WAVENUMBER PREDICTION OF WAVES IN BURIED PIPES FOR WATER LEAK DETECTION

Water leaks are a topic of great concern in Britain and many other countries, because of decreasing water supplies and the deterioration of old pipework. Correlation techniques are widely used in leak detection, but for these to be effective, the propagation wavespeeds and wave attenuation must be known. Relatively predictable for metal pipes, these are largely unknown for the newer plastic pipes, being highly dependent on the pipe wall properties and the surrounding medium. In this paper, pipe equations for n=0 axisymmetric wave motion are derived for a fluid-filled pipe, surrounded by an infinite elastic medium which can support both longitudinal and shear waves. These equations are solved for two wave types,s =1,2, which correspond to a fluid dominated wave and an axial shell wave, and expressions for a complex wavenumber for each wave are given.     

Promoting inertial cavitation by nonlinear frequency mixing in a bifrequency focused ultrasound beam

Enhancing cavitation activity with minimal acoustic intensities could be interesting in a variety of therapeutic applications where mechanical effects of cavitation are needed with minimal heating of surrounding tissues. The present work focuses on the relative efficiency of a signal combining two neighbouring frequencies and a one-frequency signal for initiating ultrasound inertial cavitation. Experiments were carried out in a water tank, using a 550 kHz piezoelectric composite spherical transducer focused on targets with 46 μm roughness. The acoustic signal scattered, either by the target or by the cavitation bubbles, is filtered using a spectral and cepstral-like method to obtain an inertial cavitation activity measurement. The ultrasound excitations consist of 1.8 ms single bursts of single frequency f₀ = 550 kHz excitation, in the monofrequency case, and of dual frequency f₁ = 535 kHz and f₂ = 565 kHz excitation, in the bifrequency case. It is shown that depending on the value of the monofrequency cavitation threshold intensity the bifrequency excitation can increase or reduce the cavitation threshold. The analysis of the thresholds indicates that the mechanisms involved are nonlinear. The progress of the cavitation activity beyond the cavitation threshold is also studied. The slope of the cavitation activity considered as a function of the acoustic intensity is always steeper in the case of the bifrequency excitation. This means that the delimitation of the region where cavitation occurs should be cleaner than with a classical monofrequency excitation.     

Entanglement dynamics for two interacting spins

We study the dynamical generation of entanglement for a very simple system: a pair of interacting spins, s₁ and s₂, in a constant magnetic field. Two different situations are considered: (a) s₁ → ∞, s₂ = 1/2 and (b) s₁ = s₂ → ∞, corresponding, respectively, to a quantum degree of freedom coupled to a semiclassical one (a qubit in contact with an environment) and a fully semiclassical system, which in this case displays chaotic behavior. Relations between quantum entanglement and classical dynamics are investigated.     

Acoustic backscattering enhancements resulting from the interaction of an obliquely incident plane wave with an infinite cylinder

Background and objective

The analysis of the acoustic backscattering enhancements from tilted cylinders is of particular importance in determining some of the (visco)elastic properties of the cylinder, and/or its surrounding fluid in ultrasonic non-destructive evaluation (NDE) and imaging (NDI) applications. Previous related investigations on an aluminum cylinder limited to incidence angles varying from 0° to 40°, revealed the existence of an anomalous “pseudo-Rayleigh” mode (above the critical Rayleigh angle) identified as the rigid-body translational dipole (n = 1) mode. The objective here is to provide a complete investigation on the backscattering enhancements for incidence angles larger than 40° for various elastic and viscoelastic cylinder materials.

Method

Using the partial-wave series solution for the linear scattering by an infinite circular cylinder, the acoustic backscattering from isotropic elastic and viscoelastic (polymer-type) cylinders excited by an obliquely incident plane acoustic wave is investigated. Total and resonance backscattering form functions are calculated for several elastic and viscoelastic cylinder materials immersed in water versus the angle of incidence 0° ? α < 90°. The “pure” resonance peaks are isolated by subtracting a rigid background from the total form function, so the associated resonance modes are properly identified.

Results and conclusion

The plots of the partial-wave series reveal acoustic backscattering enhancements (not shown in previous investigations) generally occurring at ka? 0.1 at a critical angle α_c bounded by the longitudinal and shear waves coupling angles θ_L=sin^-1(c/c_L) and θ_S=sin^-1(c/c_S) such that θ_L<α_c<θ_S (where c_L and c_S are the phase velocities of the longitudinal and shear waves inside the elastic cylinder, and c is the speed of sound in the surrounding medium). It is shown here that the backscattering enhancements with a critical angle θ_L<α_c<θ_S result from the excitation of the monopole (n = 0) resonance mode. Moreover, additional acoustic backscattering enhancements still occur in the range 1 ?ka? 6 even though the angle of tilt is greater than the Rayleigh wave coupling angle θ_R=sin^-1(c/c_R) (where c_R is the Rayleigh wave velocity in an elastic half-space). The resonance scattering theory shows that such additional enhancements are associated with the excitation of a dipole (n = 1) resonance mode which may result from the interference of meridional and/or helical waves propagating along the cylinder’s surface. It is therefore essential to consider tilt angles ranging from normal to end-on incidence for a complete analysis of the backscattering by elastic and viscoelastic cylinders.     

Quantum amplitudes in black-hole evaporation: Spins 1 and 2

Quantum amplitudes for s = 1 Maxwell fields and for s = 2 linearised gravitational-wave perturbations of a spherically symmetric Einstein/massless scalar background, describing gravitational collapse to a black hole, are treated by analogy with the previous treatment of s = 0 scalar-field perturbations of gravitational collapse at late times. Both the spin-1 and the spin-2 perturbations split into parts with odd and even parity. Their detailed angular behaviour is analysed, as well as their behaviour under infinitesimal coordinate transformations and their linearised field equations. In general, we work in the Regge-Wheeler gauge, except that, at a certain point, it becomes necessary to make a gauge transformation to an asymptotically flat gauge, such that the metric perturbations have the expected fall-off behaviour at large radii. In both the s = 1 and s = 2 cases, we isolate suitable ‘coordinate’ variables which can be taken as boundary data on a final space-like hypersurface Σ_F. (For simplicity of exposition, we take the data on the initial surface Σ_I to be exactly spherically symmetric.) The (large) Lorentzian proper-time interval between Σ_I and Σ_F, measured at spatial infinity, is denoted by T. We then consider the classical boundary-value problem and calculate the second-variation classical Lorentzian action , on the assumption that the time interval T has been rotated into the complex: T → |T| exp (−iθ), for 0 < θ ? π/2. This complexified classical boundary-value problem is expected to be well-posed, in contrast to the boundary-value problem in the Lorentzian-signature case (θ = 0), which is badly posed, since it refers to hyperbolic or wave-like field equations. Following Feynman, we recover the Lorentzian quantum amplitude by taking the limit as θ → 0₊ of the semi-classical amplitude . The boundary data for s = 1 involve the (Maxwell) magnetic field, while the data for s = 2 involve the magnetic part of the Weyl curvature tensor. These relations are also investigated, using 2-component spinor language, in terms of the Maxwell field strength ?_AB = ?_(AB) and the Weyl spinor Ψ_ABCD = Ψ_(ABCD). The magnetic boundary conditions are related to each other and to the natural boundary conditions by supersymmetry.     

The controlled excitation of forbidden transitions in the two-photon spectrum of strontium by using collisions and electric fields

We present experimental results involving controlled configuration mixing in two-photon spectroscopy of highly-excited states by exploiting a weak external electric field and collisions. The method has allowed new extensions to high members of the two-photon forbidden J = 3 odd-parity 5snf ¹F₃ and the J = 0, even-parity 5sns ¹S₀ Rydberg series of neutral strontium to be observed. We achieve resonant two-photon transverse excitation of a high density atomic jet by using a narrow bandwidth tunable dye laser in a heat pipe setup with sensitive ionization detection. Experimental term values are extended for the 5sns ¹S₀ series up to n = 46. By suitable exploitation of the composition and pressure of the buffer gases in conjunction with the electric field strength in the excitation region and the exciting laser beam intensity we have also extended observations up to n = 44 for the 5snf ¹F₃ series and up to n = 46 for the 5snp ¹P₁ series. Our results demonstrate a novel and remarkably simple experimental method to access high Rydberg states to which transitions are forbidden from the ground state by parity and other selection rules.     

Heat treatment effects on microstructure and magnetic properties of Mn-Zn ferrite powders

Mn-Zn ferrite powders (Mn_0.5Zn_0.5Fe₂O₄) were prepared by the nitrate-citrate auto-combustion method and subsequently annealed in air or argon. The effects of heat treatment temperature on crystalline phases formation, microstructure and magnetic properties of Mn-Zn ferrite were investigated by X-ray diffraction, thermogravimetric and differential thermal analysis, scanning electron microscopy and vibrating sample magnetometer. Ferrites decomposed to Fe₂O₃ and Mn₂O₃ after annealing above 550 °C in air, and had poor magnetic properties. However, Fe₂O₃ and Mn₂O₃ were dissolved after ferrites annealing above 1100 °C. Moreover, the 1200 °C annealed sample showed pure ferrite phase, larger saturation magnetization (M_s=48.15 emu g⁻¹) and lower coercivity (H_c=51 Oe) compared with the auto-combusted ferrite powder (M_s=44.32 emu g⁻¹, H_c=70 Oe). The 600 °C air annealed sample had the largest saturation magnetization (M_s=56.37 emu g⁻¹) and the lowest coercivity (H_c=32 Oe) due to the presence of pure ferrite spinel phase, its microstructure and crystalline size.     

Effects of rapid thermal annealing on structural, magnetic and optical properties of Ni-doped ZnO thin films

XPS depth profiles were used to investigate the effects of rapid thermal annealing under varying conditions on the structural, magnetic and optical properties of Ni-doped ZnO thin films. Oxidization of metallic Ni from its metallic state to two-valence oxidation state occurred in the film annealed in air at 600 °C, while reduction of Ni²⁺ from its two-valence oxidation state to metallic state occurred in the film annealed in Ar at 600 and 800 °C. In addition, there appeared to be significant diffusion of Ni from the bottom to the top surface of the film during annealing in Ar at 800 °C. Both as-deposited and annealed thin films displayed obvious room temperature ferromagnetism (RTFM) which was from metallic Ni, Ni²⁺ or both with two distinct mechanisms. Furthermore, a significant improvement in saturation magnetization (M_s) in the films was observed after annealing in air (M_s = 0.036 μ_B/Ni) or Ar (M_s = 0.033 μ_B/Ni) at 600 °C compared to that in as-deposited film (M_s = 0.017 μ_B/Ni). An even higher M_s value was observed in the film annealed in Ar at 800 °C (M_s = 0.055 μ_B/Ni) compared to that at 600 °C mainly due to the diffusion of Ni. The ultraviolet emission of the Ni-doped ZnO thin film was restored during annealing in Ar at 800 °C, which was also attributed to the diffusion of Ni.     

Acoustic scattering of a high-order Bessel beam by an elastic sphere

The exact analytical solution for the scattering of a generalized (or “hollow”) acoustic Bessel beam in water by an elastic sphere centered on the beam is presented. The far-field acoustic scattering field is expressed as a partial wave series involving the scattering angle relative to the beam axis and the half-conical angle of the wave vector components of the generalized Bessel beam. The sphere is assumed to have isotropic elastic material properties so that the nth partial wave amplitude for plane wave scattering is proportional to a known partial-wave coefficient. The transverse acoustic scattering field is investigated versus the dimensionless parameter ka(k is the wave vector, a radius of the sphere) as well as the polar angle θ for a specific dimensionless frequency and half-cone angle β. For higher-order generalized beams, the acoustic scattering vanishes in the backward (θ = π) and forward (θ = 0) directions along the beam axis. Moreover it is possible to suppress the excitation of certain resonances of an elastic sphere by appropriate selection of the generalized Bessel beam parameters.     

Effects of oxygen partial pressure and substrate temperature on the structure and optical properties of MgxZn1−xO thin films prepared by magnetron sputtering

Deposited with different oxygen partial pressures and substrate temperatures, Mg_xZn_1−xO thin films were prepared using a Mg_0.6Zn_0.4O ceramic target by magnetron sputtering. The structural and optical properties of the prepared thin films were investigated. The X-ray diffraction spectra reveal that all the films on quartz substrate are grown along (2 0 0) orientation with cubic structure. The lattice constant decreases and the crystallite size increases with the increase of substrate temperature. Both energy dispersive X-ray spectroscopy and calculated results suggest the ratio of Mg/Zn increases with increasing substrate temperature. The thin film deposited with T_s = 500 °C has a minimal rms roughness of 7.37 nm. The transmittance of all the films is higher than 85% in the visual region. The optical band gap is not sensitive to the oxygen partial pressure, while it increases from 5.63 eV for T_s = 100 °C to 5.95 eV for T_s = 700 °C. In addition, the refractive indices calculated from transmission spectra are sensitive to the substrate temperature. The photoluminescence spectra of Mg_xZn_1−xO thin films excited by 330 nm ultraviolet light indicate that the peak intensity of the spectra is influenced by the oxygen partial pressure and substrate temperature.     

Defects in nanocrystalline Nb films: Effect of sputtering temperature

Thin niobium (Nb) films (thickness 350-400 nm) were prepared on (1 0 0)Si substrate in a UHV chamber using the cathode beam sputtering. The sputtering temperature T_s was varied from 40 up to 500 °C and the influence of the sputtering temperature on the microstructure of thin Nb films was investigated. Defect studies of the thin Nb films sputtered at various temperatures were performed by slow positron implantation spectroscopy (SPIS) with measurement of the Doppler broadening of the annihilation line. SPIS was combined with transmission electron microscopy (TEM) and X-ray diffraction (XRD). We have found that the films sputtered at T_s = 40 °C exhibit elongated, column-like nanocrystalline grains. No significant increase of grain size with T_s (up to 500 °C) was observed by TEM. The thin Nb films sputtered at T_s = 40 °C contain a high density of defects. It is demonstrated by shortened positron diffusion length and a high value of the S parameter for Nb layer compared to the well-annealed (defect-free) bulk Nb reference sample. A drastic decrease of defect density was found in the films sputtered at T_s ≥ 300 °C. It is reflected by a significant increase of the positron diffusion length and a decrease of the S parameter for the Nb layer. The defect density in the Nb layer is, however, still substantially higher than in the well-annealed reference bulk Nb sample. Moreover, there is a layer at the interface between the Nb film and the substrate with very high density of defects comparable to that in the films sputtered at T_s < 300 °C. All the Nb films studied exhibit a strong (1 1 0) texture. The films sputtered at T_s < 300 °C are characterized by a compressive macroscopic in-plane stress due to lattice mismatch between the film and the substrate. Relaxation of the in-plane stress was observed in the films sputtered at T_s ≥ 300 °C. The width of the XRD profiles of the films sputtered at T_s ≥ 300 °C is significantly smaller compared to the films sputtered at lower temperatures. This is most probably due to a lower defect density which results in reduced microstrains in the films sputtered at higher temperatures.     

Synthesis and surface modified hard magnetic properties in Co0.5Pt0.5 nanocrystallites from a rheological liquid precursor

Small crystallites of a metastable phase Co_0.5Pt_0.5 are precipitated by heating a rheological liquid precursor of cobalt–hydrazine complex and platinum chloride H₂PtCl₆·xH₂O in polymer molecules of poly(vinylpyrrolidone) (PVP) in ethylene glycol. The hydrazine co-reduces nascent atoms from the Co²⁺ and Pt⁴⁺ that recombine and grow as Co_0.5Pt_0.5. The PVP molecules cap a growing Co_0.5Pt_0.5 as it achieves a critical size so that it stops growing further in given conditions. X-ray diffraction pattern of a recovered powder reveals a crystalline Co_0.5Pt_0.5 phase (average crystallite size D∼8 nm) of a well-known Fm3m-fcc crystal structure with the lattice parameter a=0.3916 nm (density ρ=14.09 g/cm³). A more ordered L1₀ phase (ρ=15.91 g/cm³) transforms (D≥25 nm) upon annealing the powder at temperature lesser than 700 °C (in vacuum). At room temperature, the virgin crystallites bear only a small saturation magnetization M_s=5.54 emu/g (D=8 nm) of a soft magnet and it hardly grows on bigger sizes (D≤31 nm) in a canted ferromagnetic structure. A rectangular hysteresis loop is markedly expanded on an optimally annealed L1₀ phase at 800 °C for 60 min, showing a surface modified coercivity H_c=7.781 kOe with remnant ratio M_r/M_s=0.5564, and M_s=39.75 emu/g. Crystallites self-assembled in an acicular shape tailor large H_c from ideal single domains and high magnetocrystalline anisotropy of a hard magnet L1₀ phase.     

CO2 adsorption on Cr(1 1 0) and Cr2O3(0 0 0 1)/Cr(1 1 0)

We attempt to correlate qualitatively the surface structure with the chemical activity for a metal surface, Cr(1 1 0), and one of its surface oxides, Cr₂O₃(0 0 0 1)/Cr(1 1 0). The kinetics and dynamics of CO₂ adsorption have been studied by low energy electron diffraction (LEED), Aug er electron spectroscopy (AES), and thermal desorption spectroscopy (TDS), as well as adsorption probability measurements conducted for impact energies of E_i = 0.1-1.1 eV and adsorption temperatures of T_s = 92-135 K. The Cr(1 1 0) surface is characterized by a square shaped LEED pattern, contamination free Cr AES, and a single dominant TDS peak (binding energy E_d = 33.3 kJ/mol, first order pre-exponential 1 × 10¹³ s⁻¹). The oxide exhibits a hexagonal shaped LEED pattern, Cr AES with an additional O-line, and two TDS peaks (E_d = 39.5 and 30.5 kJ/mol). The initial adsorption probability, S₀, is independent of T_s for both systems and decreases exponentially from 0.69 to 0.22 for Cr(1 1 0) with increasing E_i, with S₀ smaller by ∼0.15 for the surface oxide. The coverage dependence of the adsorption probability, S(Θ), at low E_i is approx. independent of coverage (Kisliuk-shape) and increases initially at large E_i with coverage (adsorbate-assisted adsorption). CO₂ physisorbs on both systems and the adsorption is non-activated and precursor mediated. Monte Carlo simulations (MCS) have been used to parameterize the beam scattering data. The coverage dependence of E_d has been obtained by means of a Redhead analysis of the TDS curves.     

Growth, microstructure and electrical properties of sputter-deposited hafnium oxide (HfO2) thin films grown using a HfO2 ceramic target

Hafnium oxide (HfO₂) thin films have been made by radio-frequency (rf) magnetron-sputtering onto Si(1 0 0) substrates under varying growth temperature (T_s). HfO₂ ceramic target has been employed for sputtering while varying the T_s from room temperature to 500 °C during deposition. The effect of T_s on the growth and microstructure of deposited HfO₂ films has been studied using grazing incidence X-ray diffraction (GIXRD), and high-resolution scanning electron microscopy (HR-SEM) coupled with energy dispersive X-ray spectrometry (EDS). The results indicate that the effect of T_s is significant on the growth, surface and interface structure, morphology and chemical composition of the HfO₂ films. Structural characterization indicates that the HfO₂ films grown at T_s < 200 °C are amorphous while films grown at T_s > 200 °C are nanocrystalline. An amorphous-to-crystalline transition occurs at T_s = 200 °C. Nanocrystalline HfO₂ films crystallized in a monoclinic structure with a (−1 1 1) orientation. An interface layer (IL) formation occurs due to reaction at the HfO₂-Si interface for HfO₂ films deposited at T_s > 200 °C. The thickness of IL increases with increasing T_s. EDS at the HfO₂-Si cross-section indicate that the IL is a (Hf, Si)-O compound. The electrical characterization using capacitance-voltage measurements indicate that the dielectric constant decreases from 25 to 16 with increasing T_s. The current-voltage characteristics indicate that the leakage current increases significantly with increasing T_s due to increased ILs.     

Influence of Nb substitution for Fe on the magnetic and magneto-impedance properties of amorphous and annealed Fe76.5−xSi13.5B9Cu1Nbx (x=0–7) ribbons

We report a systematic study of the influence of Nb substitution for Fe on the magnetic properties and magneto-impedance (MI) effect in amorphous and annealed Fe_76.5−xSi_13.5B₉Cu₁Nb_x (x=0, 1, 2, 3, 4, 5, 6, and 7) ribbons. The amorphous ribbons were annealed at different temperatures ranging from 530 to 560 °C in vacuum for different annealing times between 5 and 20 min. We have found that for the as-quenched amorphous ribbons, the substitution of Nb for Fe first increases the saturation magnetization (M_s) and decreases the coercivity (H_c) until x=3, for which the largest M_s∼152 emu/g and the smallest H_c∼1.3 Oe are obtained, then an opposite trend is found for x>3. The largest MI ratio (ΔZ/Z∼38% at f=6 MHz) is achieved in the amorphous ribbon with x=3. A similar trend has been observed for the annealed ribbons. The most desirable magnetic properties (M_s∼156 emu/g and H_c∼1.8 Oe) and the largest MI ratio (ΔZ/Z∼221% at f=6 MHz) are achieved for the x=3 sample annealed at 540 °C for 15 min. A correlation between the microstructure, magnetic properties, and MI effect in the annealed ribbons has been established.     

Adsorption dynamics of CO2 on Cu(1 1 0): A molecular beam study

Molecular beam scattering measurements have been conducted to examine the adsorption dynamics of CO₂ on Cu(1 1 0). The initial adsorption probability, S₀, decreases exponentially from 0.43 ± 0.03 to a value close to the detection limit (∼0.03) within the impact energy range of E_i = (0.12-1.30) eV. S₀ is independent of the adsorption temperature, T_s, and the impact angle, α_i, i.e., the adsorption is non-activated and total energy scaling is obeyed. The coverage, Θ, dependent adsorption probability, S(Θ), agrees with precursor-assisted adsorption dynamics (Kisliuk type) above T_s ∼ 91 K. However, below that temperature adsorbate-assisted adsorption (S increases with Θ) has been observed. That effect is most distinct at large E_i and low T_s. The S(Θ) data have been modeled by Monte Carlo simulations. No indications of CO₂ dissociation were obtained from Auger Electron Spectroscopy or the molecular beam scattering data.     

Adsorption of 1,2-diaminoethane on ZnO thin films from p-xylene

The interaction of 1,2-diaminoethane (DAE) with ZnO thin films prepared by electrodeposition and magnetron sputtering was investigated by X-ray photoelectron spectroscopy (XPS). The samples were exposed to organic solution of 0.5 M DAE-p-xylene in an Ar atmosphere glove box (O₂ and H₂O <5 ppm), directly connected to the XPS analysis chamber by an anaerobic and anhydrous transfer system. A clear interaction of DAE with the ZnO surface is evidenced by the presence of a high intensity N1s peak at BE = 399.5 ± 0.2 eV and C1s at BE = 286.3 ± 0.2 eV which are attributed to C-N bonding. The atomic ratio C:N was very close to 1:1 consistent with the molecular, non-dissociative adsorption of DAE on the ZnO layer. No significant difference in adsorption of DAE was observed for three different ZnO surfaces despite slight differences in their acid/base properties as evidenced by the O/OH ratio. The results are interpreted in terms of adsorption on Brönsted acid sites. A uniform layer model was used to approximate the DAE film thickness, which was found to be around 10 Å on three studied samples. The N1s and C1s_B signals were observed to decrease on sample exposure to vacuum and/or X-ray irradiation and additional N1s_B peak appeared at lower binding energy at around 398.5 ± 0.2 eV. This is interpreted by the desorption and modification of DAE, indicating low stability of the adsorbed state on ZnO. The exposure to water of the sample with adsorbed DAE causes a significant decrease of the N1s_A and C1s_B peak intensities attributed to the adsorbed DAE molecule, demonstrating the instability of the DAE-ZnO interface in water.     

Energy analysis during acoustic bubble oscillations: Relationship between bubble energy and sonochemical parameters

In this work, energy analysis of an oscillating isolated spherical bubble in water irradiated by an ultrasonic wave has been theoretically studied for various conditions of acoustic amplitude, ultrasound frequency, static pressure and liquid temperature in order to explain the effects of these key parameters on both sonochemistry and sonoluminescence. The Keller–Miksis equation for the temporal variation of the bubble radius in compressible and viscous medium has been employed as a dynamics model. The numerical calculations showed that the rate of energy accumulation, dE/dt, increased linearly with increasing acoustic amplitude in the range of 1.5–3.0 atm and decreased sharply with increasing frequency in the range 200–1000 kHz. There exists an optimal static pressure at which the power w is highest. This optimum shifts toward a higher value as the acoustic amplitude increases. The energy of the bubble slightly increases with the increase in liquid temperature from 10 to 60 °C. The results of this study should be a helpful means to explain a variety of experimental observations conducted in the field of sonochemistry and sonoluminescence concerning the effects of operational parameters.     

Propagation regimes of intense circularly polarized laser beam in magnetoactive plasma

This paper presents an analytical and numerical investigation of an intense circularly polarized wave propagating along the static magnetic field parallel to oscillating magnetic field in magnetoactive plasma. In the relativistic regime such a magnetic field is created by pulse itself. The authors have studied different regimes of propagation with relativistic electron mass effect for magnetized plasma. An appropriate expression for dielectric tensor in relativistic magnetoactive plasma has been evaluated under paraxial theory. Two modes of propagation as extraordinary and ordinary exist; because of the relativistic effect, ultra-strong magnetic fields are generated which significantly influence the propagation of laser beam in plasma. The nature of propagation is characterized through the critical-divider curves in the normalized beam width with power plane For given values of normalized density (ω_p/ω) and magnetic field (ω_c/ω) the regions are namely steady divergence (SD), oscillatory divergence (OD) and self-focusing (SF). Numerical computations are performed for typical parameters of relativistic laser-plasma interaction: magnetic field B = 10-100 MG; intensity I = 10¹⁶ to 10²⁰ W/cm²; laser frequency ω = 1.1 × 10¹⁵ s⁻¹; cyclotron frequency ω_c = 1.7 × 10¹³ s⁻¹; electron density n_e = 2.18 × 10²⁰ cm⁻³. From the calculations, we confirm that a circularly polarized wave can propagate in different regimes for both the modes, and explicitly indicating enhancement in wave propagation, beam focusing/self-guiding and penetration of E-mode in presence of magnetic field.