Sensitivity Analysis of MFiX PIC Parameters Using Nodeworks, PSUADE, and DAKOTA
2021 NETL Workshop on Multiphase Flow Science, Virtual, August 3-5, 2021
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2021 NETL Workshop on Multiphase Flow Science, Virtual, August 3-5, 2021
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This work is aimed at providing reliable high-quality data from fluidization experiments. Geldart Group A glass beads are used as bed material. The fluidizing medium is air at atmospheric pressure which enters the system at 40% relative humidity. The air inlet velocity is varied over a broad range from 2 U mf to 26 U mf , where the minimum fluidization velocity, U mf , is 0.608 cm/s. There is not a significant change in the mean values of differential pressure; however, there are noticeable trends in their standard deviation values. Preliminary validation studies are performed using the open-source software Multiphase Flow with Interphase eXchanges (MFiX) developed by the National Energy Technology Laboratory (NETL). The results from Eulerian-Eulerian (MFiX-TFM, two-fluid model) and Eulerian-Lagrangian (MFiX-PIC, particle-in-cell) formulations are compared. The work presented in this report highlights the applicability of MFiX-PIC for large-scale applications, and reveals that PIC simulation offers a suitable alternative to TFM simulation when effects due to multiple components or polydispersity are significant. PIC modeling provides a readily extendible framework for such systems. However, PIC models do rely on an empirical closure for inter-particle stress. Some solution discrepancies were evident in MFiX-PIC predictions which require further analysis. As such, the study underlines the need for a systematic approach to quantify the sources of numerical uncertainty within the PIC model. However, even with known empiricism, MFiX-PIC has demonstrated considerable potential in analyzing gas-solid systems. The results obtained are encouraging and warrant further investigation to improve the predictive capability of MFiX-PIC.
Finite-grid (or aliasing) instabilities are pervasive in particle-in-cell (PIC) plasma simulation algorithms, and force the modeler to resolve the smallest (Debye) length scale in the problem regardless of dynamical relevance. These instabilities originate in the aliasing of interpolation errors between mesh quantities and particles (which live in the space–time continuum). Recently, strictly energy-conserving PIC (EC-PIC) algorithms have been developed that promise enhanced robustness against aliasing instabilities. In this study, we confirm by analysis that EC-PIC is stable against aliasing instabilities for stationary plasmas. For drifting plasmas, we demonstrate by analysis and numerical experiments that, while EC-PIC algorithms are not free from these instabilities in principle, they feature a benign stability threshold for finite-temperature plasmas that make them usable in practice for a large class of problems (featuring ambipolarity and realistic ion-electron mass ratios) without the need to consider the size of the Debye length. We also demonstrate that this threshold is absent for the popular momentum-conserving PIC algorithms, which are therefore unstable for both drifting and stationary plasmas beyond a threshold in cell size compared to Debye length. Finite-grid (or aliasing) instabilities are pervasive in particle-in-cell (PIC) plasma simulation algorithms, and force the modeler to resolve the smallest (Debye) length scale in the problem regardless of dynamical relevance. These instabilities originate in the aliasing of interpolation errors between mesh quantities and particles (which live in the space–time continuum). Recently, strictly energy-conserving PIC (EC-PIC) algorithms have been developed that promise enhanced robustness against aliasing instabilities. In this study, we confirm by analysis that EC-PIC is stable against aliasing instabilities for stationary plasmas. For drifting plasmas, we demonstrate by analysis and numerical experiments that, while EC-PIC algorithms are not free from these instabilities in principle, they feature a benign stability threshold for finite-temperature plasmas that make them usable in practice for a large class of problems (featuring ambipolarity and realistic ion-electron mass ratios) without the need to consider the size of the Debye length. Finally, we also demonstrate that this threshold is absent for the popular momentum-conserving PIC algorithms, which are therefore unstable for both drifting and stationary plasmas beyond a threshold in cell size compared to Debye length.
High fidelity modeling of plasma based acceleration (PBA) requires the use of three dimensional, fully nonlinear, and kinetic descriptions based on the particle-in-cell (PIC) method. In PBA an intense particle beam or laser (driver) propagates through a tenuous plasma whereby it excites a plasma wave wake. Three-dimensional PIC algorithms based on the quasi-static approximation (QSA) have been successfully applied to efficiently model the interaction between relativistic charged particle beams and plasma. In a QSA PIC algorithm, the plasma response to a charged particle beam or laser driver is calculated based on forces from the driver and self-consistent forces from the QSA form of Maxwell's equations. These fields are then used to advance the charged particle beam or laser forward by a large time step. Since the time step is not limited by the regular Courant-Friedrichs-Lewy (CFL) condition that constrains a standard 3D fully electromagnetic PIC code, a 3D QSA PIC code can achieve orders of magnitude speedup in performance. Recently, a new hybrid QSA PIC algorithm that combines another speedup technique known as an azimuthal Fourier decomposition has been proposed and implemented. This hybrid algorithm decomposes the electromagnetic fields, charge and current density into azimuthal harmonics and only the Fourier coefficients need to be updated, which can reduce the algorithmic complexity of a 3D code to that of a 2D code. Modeling the laser-plasma interaction in a full 3D electromagnetic PIC algorithm is very computationally expensive due the enormous disparity of physical scales to be resolved. In the QSA the laser is modeled using the ponderomotive guiding center (PGC) approach. We describe how to implement a PGC algorithm compatible for the QSA PIC algorithms based on the azimuthal mode expansion. Here this algorithm permits time steps orders of magnitude larger than the cell size and it can be asynchronously parallelized. Details on how this is implemented into the QSA PIC code that utilizes an azimuthal mode expansion, QPAD, are also described. Benchmarks and comparisons between a fully 3D explicit PIC code (OSIRIS), as well as a few examples related to laser wakefield acceleration, are presented.
The three-dimensional (3D) quasi-static particle-in-cell (PIC) algorithm is a very efficient method for modeling short-pulse laser or relativistic charged particle beam–plasma interactions. In this algorithm, the plasma response, i.e., plasma wave wake, to a non-evolving laser or particle beam is calculated using a set of Maxwell’s equations based on the quasi-static approximate equations that exclude radiation. The plasma fields are then used to advance the laser or beam forward using a large time step. The algorithm is many orders of magnitude faster than a 3D fully explicit relativistic electromagnetic PIC algorithm. It has been shown to be capable to accurately model the evolution of lasers and particle beams in a variety of scenarios. Additionally, at the same time, an algorithm in which the fields, currents and Maxwell equations are decomposed into azimuthal harmonics has been shown to reduce the algorithmic complexity of a 3D explicit PIC algorithm to that of a 2D algorithm when the expansion is truncated while maintaining accuracy for problems with near azimuthal symmetry. This hybrid algorithm uses a PIC description in r–z and a gridless description in . We describe a novel method that combines the quasi-static and hybrid PIC methods. This algorithm expands the fields, charge and current density into azimuthal harmonics. A set of the quasi-static field equations is derived for each harmonic. The complex amplitudes of the fields are then solved using the finite difference method. The beam and plasma particles are advanced in Cartesian coordinates using the total fields. Details on how this algorithm was implemented using a similar workflow to an existing quasi-static code, QuickPIC, are presented. The new code is called QPAD for QuickPIC with Azimuthal Decomposition. Benchmarks and comparisons between a fully 3D explicit PIC code (OSIRIS), a full 3D quasi-static code (QuickPIC), and the new quasi-static PIC code with azimuthal decomposition (QPAD) are also presented.
Abstract We derive the kinetic theory of fluctuations in physically and numerically stable particle-in-cell (PIC) simulations of electrostatic plasmas. The starting point is the single-time correlation at the start of the simulation between the statistical fluctuations of the weighted densities of macroparticle centers in the plasma particle phase-space. The fluctuations are associated with different initial conditions, typically due to the random initial conditions (in velocity space) of the macroparticles/simulation plasma, assigned according to their initial distribution of probability. The single-time correlations at all time steps and in each spatial grid cell are then determined from the Laplace–Fourier transforms of the discretized Klimontovich-like equation for the macroparticles and Maxwell’s equations for the fields, as computed by modern PIC codes. We recover the expressions for the electrostatic field and the plasma particle density fluctuation autocorrelation spectra as well as the kinetic equations describing the average evolution of PIC-simulated plasma particles, first derived by Langdon (1970b Proc. 4th Conf. Numerical Simulation of Plasmas ) using a test macroparticle approach perturbing a discretized Vlasovian plasma and then averaging the obtained physical quantity over the initial macroparticle velocity distribution. We generalize and extend these results to the modern algorithms in PIC codes using arbitrary macroparticle weights. Analytical estimates of statistical fluctuation amplitudes are derived as a function of the plasma simulation parameters, using the central limit theorem in the limit of a large number of macroparticles per cell. The theory is then used to analyze the ensemble averaging technique of PIC simulations where statistical averages are performed over ensembles of PIC simulations, modeling the same plasma physics problem but using different statistical realizations of the initial distribution functions of the macroparticles. This method is illustrated by linear Landau damping uncovering (from noise, which is usually considered numerical) the physical fluctuations driven by a single small amplitude electrostatic wave perturbing a PIC simulation plasma in equilibrium.
Particle-in-cell (PIC) simulation methods are attractive for representing species distribution functions in plasmas. However, as a model, they introduce uncertain parameters, and for quantifying their prediction uncertainty it is useful to be able to assess the sensitivity of a quantity-of-interest (QoI) to these parameters. Such sensitivity information is likewise useful for optimization. However, computing sensitivity for PIC methods is challenging due to the chaotic particle dynamics, and sensitivity techniques remain underdeveloped compared to those for Eulerian discretizations. This challenge is examined from a dual particle–continuum perspective that motivates a new sensitivity discretization. Two routes to sensitivity computation are presented and compared: a direct fully-Lagrangian particle-exact approach provides sensitivities of each particle trajectory, and a new particle-pdf discretization, which is formulated from a continuum perspective but discretized by particles to take the advantages of the same type of Lagrangian particle description leveraged by PIC methods. Since the sensitivity particles in this approach are only indirectly linked to the plasma-PIC particles, they can be positioned and weighted independently for efficiency and accuracy. The corresponding numerical algorithms are presented here in mathematical detail. The advantage of the particle-pdf approach in avoiding the spurious chaotic sensitivity of the particle-exact approach is demonstrated for Debye shielding and sheath configurations. In essence, the continuum perspective makes implicit the distinctness of the particles, which circumvents the Lyapunov instability of the N -body PIC system. The cost of the particle-pdf approach is comparable to the baseline PIC simulation.
In this paper we present an alternative approach to the representation of simulation particles for unstructured electrostatic and electromagnetic PIC simulations. In our modified PIC algorithm we represent particles as having a smooth shape function limited by some specified finite radius, r 0 . A unique feature of our approach is the representation of this shape by surrounding simulation particles with a set of virtual particles with delta shape, with fixed offsets and weights derived from Gaussian quadrature rules and the value of r 0 . As the virtual particles are purely computational, they provide the additional benefit of increasing the arithmetic intensity of traditionally memory bound particle kernels. The modified algorithm is implemented within Sandia National Laboratories' unstructured EMPIRE-PIC code, for electrostatic and electromagnetic simulations, using periodic boundary conditions. We show results for a representative set of benchmark problems, including electron orbit, a transverse electromagnetic wave propagating through a plasma, numerical heating, and a plasma slab expansion. In this work, good error reduction across all of the chosen problems is achieved as the particles are made progressively smoother, with the optimal particle radius appearing to be problem-dependent.
We present a concept of a plasma lens in a parametric resonance ionization cooling (PIC) for extra cooling of muon colliders. The PIC concept has been developed to overcome most aberrations. However, parasitic non-linear aberrations which is induced in an ionization cooling material still reduce a dynamic aperture of the PIC. The plasma lens generates an azimuthally symmetric focusing field in gas-filled RF cavities that is several orders of magnitude stronger than the conventional superconducting magnets. It allows for reduction of the beam size at the beam expansion points. This reduces the size of the aberrations and therefore greatly simplifies their compensation.
Though both of the current Landsat instruments, Landsat-7 Enhanced Thematic Mapper+ (ETM+) and Landsat-5 Thematic Mapper (TM), include on-board calibration systems, since 2001, pseudo-invariant calibration sites (PICS) have been added to the suite of metrics to assess the instruments calibration. These sites do not provide absolute calibration data since there are no ground measurements of the sites, but in monitoring these PICS over time, the relative calibration can be tracked. The sites used by the Landsat instruments are primarily in the Saharan Desert. To date, the trending from the PICS sites has confirmed that most of the degradation seen in the ETM+ on-board calibration systems is likely not degradation of the instrument, but rather degradation of the calibration systems themselves. However, the PICS data show statistically significant degradation (at 2-sigma) in all the reflective spectral bands of up to -0.22%/year since July 2003. For the TM, the PICS were instrumental in updating the calibration in 2007 and now suggest two bands may require another update. The data show a statistically significant degradation (at 2-sigma) in Bands 1 and 3 of -0.27 and -0.15%/year, respectively, since March 1999. The data filtering and processing methods are currently being reviewed but these PICS results may lead to an update in the reflective band calibration of both Landsat-7 and Landsat-5.
We describe the structures of four related indium complexes obtained during synthesis of solid-state materials precursors. Indium adducts of halides and 4-methylpyridine, InX3(pic)3 (X = Cl, Br; pic = 4-methylpyridine) consist of octahedral molecules with meridional (mer) geometry. Crystals of mer-InCl3(pic)3 (1) are triclinic, space group P1(bar) (No. 2), with a = 9.3240(3), b = 13.9580(6), c = 16.7268 (7) A, alpha = 84.323(2), beta = 80.938(2), gamma = 78.274(3)Z = 4, R = 0.035 for 8820 unique reflections. Crystals of mer-InBr3(pic)3 (2) are monoclinic, space group P21/n (No. 14), with a = 15.010(2), b = 19.938(2), c = 16.593(3), beta = 116.44(1)Z = 8, R = 0.053 for 4174 unique reflections. The synthesis and structures of related compounds with phenylsulfide (chloride) (3) and a dimeric complex with bridging hydroxide (bromide) (4) coordination is also described. Crystals of trans-In(SC6H5)Cl2(pic)3 (3) are monoclinic, space group P21/n (No. 14), with a = 9.5265(2), b = 17.8729(6), c = 13.8296(4), beta = 99.7640(15)Z = 4, R = 0.048 for 5511 unique reflections. Crystals of [In(mu-OH)Br2(pic)22 (4) are tetragonal, space group = I41cd (No. 110) with a = 19.8560(4), b = 19.8560(4), c = 25.9528(6), Z = 8, R = 0.039 for 5982 unique reflections.
This work extends an empirical absolute calibration model initially developed for the Libya 4 Pseudo-Invariant Calibration Site (PICS) to five additional Saharan Desert PICS (Egypt 1, Libya 1, Niger 1, Niger 2, and Sudan 1), and demonstrates the efficacy of the resulting models at predicting sensor top-of-atmosphere (TOA) reflectance. It attempts to generate absolute calibration models for these PICS that have an accuracy and precision comparable to or better than the current Libya 4 model, with the intent of providing additional opportunities for sensor calibration. In addition, this work attempts to validate the general applicability of the model to other sites. The method uses Terra Moderate Resolution Imaging Spectroradiometer (MODIS) as the reference radiometer and Earth Observing-1 (EO-1) Hyperion image data to provide a representative hyperspectral reflectance profile of the PICS. Data from a region of interest (ROI) in an “optimal region” of 3% temporal, spatial, and spectral stability within the PICS are used for developing the model. The developed models were used to simulate observations of the Landsat 7 (L7) Enhanced Thematic Mapper Plus (ETM+), Landsat 8 (L8) Operational Land Imager (OLI), Sentinel 2A (S2A) MultiSpectral Instrument (MSI) and Sentinel 2B (S2B) MultiSpectral Instrument (MSI) from their respective launch date through 2018. The models developed for the Egypt 1, Libya 1 and Sudan 1 PICS have an estimated accuracy of approximately 3% and precision of approximately 2% for the sensors used in the study, comparable to the current Libya 4 model. The models developed for the Niger 1 and Niger 2 sites are significantly less accurate with similar precision.
Integrated photonics is a promising coronagraph technology option for exoplanet-imaging missions like NASA’s Habitable Worlds Observatory flagship. It is theoretically capable of achieving better performance than traditional bulk-optic coronagraphs because arrays of integrated interferometers can be combined to implement any linear operator. However, photonic coronagraphs require significant maturation to be ready for a space telescope mission. The AstroPIC project is advancing this technology by developing a proof-of-concept integrated photonic coronagraph based on silicon photonic integrated circuit (PIC) technology. Specifically, the AstroPIC program is investigating the impact of a PIC coronagraph on the predicted scientific yield of the upcoming Habitable Worlds Observatory (HWO) mission concept. In this talk, we will present the current status of the AstroPIC design, including the layout of the most recent PIC. We will also present on the status of simulations that predict the performance of the instrument and feed into scientific yield estimations for HWO Exoploratory Analytic Cases (EACs) 1-3. Finally, we will present the status of the development of a PIC testbed at NASA Ames and results from preliminary PIC laboratory testing at Stanford.