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The Open Databases Integration for Materials Design (OPTIMADE) application programming interface (API) empowers users with holistic access to a growing federation of databases, enhancing the accessibility and discoverability of materials and chemical data. Since the first release of the OPTIMADE specification (v1.0), the API has undergone significant development, leading to the upcoming v1.2 release, and has underpinned multiple scientific studies. In this work, we highlight the latest features of the API format, accompanying software tools, and provide an update on the implementation of OPTIMADE in contributing materials databases. We end by providing several use cases that demonstrate the utility of the OPTIMADE API in materials research that continue to drive its ongoing development.

This paper provides perspectives on recent progress in the understanding of the physics of devices where the external magnetic field is applied perpendicularly to the discharge current. This configuration generates a strong electric field, which acts to accelerates ions. The many applications of this set up include generation of thrust for spacecraft propulsion and the separation of species in plasma mass separation devices. These ExB plasmas are subject to plasma-wall interaction effects as well as various micro and macro instabilities, and in many devices, we observe the emergence of anomalous transport. This perspective presents the current understanding of the physics of these phenomena, state-of-the-art computational results, identifies critical questions, and suggests directions for future research, Comment: 59 pages, 25 Figures, submitted to Physics of Plasmas

A rotating plasma spoke is shown to develop in two-dimensional full-sized kinetic simulations of a Penning discharge cross-section. Electron cross-field transport within the discharge is highly anomalous and correlates strongly with the spoke phase. Similarity between collisional and collisionless simulations demonstrates that ionization is not necessary for spoke formation. Parameter scans with discharge current $I_d$, applied magnetic field strength $B$ and ion mass $m_i$ show that spoke frequency scales with $\sqrt{e E_r L_n / m_i}$, where $E_r$ is the radial electric field, $L_n$ is the gradient length scale and $e$ is the fundamental charge. This scaling suggests that the spoke may develop as a non-linear phase of the collisionless Simon-Hoh instability.

The two particle-in-cell codes EDIPIC and LSP are benchmarked and validated for a parallel-plate glow discharge in helium, in which the axial electric field had been carefully measured, primarily to investigate and improve the fidelity of their collision models. The scattering anisotropy of electron-impact ionization, as well as the value of the secondary-electron emission yield, are not well known in this case. The experimental uncertainty for the emission yield corresponds to a factor of two variation in the cathode current. If the emission yield is tuned to make the cathode current computed by each code match the experiment, the computed electric fields are in excellent agreement with each other, and within about 10\% of the experimental value. The non-monotonic variation of the width of the cathode fall with the applied voltage seen in the experiment is reproduced by both codes. The electron temperature in the negative glow is within experimental error bars for both codes, but the density of slow trapped electrons is underestimated. A more detailed code comparison done for several synthetic cases of electron-beam injection into helium gas shows that the codes are in excellent agreement for ionization rate, as well as for elastic and excitation collisions with isotropic scattering pattern. The remaining significant discrepancies between the two codes are due to differences in their electron binary-collision models, and for anisotropic scattering due to elastic and excitation collisions.

Propagation of charged particle beams in background plasma as a method of space charge neutralization has been shown to achieve a high degree of charge and current neutralization and therefore enables nearly ballistic propagation and focusing of charged particle beams. Correspondingly, use of plasmas for propagation of charged particle beams has important applications for transport and focusing of intense particle beams in inertial fusion and high energy density laboratory plasma physics. However, the streaming of beam ions through a background plasma can lead to development of the two-stream instability between the beam ions and the plasma electrons. The beam electric and magnetic fields enhanced by the two-stream instability can lead to defocusing of the ion beam. Using particle-in-cell (PIC) simulations, we study the scaling of the instability-driven self-electromagnetic fields and consequent defocusing forces with the background plasma density and beam ion mass. We identify plasma parameters where the defocusing forces can be reduced., Comment: 28 pages, submitted to Phys. Plasmas

Electrostatic particle-in-cell simulations of a Penning discharge are performed in order to investigate azimuthally asymmetric, spoke-like structures previously observed in experiments. Two-dimensional simulations show that for Penning-discharge conditions, a persistent nonlinear spoke-like structure forms readily and rotates in the direction of ExB and electron diamagnetic drifts. The azimuthal velocity is within about a factor of two of the ion acoustic speed. The spoke frequency follows the experimentally observed scaling with ion mass, which indicates the importance of ion inertia in spoke formation. The spoke provides enhanced (anomalous) radial electron transport, and the effective cross-field conductivity is several times larger than the classical (collisional) value. The level of anomalous current obtained in the simulations is in good agreement with the experimental data. The rotating spoke channels most of the radial current, observable by an edge probe as short pulses., Comment: Submitted to PoP, revised version

The reason why the half-integer quantum Hall effect (QHE) is suppressed in graphene grown by chemical vapor deposition (CVD) is unclear. We propose that it might be connected to extended defects in the material and present results for the quantum Hall effect in graphene with [0001] tilt grain boundaries connecting opposite sides of Hall bar devices. Such grain boundaries contain 5-7 ring complexes that host defect states that hybridize to form bands with varying degree of metallicity depending on grain boundary defect density. In a magnetic field, edge states on opposite sides of the Hall bar can be connected by the defect states along the grain boundary. This destroys Hall resistance quantization and leads to non-zero longitudinal resistance. Anderson disorder can partly recover quantization, where current instead flows along returning paths along the grain boundary depending on defect density in the grain boundary and on disorder strength. Since grain sizes in graphene made by chemical vapor deposition are usually small, this may help explain why the quantum Hall effect is usually poorly developed in devices made of this material., Comment: 5 pages, 4 figures

A new Jacobian approximation is developed for use in quasi-Newton methods for solving systems of nonlinear equations. The new hypersecant Jacobian approximation is intended for the special case where the evaluation of the functions whose roots are sought dominates the computation time, and additionally the Jacobian is sparse. One example of such a case is the solution of the discretized transport equation to calculate particle and energy fluxes in a fusion plasma. The hypersecant approximation of the Jacobian is calculated using function values from previous Newton iterations, similarly to the Broyden approximation. Unlike Broyden, the hypersecant Jacobian converges to the finite-difference approximation of the Jacobian. The calculation of the hypersecant Jacobian elements requires solving small, dense linear systems, where the coefficient matrices can be ill-conditioned or even exactly singular. Singular-value decomposition (SVD) is therefore used. Convergence comparisons of the hypersecant method, the standard Broyden method, and the colored finite differencing of the PETSc SNES solver are presented., Comment: 12 pages, 2 figures

This paper contains a study of ADI methods in the presence of charge and current sources. It is shown that there are four significantly distinct cases, with four more related by duality. Of those, only one preserves divergence and, thus, is guaranteed to be stable in the presence of moving charged particles. Computational verification of this property is accomplished by implementation in existing 3D-EMPIC simulation software. Of the other three cases, two are verified unstable, as expected, and one remains stable, despite the lack of divergence preservation. This other stable algorithm is shown to be related to the divergence preserving case by a similarity transformation, effectively providing the complement of the divergence preserving field in the finite-difference energy quantity., Comment: "20 pages, 2 figures. Submitted to Journal of Computation Physics"

Thermal ions in spherical tokamaks have two adiabatic invariants: the magnetic moment and the longitudinal invariant. For hot ions, variations in magnetic-field strength over a gyro period can become sufficiently large to cause breakdown of the adiabatic invariance. The magnetic moment is more sensitive to perturbations than the longitudinal invariant and there exists an intermediate regime, super-adiabaticity, where the longitudinal invariant remains adiabatic, but the magnetic moment does not. The motion of super-adiabatic ions remains integrable and confinement is thus preserved. However, above a threshold energy, the longitudinal invariant becomes non-adiabatic too, and confinement is lost as the motion becomes chaotic. We predict beam ions in present-day spherical tokamaks to be super-adiabatic but fusion alphas in proposed burning-plasma spherical tokamaks to be non-adiabatic., Comment: 6 pages, 8 figures

The recently introduced backward Monte-Carlo method [Johan Carlsson, arXiv:math.NA/0010118] is validated, benchmarked, and compared to the conventional, forward Monte-Carlo method by analyzing the error in the Monte-Carlo solutions to a simple model equation. In particular, it is shown how the backward method reduces the statistical error in the common case where the solution is of interest in only a small part of phase space. The forward method requires binning of particles, and linear interpolation between the bins introduces an additional error. Reducing this error by decreasing the bin size increases the statistical error. The backward method is not afflicted by this conflict. Finally, it is shown how the poor time convergence can be improved for the backward method by a minor modification of the Monte-Carlo equation of motion that governs the stochastic particle trajectories. This scheme does not work for the conventional, forward method., Comment: 14 pages, 9 figures. Submitted to Computer Physics Communications

A new Monte-Carlo method for solving linear parabolic partial differential equations is presented. Since, in this new scheme, the particles are followed backward in time, it provides great flexibility in choosing critical points in phase-space at which to concentrate the launching of particles and thereby minimizing the statistical noise of the sought solution. The trajectory of a particle, Xi(t), is given by the numerical solution to the stochastic differential equation naturally associated with the parabolic equation. The weight of a particle is given by the initial condition of the parabolic equation at the point Xi(0). Another unique advantage of this new Monte-Carlo method is that it produces a smooth solution, i.e. without delta-functions, by summing up the weights according to the Feynman-Kac formula., Comment: Submitted to Computer Physics Communications; 13 pages, 2 figures