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Slab geometry solid-state lasers offer significant performance improvements over conventional rod-geometry lasers. A detailed theoretical description of the thermal, stress, and beam-propagation characteristics of a slab laser is presented. The analysis includes consideration of the effects of the zig-zag optical path, which eliminates thermal and stress focusing and reduces residual birefringence.
It is noted that slab-geometry solid-state lasers potentially provide significant performance improvements relative to conventional rod-geometry lasers. Experimental measurements that use an Nd:glass test-bed slab laser are presented. A comparison is made between the results and computer-model predictions of the slab-geometry approach. The computer model calculates and displays the temperature and stress fields in the slab, and on the basis of these predicts birefringence and index-of-refraction distributions. The effect that these distributions have on optical propagation is determined in a polarization-sensitive ray-tracing section of the model. Calculations are also made of stress-induced surface curvature and the resulting focusing effects. The measurements are found to be in good agreement with the computer-model predictions. It is concluded that the slab configuration offers significant laser-performance advantages in comparison with the traditional rod-laser geometry.
Slab expansion (SLABEX) tests are conducted to validate a process for calibrating the detonation products equation of state (EOS) of a high explosive (HE). The SLABEX tests use rectangular slabs of PBX 9502, a polymer-bonded HE formulation consisting of 95 wt.% 1,3,5-triamino-2,4,6-trinitrobenzene bound with Kel F-800, a co-polymer of chlorotrifluoroethylene and vinylidene-fluoride. Three PBX 9502 slab thicknesses are examined, each confined symmetrically by two rectangular copper (Cu) plates approximately one-tenth the thickness of the HE slab. For the duration of each experiment, the detonation flow along the central axis of the PBX 9502 slab remains two-dimensional. The lateral flow velocity component of the outer surfaces of the expanding Cu plates is measured, along with the steady axial detonation speed along the central axis of the SLABEX. Hydrodynamic simulations of the Cu plate expansion in the SLABEX geometry, driven by the energy stored in the detonation products by the detonation combustion event, are conducted using a Jones–Wilkins–Lee EOS for the detonation products. This EOS form was recently parameterized for PBX 9502 in the cylinder expansion test geometry using a newly developed calibration technique [Voelkel et al., Combust. Flame 246, 112373 (2022)]. Good agreement between the experiment and prediction is found in each SLABEX test, demonstrating that the detonation product EOS calibration technique produces EOSs that are predictive when applied to other geometries.
In this work we develop the complete linearization formalism for the radiation transfer equation in slab geometry. This development was motivated by an observed convergence instability arising from the NORA code’s inner boundary while modeling a suite of simple test problems in slab geometry presented at the Line Transfer Workshop held in LLNL in May of 2019. The convergence issue was seen to emerge early on in Newton-Raphson iterations. These test problems required parameters in the former NORA inner boundary to achieve the asymptotic limit of zero incoming intensity. In this work we derive the limiting case directly to gain insight into the former algorithm’s pathology.
A flash-lamp-pumped slab Nd:YAG laser amplifier with 62 dB of gain is demonstrated. The amplifier remains linear for energy extraction up to 12 mJ, and the beam spatial quality remains good at repetition rates up to 10 Hz. The slab geometry provides for gain averaging in the zigzag dimension, thus eliminating the undesirable effects of nonuniform pumping. This averaging and the necessity for only a single compact gain element are valuable attributes that may allow for eventual laser-diode array pumping of the slab Nd:YAG amplifier.
Finite thickness infinite slab with radiation from time dependent source, solving nonhomogeneous boundary value problem for linear transport equation
This paper presents two methods for calculating the thermally induced stress, focusing, and depolarization in a pumped zigzag-slab solid-state laser. A computer program capable of detailed calculations of thermal effects in the general case is described. An approximate analysis of slab thermal effects in many cases allows calculation of these effects without use of the computer model directly. The analysis predicts that slabs of square cross section can be designed to have low depolarization and thermal focusing compared to Nd:YAG laser rods.
We propose two fractional extensions of continuous diffusion synthetic acceleration (DSA) with fractional derivative order α varying over the interval 2 ≥ α ≥ 1 . We investigate the spectral properties of the corresponding continuous families of fractional preconditioners by performing Fourier analysis for a model infinite homogeneous medium problem in slab geometry. The first family results in a fractional acceleration scheme, FrDSAo, that reduces to traditional DSA for .α = 2 and scattering ratio c limiting to a unit value (c → 1) but is otherwise optimized via the Fourier analysis, to obtain the smallest possible spectral radius, for c < 1 and 2 ≥ α ≥ 1. The second family corresponds to a fractional acceleration scheme, FrDSAs, that reduces to traditional DSA for α = 2 for all values of c. The latter scheme is not optimized but has the advantage of lending itself to a more straightforward implementation. For high values of c, the results of the Fourier analysis point to the existence of an interval 2 > α > ∼1.8 where both FrDSAo and FrDSAs can achieve a lower spectral radius than DSA. For example, DSA has a spectral radius of ∼0.2246 for c = 0.9999 while FrDSAo produces a value of ∼0.1616 at α = 1.92 and FrDSAs results in ∼0.2116 at α =1.93. (author)
The linear Boltzmann equation can be cast in a form mathematically identical to the radiation-transport equation. A multigroup procedure is used to reduce the energy (or velocity) dependence of the transport equation to a series of one-speed problems. Each of these one-speed problems is equivalent to the monochromatic radiative-transfer problem, and existing software is used to solve this problem in slab geometry. The numerical code conserves particles in elastic collisions. Generic examples are provided to illustrate the applicability of this approach. Although this formalism can, in principle, be applied to a variety of test particle or linearized gas dynamics problems, it is particularly well-suited to study the thermalization of suprathermal particles interacting with a background medium when the thermal motion of the background cannot be ignored. Extensions of the formalism to include external forces and spherical geometry are also feasible.
We investigate the solutions of the relaxed magnetohydrodynamic (MHD) model (RxMHD) of R. Dewar and Z. Qu. This model generalizes Taylor relaxation by including the ideal Ohm's law constraint using an augmented Lagrangian method, providing a pathway to extend the multi-region relaxed MHD (MRxMHD) model. We present the first numerical solution of the RxMHD model by Dewar and Qu, demonstrating that it is mathematically well-defined and computationally feasible for constructing MHD equilibria in slab geometry. We also show that a cross-field flow can exist without enforcing an arbitrary constraint on the angular momentum, as is done in the case of MRxMHD with flow. Our results also demonstrate the self-organization of fully relaxed regions during the optimization, which was an important motivation behind developing this model.
The present investigation is concerned with interferometric measurements of the thermally induced optical effects in laser crystals, taking into account crystals cut in both the zig-zag slab and the conventional rod geometries. The measurements conducted demonstrate the significant advantages obtained by replacing the rod in a Nd:YAG laser with a slab. A description is provided of simple measures designed to eliminate end and edge effects, and efficiency and threshold data for the Nd:YAG slab and the rod it replaced are presented. The only disadvantage is a small increase in cost due to the more difficult fabrication of the slab and the greater amount of Nd:YAG which is needed to allow the ends to be unpumped.
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We apply our self-consistent accretion disk corona (ADC) model, with two different geometries, to the broadband X-ray spectrum of the black hole candidate Cygnus X-1. As shown in a companion paper, models in which the Comptonizing medium is a slab surrounding the cold accretion disk cannot have a temperature higher than about 140 keV for optical depths greater than 0.2, resulting in spectra that are much softer than the observed 10-30 keV spectrum of Cyg X-1. In addition, the slab-geometry models predict a substantial "soft excess" at low energies, a feature not observed for Cyg X-1, and Fe K-alpha fluorescence lines that are stronger than observed. Previous Comptonization models in the literature have invoked a slab geometry with optical depth tau(sub T) approx. greater than 0.3 and coronal temperature T(sub c) approx. 150 keV, but they are not self-consistent. Therefore, ADC models with a slab geometry are not appropriate for explaining the X-ray spectrum of Cyg X-1. Models with a spherical corona and an exterior disk, however, predict much higher self-consistent coronal temperatures than the slab-geometry models. The higher coronal temperatures are due to the lower amount of reprocessing of coronal radiation in the accretion disk, giving rise to a lower Compton cooling rate. Therefore, for the sphere-plus-disk geometry, the predicted spectrum can be hard enough to describe the observed X-ray continuum of Cyg X-1 while predicting Fe fluorescence lines having an equivalent width of approx. 40 eV. Our best-fit parameter values for the sphere-plus-disk geometry are tau(sub T) approx. equal to 1.5 and T(sub c) approx. equal to 90 keV.
Recent progress in slab-geometry and conventional rod Nd:YAG solid-state lasers for applications in remote sensing is presented. Developments in slab geometry lasers, which were aimed at improving pulse energy and tuning range, have been based on the use of a Nd:glass substrate with a zig-zag optical path, with selective Raman shifting in gases and harmonic generation in LiNbO3 and KDP to extend the tuning range into the UV and visible regions. The theoretically predicted advantages of the elimination of birefringence and thermal and stress-induced focusing in the slab-geometry laser have been confirmed in measurements on a test-bed Nd:glass system, and a CW lamp pumped Nd:YAG oscillator, which have also demonstrated an order of magnitude improvement in laser performance. A single axial mode Nd:YAG oscillator has also been designed which, operating in a 3-msec quasi-CW mode, has a chirp rate of 30 kHz/microsec and a free-running stability of + or - 20 MHz. With chirp compensation, this stability is adequate for wind velocity measurements by coherent lidar.
The presentation outline includes motivation, radiation transport codes being considered, space radiation cases being considered, results for slab geometry, results from spherical geometry, and summary. ///////// main physics in radiation transport codes hzetrn uprop fluka geant4, slab geometry, spe, gcr,
Three-dimensional numerical simulations of compressible turbulent thermally driven convection, in both slab and spheroidal geometries, are reviewed and analyzed in terms of velocity spectra and mixing-length theory. The same ideal gas model is used in both geometries, and resulting flows are compared. The piecewise-parabolic method (PPM), with either thermal conductivity or photospheric boundary conditions, is used to solve the fluid equations of motion. Fluid motions in both geometries exhibit a Kolmogorov-like k(sup -5/3) range in their velocity spectra. The longest wavelength modes are energetically dominant in both geometries, typically leading to one convection cell dominating the flow. In spheroidal geometry, a dipolar flow dominates the largest scale convective motions. Downflows are intensely turbulent and up drafts are relatively laminar in both geometries. In slab geometry, correlations between temperature and velocity fluctuations, which lead to the enthalpy flux, are fairly independent of depth. In spheroidal geometry this same correlation increases linearly with radius over the inner 70 percent by radius, in which the local pressure scale heights are a sizable fraction of the radius. The effects from the impenetrable boundary conditions in the slab geometry models are confused with the effects from non-local convection. In spheroidal geometry nonlocal effects, due to coherent plumes, are seen as far as several pressure scale heights from the lower boundary and are clearly distinguishable from boundary effects.
Sparse-grid methods have recently gained interest in reducing the computational cost of solving high-dimensional kinetic equations. In this paper, we construct adaptive and hybrid sparse-grid methods for the Vlasov–Poisson–Lenard–Bernstein (VPLB) model. This model has applications to plasma physics and is simulated in two reduced geometries: a 0x3v space homogeneous geometry and a 1x3v slab geometry. Here we use the discontinuous Galerkin (DG) method as a base discretization due to its high-order accuracy and ability to preserve important structural properties of partial differential equations. We utilize a multiwavelet basis expansion to determine the sparse-grid basis and the adaptive mesh criteria. We analyze the proposed sparse-grid methods on a suite of three test problems by computing the savings afforded by sparse-grids in comparison to standard solutions of the DG method. The results are obtained using the adaptive sparse-grid discretization library ASGarD.
Papers are presented on solid-state lasers for remote sensing, diode-pumped Nd:YAG lasers, and tunable solid-state-laser systems. Topics discussed include titanium-sapphire tunable laser systems, the performance of slab geometry, and the development of slab lasers. Consideration is given to garnet host solid-state lasers, the growth of lasers and nonlinear materials, and nonlinear frequency conversion and tunable sources.