Self-focusing of Hermite–Gaussian laser beams in plasma under plasma density ramp

Self-focusing of Hermite–Gaussian laser beams in plasma under plasma density ramp has been investigated. It is known that a laser beam shows an oscillatory self-focusing and defocusing behavior with the propagation distance. To overcome the defocusing, localized upward plasma density ramp is introduced, so that the laser beam attains a minimum spot size and maintains it with only a mild ripple. The density ramp could be important for the self-focusing of a Hermite–Gaussian laser by choosing the laser and plasma parameters appropriately. Self-focusing becomes stronger as the propagation distance increases. The behavior of beam-width parameters with the distance of propagation is presented graphically.     

Self-focusing and defocusing of cosh Gaussian laser beam in the presence of nonlinearity of ponderomotive force and temperature gradient

In this paper, the propagation of Cosh Gaussian laser beam and its interaction with isothermal plasma without temperature gradient as well as the effect of the exponential electron temperature gradient are investigated. Here the ponderomotive nonlinearity force is effective mechanism. This force can modify the electron density distribution. All the investigations are carried out for different initial plasma temperatures. Using Maxwell’s equations we obtained the nonlinear second-order differential equation of the dimensionless beam-width parameter (f) on the distance of propagation for several initial electron temperatures and exponential temperature variations. These equations are solved numerically by taking WKB and paraxial approximation. Under the effect of initial electron temperature, self-focusing and defocusing of hyperbolic cosine (cosh) Gaussian laser beam is distinguished. Furthermore, the exponential temperature gradient cause to stationary propagation mode breaks, and self-focusing or defocusing properties is observable.     

Propagation of cosh Gaussian laser beam in plasma with density ripple in relativistic – ponderomotive regime

Self-focusing of cosh Gaussian laser beam in plasma with periodic density ripple has been investigated. The pondermotive force on electron and the relativistic oscillation of the electron mass causes periodic self-focusing/defocusing of the cosh Gaussian laser beam. The beam converges in the region of high plasma density due to dominance of self-focusing effect over diffraction effect and diverges in the low density region. Non-linear partial differential equation governing the evolution of complex envelope in slowly varying approximation is solved using paraxial ray approximation. The variation of beam-width parameter is studied with distance of propagation for different values of ripple wave number d and decentred parameter b. In order to get strong self-focusing, wavelength and intensity parameters of cosh Gaussian laser beam are optimized.     

Nonlinear oscillatory waveguide propagation in a plasma

The presence of an intense Gaussian laser beam gives rise to a ponderomotive force on electrons in a collisionless plasma, leading to a redistribution of electron density along the wave-front and consequently to an intensity dependent dielectric constant which saturates with increasing intensity. The intensity dependent dielectric constant is responsible for beam propagation in an oscillatory waveguide. It is seen that (i) a beam of radiusr ₀ less thanr _0min (?c/ω _p) cannot be focused in the plasma regardless of its power, (ii) minimum dimension of oscillatory waveguide increases with increasing power of the beam. Similar results are also obtained for collisional plasma where nonlinearity arises due to nonuniform heating and consequent redistribution of carriers.     

Study of dust ion-acoustic wave propagation in the Lorentzian magnetized dusty plasma

Dust ion-acoustic waves propagation in the magnetized dusty plasma including ions, electrons and dust particulates are studied by using kinetic equation. For unbounded and collisionless plasma and in the presence of uniform external magnetic field B₀, electrons and ions with Lorentzian distribution function and dust particles with Maxwellian one are considered. Calculating dielectric tensor through the Vlasov equation solution, in the parallel propagation, dispersion relation is derived and suprathermal particle effects on the Landau damping is studied. It is shown that the Landau damping effect vanishes for parallel propagation.     

Distribution regimes of intense laser beam in a self-consistent plasma channel

In the present work, we investigate the distributed regimes of an intense laser beam in a self-consistent plasma channel. As the intensity of the laser beam increases, the relativistic mass effect as well as the ponderomotive expulsion of electrons modifies the dielectric function of the medium due to which the medium exhibits nonlinearity. Based on Wentzel–Kramers–Brillouin and paraxial ray theory, the steady-state solution of an intense, Gaussian electromagnetic beam is studied. A differential equation of the beamwidth parameter with the distance of propagation is derived, including the effects of relativistic self-focusing (SF) and ponderomotive self-channeling. The nature of propagation and radial dynamics of the beam in plasma depend on the power, width of the beam, and Ω _p, the ratio of plasma to wave frequency. For a given value of Ω _p (<1), the distribution regimes have been obtained in beampower–beamwidth plane, characterizing the regimes of propagation as steady divergence, oscillatory divergence, and SF. The related focusing parameters are optimized introducing plasma density ramp function, and spot size of the laser beam is analyzed for inhomogeneous plasma. This results in overcoming the diffraction and guiding the laser beam over long distance. Numerical computations are performed for typical parameters of relativistic laser–plasma interaction studies.     

Spin resonant optical four wave mixing in Pb1−xSnxTTe epitaxial layers and in Pb1−xSnx/PbTe superlattices

Spin resonances of the third-order non-linear susceptibility of epitaxial layers of n- and p-type Pb_1?xSn_xTe and Pb_1?xSn_xTe/PbTe superlatttices have been observed by four photon mixing of the radiation of two CO₂-lasers. Precise data on the effective g-values of the electrons and holes of Pb_1?xSn_xTe were obtained. These data and the results of magneto-optical interband absorption measurements are used to obtain k·p parameters within the Mitchell and Wallis band model. In the Pb_1?xSn_xTe/PbTe superlattices, the same g-values for electrons as in the Pb_1?xSn_xTe films with the same composition x are found. Consequently, the electrons in the superlattices are confined within the Pb_1?xSn_xTe layers. Therefore the Pb_1?xSn_xTe/PbTe system forms a type I and not a staggered superlattice.     

Influence of collisions and pulse intensity on multiple photon absorption in SF6

Using a pyroelectric detector, the multiple photon absorption (MPA) of the SF₆ molecule in a wide range of pressures (10^-3 -1 torr) has been studied. The significant role of collisions in MPA has been shown. The fraction of molecules excited under essentially collisionless conditions has been defined. It is shown that under collisionless excitation of SF₆ (p < 10^-2 torr) at energy fluences E < 10^-1 J/cm² the intensity of the laser pulse plays the essential role, while in presence of collisions MPA is determined mainly by the energy fluence in the pulse.     

Propagation and conversion of non-axisymmetric modes in non-uniform helicon-sustained plasma

An effect of the radial plasma density gradient on the oblique wave propagation in the helicon-frequency range is investigated. It is shown that the dispersion features of electrostatic and electromagnetic modes are essentially changed in strongly non-uniform helicon plasma. In particular, the transition between helicon eigenmode frequency scales ω ～ k _z and ω ～ k _z ² is demonstrated. The process of total conversion of long-wavelength helicon mode into short-wavelength electrostatic wave in near-axis region of a plasma column is analysed. Due to modification of the wave dispersion relations, the densities at which the mode conversion occurs are considerably reduced if the density gradient is steep enough. The estimation of collisionless axial damping rate of helicon mode connected with linear mode conversion is presented. This damping is compared with the usual collision damping.     

Propagation of Hermite-cosh-Gaussian laser beams in n-InSb

The propagation of Hermite-cosh-Gaussian (HChG) laser beams in n-InSb are investigated for 0, 1 and 2 mode indices. The field distribution in the medium is expressed in terms of beam-width parameter f and decentred parameter b. The differential equations for f-parameter are established by parabolic wave equation approach under paraxial approximation. Analytical solutions are obtained under the condition R_n < R_d, where, R_n is the self-focusing length and R_d is the diffraction length. The behaviour of f-parameter with the dimensionless distance of propagation η for various b values is examined by numerical estimates. The results are presented graphically.     

Ferrodistortiv geordnete tetragonal gedehnte AgIIF6-oktaeder in den verbindungen AgMIVF6[MIV = Sn,Zr]

From EPR measurements on polycrystalline samples of the complex flourides AgM^IVF₆ [M^IV = Sn, Zr] a coupling of tetragonal elongated AgF₆-octrahedral corresponding to an undisturbed ferrodistortive order can be deduced. The spectroscopic dáta (g-values and ligand field parameters) are consistent with reasonable covalency parameters (k_[, k_⊥) for the Ag^II-F-bonding.     

Effect of neutral pressure on the He plasma flow measurement in a linear device

Axial and azimuthal flow velocities have been measured in a linear plasma device called NAGDIS-II (NAGoya DIvertor Simulator-II), along with plasma density and electron temperature, using a vector Mach probe composed of two Mach probes, one of which is for the axial flow, and the other is for the azimuthal flow. To study the effect of neutral pressure on the deduction of the Mach numbers, the ratio of upstream to downstream currents are measured by changing the neutral pressure for the deduction of flow velocities. Helium plasma was generated with pressure of 2–35 mTorr. Since the ion gyro-radius at the magnetic flux of 300 G is larger than the probe size, an unmagnetized collisionless Mach probe theory was used for the deduction of Mach numbers and their variations. In order to check the range of collisionality, plasma density (n_e = 10¹⁰–10¹¹ cm^?3) and electron temperature (T_e = 2–9 eV) are measured by a single electric probe using a conventional collisionless probe theory. Variations of Mach number, electron temperature and plasma density with collisionless models are to be compared with those using collisional models for different pressures where ionization and ion-neutral collision are included. Mach numbers by the collisionless model are found to be overestimated by 120% for the maximum difference even in weakly collisional plasmas. A clear flow reversal exists in the axial direction with higher pressure plasma, even in the linear machine. Azimuthal flows are also measured simultaneously along with axial flows, yet they seem to be very small in the present cold ion plasma (T_i/T_e << 1).     

Absolute and relative line intensity measurements when the spectral lines are not optically thin

The curves of growth were used in order to determine the Doppler absorption coefficient at the line center, k_D0, from absolutely measured line intensities (equivalent widths) and theoretical widths. It is shown that the relative line intensities from a single path and a double path may be used for the determination of absorption coefficients and absolute oscillator strengths, for estimating absorption at the inhomogeneous ends of a plasma column, and for assessing the approach to thermal equilibrium.Measurements were carried out on the red argon lines arising from the 4s–4p transition arrays. The influence of plasma diagnostics on the f-value is considered, and our f-values are compared with other measurements.     

Charged particle production at the CERN ISR as a function of transverse momentum

Experimental results are presented on the production of charged particles in inclusive reactions at ISR energies. The data have been taken as function of transverse momentum p_t at the fixed x-values of 0.08, 0.16 and 0.32. The behaviour of the p_t-distributions for the different particles is discussed.     

Self-focusing of cosh-Gaussian laser beams in a parabolic medium with linear absorption

The authors have investigated self-focusing of cosh-Gaussian laser beams in a parabolic medium with linear absorption. The field distribution in the medium is expressed in terms of beam-width parameter f, decentred parameter b and absorption coefficient k_i. The differential equation for f parameter is established by following Wentzel–Kramers–Brillouin (WKB) and paraxial approximations through parabolic wave equation approach and analytical solution is obtained for the same. The behavior of f parameter with the normalized distance of propagation η is studied at various values of b with different absorption levels in the medium. The results are presented graphically and discussed.     

Dust-acoustic solitons in quantum plasma with kappa-distributed ions

Arbitrary amplitude dust-acoustic (DA) solitary waves in an unmagnetized and collisionless quantum dusty plasma comprising cold dust particles, kappa (κ)-distributed ions and degenerate electrons are investigated. The influence of suprathermality and quantum effects on the linear dispersion relation of DA waves is investigated. Then, the effect of κ-distributed ions and degenerate electrons on the existence domain of solitons is discussed in the space of (M, f). The comparison of the existence domain for higher and lower values of κ shows that suprathermality results in propagation of solitons with lower Mach number, and the quantum effects, lead to a higher values of Mach number. The existence domain of solitons for nondegenerate κ-distributed electrons is considered for comparison with effect of degenerate electrons. Also, we found that the Sagdeev potential well becomes deeper and wider as ε _F???i decreases, as for lower κ values, the influence of quantum effects on the Sagdeev pseudopotential profile is smaller.     

Axial contraction in toroidal pinches with non-circular plasma cross-sections

The axial contraction of linear pinches with racetrack-shaped and elliptic cross sections is studied byδW-analysis near the equilibrium shape. A surface current profile and a fixed plasma cross-section area are assumed. It is shown for the corresponding special perturbation thatδW is given by the variation of the surface energy(δW=δW _s =1/8B _p ² ξ _b ² ), and thatδW is nearly independent of the shape of the plasma (racetrack or ellipse). The axial oscillation frequency is found to beΩ _ax=1/2√CB _p /√ρ_l with a constantC<1. The model correctly predicts theB _p and ρ_l-dependences of the experimental belt-pinch results and yields theoreticalΩ _ax-values a factor of 2 above the experimental ones.     

Tailored TEMp0 beams for large size 3-D laser prototyping

The Laser-Lithography technique allows the fabrication of complex objects having microsizes by selectively solidifying polymeric materials layer by layer upon exposure to a focused Gaussian laser beam having a beam propagation factor M²=1. We can expect that extension of this technique to large sizes 3-D prototyping comes up against a large increase in the design time. A possible solution is the increase in the focused spot size, but unfortunately at the price of a great reduction in the longitudinal resolution due to the resulting increase in the depth of focus. To overcome these difficulties, we propose the use of a rectified TEM_p0 beam allowing the obtaining of a Gaussian beam intensity profile in the focus plane of a lens. The reshaped TEM_p0 beam has a beam propagation factor M²≈(2p+1), and this yields to a relative improvement of the longitudinal resolution although the spot size is increased for reducing the processing time.     

Trivelpiece-Gould-Modes in an Axial Inhomogeneous Plasma

Experiments on the propagation of TG-modes in a weakly inhomogeneous plasma are reported. The modes travel from the high density part (ω < ω_pe) to that of lower density (ω > ω_pe). The wavelength decreases as expected but an increase of the longitudinal fieldstrength predicted by collisionless theory could not be observed. Two nonlinear effects appear one after another with increasing wave amplitude. These are the sideband instability and a decay into the drift frequency range occuring in the whole plasma column. Neither the region ω ≈ ω_pe nor the very vicinity of the exciter antenna are distinguished. The second instability is accompanied by effective electron heating.     

Determination of the internal structure of valons

We determine the internal structure functions of the valons introduced by Hwa and coworkers, using low-p _t data and Regge model constraints. Our calibration reaction is the fragmentation processp→π^? observed in 70 GeV/cK ⁺ p interactions. The fitted valon structure parameters are used to make successful predictions for various other fragmentation processes (p→π⁺ andp→K ⁺). A comparison with experimental data of the DISvW ₂ (x)-values implied by this same fit, indicates that soft processes probe the nucleon typically at aQ ²-value of ～1 GeV². This finding supports the hypothesis that soft hadronic reactions are useful (and often unique) tools to learn about hadron quark structure.