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DOE OSTI2026

Quantum kinetic modeling of KEEN waves in a warm-dense regime

We report the first fully kinetic, quantum study of kinetic electrostatic electron nonlinear (KEEN) waves, showing that quantum diffraction systematically erodes the classical trapping mechanism, narrows harmonic locking to the fundamental, and hastens post-drive decay. Electrons are evolved with a second-order Strang-split 1D1V Wigner–Poisson solver that couples conservative semi-Lagrangian WENO advection to an analytic Fourier space update for the non-local Wigner term, while ions remain classical. We focus on collisionless dynamics in a weakly coupled regime, providing a controlled baseline before collisional extensions. Short, frequency-tuned ponderomotive pulses drive KEEN formation in a uniform Maxwellian plasma; as the dimensionless quantum parameter H rises from the classical limit to values relevant to warm-dense matter, doped semiconductors, and 2D electron systems, the drive threshold increases, higher harmonics are damped, trapped electron vortices diffuse, and the subplasma electrostatic energy relaxes to a lower stationary level, as confirmed by continuous wavelet analysis. These microscopic changes carry macroscopic weight. Ignition-scale capsules now compress matter to regimes where the electron de Broglie wavelength rivals the Debye length, making classical kinetic descriptions insufficient. By extending KEEN physics into this quantum domain, our results offer a potential diagnostic of non-equilibrium electron dynamics for next-generation inertial-confinement designs and high-energy-density platforms, indicating that predictive fusion modeling may benefit from the integration of kinetic fidelity with quantum effects.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

A fast, matrix-based method to perform omnidirectional pressure integration

Abstract Experimentally-measured pressure fields play an important role in understanding many fluid dynamics problems. Unfortunately, pressure fields are difficult to measure directly with non-invasive, spatially resolved diagnostics, and calculations of pressure from velocity have proven sensitive to error in the data. Omnidirectional line integration methods are usually more accurate and robust to these effects as compared to implicit Poisson equations, but have seen slower uptake due to the higher computational and memory costs, particularly in 3D domains. This paper demonstrates how omnidirectional line integration approaches can be converted to a matrix inversion problem. This novel formulation uses an iterative approach so that the boundary conditions are updated each step, preserving the convergence behavior of omnidirectional schemes while also keeping the computational efficiency of Poisson solvers. This method is implemented in Matlab and also as a GPU-accelerated code in CUDA-C++. The behavior of the new method is demonstrated on 2D and 3D synthetic and experimental data. Three-dimensional grid sizes of up to 125 million grid points are tractable with this method, opening exciting opportunities to perform volumetric pressure field estimation from 3D PIV measurements.

42 ENGINEERING↗

DOE OSTI2022

A self-consistent hybrid model of kinetic striations in low-current argon discharges

A self-consistent hybrid model of standing and moving striations was developed for low-current DC discharges in noble gases. We introduced the concept of surface diffusion in phase space ( r , u ) (where u denotes the electron kinetic energy) described by a tensor diffusion in the nonlocal Fokker–Planck kinetic equation for electrons in the collisional plasma. Electrons diffuse along surfaces of constant total energy ε = u - eφ ( r ) between energy jumps in inelastic collisions with atoms. Numerical solutions of the 1d1u kinetic equation for electrons were obtained by two methods and coupled to ion transport and Poisson solver. We studied the dynamics of striation formation in Townsend and glow discharges in argon gas at low discharge currents using a two-level excitation-ionization model and a ‘full-chemistry’ model, which includes stepwise and Penning ionization. Standing striations appeared in Townsend and glow discharges at low currents, and moving striations were obtained for the discharge currents exceeding a critical value. These waves originate at the anode and propagate towards the cathode. We have seen two types of moving striations with the two-level and full-chemistry models, which resemble the s and p striations previously observed in the experiments. Simulations indicate that processes in the anode region could control moving striations in the positive column plasma. The developed model helps clarify the nature of standing and moving striations in DC discharges of noble gases at low discharge currents and low gas pressures.

Physics↗

DOE OSTI2025

Noncollinear ground states of solids with a source-free exchange correlation functional

In this paper, we expand upon the source-free (SF) exchange correlation (XC) functional developed by Sangeeta Sharma and coworkers to plane-wave density functional theory (DFT) based on the projector augmented wave (PAW) method. This constraint is implemented by the current authors within the VASP source code, using a fast Poisson solver that capitalizes on the parallel three-dimensional fast Fourier transforms (FFTs) implemented in VASP. Using this modified XC functional, we explore the improved convergence behavior that results from applying this constraint to the GGA-PBE+U+J functional. In the process, we compare the noncollinear magnetic ground state computed by each functional and their SF counterpart for a select number of magnetic materials in order to provide a metric for comparing with experimentally determined magnetic orderings. We observe significantly improved agreement with experimentally measured magnetic ground-state structures after applying the source-free constraint. Furthermore, we explore the importance of considering probability current densities in spin-polarized systems, even under no applied field. We analyze the XC torque as well, in order to provide theoretical and computational analyses of the net XC magnetic torque induced by the source-free constraint. Along these lines, we highlight the importance of properly considering the real-space integral of the source-free local magnetic XC field. Our analyses on probability currents, net torque, and constant terms draw additional links to the rich body of previous research on spin-current density functional theory (SCDFT), and pave the way for future extensions and corrections to the SF corrected XC functional.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

LW3D v1

LW3D is code for modeling beam dynamics in particle accelerators including Lienard-Wiechert self-fields. It is similar to codes like IMPACT-T except that the Poisson solver is replaced by a Lienard-Wiechert solver. Along with space-charge effects, the code can model effects like coherent synchrotron radiation.

Ryne, Robert↗

NASA NTRS1976

Accelerated iterative calculation of transonic nacelle flowfields

A method is presented for the calculation of inviscid, supercritical flowfields about axisymmetric inlet cowls. A finite-difference calculation is performed in a simple, rectangular domain obtained from the nacelle geometry by a nearly-conformal mapping procedure. Type-dependent finite-differences are constructed using a coordinate-independent, 'rotated' differencing scheme. Methods of accelerating convergence of the iterative solution are demonstrated including a hybrid fast-Poisson-solver/relaxation scheme and an extrapolated relaxation procedure. Calculated pressure distributions are compared with experimental data for a variety of Mach numbers and mass-flow ratios, and show generally good agreement.

Caughey, D. A.↗

NASA NTRS1977

Supercritical wing sections III

The book describes recent computational flow research on the design and analysis of supercritical wing sections. The central object is a detailed description of a supercritical wing design code based on the concept of designing a shockless airfoil so that its pressure distribution very nearly takes on prescribed data. The accompanying two-dimensional analysis code with fast Poisson solver is also described. FORTRAN listings are included along with a users manual for the design code. Airfoils designed with the new code and data from analysis and experiment are provided. A brief description of the method of complex characteristics is also given.

Bauer, F.↗

NASA NTRS1981

Rapid, high-order accurate calculation of flows due to free source or vortex distributions

Fast Fourier transform (FFT) techniques are applied to the problem of finding the flow due to source or vortex distributions in the field outside an airfoil or other two-dimensional body. Either the complex potential or the complex velocity may be obtained to a high order of accuracy, with computational effort similar to that required by second-order fast Poisson solvers. These techniques are applicable to general flow problems with compressibility and rotation. An example is given of their use for inviscid compressible flow.

Halsey, D.↗

NASA NTRS1983

Semidirect computations for transonic flow

A semidirect method, driven by a Poisson solver, was developed for inviscid transonic flow computations. It is an extension of a recently introduced algorithm for solving subsonic rotational flows. Shocks are captured by implementing a form of artificial compressibility. Nonisentropic cases are computed using a shock tracking procedure coupled with the Rankine-Hugoniot relationships. Results are presented for both subsonic and transonic flows. For the test geometry, an unstaggered cascade of 20 percent thick circular arc airfoils at zero angle of attack, shocks are crisply resolved in supercritical situations and the algorithm converges rapidly. In addition, the convergence rate appears to be nearly independent of the entropy and vorticity production at the shock.

Swisshelm, J. M.↗

NASA NTRS1984

Plasma response to the injection of an electron beam

The results of Vlasov-Poisson-solver numerical simulations of the detailed temporal response of a Maxwellian plasma to the sudden injection of an electron beam are presented in graphs and maps and discussed. Phenomena characterized include ion bursts, electron shocks and holes, plasma heating and expulsion, density gradients; cavitons, deep-density-front and solitary-pulse propagation down the density gradient, and Bunemann-mode excitation leading to formation of a virtual cathode and double layers which are at first monotonic or have low-potential-side dips or high-potential-side bumps and become strong as the electron-current density decreases. The strength of the double layer is found to be roughly proportional to the beam energy.

Singh, N.↗

NASA NTRS1986

Research in computer science

Various graduate research activities in the field of computer science are reported. Among the topics discussed are: (1) failure probabilities in multi-version software; (2) Gaussian Elimination on parallel computers; (3) three dimensional Poisson solvers on parallel/vector computers; (4) automated task decomposition for multiple robot arms; (5) multi-color incomplete cholesky conjugate gradient methods on the Cyber 205; and (6) parallel implementation of iterative methods for solving linear equations.

Ortega, J. M.↗

NASA NTRS1989

A dual potential formulation of the Navier-Stokes equations

A dual potential formulation for numerically solving the Navier-Stokes equations is developed and presented. The velocity field is decomposed using a scalar and vector potential. Vorticity and dilatation are used as the dependent variables in the momentum equations. Test cases in two dimensions verify the capability to solve flows using approximations from potential flow to full Navier-Stokes simulations. A three-dimensional incompressible flow formulation is also described. An interesting feature of this approach to solving the Navier-Stokes equations is the decomposition of the velocity field into a rotational part (vector potential) and an irrotational part (scalar potential). The Helmholtz decomposition theorem allows this splitting of the velocity field. This approach has had only limited use since it increases the number of dependent variables in the solution. However, it has often been used for incompressible flows where the solution scheme is known to be fast and accurate. This research extends the usage of this method to fully compressible Navier-Stokes simulations by using the dilatation variable along with vorticity. A time-accurate, iterative algorithm is used for the uncoupled solution of the governing equations. Several levels of flow approximation are available within the framework of this method. Potential flow, Euler and full Navier-Stokes solutions are possible using the dual potential formulation. Solution efficiency can be enhanced in a straightforward way. For some flows, the vorticity and/or dilatation may be negligible in certain regions (e.g., far from a viscous boundary in an external flow). It is possible to drop the calculation of these variables then and optimize the solution speed. Also, efficient Poisson solvers are available for the potentials. The relative merits of non-primitive variables versus primitive variables for solution of the Navier-Stokes equations are also discussed.

Gegg, S. G.↗

NASA NTRS1989

Numerical solution of unsteady incompressible viscous flows in generalized moving coordinate systems

A solution method of the time-accurate, incompressible Navier-Stokes equations in generalized curvilinear moving coordinate systems is presented in this paper. Accuracy is achieved by a conservative finite-volume discretization which satisfies the geometric conservation laws in generalized moving coordinate systems. The solution method is second-order accurate in space and first-order accurate in time. A fractional step solution method is used to efficiently solve the discrete equations. The unknowns, namely the pressure and the volume-fluxes, are chosen to facilitate the formulation of a consistent Poisson equation and to obtain a robust Poisson solver with favorable convergence properties. The method is validated by comparisons to other numerical and experimental solutions. The comparisons show good agreement.

Rosenfeld, Moshe↗

NASA NTRS1990

Application of the TRANAIR rectangular grid approach to the aerodynamic analysis of complex configurations

A numerical method is described which uses a rectangular grid to solve the nonlinear full potential equation about complex configurations. The grid is locally refined to resolve high velocity gradients arising from leading edge expansions or shock waves. The grid penetrates the boundary (described by networks of quadrilateral panels) and is generated automatically. Discrete operators are constructed using the finite element method. The system of nonlinear discrete equations is solved iteratively using a Krylov subspace method preconditioned by an exterior Poisson solver and a direct sparse solver. The primary emphasis is to provide design engineers with an aerodynamic analysis tool (the TRANAIR code) which is accurate, reliable, economical, and flexible to use. Computational results for many interesting configurations are presented.

Johnson, Forrester T.↗

NASA NTRS1992

A numerical code for a three-dimensional magnetospheric MHD equilibrium model

Two dimensional and three dimensional MHD equilibrium models were begun for Earth's magnetosphere. The original proposal was motivated by realizing that global, purely data based models of Earth's magnetosphere are inadequate for studying the underlying plasma physical principles according to which the magnetosphere evolves on the quasi-static convection time scale. Complex numerical grid generation schemes were established for a 3-D Poisson solver, and a robust Grad-Shafranov solver was coded for high beta MHD equilibria. Thus, the effects were calculated of both the magnetopause geometry and boundary conditions on the magnetotail current distribution.

Voigt, G.-H.↗

NASA NTRS1991

Time-dependent solutions of viscous incompressible flows in moving co-ordinates

A time-accurate solution method for the incompressible Navier-Stokes equations in generalized moving coordinates is presented. A finite-volume discretization method that satisfies the geometric conservation laws for time-varying computational cells is used. The discrete equations are solved by a fractional-step solution procedure. The solution is second-order-accurate in space and first-order-accurate in time. The pressure and the volume fluxes are chosen as the unknowns to facilitate the formulation of a consistent Poisson equation and thus to obtain a robust Poisson solver with favorable convergence properties. The method is validated by comparing the solutions with other numerical and experimental results. Good agreement is obtained in all cases.

Rosenfeld, Moshe↗

NASA NTRS1993

Numerical simulation using vorticity-vector potential formulation

An accurate and efficient computational method is needed for three-dimensional incompressible viscous flows in engineering applications. On solving the turbulent shear flows directly or using the subgrid scale model, it is indispensable to resolve the small scale fluid motions as well as the large scale motions. From this point of view, the pseudo-spectral method is used so far as the computational method. However, the finite difference or the finite element methods are widely applied for computing the flow with practical importance since these methods are easily applied to the flows with complex geometric configurations. However, there exist several problems in applying the finite difference method to direct and large eddy simulations. Accuracy is one of most important problems. This point was already addressed by the present author on the direct simulations on the instability of the plane Poiseuille flow and also on the transition to turbulence. In order to obtain high efficiency, the multi-grid Poisson solver is combined with the higher-order, accurate finite difference method. The formulation method is also one of the most important problems in applying the finite difference method to the incompressible turbulent flows. The three-dimensional Navier-Stokes equations have been solved so far in the primitive variables formulation. One of the major difficulties of this method is the rigorous satisfaction of the equation of continuity. In general, the staggered grid is used for the satisfaction of the solenoidal condition for the velocity field at the wall boundary. However, the velocity field satisfies the equation of continuity automatically in the vorticity-vector potential formulation. From this point of view, the vorticity-vector potential method was extended to the generalized coordinate system. In the present article, we adopt the vorticity-vector potential formulation, the generalized coordinate system, and the 4th-order accurate difference method as the computational method. We present the computational method and apply the present method to computations of flows in a square cavity at large Reynolds number in order to investigate its effectiveness.

Tokunaga, Hiroshi↗

NASA NTRS1993

Characteristics of 0.8- and 0.2-microns gate length In(x)Ga(1-x) As/In(0.52)Al(0.48)As/InP (0.53 less than or equal to x less than or equal to 0.70) modulation-doped field-effect transistors at cryogenic temperatures

The performance characteristics of InP-based In(x)Ga(1-x)As/In(0.52)Al(0.48)As (0.53 is less than or equal to x is less than or equal to 0.70) pseudomorphic modulation-doped field-effect transistors (MODFET's) as a function of strain in the channel, gate, length, and temperature were investigated analytically and experimentally. The strain in the channel was varied by varying the In composition x. The temperature was varied in the range of 40-300 K and the devices have gate lengths L(sub g) of 0.8 and 0.2 microns. Analysis of the device was done using a one-dimensional self consistent solution of the Poisson and Schroedinger equations in the channel, a two-dimensional Poisson solver to obtain the channel electric field, and a Monte Carlo simulation to estimate the carrier transit times in the channel. An increase in the value of the cutoff frequency is predicted for an increase in In composition, a decrease in temperature, and a decrease in gate length. The improvements seen with decreasing temperature, decreasing gate length, and increased In composition were smaller than those predicted by analysis. The experimental results on pseudomorphic InGaAs/InAlAs MODFET's showed that there is a 15-30 percent improvement in cutoff frequency in both the 0.8- and 0.2-micron gate length devices when the temperature is lowered from 300 to 40 K.

Lai, Richard↗