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At least 541 records · Page 30
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Conformation of ionizable poly Para phenylene ethynylene in dilute solutions

The conformation of dinonyl poly para phenylene ethynylenes (PPEs) with carboxylate side chains, equilibrated in solvents of different quality is studied using molecular dynamics simulations. PPEs are of interest because of their tunable electro-optical properties, chemical diversity, and functionality which are essential in wide range of applications. The polymer conformation determines the conjugation length and their assembly mode and affects electro-optical properties which are critical in their current and potential uses. The current study investigates the effect of carboxylate fraction on PPEs side chains on the conformation of chains in the dilute limit, in solvents of different quality. The dinonyl PPE chains are modeled atomistically, where the solvents are modeled both implicitly and explicitly. Dinonyl PPEs maintained a stretched out conformation up to a carboxylate fraction f of 0.7 in all solvents studied. The nonyl side chains are extended and oriented away from the PPE backbone in toluene and in implicit good solvent whereas in water and implicit poor solvent, the nonyl side chains are collapsed towards the PPE backbone. Thus, rotation around the aromatic ring is fast and no long range correlations are seen within the backbone.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1979

Modern estimation techniques applied to microwave sensing of the marine boundary layer

Previous efforts in the area of satellite microwave sensing of the marine boundary layer have relied upon linear regression techniques to extract geophysical parameters from the microwave measurement data. The approach used in the present paper shifts emphasis away from the generation of regression weighting matrices which implicitly assume that the data are linear in the parameters to be determined and that the problem is statistically stationary. The idea is simply to employ modern computational estimation techniques to obtain parameter estimates from nonlinear noisy measurements. The approach is limited only to the region of validity of Grody's (1976) model. Attention is focused on documenting how estimation techniques, in particular the square root information filter (SRIF), are used to solve a nonlinear function optimization problem.

Bierman, G. J.↗
NASA NTRS1988

Analytical study of the liquid phase transient behavior of a high temperature heat pipe

The transient operation of the liquid phase of a high temperature heat pipe is studied. The study was conducted in support of advanced heat pipe applications that require reliable transport of high temperature drops and significant distances under a broad spectrum of operating conditions. The heat pipe configuration studied consists of a sealed cylindrical enclosure containing a capillary wick structure and sodium working fluid. The wick is an annular flow channel configuration formed between the enclosure interior wall and a concentric cylindrical tube of fine pore screen. The study approach is analytical through the solution of the governing equations. The energy equation is solved over the pipe wall and liquid region using the finite difference Peaceman-Rachford alternating direction implicit numerical method. The continuity and momentum equations are solved over the liquid region by the integral method. The energy equation and liquid dynamics equation are tightly coupled due to the phase change process at the liquid-vapor interface. A kinetic theory model is used to define the phase change process in terms of the temperature jump between the liquid-vapor surface and the bulk vapor. Extensive auxiliary relations, including sodium properties as functions of temperature, are used to close the analytical system. The solution procedure is implemented in a FORTRAN algorithm with some optimization features to take advantage of the IBM System/370 Model 3090 vectorization facility. The code was intended for coupling to a vapor phase algorithm so that the entire heat pipe problem could be solved. As a test of code capabilities, the vapor phase was approximated in a simple manner.

Roche, Gregory Lawrence↗
NASA NTRS2000

Discontinuous dual-primal mixed finite elements for elliptic problems

We propose a novel discontinuous mixed finite element formulation for the solution of second-order elliptic problems. Fully discontinuous piecewise polynomial finite element spaces are used for the trial and test functions. The discontinuous nature of the test functions at the element interfaces allows to introduce new boundary unknowns that, on the one hand enforce the weak continuity of the trial functions, and on the other avoid the need to define a priori algorithmic fluxes as in standard discontinuous Galerkin methods. Static condensation is performed at the element level, leading to a solution procedure based on the sole interface unknowns. The resulting family of discontinuous dual-primal mixed finite element methods is presented in the one and two-dimensional cases. In the one-dimensional case, we show the equivalence of the method with implicit Runge-Kutta schemes of the collocation type exhibiting optimal behavior. Numerical experiments in one and two dimensions demonstrate the order accuracy of the new method, confirming the results of the analysis.

Bottasso, Carlo L.↗
DOE OSTI2024

Learning Constitutive Relations From Soil Moisture Data via Physically Constrained Neural Networks

Abstract The constitutive relations of the Richardson‐Richards equation encode the macroscopic properties of soil water retention and conductivity. These soil hydraulic functions are commonly represented by models with a handful of parameters. The limited degrees of freedom of such soil hydraulic models constrain our ability to extract soil hydraulic properties from soil moisture data via inverse modeling. We present a new free‐form approach to learning the constitutive relations using physically constrained neural networks. We implemented the inverse modeling framework in a differentiable modeling framework, JAX, to ensure scalability and extensibility. For efficient gradient computations, we implemented implicit differentiation through a nonlinear solver for the Richardson‐Richards equation. We tested the framework against synthetic noisy data and demonstrated its robustness against varying magnitudes of noise and degrees of freedom of the neural networks. We applied the framework to soil moisture data from an upward infiltration experiment and demonstrated that the neural network‐based approach was better fitted to the experimental data than a parametric model and that the framework can learn the constitutive relations.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2016

Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review

A review of diagonally implicit Runge-Kutta (DIRK) methods applied to rst-order ordinary di erential equations (ODEs) is undertaken. The goal of this review is to summarize the characteristics, assess the potential, and then design several nearly optimal, general purpose, DIRK-type methods. Over 20 important aspects of DIRKtype methods are reviewed. A design study is then conducted on DIRK-type methods having from two to seven implicit stages. From this, 15 schemes are selected for general purpose application. Testing of the 15 chosen methods is done on three singular perturbation problems. Based on the review of method characteristics, these methods focus on having a stage order of two, sti accuracy, L-stability, high quality embedded and dense-output methods, small magnitudes of the algebraic stability matrix eigenvalues, small values of aii, and small or vanishing values of the internal stability function for large eigenvalues of the Jacobian. Among the 15 new methods, ESDIRK4(3)6L[2]SA is recommended as a good default method for solving sti problems at moderate error tolerances.

Kennedy, Christopher A.↗
DOE OSTI2015

Charged patchy particle models in explicit salt: Ion distributions, electrostatic potentials, and effective interactions

We introduce a set of charged patchy particle models (CPPMs) in order to systematically study the influence of electrostatic charge patchiness and multipolarity on macromolecular interactions by means of implicit-solvent, explicit-ion Langevin dynamics simulations employing the Gromacs software. We consider well-defined zero-, one-, and two-patched spherical globules each of the same net charge and (nanometer) size which are composed of discrete atoms. The studied mono- and multipole moments of the CPPMs are comparable to those of globular proteins with similar size. We first characterize ion distributions and electrostatic potentials around a single CPPM. Although angle-resolved radial distribution functions reveal the expected local accumulation and depletion of counter- and co-ions around the patches, respectively, the orientation-averaged electrostatic potential shows only a small variation among the various CPPMs due to space charge cancellations. Furthermore, we study the orientation-averaged potential of mean force (PMF), the number of accumulated ions on the patches, as well as the CPPM orientations along the center-to-center distance of a pair of CPPMs. We compare the PMFs to the classical Derjaguin-Verwey-Landau-Overbeek theory and previously introduced orientation-averaged Debye-Hückel pair potentials including dipolar interactions. Our simulations confirm the adequacy of the theories in their respective regimes of validity, while low salt concentrations and large multipolar interactions remain a challenge for tractable theoretical descriptions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Coarse-grained molecular simulations of allosteric cooperativity

Interactions between a protein and a ligand are often accompanied by a redistribution of the population of thermally accessible conformations. This dynamic response of the protein’s functional energy landscape enables a protein to modulate binding affinities and control binding sensitivity to ligand concentration. In this paper, we investigate the structural origins of binding affinity and allosteric cooperativity of binding two Ca{sup 2+} ions to each domain of Calmodulin (CaM) through simulations of a simple coarse-grained model. In this model, the protein’s conformational transitions between open and closed conformational ensembles are simulated explicitly and ligand binding and unbinding are treated implicitly within the grand canonical ensemble. Ligand binding is cooperative because the binding sites are coupled through a shift in the dominant conformational ensemble upon binding. The classic Monod-Wyman-Changeux model of allostery with appropriate binding free energies to the open and closed ensembles accurately describes the simulated binding thermodynamics. The simulations predict that the two domains of CaM have distinct binding affinity and cooperativity. In particular, the C-terminal domain binds Ca{sup 2+} with higher affinity and greater cooperativity than the N-terminal domain. From a structural point of view, the affinity of an individual binding loop depends sensitively on the loop’s structural compatibility with the ligand in the bound ensemble, as well as the conformational flexibility of the binding site in the unbound ensemble.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Mixing Cell Model: A One-Dimensional Numerical Model for Assessment of Water Flow and Contaminant Transport in the Unsaturated Zone

This report describes the Mixing Cell Model code, a one dimensional model for water flow and solute transport in the unsaturated zone under steady state or transient flow conditions. The model is based on the principles and assumptions underlying mixing-cell model formulations. The unsaturated zone is discretized into a series of independent mixing cells. Each cell may have unique hydrologic, lithologic, and sorptive properties. Ordinary differential equations describe the material (water and solute) balance within each cell. Water-flow equations are derived from the continuity equation, assuming that unit gradient conditions exist at all times in each cell. Pressure gradients are considered implicitly through model discretization. Unsaturated hydraulic conductivity and moisture contents are determined by the material specific moisture-characteristic curves. Solute-transport processes include explicit treatment of advective processes, first order chain decay, and linear sorption reactions. Dispersion is addressed through implicit and explicit dispersion. Implicit dispersion is an inherent feature of all mixing-cell models and originates from the formulation of the problem in terms of mass balance around fully mixed volume elements. Expressions are provided that relate implicit dispersion to the physical dispersion of the system. Two FORTRAN codes were developed to solve the water flow and solute-transport equations: (1) the Mixing Cell Model for Flow (MCMF) solves transient water-flow problems and (2) the Mixing Cell Model for Transport (MCMT) solves the solute-transport problem. The transient water-flow problem is typically solved first by estimating the water flux through each cell in the model domain as a function of time using the MCMF code. These data are stored in either ASCII or binary files that are later read by the solute transport code (MCMT). Code output includes solute pore water concentrations, water and solute inventories in each cell and at each specified output time, and water and solute fluxes through each cell and specified output time. Computer run times for coupled transient water flow and solute transport were typically several seconds on a 2 GHz Intel Pentium IV desktop computer. The model was benchmarked against analytical solutions and finite element approximations to the partial differential equations (PDE) describing unsaturated flow and transport. Differences between the maximum solute flux estimated by the mixing cell model and the PDE models were typically less than two percent. This revision includes an option for a fixed concentration lower boundary condition for diffusive fluxes for versions 020321 and later.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

An asymptotic preserving unified gas kinetic scheme for frequency-dependent radiative transfer equations

This paper presents an extension of previous work (Sun et al., 2015 [22]) of the unified gas kinetic scheme (UGKS) for the gray radiative transfer equations to the frequency-dependent (multi-group) radiative transfer system. Different from the gray radiative transfer equations, where the optical opacity is only a function of local material temperature, the simulation of frequency-dependent radiative transfer is associated with additional difficulties from the frequency-dependent opacity. For the multiple frequency radiation, the opacity depends on both the spatial location and the frequency. For example, the opacity is typically a decreasing function of frequency. At the same spatial region the transport physics can be optically thick for the low frequency photons, and optically thin for high frequency ones. Therefore, the optical thickness is not a simple function of space location. In this paper, the UGKS for frequency-dependent radiative system is developed. The UGKS is a finite volume method and the transport physics is modeled according to the ratio of the cell size to the photon's frequency-dependent mean free path. When the cell size is much larger than the photon's mean free path, a diffusion solution for such a frequency radiation will be obtained. On the other hand, when the cell size is much smaller than the photon's mean free path, a free transport mechanism will be recovered. In the regime between the above two limits, with the variation of the ratio between the local cell size and photon's mean free path, the UGKS provides a smooth transition in the physical and frequency space to capture the corresponding transport physics accurately. The seemingly straightforward extension of the UGKS from the gray to multiple frequency radiation system is due to its intrinsic consistent multiple scale transport modeling, but it still involves lots of work to properly discretize the multiple groups in order to design an asymptotic preserving (AP) scheme in all regimes. The current scheme is tested in a few frequency-dependent radiation problems, and the results are compared with the solutions from the well-defined implicit Monte Carlo (IMC) method. The UGKS is much more efficient than IMC, and the computational times of both schemes for all test cases are listed. The UGKS seems to be the first discrete ordinate method (DOM) for the accurate capturing of multiple frequency radiative transport physics from ballistic particle motion to the diffusive wave propagation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1976

An implicit finite-difference algorithm for hyperbolic systems in conservation-law form

An implicit finite-difference scheme is developed for the efficient numerical solution of nonlinear hyperbolic systems in conservation-law form. The algorithm is second-order time-accurate, noniterative, and in a spatially factored form. Second- or fourth-order central and second-order one-sided spatial differencing are accommodated within the solution of a block tridiagonal system of equations. Significant conceptual and computational simplifications are made for systems whose flux vectors are homogeneous functions (of degree one), e.g., the Eulerian gasdynamic equations. Conservative hybrid schemes, which switch from central to one-sided spatial differencing whenever the local characteristic speeds are of the same sign, are constructed to improve the resolution of weak solutions. Numerical solutions are presented for a nonlinear scalar model equation and the two-dimensional Eulerian gasdynamic equations.

Beam, R. M.↗
NASA NTRS2015

Development of the US3D Code for Advanced Compressible and Reacting Flow Simulations

Aerothermodynamics and hypersonic flows involve complex multi-disciplinary physics, including finite-rate gas-phase kinetics, finite-rate internal energy relaxation, gas-surface interactions with finite-rate oxidation and sublimation, transition to turbulence, large-scale unsteadiness, shock-boundary layer interactions, fluid-structure interactions, and thermal protection system ablation and thermal response. Many of the flows have a large range of length and time scales, requiring large computational grids, implicit time integration, and large solution run times. The University of Minnesota NASA US3D code was designed for the simulation of these complex, highly-coupled flows. It has many of the features of the well-established DPLR code, but uses unstructured grids and has many advanced numerical capabilities and physical models for multi-physics problems. The main capabilities of the code are described, the physical modeling approaches are discussed, the different types of numerical flux functions and time integration approaches are outlined, and the parallelization strategy is overviewed. Comparisons between US3D and the NASA DPLR code are presented, and several advanced simulations are presented to illustrate some of novel features of the code.

CFD↗
DOE OSTI2022

How to Obtain the Redshift Distribution from Probabilistic Redshift Estimates

Abstract A reliable estimate of the redshift distribution n ( z ) is crucial for using weak gravitational lensing and large-scale structures of galaxy catalogs to study cosmology. Spectroscopic redshifts for the dim and numerous galaxies of next-generation weak-lensing surveys are expected to be unavailable, making photometric redshift (photo- z ) probability density functions (PDFs) the next best alternative for comprehensively encapsulating the nontrivial systematics affecting photo- z point estimation. The established stacked estimator of n ( z ) avoids reducing photo- z PDFs to point estimates but yields a systematically biased estimate of n ( z ) that worsens with a decreasing signal-to-noise ratio, the very regime where photo- z PDFs are most necessary. We introduce Cosmological Hierarchical Inference with Probabilistic Photometric Redshifts ( CHIPPR ), a statistically rigorous probabilistic graphical model of redshift-dependent photometry that correctly propagates the redshift uncertainty information beyond the best-fit estimator of n ( z ) produced by traditional procedures and is provably the only self-consistent way to recover n ( z ) from photo- z PDFs. We present the chippr prototype code, noting that the mathematically justifiable approach incurs computational cost. The CHIPPR approach is applicable to any one-point statistic of any random variable, provided the prior probability density used to produce the posteriors is explicitly known; if the prior is implicit, as may be the case for popular photo- z techniques, then the resulting posterior PDFs cannot be used for scientific inference. We therefore recommend that the photo- z community focus on developing methodologies that enable the recovery of photo- z likelihoods with support over all redshifts, either directly or via a known prior probability density.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Ab initio molecular dynamics free energy study of enhanced copper (II) dimerization on mineral surfaces

Understanding the adsorption of isolated metal cations from water on to mineral surfaces is critical for toxic waste retention and cleanup in the environment. Heterogeneous nucleation of metal oxyhydroxides and other minerals on material surfaces is key to crystal growth and dissolution. The link connecting these two areas, namely cation dimerization and polymerization, is far less understood. In this work we apply ab initio molecular dynamics calculations to examine the coordination structure of hydroxide-bridged Cu(II) dimers, and the free energy changes associated with Cu(II) dimerization on silica surfaces. The dimer dissociation pathway involves sequential breaking of two Cu 2+ -OH – bonds, yielding three local minima in the free energy profiles associated with 0-2 OH – bridges between the metal cations, and requires the design of a (to our knowledge) novel reaction coordinate for the simulations. Cu(II) adsorbed on silica surfaces are found to exhibit stronger tendency towards dimerization than when residing in water. Cluster-plus-implicit-solvent methods yield incorrect trends if OH – hydration is not correctly depicted. The predicted free energy landscapes are consistent with fast equilibrium times (seconds) among adsorbed structures, and favor Cu 2+ dimer formation on silica surfaces over monomer adsorption.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

On the Rapid Calculation of Binding Affinities for Antigen and Antibody Design and Affinity Maturation Simulations

The accurate and efficient calculation of protein-protein binding affinities is an essential component in antibody and antigen design and optimization, and in computer modeling of antibody affinity maturation. Such calculations remain challenging despite advances in computer hardware and algorithms, primarily because proteins are flexible molecules, and thus, require explicit or implicit incorporation of multiple conformational states into the computational procedure. The astronomical size of the amino acid sequence space further compounds the challenge by requiring predictions to be computed within a short time so that many sequence variants can be tested. In this study, we compare three classes of methods for antibody/antigen (Ab/Ag) binding affinity calculations: (i) a method that relies on the physical separation of the Ab/Ag complex in equilibrium molecular dynamics (MD) simulations, (ii) a collection of 18 scoring functions that act on an ensemble of structures created using homology modeling software, and (iii) methods based on the molecular mechanics-generalized Born surface area (MM-GBSA) energy decomposition, in which the individual contributions of the energy terms are scaled to optimize agreement with the experiment. When applied to a set of 49 antibody mutations in two Ab/HIV gp120 complexes, all of the methods are found to have modest accuracy, with the highest Pearson correlations reaching about 0.6. In particular, the most computationally intensive method, i.e., MD simulation, did not outperform several scoring functions. The optimized energy decomposition methods provided marginally higher accuracy, but at the expense of requiring experimental data for parametrization. Within each method class, we examined the effect of the number of independent computational replicates, i.e., modeled structures or reinitialized MD simulations, on the prediction accuracy. We suggest using about ten modeled structures for scoring methods, and about five simulation replicates for MD simulations as a rule of thumb for obtaining reasonable convergence. We anticipate that our study will be a useful resource for practitioners working to incorporate binding affinity calculations within their protein design and optimization process.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1995

Electron distributions in quasi-perpendicular shocks: Simulations

One of the outstanding problems of collisionless shock physics is the microphysical description of electron thermalization and associated wave processes. Observations at the Earth's bow shock have shown various features in the electron velocity distribution such as a loss-cone, temperature anisotropies, and beams before a thermalized, flat-topped distribution is reached downstream. It is generally believed that in addition to the macroscopic fields, which determine the overall mapping of the distribution function, electromagnetic whistler waves and lower hybrid waves are responsible for the pitch-angle scattering and thermalization of the electrons. However, a genuine physical explanation requires analysis of the evolution of the electron distribution in the self-consistent wave fields. Particle simulations are ideally suited to do this, and include processes in which both electrons and ions are involved, such as cross-field streaming instabilities. We show results from l-D and 2-D simulations using an implicit code, which allows time steps large compared to the inverse electron plasma frequency. It is shown that in order to capture the correct propagation characteristics of the waves, a large mass ratio between the protons and electrons is generally necessary. Detailed diagnostics of the waves as well as the evolution of the electron velocity distribution will be presented and will be discussed in the frame work of satellite observations.

Pantellini, F.↗
DOE OSTI2021

Density functional theory calculations of the thermodynamic and kinetic properties of point defects in β -U

Density functional theory (DFT) calculations of the thermodynamic and kinetic properties of point defects in the β phase of uranium are reported. Defect energies and entropies were calculated using 2 x 2 x 2 supercells and the Generalized Gradient Approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) for the exchange-correlation potential. Due to computational cost, calculations of the vibrational properties governing entropies were performed by only displacing atoms within (roughly) the 3rd or 4th nearest neighbor shell of the defect, which implicitly assumes that atoms beyond this distance are unaffected by the defect. Migration barriers were estimated by nudged elastic band (NEB) calculations. The low symmetry of the β-U phase (the unit cell is tetragonal and contains 30 atoms) results in many point defect configurations and even more migration pathways. A connectivity map, starting from the most stable point defects, was developed in order to identify the rate-limiting step controlling the net diffusion rate in each crystallographic direction. The uranium self-diffusivity tensor was calculated by combining the defect formation energies, entropies, migration barriers and attempt frequencies. The fastest diffusion rate was determined to be a vacancy mechanism in the z crystallographic direction. The predicted uranium self-diffusivity for this mechanism agrees well with available experimental data. Finally, the diffusion mechanisms and rates identified in this study will inform fuel performance models of swelling and gas evolution.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2015

Asymmetric kinetic equilibria: Generalization of the BAS model for rotating magnetic profile and non-zero electric field

Finding kinetic equilibria for non-collisional/collisionless tangential current layers is a key issue as well for their theoretical modeling as for our understanding of the processes that disturb them, such as tearing or Kelvin Helmholtz instabilities. The famous Harris equilibrium [E. Harris, Il Nuovo Cimento Ser. 10 23, 115–121 (1962)] assumes drifting Maxwellian distributions for ions and electrons, with constant temperatures and flow velocities; these assumptions lead to symmetric layers surrounded by vacuum. This strongly particular kind of layer is not suited for the general case: asymmetric boundaries between two media with different plasmas and different magnetic fields. The standard method for constructing more general kinetic equilibria consists in using Jeans theorem, which says that any function depending only on the Hamiltonian constants of motion is a solution to the steady Vlasov equation [P. J. Channell, Phys. Fluids (1958–1988) 19, 1541 (1976); M. Roth et al., Space Sci. Rev. 76, 251–317 (1996); and F. Mottez, Phys. Plasmas 10, 1541–1545 (2003)]. The inverse implication is however not true: when using the motion invariants as variables instead of the velocity components, the general stationary particle distributions keep on depending explicitly of the position, in addition to the implicit dependence introduced by these invariants. The standard approach therefore strongly restricts the class of solutions to the problem and probably does not select the most physically reasonable. The BAS (Belmont-Aunai-Smets) model [G. Belmont et al., Phys. Plasmas 19, 022108 (2012)] used for the first time the concept of particle accessibility to find new solutions: considering the case of a coplanar-antiparallel magnetic field configuration without electric field, asymmetric solutions could be found while the standard method can only lead to symmetric ones. These solutions were validated in a hybrid simulation [N. Aunai et al., Phys. Plasmas (1994-present) 20, 110702 (2013)], and more recently in a fully kinetic simulation as well [J. Dargent and N. Aunai, Phys. Plasmas (submitted)]. Nevertheless, in most asymmetric layers like the terrestrial magnetopause, one would indeed expect a magnetic field rotation from one direction to another without going through zero [J. Berchem and C. T. Russell, J. Geophys. Res. 87, 8139–8148 (1982)], and a non-zero normal electric field. In this paper, we propose the corresponding generalization: in the model presented, the profiles can be freely imposed for the magnetic field rotation (although restricted to a 180 rotation hitherto) and for the normal electric field. As it was done previously, the equilibrium is tested with a hybrid simulation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗