Parabolic Density Research Articles

TODGINV—A code for optimization of gravity anomalies due to anticlinal and synclinal structures with parabolic density contrast

A code, TODGINV, to determine the parameters of 2D anticlinal and synclinal structures besides estimating linear regional gravity background is presented wherein the density contrast varies with depth based on a parabolic equation. The main program, TODGINV, is supported by five subroutines namely GANTCLINE, GSYNCLINE, PDSANT, PDSSYN and NOREQS. Forward modeling is realized through the subroutine GANTCLINE in case of an anticlinal structure while GSYNCLINE in case of a synclinal structure. PDSANT and PDSSYN compute the partial derivatives of anticlinal and synclinal structures, respectively, whereas NOREQS solves the system of normal equations. The efficiency of the code is illustrated with a set of synthetic gravity anomalies over an anticlinal and a synclinal structure both with and without regional background. Further, the code is exemplified with the gravity anomalies of the Pays De Bray anticline, France, and the results are found to be more consistent with borehole information rather than with those of Alessandrello et al. (1983, Automatic three-layer, three-dimensional deconvolution of the Pays De Bray anticline. Geophysical Prospecting 31, 608–626).

Simultaneous evolution of spot size and length of short laser pulses in a plasma channel

Nonlinear, nonparaxial propagation of an intense, short, Gaussian laser pulse in a preformed plasma channel having a parabolic radial density profile is analyzed. The variational technique is used to obtain equations describing the evolution of laser spot size and pulse length in the channel. Relativistic nonlinearity and group velocity dispersion effects have been taken into account and numerical methods are used to study the simultaneous evolution of the laser spot and pulse length.

Propagation of sinusoidal pulse laser beam in a plasma channel

The propagation of an intense sinusoidal pulse laser beam, in a preformed plasma channel having a parabolic density profile, is analyzed. Considering a nonparaxial, nonlinear wave equation and using a variational technique, simultaneous equations describing the evolution of laser spot and pulse length are obtained. Numerical methods are used to study the effect of pulse length variation on betatron oscillations of the laser spot size as it propagates in the plasma channel. Approximate conditions for propagation of the laser pulse with a constant spot size and pulse length (matched beam propagation) are obtained.

Lowest-Landau-level description of a Bose-Einstein condensate in a rapidly rotating anisotropic trap

A rapidly rotating Bose-Einstein condensate in a symmetric two-dimensional trap can be described with the lowest Landau-level set of states. In this case, the condensate wave function $\ensuremath{\psi}(x,y)$ is a Gaussian function of ${r}^{2}={x}^{2}+{y}^{2}$, multiplied by an analytic function $P(z)$ of the single complex variable $z=x+iy$; the zeros of $P(z)$ denote the positions of the vortices. Here, a similar description is used for a rapidly rotating anisotropic two-dimensional trap with arbitrary anisotropy $({\ensuremath{\omega}}_{x}∕{\ensuremath{\omega}}_{y}\ensuremath{\leqslant}1)$. The corresponding condensate wave function $\ensuremath{\psi}(x,y)$ has the form of a complex anisotropic Gaussian with a phase proportional to $xy$, multiplied by an analytic function $P(\ensuremath{\zeta})$, where $\ensuremath{\zeta}\ensuremath{\propto}x+i{\ensuremath{\beta}}_{\ensuremath{-}}y$ and $0\ensuremath{\leqslant}{\ensuremath{\beta}}_{\ensuremath{-}}\ensuremath{\leqslant}1$ is a real parameter that depends on the trap anisotropy and the rotation frequency. The zeros of $P(\ensuremath{\zeta})$ again fix the locations of the vortices. Within the set of lowest Landau-level states at zero temperature, an anisotropic parabolic density profile provides an absolute minimum for the energy, with the vortex density decreasing slowly and anisotropically away from the trap center.

INV2P5DSB—A code for gravity inversion of 2.5-D sedimentary basins using depth dependent density

A program, INV2P5DSB, has been developed to simultaneously estimate the depth of a 2.5-D sedimentary basin and regional background from observed gravity anomalies. The density contrast is assumed to be varying parabolically with depth above the basement interface. The main program is supported with two subroutines GRAV2P5D and SIMEQ and a function GPRM. The analysis of gravity anomalies due to a synthetic model of a 2.5-D sedimentary basin with and without regional background illustrates that the code is insensitive to regional background. Interpretation of gravity anomalies over the Gediz graben, Western Anatolia with parabolic density function yields geologically plausible model.

Quasistatic capillary discharge plasma model

A one-dimensional, quasistatic model of a capillary discharge plasma has been developed. Such a plasma is useful as a medium to generate plasma waves for acceleration of electrons via processes such as laser wakefield acceleration or plasma wakefield acceleration. Another important characteristic of the plasma is its intrinsic parabolic density distribution near the center of the capillary, which can channel a laser beam along the capillary. The model is intended to be a design tool to aid in the selection of the capillary parameters in order to obtain desired plasma characteristics, e.g., plasma density and matched laser beam radius for guiding. An optional external axial magnetic field can be included, which improves the laser-channeling effect in some cases. The model also enables a measure of the potential for laser damage of the capillary wall. Results are presented for the design of a gas-filled capillary that will be tested during the staged electron laser acceleration--laser wakefield (STELLA-LW) experiment.

Gravity Anomalies of 2.5-D Multiple Prismatic Structures with Variable Density: A Marquardt Inversion

We present an inversion technique based on the Marquardt algorithm to estimate the depth of a 2.5-D sedimentary basin in addition to the regional gravity anomaly that is associated with the residual gravity anomaly, wherein the density contrast varies parabolically with depth. Forward modeling is carried out through a derived analytical gravity expression of a 2.5-D vertical prism. Inversion of a theoretical gravity anomaly with and without a regional gravity anomaly illustrates the procedure that it is found to be insensitive to the regional gravity effect. Furthermore, the algorithm is exemplified with the gravity anomalies of the derived density-depth model of the Godavari subbasin, India with a parabolic density profile resulting in a more consistent geological model rather than a constant density profile. The main advantage of this method is that it works well even when the profile of interpretation does not bisect the strike length of the sedimentary basin.

Dependence of electron density on Fermi energy in compensated n-type gallium antimonide

The majority electron density as a function of the Fermi energy is calculated in zinc blende, compensated n-type GaSb for donor densities between 1016 and 1019cm−3. The compensation acceptor density is 1016cm−3. These calculations solve the charge neutrality equation self-consistently for a four-band model (three conduction subbands at Γ, L, and X and one equivalent valence band at Γ) of GaSb. Our calculations assume parabolic densities of states and thus do not treat the density-of-states modifications due to high concentrations of dopants, many-body effects, and nonparabolicity of the bands. Even with these assumptions, the results are important for interpreting optical measurements such as Raman scattering measurements that are proposed as a nondestructive method for wafer acceptance tests.

Discrete Langmuir waves in density structure

Recent wideband observations of Langmuir waves in the auroral ionosphere show complex structure (McAdams and LaBelle, 1999) interpreted as resulting from discretization of the normal modes in the presence of a parabolic density cavity (McAdams et al., 2000). We formalize the theory of discrete Langmuir waves trapped within a one‐dimensional density cavity or enhancement in a magnetized plasma, assuming a Lorentzian density profile, and show that discrete spectrum of electric field is largely determined by the electrostatic wave equation although a very low level of electromagnetic waves is also present. In the overdense case (fpe > fce), the Langmuir waves are trapped in density depletions, and the predicted frequency spacings of the eigenmodes are comparable to those estimated by McAdams et al. (2000) using an approximate theory. We furthermore calculate the eigenfunctions associated with the first four eigenmodes in a Lorentzian density structure, showing that an Airy function approximation provides a close match to the exact solutions obtained numerically. Finally, we analyze synthesized time series simulating the signals which would be obtained by a rocket electric field receiver traversing the wave structures. This analysis reveals subtle predictions of the theory which can be measured with appropriate rocket or satellite observations. Specifically, the analysis predicts that there are nulls in the spectral lines of observed discrete emission which should be detectable in principle.

Microwave Correlation Reflectometry for Tokamak CASTOR

A correlation reflectometer in 8-mm wavelength range has been constructed and installed on CASTOR tokamak. The reflectometer can operate on three fixed frequencies (29, 33, and 35 GHz). This is universal correlation sine-cosine reflectometer, which can work in poloidal or toroidal correlation regime and in ordinary mode (O-mode) and/or extraordinary mode (X-mode). A computational method of a direct evaluation of the phase fluctuations as well as absolute value of the phase from sine-cosine data has been developed. Using this method the relative plasma density fluctuations in the CASTOR core plasma has been determined in the range of few percent under assumption of parabolic density distribution.

Invariant imbedding theory of mode conversion in inhomogeneous plasmas. I. Exact calculation of the mode conversion coefficient in cold, unmagnetized plasmas

This is the first of a series of papers devoted to the development of the invariant imbedding theory of mode conversion in inhomogeneous plasmas. A new version of the invariant imbedding theory of wave propagation in inhomogeneous media allows one to solve a wide variety of coupled wave equations exactly and efficiently, even in the cases where the material parameters change discontinuously at the boundaries and inside the inhomogeneous medium. In this paper, the invariant imbedding method is applied to the mode conversion of the simplest kind, that is, the conversion of p-polarized electromagnetic waves into electrostatic modes in cold, unmagnetized plasmas. The mode conversion coefficient and the field distribution are calculated exactly for linear and parabolic plasma density profiles and compared quantitatively with previous results.

Gravity modeling of 2 1/2-D sedimentary basins — a case of variable density contrast

An algorithm and associated codes are developed to determine the depths to bottom of a 2 1/2-D sedimentary basin in which the density contrast varies parabolically with depth. This algorithm estimates initial depths of a sedimentary basin automatically and modifies thereafter appropriately within the permissible limits in an iterative approach as described in the text. Efficacy of the method as well as the code is illustrated by interpreting a gravity anomaly of a synthetic model. Further, the applicability of the method is exemplified with the derived density–depth model of the Godavari sub-basin, India to interpret the gravity anomalies due to the basin. Interpretations based on parabolic density profile are more consistent with existing geological information rather than with those obtained with constant density profile.

Atomic Force Microscopy Study of the Interaction between Adsorbed Poly(ethylene oxide) Layers: Effects of Surface Modification and Approach Velocity

The interaction forces between layers of the triblock copolymer Pluronic F108 adsorbed onto hydrophobic radio frequency glow discharge (RFGD) thin film surfaces and hydrophilic silica, in polymer-free 0.15 M NaCl solution, have been measured using the atomic force microscope (AFM) colloid probe technique. Compression of Pluronic F108 layers adsorbed on the hydrophobic RFGD surfaces results in a purely repulsive force due to the steric overlap of the layers, the form of which suggests that the PEO chains adopt a brush conformation. Subsequent fitting of these data to the polymer brush models of Alexander-de Gennes and Milner, Witten, and Cates confirms that the adsorbed Pluronic F108 adsorbs onto hydrophobic surfaces as a polymer brush with a parabolic segment density profile. In comparison, the interaction between Pluronic F108 layers adsorbed on silica exhibits a long ranged shallow attractive force and a weaker steric repulsion. The attractive component is reasonably well described by van der Waals forces, but polymer bridging cannot be ruled out. The weaker steric component of the force suggests that the polymer is less densely packed on the surface and is less extended into solution, existing as polymeric isolated mushrooms. When the surfaces are driven together at high piezo ramp velocities, an additional repulsive force is measured, attributable to hydrodynamic drainage forces between the surfaces. In comparing theoretical predictions of the hydrodynamic force to the experimentally obtained data, agreement could only be obtained if the flow profile of the aqueous solution penetrated significantly into the polymer brush. This finding is in line with the theoretical predictions of Milner and provides further evidence that the segment density profile of the adsorbed polymer brush is parabolic. A velocity dependent additional stepped repulsive force, reminiscent of a solvation oscillatory force, is also observed when the adsorbed layers are compressed under high loads. This additional force is presumably a result of hindered drainage of water due to the presence of a high volume fraction of polymer chains between the surfaces.

Electron-hopping modes in NiMn2O4+δ materials

The resistance versus temperature (R–T) characteristics of NiMn2O4+δ thermistors have been analyzed. In the literature, electron transport in manganate spinels is commonly described by a small-polaron model for nearest neighbor hopping, but variable range hopping (VRH) has not been considered so far. In this study differentiated R–T data were analyzed, allowing a clear distinction between different modes of hopping. In pressed pellets and thick screen printed films conduction was well described by a VRH model for a parabolic density of states, which was confirmed by scanning tunneling spectroscopy.

Ridge‐regression algorithm for gravity inversion of fault structures with variable density

We derive an analytical expression for gravity anomalies of an inclined fault with density contrast decreasing parabolically with depth. The effect of the regional background, particularly the interference from neighboring sources of a fault structure, is ascribed by a polynomial equation. We have developed an inversion technique employing the ridge‐regression iterative algorithm to infer the shape parameters of the fault structure, in addition to the effect of regional background. We demonstrate the validity of the proposed technique by inverting a gravity anomaly of a theoretical model, both with and without adding a regional background. The technique is insensitive to the effect of regional background. Two density‐depth models of the Godavari subbasin in India are used in our interpretation of the gravity anomalies of the Ahiri‐Cherla master fault. The interpreted results of a parabolic density model are found to be more geologically reasonable in comparison with the constant density model. The variations of the misfit function of the theoretical and observed gravity anomalies, the damping factor, and the shape parameters of the fault against the iteration number indicate the reliability of the interpretation.

Localization of wave fields in lower hybrid cavities

Abstract. We investigate lower hybrid wave trapping in cylindrically symmetric density depletions in the electrostatic approximation. Our investigation is inspired by previous observations of such trapping by spacecraft in the auroral region at altitudes up to about 2000km, and the recent discovery of this phenomenon at altitudes above 20000km in the inner magnetosphere. No particular shape is assumed for the density depletion, which need not be strictly zero outside some value of the radial coordinate r. Important previously known properties concerning parabolic density depletions extending to finite r are shown to hold also for arbitrary shapes and infinite extent: for a given parallel wave number kz, modes below the ambient lower hybrid frequency fLH are trapped in the density depletion (in the sense that they are evanescent outside the cavity), have a discrete spectrum and rotate in a left-handed sense, while there is a continuous spectrum of freely propagating right-handed rotating modes above fLH. New results are such that even though the density depletion may go to zero slowly with increasing r, and thus be essentially infinite in extent, there is a maximum distance within which a trapped mode with given kz and azimuthal mode number m may propagate. Furthermore, we find that for any monotonic density cavity and given kz, there is a local relation between plasma density gradient and the lowest possible frequency that can be trapped. We combine our theoretical results with spacecraft observations to find an upper bound on kz. Our examples indicate that the length of the cavities is larger than the width by a factor of at least 100.

Self-focusing and channel-coupling effects on short laser pulses propagating in a plasma channel

Nonparaxial, nonlinear propagation of a relativistic laser pulse in a preformed plasma channel having a parabolic density profile is analyzed. Nonlinearity arises due to relativistic motion of plasma electrons and their coupling with plasma channel. The effect of nonlinearities on betatron oscillations is analyzed and the nonlinear critical channel depth required for propagation of a matched laser pulse is evaluated. Mismatch due to nonlinear effects and additional condition for matched pulse propagation are obtained. Amplitude of the matched, as well as mismatched, beam is derived and finite pulse effects are studied.

Electron trapping and acceleration across a parabolic plasma density profile.

It is known that as a laser wakefield passes through a downward density transition in a plasma some portion of the background electrons are trapped in the laser wakefield and the trapped electrons are accelerated to relativistic high energies over a very short distance. In this study, by using a two-dimensional (2D) particle-in-cell (PIC) simulation, we suggest an experimental scheme that can manipulate electron trapping and acceleration across a parabolic plasma density channel, which is easier to produce and more feasible to apply to the laser wakefield acceleration experiments. In this study, 2D PIC simulation results for the physical characteristics of the electron bunches that are emitted from the parabolic density plasma channel are reported in great detail.

Excitation of electron Bernstein waves by a gyrating relativistic electron beam in a plasma slab

A nonlocal theory of excitation of electron Bernstein waves in a magnetized plasma column by a gyrating relativistic electron beam has been developed. The beam response is obtained using the Vlasov equation. For a one-dimensional parabolic density profile of the background plasma, the mode structure equation yields Hermite polynomial eigenfunctions. The growth of the Bernstein wave occurs via a fast cyclotron interaction. For a typical case when the electron cyclotron frequency is comparable to the electron plasma frequency and beam velocity vb≈0.8c, the growth rate is maximum for k⊥ρ0≈5. The nonlocal effects reduce the growth rate.

Linear mode conversion in inhomogeneous magnetized plasmas during ionospheric modification by HF radio waves

The propagation of high‐frequency (HF) radio waves in an inhomogeneous magnetoactive plasma and generation of plasma waves at the resonance layer near the reflection layer of the ordinary mode are studied using one‐dimensional (1‐D) and two‐dimensional full‐wave codes. The characteristics of the mode‐conversion process are investigated in linear and parabolic density profiles as the angle of incidence is varied. We present the 1‐D results for the wave propagation relevant to the high‐latitude heater facility at Tromsø and the midlatitude facility at Arecibo. For the facility at Arecibo, the 2‐D wave propagation in a plasma density approximating an overdense sporadic‐E patch is investigated to determine the localized regions of amplified intensity, where plasma waves can facilitate acceleration of fast energetic electrons, resulting in observed enhanced airglow.