Azimuthal Symmetry Research Articles

Preliminary experimental investigation on small-aspect-ratio cylindrical solid liner implosion using compact pulsed power generator

Small-aspect-ratio cylindrical liner implosion on timescales of the order of hundreds of nanoseconds is important in the fields of high-energy-density physics, implosion dynamics, and inertial confinement fusion. This paper describes the design and development of a cylindrical liner load that has a low inductance and uniform magnetic field and its application in the CQ7 compact pulsed power generator. The dynamic response properties and implosion symmetry of liners with aspect ratios ranging from 5 to 9 are investigated. The experimental results show that the azimuthal symmetry of the liner remains intact, and that a liner with an inner diameter of 6.2 mm and a thickness of 0.4 mm can be accelerated up to 10 km/s before the reflected beam is lost. The demonstrated high performance of the experimental technique used for imploding the liner could be beneficial for studying the implosion and dynamics of materials on compact pulse power generators in the future.

Formation of Unstable Shocks for 2D Isentropic Compressible Euler

In this paper we construct unstable shocks in the context of 2D isentropic compressible Euler in azimuthal symmetry. More specifically, we construct initial data that when viewed in self-similar coordinates, converges asymptotically to the unstable $$C^{\frac{1}{5}}$$ self-similar solution to the Burgers’ equation. Moreover, we show the behavior is stable in $$C^8$$ modulo a two dimensional linear subspace. Under the azimuthal symmetry assumption, one cannot impose additional symmetry assumptions in order to isolate the corresponding manifold of initial data leading to stability: rather, we rely on modulation variable techniques in conjunction with a Newton scheme.

Interpolarization Forward Stimulated Brillouin Scattering in Standard Single‐Mode Fibers

AbstractForward stimulated Brillouin scattering in standard single‐mode fibers draws increasing interest toward sensing and signal processing applications. The process takes place through two classes of guided acoustic modes: purely radial ones and torsional‐radial modes with twofold azimuthal symmetry. The latter case cannot be described in terms of scalar models alone. In this work, the polarization attributes of forward stimulated Brillouin scattering in single‐mode fibers are investigated in analysis and experiment. Torsional‐radial acoustic modes are stimulated by orthogonally polarized pump tones, a first such report in standard single‐mode fibers. The scattering of optical probe waves by torsional‐radial modes may take up the form of phase modulation, cross‐polarization coupling, or a combination of both, depending on polarization. Lastly, this analysis predicts that circular and orthogonal pump tones may stimulate acoustic vortex beams: torsional‐radial modes that are rotating. The rotation represents the transfer of angular momentum between the polarization degree of freedom of the light field and the acoustic wave.

Computational Study of the Dynamics of the Taylor Bubble

We perform high-resolution numerical simulations of three-dimensional dynamics of an elongated bubble in a microchannel at moderate Reynolds numbers up to 1800. For this purpose, we use the coupled Brinkman penalization and volume of fluid methods implemented in the open-source framework Basilisk. The new results are validated with available experimental data and compared with previous numerical and theoretical predictions. We extend existing results to regimes with significant inertia, which are characterized by intense deformations of the bubble, including cases with azimuthal symmetry breaking. Various dynamical features are analyzed in terms of their spatiotemporal characteristics, such as frequencies and wavelengths of the bubble surface undulations and vortical structures in the flow.

Shallow Donor Impurity States with Excitonic Contribution in GaAs/AlGaAs and CdTe/CdSe Truncated Conical Quantum Dots under Applied Magnetic Field.

Using the effective mass approximation in a parabolic two-band model, we studied the effects of the geometrical parameters, on the electron and hole states, in two truncated conical quantum dots: (i) GaAs-(Ga,Al)As in the presence of a shallow donor impurity and under an applied magnetic field and (ii) CdSe–CdTe core–shell type-II quantum dot. For the first system, the impurity position and the applied magnetic field direction were chosen to preserve the system’s azimuthal symmetry. The finite element method obtains the solution of the Schrödinger equations for electron or hole with or without impurity with an adaptive discretization of a triangular mesh. The interaction of the electron and hole states is calculated in a first-order perturbative approximation. This study shows that the magnetic field and donor impurities are relevant factors in the optoelectronic properties of conical quantum dots. Additionally, for the CdSe–CdTe quantum dot, where, again, the axial symmetry is preserved, a switch between direct and indirect exciton is possible to be controlled through geometry.

Evaluating applicability of an azimuthally symmetric model in a laboratory tank with absorptive panels

In our lab at Brigham Young University, a tank of water will be used to help validate machine learning algorithms that could be applied to ocean acoustics. A model for sound propagation in the tank is required, and we are exploring the possibility of using ORCA, a range-independent normal mode model [Westwood et al., JASA (1996)]. Because ORCA assumes azimuthal symmetry in cylindrical coordinates, reflections from the tank walls must be significantly attenuated for ORCA to be a good model. To compare our measurements to ORCA, two approaches have been tried: (1) timegating and (2) absorptive panels on the walls. The layering used in ORCA is air on top, water with a maximum depth of 0.91 m, 3 cm thick acrylic bottom, a lower air layer, and then concrete on bottom. A simpler model excluding the air between the acrylic and the concrete was also tested. Both models were compared to measured data; both relative and absolute transmission loss were compared across a large frequency band and as a function of source/receiver distances at set depths. If ORCA is a good model for the tank, then we could easily generate training data for machine learning applications.

Weak magnetohydrodynamic turbulence

Low-frequency hydromagnetic turbulence is thought to play an important role in charged particle energization in space and astrophysical environments. For understanding large-scale turbulence in magnetized plasmas, low-frequency electromagnetic turbulence has been widely investigated within the theoretical framework of incompressible magnetohydrodynamic (MHD) theory. Among the existing works is the weak turbulence formalism of incompressible MHD turbulence. The present paper revisits the existing formalism under the assumption of zero residual energy. Under the strict assumption of turbulence taking place in a two-dimensional plane, which can be interpolated to a three-dimensional situation with azimuthal symmetry, the well-known steady-state turbulent spectrum of k⊥−2 is recovered, where k⊥ denotes the wave number perpendicular to the ambient magnetic field.

Injector Effects on Hybrid Polymethylmethacrylate Combustion Assessed by Thermochemical Tomography

In this work, two representative hybrid rocket injector designs, a single-port and an axial showerhead design, were examined experimentally to determine the comparative influence on the development of the downstream combustion zone with polymethylmethacrylate (PMMA) fuel. One-dimensional laser absorption tomography was employed to obtain the thermochemical structure of the PMMA–gaseous oxygen reaction layer via quantitative in situ species and temperature measurements. Optical measurements were performed with tunable semiconductor lasers in the midwave infrared to target absorption features in the fundamental vibrational bands of CO, , and . Planar measurements were conducted at the exit plane of cylindrical fuel grains () at axial distances () ranging from 2 to 11 with a constant gaseous oxygen flow for each of the injectors. Assuming azimuthal symmetry, a Tikhonov-regularized Abel inversion technique was used to obtain the radially resolved absorption coefficient, from which temperature and mole fractions were extracted. One-dimensional measurements over all fuel-grain lengths were consolidated to obtain spatially resolved two-dimensional images of the reaction layer thermochemical structure in a hybrid rocket motor geometry. Significant variations in experimental results were observed between the two injectors, suggesting the importance of injection fluid dynamics in hybrid rocket combustion performance. Explanations of the variations are offered from both a theoretical and a computational analysis.

Azimuthal flame response and symmetry breaking in a forced annular combustor

In the current study azimuthal forcing of an annular combustor with swirling flames has been performed to present for the first time the Heat Release Rate (HRR) response to all possible pressure fields of the first azimuthal mode up to a finite amplitude limit. The response is first quantified through the conventional Flame Describing Function (FDF) framework, showing a difference in response which depends on whether the acoustic field rotates anti-clockwise or clockwise, albeit with some scatter. Additionally and somewhat surprisingly, a finite HRR response is observed for flames exactly in the pressure node. An Azimuthal FDF is introduced, based on the decomposition of the spatial HRR response through Bloch theory, to better highlight the difference in HRR response to the anti-clockwise and clockwise components of the acoustic field and reduce scatter. A clear difference in response is observed, with a significantly higher response to the anti-clockwise forcing component compared to the clockwise component, independent of the prescribed pressure mode. The difference is attributed to the systematic symmetry breaking introduced by using an annular enclosure of finite curvature and width with swirling flames. It is argued that the finite curvature and width of the geometry and the swirl need to be both present to observe this effect. The difference in response results in a difference between the nature angle of the HRR mode and that of the acoustic field, explaining the relatively large HRR response observed for flames in the pressure node. The Azimuthal FDF describe all of these phenomena well, and is therefore considered more suitable than the conventional FDF to characterise the response in an annular combustor.

The Dynamical Structure of a Warm Core Ring as Inferred from Glider Observations and Along-Track Altimetry

This study investigates the vertical structure of the dynamical properties of a warm-core ring in the Gulf of Mexico (Loop Current ring) using glider observations. We introduce a new method to correct the glider’s along-track coordinate, which is, in general, biased by the unsteady relative movements of the glider and the eddy, yielding large errors on horizontal derivatives. Here, we take advantage of the synopticity of satellite along-track altimetry to apply corrections on the glider’s position by matching in situ steric height with satellite-measured sea surface height. This relocation method allows recovering the eddy’s azimuthal symmetry, precisely estimating the rotation axis position, and computing reliable horizontal derivatives. It is shown to be particularly appropriate to compute the eddy’s cyclo-geostrophic velocity, relative vorticity, and shear strain, which are otherwise out of reach when using the glider’s raw traveled distance as a horizontal coordinate. The Ertel potential vorticity (PV) structure of the warm core ring is studied in details, and we show that the PV anomaly is entirely controlled by vortex stretching. Sign reversal of the PV gradient across the water column suggests that the ring might be baroclinically unstable. The PV gradient is also largely controlled by gradients of the vortex stretching term. We also show that the ring’s total energy partition is strongly skewed, with available potential energy being 3 times larger than kinetic energy. The possible impact of this energy partition on the Loop Current rings longevity is also discussed.

Nd-doped ZnO films grown on c-cut sapphire by pulsed-electron beam deposition under oblique incidence

Nd-doped ZnO thin films were grown by pulsed-electron beam deposition (PED) on c-cut sapphire substrates under oblique angle incidence, at 10-2 mbar oxygen pressure and for a substrate temperature of 500 °C. The films were smooth, compact and constituted with columnar grains inclined at about 17°±4° from the normal to the substrate surface. From X-ray diffraction and transmission electron microscopy experiments, it was found that the wurtzite phase of Nd-doped ZnO thin films is observed with the c-axis inclined around 35° with respect to the normal axis of the substrate, with a three-fold azimuthal symmetry. Epitaxial relationships between Nd-doped ZnO films and sapphire substrate were determined from the asymmetric X-ray diffraction and are presented compared with those obtained for the films grown by non-oblique PED. The tilt of the ZnO c-axis has been explained by the epitaxy of the (2 2 9) ZnO plane on the (0 0 l) sapphire plane, such particular epitaxial growth having never been reported previously.

Clarifying Analytically Calculated Dispersion Relations of Finite-Length Overmoded Corrugated Cylindrical Azimuthally Symmetric Slow Wave Structures Using Numerical Simulations

We numerically calculate using the 2-D electromagnetic solver SUPERFISH the dispersion relation for electromagnetic modes supported by finite-length, overmoded, corrugated, cylindrical slow wave structures (SWSs) with azimuthal symmetry by first enforcing electric, and thereafter magnetic boundary conditions on both the left and right boundaries of the SWS. We construct the dispersion relation as a set of dispersion curves related to azimuthally symmetric TM ${}_{{0}{n}}$ modes of the finite-length SWS and compare it with the analytically calculated dispersion relation. It is shown as a result of the numerical calculations that the analytically calculated dispersion curves of higher order TM ${}_{{0}{n}}$ modes of the infinite-length SWS are not the dispersion curves defining each single TM ${}_{{0}{n}}$ mode, but rather are combinations of dispersion curves defining those high-order TM ${}_{{0}{n}}$ modes with some parts of dispersion curves defining lower order TM ${}_{0({n-k})}$ modes, where ${k}={1}\ldots ({n}-{1})$ .

Laguerre-Gaussian modes generated vector beam via nonlinear magneto-optical rotation

Laguerre-Gaussian (LG) beams contain a helical phase front with a doughnut-like intensity profile. We use the LG beam to introduce a rather simple method for generation of a vector beam (VB), a beam with spatially-dependent polarization in the beam cross section, via the nonlinear magneto-optical rotation (NMOR). We consider the NMOR of the polarization of a linearly polarized probe field passing through an inverted Y-type four-level quantum system interacting with a LG control field and a static magnetic field. It is shown that the polarization of the transmitted field is spatially distributed by the orbital angular momentum (OAM) of the LG control field, leading to generation of the VB with azimuthally symmetric polarization distribution. We show that the polarization and intensity distributions of the VB spatially vary by changing the OAMs of the LG control field. Moreover, the radial index of the LG control field has a major role in more spatially polarization distributing of the VB. It is shown that the intensity of the generated VBs in different points of the beam cross section can be controlled by the OAM as well as the radial index of the LG control field. However, the VB with highly spatially distributed can be generated for higher values of the radial index of LG control field. The analytical calculations determine the contribution of the different nonlinear (cross-Kerr effect) phenomena on the generation of the VB. We show that the VB is mainly generated via birefringence induced by the applied fields. Finally, we use asymmetric LG (aLG) beams for making the VBs with asymmetric polarization distribution. It is shown that by applying aLG beams, the azimuthal symmetry of the polarization distribution breaks and the asymmetric polarization distribution can be controlled by OAM and radial index of the aLG control field. The obtained results may find more interesting applications in fiber/free space optical communication to enhance the capacity of the information transmission.

A three-dimensional matching localization algorithm based on helix triangular pyramid array

On the eve of the occurrence of geological hazards, part of the rock and soil body begins to burst, rub, and fracture, generating infrasound signals propagating outward. 3D advanced positioning of the landslide has remained unsolved, which is important for disaster prevention. Through the Fourier transform and Hankel transform of the wave equation in cylindrical coordinates, this work established a three-dimensional axisymmetric sound field model based on normal waves, and designed a 4-element helix triangular pyramid array with vertical and horizontal sampling capabilities. Based on this, the three-dimensional matching localization algorithm of infrasound for geological hazards is proposed. Applying the algorithm to the infrasound signal localization of rock and soil layers, it was found that the helix triangular pyramid array can achieve accurate estimation of depth and distance with a smaller number of array elements than the traditional array, and may overcome the azimuth symmetry ambiguity. This study shows the application prospects of this method for predicting geohazards position several hours in advance.

Stability of Capillary Waves of an Arbitrary Symmetry on a Jet in a Uniform Electrostatic Field

The dispersion relation for capillary waves of an arbitrary azimuthal symmetry on an elliptic cross-section jet in a uniform electrostatic field which is perpendicular to the axis of symmetry of the jet is derived. The stability of the first three azimuthal modes is investigated. It is shown that the stability of capillary waves on the jet reduces with increase in the external electrostatic field strength and the related eccentricity of transverse jet cross-section, as well as with increase in the polarization charge on the jet surface. Comparison with a jet in a radial electrostatic field is carried out. In the case of the transverse electrostatic field the instability growth rates of the capillary waves of any symmetry on the jet surface are turned out to be significantly higher than those in the case of the radial electrostatic field.

Eigenvalue solution for the ion-collisional effects on the fast and slow ion acoustic waves in multi-ion species plasmas

The fast and slow waves in multi-ion species collisionless plasmas have been widely studied, but the collision effect on ion acoustic waves is a difficult problem. In this paper, plasmas with azimuthal symmetry velocity distribution in different collisional regimes are studied by eigenvalue solution of the linearized Fokker–Planck equation. The frequency, damping rate and distribution function from the solutions are consistent with the analytical result in collisionless limit. For the fast wave, the damping rate agrees well with the prediction of both fluid theory in collision limit and kinetic theory in collisionless limit. But for the slow wave, the frequency and damping rate predicted by fluid theory are not accurate. In two-ion species plasmas, the light and heavy ion density perturbation phases of two-ion species are the same for the fast wave, but opposite for the slow wave. Polytropic index of C5H12 plasmas is also calculated, which is simply affected by mean-free paths of ions for the fast wave, but affected by multiple factors, such as mean-free paths, heat transfer and the opposite phases for the slow wave.

Local electron and ion density control using passive resonant coils in inductively coupled plasma

Control of local electron and ion density using passive resonant coils is experimentally investigated in an inductive argon discharge. Four passive resonant coils are installed under a powered coil; each coil has a fan shape and good azimuthal symmetry. Electron energy probability functions and two-dimensional ion density profiles were measured under both resonant and non-resonant regimes. At non-resonance, almost all of the current flows through the powered coil located in the center of the reactor, and the profiles of the electron and ion density are convex. However, at resonance, a large current flows through the passive resonant coil, and dramatic changes are observed in the electron and ion density profiles. At resonance, the electron and ion densities near the passive resonant coil are increased by 300% compared to the non-resonant condition, and radial distributions become almost flat. Experimental results show that the electron and ion density profiles can be effectively controlled by a passive resonant coil at both low pressure (5 mTorr) and high pressure (50 mTorr). These changes in electron and ion density profiles can be understood by the changes of the electron heating and ionization regions.

Generation of excited species in a streamer discharge

At or near atmospheric pressure, most transient discharges, particularly in molecular gases or gas mixture containing molecular gases, result in a space charge dominated transport called a streamer discharge. The excited species generation in such discharges forms the basis for plasma chemistry in most technological applications. In this paper, we simulate the propagation of streamers in atmospheric pressure N2 to understand the energy partitioning in the formation of various excited species and compare the results to a uniform Townsend discharge. The model is fully two-dimensional with azimuthal symmetry. The results show a significantly larger fraction of the energy goes into vibrational excitation of the N2 ground state in a streamer-type discharge in comparison to a Townsend discharge. For lower applied voltages, the anode-directed (negative) steamer is slightly more efficient in channeling energy for excited species production in comparison to a cathode-directed (positive) streamer. Near 70% overvoltage, both types of streamers show very similar energy partitioning, but quite different from a Townsend discharge.

An exact inversion method for extracting orientation ordering by small-angle scattering

We outline a nonparametric inversion strategy for determining the orientation distribution function (ODF) of sheared interacting rods using small-angle scattering techniques. With the presence of direct inter-rod interaction and fluid mechanical forces, the scattering spectra are no longer characterized by the azimuthal symmetry in the coordinates defined by the principal directions of simple shear conditions, which severely compounds the reconstruction of ODFs based on currently available methods developed for dilute systems. Using a real spherical harmonic expansion scheme, the real-space ODFs are uniquely determined from the anisotropic scattering spectra and their numerical accuracy is verified computationally. Our method can be generalized to extract ODFs of uniaxially anisotropic objects under different flow conditions in a properly transformed reference frame with suitable basis vectors.

Four-Frequency Solution in a Magnetohydrodynamic Couette Flow as a Consequence of Azimuthal Symmetry Breaking.

The occurrence of magnetohydrodynamic quasiperiodic flows with four fundamental frequencies in differentially rotating spherical geometry is understood in terms of a sequence of bifurcations breaking the azimuthal symmetry of the flow as the applied magnetic field strength is varied. These flows originate from unstable periodic and quasiperiodic states with broken equatorial symmetry, but having fourfold azimuthal symmetry. A posterior bifurcation gives rise to twofold symmetric quasiperiodic states, with three fundamental frequencies, and a further bifurcation to a four-frequency quasiperiodic state which has lost all the spatial symmetries. This bifurcation scenario may be favored when differential rotation is increased and periodic flows with m-fold azimuthal symmetry, m being a product of several prime numbers, emerge at sufficiently large magnetic field.