Slab Approximation Research Articles

Acoustic wave propagation and scattering in visco-acoustic medium: Integral equation representation and De Wolf approximation

A visco-acoustic medium is an approximate representation of the absorption and attenuation characteristics of the actual earth medium, which will cause energy attenuation and velocity dispersion of seismic waves. The propagation law of scattered waves in viscoelastic media can be revealed through seismic wave forward simulation. However, the numerical simulation of scattered waves in a visco-acoustic medium using the De Wolf approximation method based on the Lippmann-Schwingr (L-S) equation has not been studied. Therefore, based on the Futterman dispersion relation, the mathematical expression of the integral equation of acoustic wave propagation and scattering in the visco-acoustic medium is derived. We combine the De Wolf approximation with the quality factor Q. The thin slab approximation and screen approximation methods are two realizations of the De Wolf approximation. The thin slab approximation and the screen approximation continuation operator in the viscous-acoustic medium are constructed and applied to the numerical simulation of the scattered wave field. The research results of the concave model and complex model indicate that due to the influence of medium viscosity, the energy of the deep reflected waves is weaker in the forward modeling records of the thin slab approximation method and screen approximation method, and the dominant frequency of seismic waves moves towards the low-frequency direction; Compared with the finite difference results, they only calculate one reflection, and there are no multiple wave signals in the seismic records. Finally, We discuss the thin slab approximation and the screen approximation method for detail around the division of the thickness of the thin slab, the selection of the reference frequency, and the non-uniformity of the medium.

A Generalized Slab Model

Abstract We construct a generalized slab model to calculate the ocean’s linear response to an arbitrary, depth-variable forcing stress profile. To introduce a first-order improvement to the linear stress profile of the traditional slab model, a nonlinear stress profile, which allows momentum to penetrate into the transition layer (TL), is used [denoted mixed layer/transition layer (MLTL) stress profile]. The MLTL stress profile induces a twofold reduction in power input to inertial motions relative to the traditional slab approximation. The primary reduction arises as the TL allows momentum to be deposited over a greater depth range, reducing surface currents. The secondary reduction results from the production of turbulent kinetic energy (TKE) beneath the mixed layer (ML) related to interactions between shear stress and velocity shear. Direct comparison between observations in the Iceland Basin, the traditional slab model, the generalized slab model with the MLTL stress profile, and the Price–Weller–Pinkel (PWP) model suggest that the generalized slab model offers improved performance over a traditional slab model. In the Iceland Basin, modeled TKE production in the TL is consistent with observations of turbulent dissipation. Extension to global results via analysis of Argo profiling float data suggests that on the global, annual mean, ∼30% of the total power input to near-inertial motions is allocated to TKE production. We apply this result to the latest global, annual-mean estimates for near-inertial power input (0.27 TW) to estimate that 0.08 ± 0.01 TW of the total near-inertial power input are diverted to TKE production.

Analytical Modeling of Magnetization Losses in Twisted Stacked HTS Conductors

The European post-ITER fusion demonstrator reactor (DEMO) design activities have been ongoing for several years in the framework of the EUROfusion Consortium. The designs proposed for the DEMOnstration Fusion Power Plants (DEMO) magnets include options based on high-temperature superconducting (HTS) technology, namely as an Insert in the Central Solenoid (CS). This work describes the development of tools for the calculation of magnetisation losses in a twisted-stacked HTS cable, which represents one of the most promising configurations of HTS fusion Cable-in-Conduit conductors (CICC). This geometry cannot be tackled with the straightforward application of 1D or 2D models, given their inability to describe the twisting of the tape stacks. However, the methodology proposed in this work allows one to treat the twisting of the conductors by discretizing them in a set of straight pieces. A set of analytical equations is developed to compute the instantaneous power losses in the slab approximation. This fast, easy-to-use, open-access tool, can be employed for the computation of AC losses in the central solenoid modules of a tokamak. In particular, we have applied the model to study the HTS insert of the DEMO central solenoid.

Discrepancy in Grain Size Estimation of H2O Ice in the Outer Solar System

Radiative transfer models (RTMs) have been used to estimate grain size of amorphous and crystalline water (H2O) ice in the outer solar system from near-infrared (NIR) wavelengths. We use radiative scattering models to assess the discrepancy in grain size estimation of H2O ice at a temperature of 15, 40, 60, and 80 K (amorphous) and 20, 40, 60, and 80 K (crystalline)—relevant to the outer solar system. We compare the single scattering albedos of H2O ice phases using the Mie theory and Hapke approximation models from the optical constant at NIR wavelengths (1–5 μm). This study reveals that Hapke approximation models—Hapke slab and internal scattering model (ISM)—predict grain size of crystalline phase slightly closer to Mie model than amorphous phase at temperatures of 15–80 K. However, the Hapke slab model predicts, in general, grain sizes much closer to those of the Mie model's estimations while ISM predicted grain sizes exhibit a higher uncertainty. We recommend using the Mie model for unknown spectra of outer solar system bodies to estimate H2O ice grain sizes. While choosing the approximation model for employing RTMs, we recommend using a Hapke slab approximation model over the ISM.

Assessment of Radiative Heating for Hypersonic Earth Reentry Using Nongray Step Models

Accurate prediction of the aerothermal environment is of great significance to space exploration and return missions. The canonical Fire II trajectory points are simulated to investigate the radiative transfer in the shock layer for Earth reentry at hypervelocity above 10 km/s using a developed radiation–flowfield uncoupling method. The thermochemical nonequilibrium flow is solved by an in-house PHAROS Navier–Stokes code, while the nongray radiation is integrated by the tangent slab approximation, respectively, combined with the two-, five-, and eight-step models. For the convective heating, the present results agree well with the data of Anderson’s relation. For the radiative heating, the two-step model predicts the closest values with the results of Tauber and Sutton’s relationship, while the five- and eight-step models predict far greater. The three-step models all present the same order of magnitude of radiative heating of 1 MW/m2 and show a consistent tendency with the engineering estimation. The Planck-mean absorption coefficient is calculated to show the radiative transfer significantly occurs in the shock layer. By performing the steady simulation at each flight trajectory point, the present algorithm using a nongray step model with moderate efficiency and reasonable accuracy is promising to solve the real-time problem in engineering for predicting both convective and radiative heating to the atmospheric reentry vehicle in the future.

Uncertainty in Grain Size Estimations of Volatiles on Trans-Neptunian Objects and Kuiper Belt Objects

Abstract We analyze the uncertainty in grain size estimation of pure methane (CH4) and nitrogen saturated with methane (N2:CH4) ices, the most abundant volatile materials on trans-Neptunian objects (TNOs) and Kuiper Belt objects (KBOs). We compare the single scattering albedo, which determines the grain size estimation of outer solar system regolith, of these ices using the Mie scattering model and two other Hapke approximations (Hapke 1993) in radiative transfer scattering models (RTMs) at near-infrared (NIR) wavelengths (1–5 μm). The equivalent slab (Hapke slab) approximation model predicts results much closer to Mie scattering over the NIR wavelengths at a wide range of grain sizes. In contrast, even though the internal scattering model predicts an approximate particle diameter close to the Mie model for particles with a 10 μm radii, it exhibits higher discrepancies in the predicted estimation for larger grain sizes (e.g., 100 and 1000 μm radii). Owing to the Rayleigh effect on single-scattering properties, neither Hapke approximate models could predict an accurate grain size estimation for the small particles (radii ≤5 μm). We recommend that future studies should favor the Hapke slab approximation when employing RTMs for estimating grain sizes of the vast number of TNOs and KBOs in the outer solar system.

Improving Groundwater Model Calibration with Repeat Microgravity Measurements.

Groundwater-flow models depend on hydraulic head and flux observations for evaluation and calibration. A different type of observation-change in storage measured using repeat microgravity-can also be used for parameter estimation by simulating the expected change in gravity from a groundwater model and including the observation misfit in the objective function. The method is demonstrated using new software linked to MODFLOW input and output files and field data from the vicinity of the All American Canal in southeast California, USA. Over a 10-year period following lining of the previously highly permeable canal with concrete, gravity decreased by over 100 μGal (equivalent to about 2.5m of free-standing water) at some locations as seepage decreased and the remnant groundwater mound dissipated into the aquifer or was removed by groundwater pumping. Simulated gravity from a MODFLOW model closely matched observations, and repeat microgravity data proved useful for constraining both hydraulic conductivity and specific yield estimates. Specific yield estimated using the infinite-horizontal slab approximation agreed well with model-derived values, and the departure from the linear, flat-water-table approximation was small, less than 2%, despite relatively large and dynamic water-table slope. First-order second-moment parameter uncertainty analysis shows reduction in uncertainty for all hydraulic conductivity and specific yield parameter estimates with the addition of repeat microgravity data, as compared to drawdown data alone.

First evaluation of an absolute quantum gravimeter (AQG#B01) for future field experiments

Abstract. Quantum gravimeters are a promising new development allowing for continuous absolute gravity monitoring while remaining user-friendly and transportable. In this study, we present experiments carried out to assess the capacity of the AQG#B01 in view of future deployment as a field gravimeter for hydrogeophysical applications. The AQG#B01 is the field version follow-up of the AQG#A01 portable absolute quantum gravimeter developed by the French quantum sensor company Muquans. We assess the instrument's performance in terms of stability (absence of instrumental drift) and sensitivity in relation to other gravimeters. No significant instrumental drift was observed over several weeks of measurement. We discuss the observations concerning the accuracy of the AQG#B01 in comparison with a state-of-the-art absolute gravimeter (Micro-g-LaCoste, FG5#228). We report the repeatability to be better than 50 nm s−2. This study furthermore investigates whether changes in instrument tilt and external temperature and a combination of both, which are likely to occur during field campaigns, influence the measurement of gravitational attraction. We repeatedly tested external temperatures between 20 and 30 ∘C and did not find any significant effect. As an example of a geophysical signal, a 100 nm s−2 gravity change is detected with the AQG#B01 after a rainfall event at the Larzac geodetic observatory (southern France). The data agreed with the gravity changes measured with a superconducting relative gravimeter (GWR, iGrav#002) and the expected gravity change simulated as an infinite Bouguer slab approximation. We report 2 weeks of stable operation under semi-terrain conditions in a garage without temperature-control. We close with operational recommendations for potential users and discuss specific possible future field applications. While not claiming completeness, we nevertheless present the first characterization of a quantum gravimeter carried out by future users. Selected criteria for the assessment of its suitability in field applications have been investigated and are complemented with a discussion of further necessary experiments.

Superwide-angle seismic migration by including the back-scattered wave through domain decomposition and biaxial parabolic approximation

Using ideas from computational electromagnetics and the basic procedure from the domain decomposition method, we present a biaxial parabolic approximation method for enlarging the angle domain in which the parabolic approximation to the acoustic wave equation is multiple applied and that can be used for migrating data with super-wide angles. Mathematically, the biaxial approximation is a special case of the multiaxial parabolic approximation, and thus can be straightforwardly extended to multiaxial approximations. In detail, we first divide the subsurface into several fan-shaped subdomains and use the axis of each subdomain as the local wave propagation direction. Then, we make a parabolic approximation to the wave equation in each subdomain with respect to the corresponding symmetry axis and compute the forward-propagating wave alternately using a high-order parabolic approximated wave equation in two subdomains. Finally, we use the computed forward-propagating wave as the boundary condition for calculating the back-scattered wave and Green's function by applying the thin slab approximation. Compared with most one-way methods, the proposed method can deal with the strong velocity contrast in the horizontal direction at a large scattering angles. Moreover, compared with certain full-wave methods that have been published in recent years, the proposed method is considerably more efficient and sacrifices only a little in terms of accuracy. Numerical results from comparisons with models of different complexities demonstrate that our method is cost-effective and has considerable potential for use in seismic modeling and imaging.

A Coupled A–H Formulation for Magneto-Thermal Transients in High-Temperature Superconducting Magnets

The application of high-temperature superconductors to accelerator magnets for future particle colliders is under study. Numerical methods are crucial for an accurate evaluation of the complex dynamical behavior of the magnets, especially concerning the magnetic field quality and thermal behavior. We present a coupled $\textbf{A}$-$\textbf{H}$ field formulation for the analysis of magneto-thermal transients in accelerator magnets. The magnetic field strength $\textbf{H}$ accounts for the eddy current problem in the source regions containing the superconducting domains, while the magnetic vector potential $\textbf{A}$ represents the magnetoquasistatic problem in the normal and non-conducting domains. Furthermore, we include a slab approximation for the source regions, making the formulation suitable for large scale models composed of thousands of tapes. In this work, the relevant equations are derived and discussed, with emphasis on the coupling conditions. The weak formulation is derived, and numerical results are provided in order to both, verify the formulation and scale it to the size of an accelerator magnet.

Optimisation of the input polarisation angle on lines of sights of a polarimetry system for a fusion reactor

The study is dedicated to the evaluation of the effects of the input polarisation angle with respect to the toroidal magnetic field on the values of the Faraday Rotation, Cotton-Mouton phase shift angle (and then ellipticity). The need of this evaluation is connected to the optimisation of the polarimetry quantities in view of having a complete information related to magnetic fields, plasma density and electron temperature. A polarimeter with vertical as well as horizontal lines of sights at various angle with respect to the equatorial axis is considered. The equilibrium used is a circular analytic model which considers a tokamak in the slab approximation. The plasma parameters considered are B0=3.1 T (toroidal magnetic field), I0=3.5 MA (plasma current), N0=2⋅ 1020 m−3 (plasma density), R0=3 m (major radius) and a=1 m (plasma radius), so R0/a=3 (aspect ratio). The input polarisation angle is varied between −90̂ and 90̂. It is found that the polarimetry signals of horizontal lines of sights are very sensible to the polarisation input angle leading to strengthening the capability of measuring the plasma density and electron temperature in these lines. Numerical calculations show that the largest change in the polarization state, leading to the reduction of the measurement errors, is for the beam with initial Stokes vector s⃗0=(0,± 1,0) (polarization angle ψ0=± 45̂).

3D Gravity Analysis in the Spatial Domain: Model Simulation by Multiple Polygonal Cross-Sections Coupled with Exponential Density Contrast

An automatic 3D modeling technique is developed in the spatial domain to analyze the gravity anomalies produced by a concealed density interface with mass density contrast differing exponentially with depth. The sedimentary column above the interface is described with a stack of multiple vertical polygonal sections of unit thickness each. For such a case, the depth ordinates of the vertices of the cross-sections become the unknown parameters to be estimated from gravity data. Forward solution of the model space is realized in the spatial domain by a technique that combines both analytic and numeric approaches. Initial depths to the interface are calculated based on the Bouguer slab approximation and subsequently improved, iteratively, based on the ratio of the product of the observed gravity anomaly and existing depth parameter to the corresponding model gravity response. The iterative process continues until one of the predefined termination criteria is accomplished. Unlike the existing methods, the advantage of the proposed method is that the observed gravity anomalies need not necessarily be sampled/available at regular spatial grid intervals. The applicability of the proposed model is exemplified with a set of noisy gravity anomalies attributable to a synthetic structure before being applied to a real world gravity data. In the case of the synthetic example, the method has yielded a structure that was compatible with the assumed structure even in the presence of random noise. Application of the proposed method to the gravity data set from the Los Angeles Basin, California, using a prescribed exponential density function has yielded a model that concurs reasonably well with the published models.

Stability of scrape-off layer plasma: A modified Rayleigh–Bénard problem

We present an extensive linear stability analysis of a two-dimensional fluid model used to study the plasma dynamics in the scrape-off layer of tokamaks. The model equations are based on the Braginskii fluid equations under the assumptions of drift ordering and electrostatic plasma. The model also employs the commonly used slab geometry approximation, whereby the magnetic field is assumed constant and straight, with the effects of curvature reintroduced as effective gravitational terms. We study the linear instability in the system by solving a boundary value problem, thereby extending previous studies, which focused on a local analysis. Furthermore, we demonstrate that the governing plasma equations for the scrape-off layer can be viewed as describing a thermal convection problem with additional effects. The new features include a non-uniform basic state gradient, linear damping terms, and additional advective terms. We characterize the conditions at the onset of instability and perform an extensive parameter scan to describe how the stability threshold varies as a function of plasma parameters.

Small deformations of kinks and walls

A Rayleigh–Schrödinger type of perturbation scheme is employed to study weak self-interacting scalar potential perturbations occurring in scalar field models describing 1D domain kinks and 3D domain walls. The solutions for the unperturbed defects are modified by the perturbing potentials. An illustration is provided by adding a cubic potential to the familiar quartic kink potential and solving for the first order correction to the kink solution, using a “slab approximation”. A result is the appearance of an asymmetric scalar potential with different, nondegenerate, vacuum values and the subsequent formation of vacuum bubbles.

Electron heating in the laser and static electric and magnetic fields

A 2D slab approximation of the interactions of electrons with intense linearly polarized laser radiation and static electric and magnetic fields is widely used for both numerical simulations and simplified semi-analytical models. It is shown that in this case, electron dynamics can be conveniently described in the framework of the 3/2 dimensional Hamiltonian approach. The electron acceleration beyond a standard ponderomotive scaling, caused by the synergistic effects of the laser and static electro-magnetic fields, is due to an onset of stochastic electron motion.

Identifying the source of super-high energetic electrons in the presence of pre-plasma in laser–matter interaction at relativistic intensities

The generation of super-high energetic electrons influenced by pre-plasma in relativistic intensity laser–matter interaction is studied in a one-dimensional slab approximation with particle-in-cell simulations. Different pre-plasma scale lengths and laser intensities are considered, showing an increase in both particle number and cut-off kinetic energy of electrons with the increase of pre-plasma scale length and laser intensity, the cut-off kinetic energy greatly exceeding the corresponding laser ponderomotive energy. A two-stage electron acceleration model is proposed to explain the underlying physics. The first stage is attributed to the synergetic acceleration by longitudinal electric field and counter-propagating laser pulses, and a scaling law is obtained with efficiency depending on the pre-plasma scale length and laser intensity. These electrons pre-accelerated in the first stage could build up an intense electrostatic potential barrier with maximal value several times as large as the initial electron kinetic energy. Some of the energetic electrons could be further accelerated by reflection off the electrostatic potential barrier, with their finial kinetic energies significantly higher than the values pre-accelerated in the first stage.

Time resolved diffuse optical spectroscopy with geometrically accurate models for bulk parameter recovery.

A novel straightforward, accessible and efficient approach is presented for performing hyperspectral time-domain diffuse optical spectroscopy to determine the optical properties of samples accurately using geometry specific models. To allow bulk parameter recovery from measured spectra, a set of libraries based on a numerical model of the domain being investigated is developed as opposed to the conventional approach of using an analytical semi-infinite slab approximation, which is known and shown to introduce boundary effects. Results demonstrate that the method improves the accuracy of derived spectrally varying optical properties over the use of the semi-infinite approximation.

AC loss evaluation of an HTS insert for high field magnet cooled by cryocoolers

AC losses in a high temperature superconducting (HTS) insert coil for 25-T cryogen-free superconducting magnet during its initial energization are numerically calculated under the assumption of slab approximation. The HTS insert consisting of 68 single pancakes wound using coated conductors generates a central magnetic field of 11.5T in addition to the contribution of 14.0T from a set of low temperature superconducting (LTS) outsert coils. Both the HTS insert and the LTS coils are cooled using cryocoolers, and energized simultaneously up to the central field of 25.5T with a constant ramp rate for 60min. The influences of the magnitudes and orientations of locally applied magnetic fields, magnetic interactions between turns and transport currents flowing in the windings are taken into account in the calculations of AC losses. The locally applied fields are separated into axial and radial components, and the individual contributions of these field components to the AC losses are simply summed up to obtain the total losses. The AC losses due to the axial fields become major in the beginning of energization, whereas the total losses monotonically increase with time after the AC losses due to the radial fields become major.

View-Factor Approach as a Radiation Model for the Reentry Flowfield

An accurate and efficient radiation transfer model, based on the view-factor approach, is proposed for the reentry flowfield. The radiation transfer equation is coupled to the gasdynamic system of equations in order to describe the energy transfer in the absorbing and emitting air plasma in two-dimensional axisymmetric and three-dimensional geometries. A newly derived semi-analytical expression for the radiative flux density dramatically simplifies the calculation of the spectral and integral characteristics of the radiation flowfield in the axisymmetric geometry. The comparison with the ray-tracing method and tangent slab approximation revealed an asymptotic accuracy of radiation flux density.

AC Losses of an HTS Insert in a 25-T Cryogen-Free Superconducting Magnet

A 25-T cryogen-free superconducting magnet (25T-CSM) is being developed at the High Field Laboratory for Superconducting Materials, Institute for Materials Research, Tohoku University. In the case of a cryogen-free superconducting magnet, the coil temperature rises during a sweep of an operating current due to ac losses. Hence, the ac loss estimation is very important for the cooling design. The critical current density and the magnetization of Gd123 tapes at 4.2 K were measured in order to estimate the ac loss of a Gd123 insert of the 25T-CSM. The ac loss is actually the hysteresis loss, which are calculated from the J c properties taking the magnetic field distribution in the Gd123 coil into account. Regarding the effect of tape stacking (or winding) in a pancake coil, the slab approximation can be used for hysteresis loss calculation. In the case of slab model, the full penetration field at the center of the tape becomes higher than the maximum applied magnetic field in the most part of the coil. As a result, the hysteresis loss increases with increasing a magnetic field when the magnet energizes. The hysteresis losses assuming the slab model, however, show an opposite field dependence to those calculated from the strip model without the stacking effect. Hence, the ac loss of 5 W is estimated when the magnet energizes to 25.5 T within 60 min.