Volume Ray casting with peak finding and differential sampling

Journal ArticleDirect volume rendering and isosurfacing are ubiquitous rendering techniques in scientific visualization, commonly employed in imaging 3D data from simulation and scan sources. Conventionally, these methods have been treated as separate modalities, necessitating different sampling strategies and rendering algorithms. In reality, an isosurface is a special case of a transfer function, namely a Dirac impulse at a given isovalue. However, artifact-free rendering of discrete isosurfaces in a volume rendering framework is an elusive goal, requiring either infinite sampling or smoothing of the transfer function. While preintegration approaches solve the most obvious deficiencies in handling sharp transfer functions, artifacts can still result, limiting classification. In this paper, we introduce a method for rendering such features by explicitly solving for isovalues within the volume rendering integral. In addition, we present a sampling strategy inspired by ray differentials that automatically matches the frequency of the image plane, resulting in fewer artifacts near the eye and better overall performance. These techniques exhibit clear advantages over standard uniform ray casting with and without preintegration, and allow for high-quality interactive volume rendering with sharp C0 transfer functions

Interactive isosurface ray tracing of large octree volumes

Journal ArticleWe present a technique for ray tracing isosurfaces of large compressed structured volumes. Data is first converted into a losslesscompression octree representation that occupies a fraction of the original memory footprint. An isosurface is then dynamically rendered by tracing rays through a min/max hierarchy inside interior octree nodes. By embedding the acceleration tree and scalar data in a single structure and employing optimized octree hash schemes, we achieve competitive frame rates on common multicore architectures, and render large time-variant data that could not otherwise be accomodated

Interactive ray tracing of arbitrary implicits with SIMD interval arithmetic

Journal ArticleWe present a practical and efficient algorithm for interactively ray tracing arbitrary implicit surfaces. We use interval arithmetic (IA) both for robust root computation and guaranteed detection of topological features. In conjunction with ray tracing, this allows for rendering literally any programmable implicit function simply from its definition. Our method requires neither special hardware, nor preprocessing or storage of any data structure. Efficiency is achieved through SIMD optimization of both the interval arithmetic computation and coherent ray traversal algorithm, delivering interactive results even for complex implicit functions

Effects of the applied fields' strength on the plasma behavior and processes in ExB plasma discharges of various propellants: II. Magnetic field

We present in this part II the effects of the magnetic field intensity on the properties of the plasma discharge and the underlying phenomena for different propellant's ion mass. The plasma setup represents a perpendicular configuration of the electric and magnetic fields, with the electric field along the axial direction and the magnetic field along the radial direction. The magnetic field intensity is changed from 5 to 30 mT, with 5 mT increments. The propellant gases are xenon, krypton, and argon. The simulations are carried out using a particle-in-cell (PIC) code based on the computationally efficient reduced-order PIC scheme. Similar to the observations in part I, we show that, across all propellants, the variation in the intensity of the magnetic field yields two distinct regimes of the plasma, where either the Modified Two Stream Instability (MTSI) or the Electron Cyclotron Drift Instability (ECDI) are present. Nonetheless, a third plasma regime is also observed for cases with moderate values of the magnetic field intensity (15 and 20 mT), in which the ECDI and the MTSI co-exist with comparable amplitudes. This described change in the plasma regime becomes clearly reflected in the radial distribution of the axial electron current density and the electron temperature anisotropy. Contrary to the effect of the electric field magnitude in part I, we observed here that the MTSI is absent at the relatively low magnetic field intensities (5 and 10 mT). At the relatively high magnitudes of the magnetic field (25 and 30 mT), the MTSI becomes strongly present, a long-wavelength wave mode develops, and the ECDI does not excite. An exception to this latter observation was noticed for xenon, for which the ECDI's presence persists up to the magnetic field peak value of 25 mT.Comment: 17 pages, 15 figure

Influence of the magnetic field's curvature on the radial-azimuthal dynamics of a Hall thruster plasma discharge with different propellants

The topology of the applied magnetic field is an important design aspect of Hall thrusters. For modern Hall thrusters, the field topology most often features curved lines with a concave (negative) curvature upstream of the field peak and a convex (positive) curvature downstream. Additionally, the advent of the magnetic shielding technique has resulted in the design of Hall thrusters with non-conventional magnetic fields that exhibit high degrees of concavity upstream of the field's peak. We carry out a rigorous and detailed study of the effects that the magnetic field's curvature has on the plasma properties and the underlying processes in a 2D configuration representative of a Hall thruster's radial-azimuthal cross-section. The analyses are performed for plasma discharges of three propellants: xenon, krypton, and argon. For each propellant, we have carried out high-fidelity reduced-order particle-in-cell (PIC) simulations with various degrees of positive and negative curvatures of the magnetic field. Corresponding 1D radial PIC simulations were also performed for xenon to compare the observations between 1D and 2D simulations. We observed that there are distinct differences in the plasma phenomena between the cases with positive and negative field curvatures. The instability spectra in the cases of positive curvature is mostly dominated by the Electron Cyclotron Drift Instability, whereas the Modified Two Stream Instability is dominant in the negative-curvature cases. The distribution of the plasma properties, particularly the electron and ion temperatures, and the contribution of various mechanisms to electrons' cross-field transport showed notable variations with the field's curvature, especially between the positive and the negative values. Finally, the magnetic field curvature was observed to majorly influence the ion beam divergence along the radial and azimuthal coordinates.Comment: 25 pages, 24 figure

Effects of the neutral dynamics model on the particle-in-cell simulations of a Hall thruster plasma discharge

The dynamics of the neutral atoms in Hall thrusters affect several plasma processes, from the ionization to the electrons' mobility. In the context of Hall thruster's particle-in-cell (PIC) modeling, the neutrals are often treated kinetically, similar to the plasma species, and their interactions with themselves and the ions are resolved using the Direct-Simulation Monte-Carlo (DSMC) algorithm. However, the DSMC approach is computationally resource demanding. Therefore, modeling the neutrals as a 1D fluid has been also pursued in simulations that do not involve the radial coordinate and, hence, do not resolve the neutrals' radial expansion. In this article, we present an extensive study on the sensitivity of the PIC simulations of Hall thruster discharge to the model used for the neutral dynamics. We carried out 1D axial PIC simulations with various fluid and kinetic models of the neutrals as well as self-consistent quasi-2D axial-azimuthal simulations with different neutrals' fluid descriptions. Our results show that the predictions of the simulations in either 1D or 2D configurations are highly sensitive to the neutrals' model, and that different treatments of the neutrals change the spatiotemporal evolution of the discharge. Moreover, we observed that considering the ion-neutral collisions causes a significant variation in the neutral temperature, thus requiring that the neutrals' energy equation to be included as well in their fluid system of equations. Finally, the self-consistent axial-azimuthal simulations highlighted that a neutrals' model based on the continuity conservation equation only is not an appropriate choice and leads to physically unexpected high-frequency global discharge oscillations.Comment: 32 pages, 30 figure

Effects of the applied fields' strength on the plasma behavior and processes in ExB plasma discharges of various propellants: I. Electric field

We present, in this two-part article, an extensive study on the influence that the magnitudes of the applied electric (E) and magnetic (B) fields have on a collisionless plasma discharge of xenon, krypton, and argon in a 2D radial-azimuthal configuration with perpendicular orientation of the fields. The dependency of the behavior and the underlying processes of ExB discharges on the strength of electromagnetic field and ion mass has not yet been studied in depth and in a manner that can distinguish the role of each individual factor. This has been, on the one hand, due to the significant computational cost of conventional high-fidelity particle-in-cell (PIC) codes that do not allow for extensive simulations over a broad parameter space within practical timeframes. On the other hand, the experimental efforts have been limited, in part, by the measurements' spatial and temporal resolution. In this sense, the notably reduced computational cost of the reduced-order PIC scheme enables to numerically cast light on the parametric variations in various aspects of the physics of ExB discharges, such as high resolution spatial-temporal mappings of the plasma instabilities. In part I of the article, we focus on the effects of the E-field intensity. We demonstrate that the intensity of the field determines two distinct plasma regimes, which are characterized by different dominant instability campaigns. At relatively low E-field magnitudes, the Modified Two Stream Instability (MTSI) is dominant, whereas, at relatively high E-field magnitudes, the MTSI is mitigated, and the Electron Cyclotron Drift Instability (ECDI) becomes dominant. These two regimes are identified for all studied propellants. Consequent to the change in the plasma regime, the radial distribution of the axial electron current density and the electron temperature anisotropy vary.Comment: 20 pages, 16 figure

Effects of magnetic field gradient and secondary electron emission on instabilities and transport in an ExB plasma configuration

Today, partially magnetized low-temperature plasmas (LTP) in an ExB configuration, where the applied magnetic field is perpendicular to the self-consistent electric field, have important industrial applications. Hall thrusters, a type of electrostatic plasma propulsion, are one of the main LTP technologies whose advancement is hindered by the not-fully-understood underlying physics of operation, particularly, with respect to the plasma instabilities and the associated electron cross-field transport. The development of Hall thrusters with unconventional magnetic field topologies has imposed further questions regarding the instabilities' characteristics and the electrons' dynamics in these modern cross-field configurations. Accordingly, we present in this effort a series of studies on the influence of four factors on the plasma processes in the radial-azimuthal coordinates of a Hall thruster, namely, the magnetic field gradient, Secondary Electron Emission, electron-neutral collisions, and plasma number density. The studies are carried out using the reduced-order particle-in-cell (PIC) code developed by the authors. The setup of the radial-azimuthal simulations largely follows a well-defined benchmark case from the literature in which the magnetic field is oriented along the radius and a constant axial electric field is applied perpendicular to the simulation plane. The salient finding from our investigations is that, in the studied cases corresponding to elevated plasma densities, an inverse energy cascade leads to the formation of a long-wavelength, high-frequency azimuthal mode. Moreover, in the presence of strong magnetic field gradients, this mode is fully developed and induces a significant electron cross-field transport as well as a notable heating of the ion population.Comment: 22 pages, 24 figures. This article has been submitted to Journal of Applied Physic

Fourier series of atomic radial distribution functions: A molecular fingerprint for machine learning models of quantum chemical properties

We introduce a fingerprint representation of molecules based on a Fourier series of atomic radial distribution functions. This fingerprint is unique (except for chirality), continuous, and differentiable with respect to atomic coordinates and nuclear charges. It is invariant with respect to translation, rotation, and nuclear permutation, and requires no pre-conceived knowledge about chemical bonding, topology, or electronic orbitals. As such it meets many important criteria for a good molecular representation, suggesting its usefulness for machine learning models of molecular properties trained across chemical compound space. To assess the performance of this new descriptor we have trained machine learning models of molecular enthalpies of atomization for training sets with up to 10k organic molecules, drawn at random from a published set of 134k organic molecules. We validate the descriptor on all remaining molecules of the 134k set. For a training set of 5k molecules the fingerprint descriptor achieves a mean absolute error of 8.0 kcal/mol, respectively. This is slightly worse than the performance attained using the Coulomb matrix, another popular alternative, reaching 6.2 kcal/mol for the same training and test sets