to reorientation (about the short axis) of the nematic dipole to the external field. The temperature variation of the nematic relaxation frequencyf _R is found to follow an Arrhenius shift, with an activation energy of 1.7?eV. Temperature variation of the dielectric strength (Δε = ε _o ? ε_∞) and the distribution parameter α in the nematic phase are discussed. The dynamic response of the nematic dipoles and growth of pre-transitional fluctuations are found to be nonlinear in the vicinity of the IN transition. The value of the exponent α_eff = 0.072 indicates weak growth of transitional fluctuations across the IN transition.     

Magnetische Suszeptibilität von Spinsystemen mit mehreren zeitabhängigen Temperaturen

The longitudinal susceptibility of a spin system in contact with a lattice is calculated from quantum statistics in the high temperature approximation. The method is based on the concept of time dependent temperatures describing the relaxation of several partial energies 〈þ _v 〉(t). The result forχ _∥ (Ω) is a sum of Debye functions. Explicit formulas for the relaxation times and the coefficients of the Debye functions are given in terms of the Hamiltonians. Three cases are especially discussed: 1. A part of the spin system is strongly coupled to the Zeeman system. 2. The lattice is weakly coupled to the total spin system. It is shown that on certain conditions the total spin systems may be treated as isolated from the lattice. 3. A part of the spin system dependent on the static magnetic field is isolated from the rest. An example is discussed which explains recent measurements obtained in CeCl₃ · 7H₂O.     

Effect of chirality on the dynamics of domain walls in the molecular ferrimagnet [MnII(HL-pn)(H2O)][MnIII(CN)6] · 2H2O

The contributions from modes of switching, sliding, creep, and Debye relaxation of pinned domain walls to the low-frequency magnetic properties of the chiral and racemic molecular ferrimagnets [Mn^II(HL-pn)(H₂O)][Mn^III(CN)₆] · 2H₂O have been separated. It has been found that the chirality of the atomic and spin structures affects the temperatures of the transitions from the sliding mode to the creep mode and from the creep mode to the mode of Debye relaxation. In the chiral crystals, transitions to the creep and Debye relaxation modes have been observed at temperatures T = 7 and 5 K, respectively. In the racemic crystals, these transitions have been observed at temperatures T = 13 and 9 K, respectively, all other factors being equal.     

Längsfeldstärke,Elektronentemperatur, mittlere Neutralgasdichte,Ionenstromdichte auf die Wand und mittlere Entladungsstromdichte in der Freifallsäule bei hohem Ionisationsgrad

On the basis of a foregoing paper new theoretical results for the positive column at low pressure and strong ionization, especially for discharges in noble gas ion lasers, are given. The mean velocity v_n0 of the neutral atoms reemitted from the wall is taken into account. The electric conductivity is calculated for an argon plasma. The formulas connecting the electron temperature, the mean neutral gas density, and the electric field strength are derived. The electron temperature, the axial electric field intensity, the degree of ionization, the axial electron drift velocity, the ion flux to the wall, and the force density causing the main part of gas pumping along the column are calculated as functions of the product of the mean current density and the tube radius, and of v_n0 for argon. The axial drift velocity of the electrons is still smaller than the mean thermal electron velocity for high discharge currents, except at very low gas pressures. In general, the ion flux to the wall is not directly proportional to the discharge current. The factor for the determination of the charged particle density by means of probe measurements at the wall is discussed. The self-magnetic field affects the discharge only at high electron temperature, high degree of ionization, and relatively large tube radius, i.e. at high current density and low gas pressure in not too narrow discharge channels.