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At least 703 records · Page 39
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Comparative H-mode density limit studies in JET and AUG

Identification of the mechanisms for the H-mode density limit in machines with fully metallic walls, and their scaling to future devices is essential to find for these machines the optimal operational boundaries with the highest attainable density and confinement. Systematic investigations of H-mode density limit plasmas in experiments with deuterium external gas fuelling have been performed on machines with fully metallic walls, JET and AUG and results have been compared with one another. Basically, the operation phases are identical for both tokamaks: the stable H-mode phase, degrading H-mode phase, breakdown of the H-mode with energy confinement deterioration usually accompanied by a dithering cycling phase, followed by the l-mode phase. The observed H-mode density limit on both machines is found close to the Greenwald limit (n/n GW = 0.8–1.1 in the observed magnetic configurations). The similar behavior of the radiation on both tokamaks demonstrates that the density limit (DL) is neither related to additional energy losses from the confined region by radiation, nor to an inward collapse of the hot discharge core induced by overcooling of the plasma periphery by radiation. It was observed on both machines that detachment, as well as the X-point MARFE itself, does not trigger a transition in the confinement regime and thus does not present a limit on the plasma density. It is the plasma confinement, most likely determined by edge parameters, which is ultimately responsible for the transition from H- to l-mode. The measured Greenwald fractions are found to be consistent with the predictions from different theoretical models, based on MHD instability theory in the near-SOL.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Intermolecular Interactions in Direct Air Capture Materials: Insights from Charge Density Analysis

Direct air capture (DAC) materials enable the removal of CO 2 from the atmosphere, but improving their efficiency requires a detailed understanding of the intermolecular interactions that govern CO 2 sorption and release. Here, we present an experimental electron density study of methylglyoxal-bis(iminoguanidine) (MGBIG), a promising DAC material, using high-resolution X-ray and neutron diffraction data combined with quantum crystallographic analysis. This approach bridges theoretical and experimental data by quantifying electron density distributions and revealing how hydrogen bonds stabilize CO 2 -derived carbonate phases and may influence the desorption behavior. We identify distinct hydrogen-bonding environments in two crystalline carbonate phases: P1, a transient kinetic product, and P3, a thermodynamically stable phase. Multipolar refinement and electrostatic potential and multipole moment calculations precisely map electron density distributions, revealing key hydrogen bonds involved in CO 2 capture. Topological analysis of electron density highlights a cooperative hydrogen-bonding network in the thermodynamically favored P3 phase, where enhanced electron density delocalization and water-mediated interactions contribute to a more stable lattice. Energetic analyses confirm that stronger hydrogen bonding networks enhance the stability of P3 with a binding energy of −607.0 kJ/mol and greater lattice stability (−847.3 kJ/mol) compared to P1 (−302.5 and −571.0 kJ/mol, respectively). Electrostatic potential maps further illustrate polarization patterns that may influence the stability of the binding of CO 2 and release conditions. These findings establish a direct experimental framework for linking electron density distributions to intermolecular interactions in DAC materials, providing a rational design strategy for optimizing sorbents with improved CO 2 capture efficiency and reduced energy demands.

Electron density↗
DOE OSTI2016

Scattering of radio frequency waves by cylindrical density filaments in tokamak plasmas

In tokamak fusion plasmas, coherent fluctuations in the form of blobs or filaments are routinely observed in the scrape-off layer. Radio frequency (RF) electromagnetic waves, excited by antenna structures placed near the wall of a tokamak, have to propagate through the scrape-off layer before reaching the core of the plasma. While the effect of fluctuations on the properties of RF waves has not been quantified experimentally, it is of interest to carry out a theoretical study to determine if fluctuations can affect the propagation characteristics of RF waves. Usually, the difference between the plasma density inside the filament and the background plasma density is sizable, the ratio of the density difference to the background density being of order one. Generally, this precludes the use of geometrical optics in determining the effect of fluctuations, since the relevant ratio has to be much less than one, typically, of the order of 10% or less. In this study, a full-wave, analytical model is developed for the scattering of a RF plane wave by a cylindrical plasma filament. It is assumed that the plasma inside and outside the filament is cold and uniform and that the major axis of the filament is aligned along the toroidal magnetic field. The ratio of the density inside the filament to the density of the background plasma is not restricted. The theoretical framework applies to the scattering of any cold plasma wave. In order to satisfy the boundary conditions at the interface between the filament and the background plasma, the electromagnetic fields inside and outside the filament need to have the same k ∥ , the wave vector parallel to the ambient magnetic field, as the incident plane wave. Consequently, in contrast to the scattering of a RF wave by a spherical blob [Ram et al., Phys. Plasmas 20, 056110-1–056110-10 (2013)], the scattering by a field-aligned filament does not broaden the k ∥ spectrum. However, the filament induces side-scattering leading to surface waves and can also couple some power to the cold plasma wave different from the incident wave. The changes induced by a filament in the propagation of electron cyclotron waves and lower hybrid waves are illustrated by numerical results displaying the properties of the Poynting vector. The Poynting flux in the wake of the filament, and directed towards the core of the plasma, develops a spatial structure due to diffraction and shadowing. Finally and thus, the fluctuations affect the uniformity of power flow into the plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

A numerical study of the effect of various reactions, pressure and gas mixture ratio on the density distribution of etchant species (H, Br, Br{sup +}, and HBr{sup +}) in HBr/He plasma

In this study, a fluid model has been used to study the effect of gas mixing ratio and pressure on the density distribution of important etchant species, i.e., hydrogen (H), bromine (Br), Br{sup +}, and HBr{sup +} in HBr/He plasma. Our simulation results show that the densities of active etchant species H, Br, and HBr{sup +} increase with the increase in pressure as well as the HBr fraction in HBr/He mixture. On the contrary, the density of Br{sup +} decreases with the increase in He percentage in HBr/He mixture and with the increase in the pressure. Time averaged reaction rates (of the reactions involved in the production and consumption of these species) have been calculated to study the effect of these reactions on the density distribution of these species. The spatial distribution of these species is explained with the help of the time averaged reaction rates. Important reactions have been identified that contribute considerably to the production and consumption of these active species. The code has been optimized by identifying 26 reactions (out of 40 reactions which contribute in the production and consumption of these species) that have insignificant effect on the densities of H, Br, Br{sup +}, and HBr{sup +}. This shows that out of 40 reactions, only 14 reactions can be used to calculate the density and distribution of the important species in HBr/He plasma discharge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Measurement of 2D density profiles using a second-harmonic, dispersion interferometer

A second-harmonic, dispersion interferometer is used to image large-area (≃5 cm 2 ) plasma-jet and gas-jet density profiles. Achromatic telescopes magnify the diameters of the primary-laser beam (1064 nm) and its second-harmonic (532 nm) before probing the sample and de-magnify the beam diameters after the sample, where the primary beam transfers its phase change to a second, second-harmonic beam, allowing the sample’s dispersive-phase change to be measured between two, orthogonally polarized second harmonic beams. The telescopes produce an azimuthally symmetric, dispersive-phase shift in the sample + background phase-change image and in the background phase-change image, which is removed by digital subtraction. The interferometer’s performance was verified using standard-optical components as dispersive elements (BK7 lenses and wedge plates), resolving a minimum, phase-change sensitivity of ΔΦ min ≳ 15 mrad and spatial resolution of Δx res ≃ 100 μm. The phase change produced by unknown-density objects (a pulsed-plasma-jet and a pulsed-gas-jet) was measured, and their data were used to recover the original, 2D density profiles using an inverse Abel transform: peak-number density, N gas ≃ 6 × 10 20 cm –3 and N e ≃ 5 × 10 16 cm –3 ; line-integrated density, ∫N gas dl ~ 2 × 10 19 cm –2 and ∫N e dl ~ 1 × 10 16 cm –2 . The techniques and methods developed here are scalable to even larger probe-beam diameters and frame-capture rates, leading to a diagnostic capability that is well-suited for applications involving the real-time measurement of density.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Identification of a nematic pair density wave state in Bi 2 Sr 2 CaCu 2 O 8+x

Electron-pair density wave (PDW) states are now an intense focus of research in the field of cuprate correlated superconductivity. PDWs exhibit periodically modulating superconductive electron pairing that can be visualized directly using scanned Josephson tunneling microscopy (SJTM). Although from theory, intertwining the d-wave superconducting (DSC) and PDW order parameters allows a plethora of global electron-pair orders to appear, which one actually occurs in the various cuprates is unknown. In this work, we use SJTM to visualize the interplay of PDW and DSC states in Bi 2 Sr 2 CaCu 2 O 8+x at a carrier density where the charge density wave modulations are virtually nonexistent. Simultaneous visualization of their amplitudes reveals that the intertwined PDW and DSC are mutually attractive states. Then, by separately imaging the electron-pair density modulations of the two orthogonal PDWs, we discover a robust nematic PDW state. Its spatial arrangement entails Ising domains of opposite nematicity, each consisting primarily of unidirectional and lattice commensurate electron-pair density modulations. Further, we demonstrate by direct imaging that the scattering resonances identifying Zn impurity atom sites occur predominantly within boundaries between these domains. This implies that the nematic PDW state is pinned by Zn atoms, as was recently proposed [Lozano et al., Phys. Rev. B 103, L020502 (2021)]. Taken in combination, these data indicate that the PDW in Bi 2 Sr 2 CaCu 2 O 8+x is a vestigial nematic pair density wave state [Agterberg et al. Phys. Rev. B 91, 054502 (2015); Wardh and Granath arXiv:2203.08250].

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Application of an Empirical Density Law via Python for Aqueous Plutonium Chloride Systems for MCNP6

Criticality safety models for aqueous plutonium chloride systems often contain a significant bias due to assumptions in material compositions. These systems are currently modeled as a fictitious metal-water mixture because little is known about the true solution density. Furthermore, no predictive density tools or capabilities for modeling aqueous plutonium chloride systems are approved for use at Los Alamos National Laboratory. Recent density measurements of this ternary system (PuCl 3 -HCl-H 2 O) have allowed for the development of a more realistic density law, which is applied in this work via an empirical method based in Python. This tool, entitled PuCS (Plutonium Chloride Solution tool) may be used to determine solution density and composition based on the plutonium content, acid content, and temperature for MCNP6 inputs. PuCS has been found to predict density within 2% of experimental data. In conclusion, MCNP6 calculations have found that crediting minimal amounts of free acid (0.5 M) may correspond to a ~12% decrease in peak reactivity in comparison to current modeling methods.

42 ENGINEERING↗
DOE OSTI2024

Bayesian inference of electron density and ion temperature profiles from neutral beam and halo Balmer- α emission at Wendelstein 7-X

By employing Bayesian inference techniques, the full electron density profile from the plasma core to the edge of Wendelstein 7-X (W7-X) is inferred solely from neutral hydrogen beam and halo Balmer- α (H α ) emission data. The halo is a cloud of neutrals forming in the vicinity of the injected neutral beam due to multiple charge exchange reactions. W7-X is equipped with several neutral hydrogen beam heating sources and an H α spectroscopy system that views these sources from different angles and penetration depths in the plasma. As the beam and halo emission form complex spectra for each spatial point that are non-linearly dependent on the plasma density profile and other parameters, a complete model from the neutral beam injection and halo formation through to the spectroscopic measurements is required. The model is used here to infer electron density profiles for a range of common W7-X plasma scenarios. The inferred profiles show good agreement with profiles determined by the Thomson scattering and interferometry diagnostics across a broad range of absolute densities without any changes to the input or fitting parameters. The time evolution of the density profile in a discharge with continuous core density peaking is successfully reconstructed, demonstrating sufficient spatial resolution to infer strongly shaped profiles. Furthermore, it is shown as a proof of concept that the model is also able to infer the main ion temperature profile using the same data set.

forward modeling↗
DOE OSTI2020

Role of 3D neoclassical particle flux in density pump-out during ELM control by RMP in DIII-D

Application of three-dimensional (3-D) resonant magnetic perturbations, for the purpose of controlling edge localized modes (ELMs) in high confinement (H-mode) tokamak fusion operations, routinely leads to significantly reduction of the plasma density during the discharge, a phenomenon termed 'density pump-out'. Understanding the density pump-out phenomenon due to 3-D fields is a longstanding challenging issue. This work discusses a self-consistent toroidal model that allows initial value simulation of the density pump-out effect. The model successfully reproduces pump-out phenomenology in DIII-D ELM suppression experiments. The radial particle flux, associated with the 3-D neoclassical effects (the neoclassical toroidal viscosity, NTV), is discovered to play an important role in producing the observed large density pump- out. The key physics is associated with the drift kinetic Landau resonances between the toroidal precession of trapped thermal ions and electrons from one side, and the magnetic field perturbation from the other side. Such resonances, occurring near the top of the pedestal region, substantially enhances the radial particle flux associated with NTV. As a general consequence of the resonant NTV flux, larger density pump- out occurs in plasmas with lower collisionality and slower toroidal rotation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Validation of density pump-out by pedestal-foot magnetic island formation prior to ELM suppression in KSTAR and DIII-D tokamaks

Abstract TM1 nonlinear two-fluid simulations reveal key characteristics of density pump-out caused by pedestal-foot island formation when applying resonant magnetic perturbation (RMP). These characteristics include a bifurcation in pump-out with a low RMP coil current threshold, a sensitivity of pump-out magnitude to q 95 , and the magnitude of pump-out scaling as the square root of the RMP coil current. Dedicated experiments are carried out in the KSTAR and DIII-D tokamaks to validate these features and show that: (1) a staircase bifurcation in density pump-out is observed when slowly ramping up the n = 1 RMP current, and the density fluctuations are found to be slightly decreased from the pedestal-foot to the pedestal-top; (2) the magnitude of density pump-out becomes weaker when decreasing q 95 from 5.5 to 4.9, and a partial recovery of density pump-out is observed when q 95 is ramped down to lower than 4.9; and (3) analysis of a DIII-D database of n = 3 RMP edge-localized mode control experiments finds that the magnitude of density pump-out is proportional to the square root of RMP coil current Δ n e / n e ∝ I RMP 0.5 . These experimental observations are consistent with TM1 simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Assessment of the Tao-Mo nonempirical semilocal density functional in applications to solids and surfaces

Recently, Tao and Mo developed a semilocal exchange-correlation density functional. The exchange part of this functional is derived from a density-matrix expansion corrected to reproduce the fourth-order gradient expansion of the exchange energy in the slowly-varying-density limit, while the correlation part is based on the Tao-Perdew-Staroverov-Scuseria (TPSS) correlation functional, with a modification for the low-density limit. In this work, the Tao-Mo (TM) functional is assessed by computing various properties of solids and jellium surfaces. This includes 22 lattice constants and bulk moduli, 30 band gaps, seven cohesive energies, and jellium surface exchange and correlation energies for the density parameter r s in the range from 2 to 3 bohr. Our calculations show that the TM approximation can yield consistently high accuracy for most properties considered here, with mean absolute errors (MAEs) of 0.025 Å for lattice constants, 7.0 GPa for bulk moduli, 0.08 eV/atom for cohesive energies, and 35 erg / cm 2 for surface exchange-correlation energies. The MAE in band gaps is larger than that of TPSS, but slightly smaller than the errors of the local spin-density approximation, Perdew-Burke-Ernzerhof generalized gradient approximation, and revised TPSS. However, band gaps are still underestimated, particularly for large-gap semiconductors, compared to the Heyd-Scuseria-Ernzerhof nonlocal screened hybrid functional.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Level Densities of 74,76 Ge from compound nuclear reactions

The level densities of 74,76 Ge nuclei are studied with 68,70 Zn( 7 Li , Xp ) reactions. Proton evaporation spectra are measured at backward angles in a wide energy region, from about 2 to 25 MeV. The analysis of spectra allows for the testing of level density models used in modern reaction codes for practical cross-section calculations. Our results show that at excitation energies above the discrete level region, all level density models tested in this work overestimate the level densities that are needed to reproduce proton spectra from these reactions. The Gilbert and Cameron model, which includes the constant-temperature energy dependence of the level density, shows the best agreement with experiment, however, its parameters need to be adjusted to reflect the observed reduction of the level density at higher excitation energies.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Density modification of cryo-EM maps

Density modification uses expectations about features of a map such as a flat solvent and expected distributions of density in the region of the macromolecule to improve individual Fourier terms representing the map. This process transfers information from one part of a map to another and can improve the accuracy of a map. Here, the assumptions behind density modification for maps from electron cryomicroscopy are examined and a procedure is presented that allows the incorporation of model-based information. Density modification works best in cases where unfiltered, unmasked maps with clear boundaries between the macromolecule and solvent are visible, and where there is substantial noise in the map, both in the region of the macromolecule and the solvent. It also is most effective if the characteristics of the map are relatively constant within regions of the macromolecule and the solvent. Model-based information can be used to improve density modification, but model bias can in principle occur. Here, model bias is reduced by using ensemble models that allow an estimation of model uncertainty. A test of model bias is presented that suggests that even if the expected density in a region of a map is specified incorrectly by using an incorrect model, the incorrect expectations do not strongly affect the final map.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Ultra-high energy density relativistic plasmas from nanostructures: scaling to ultra-high intensities (Final Report)

This project investigated the ultra-high energy density (UHED) regime of matter found in the center of stars, using a compact PW-class laser. These extreme conditions are typically only obtained in the laboratory in the central hot-spot of spherically imploded capsules in inertial confinement fusion experiments driven by the world’s largest lasers. We have shown that near-solid density arrays of aligned nanostructures can be volumetrically heated to multi-keV temperatures by irradiation at relativistic intensity with ultrafast laser pulses of modest energy, opening a path for the generation of UHED plasmas with compact lasers. This new UHED plasma generation approach promises to create an environment with extreme energy densities and degrees of ionization, record conversion of optical laser light into ultrafast x-ray pulses, gigantic magnetic fields and pressures, and directed beams of high energy particles . In this project we achieved record degree of ionization in volumetric heating solid density and near-solid density plasmas. Gold plasmas which spectra is characterized by L shell transition emission from ions with charge up to the Ne-like state, Au+ 72 were generated using ultrafast laser pulses of less than 10 J of energy from a compact laser focused to an intensity of ~ 3x10 21 Wcm -2 . We also conducted measurements to determine the heat penetration depth in Ni nanowire arrays as compared to Ni foil targets by monitoring the line emission of a Co buried tracer underneath a variable amount of Ni. The measurements revealed that the nanowire plasmas are roughly six times larger in depth than the solid density target plasmas. A result of this increased plasma in nanowire arrays is a greatly increased conversion of optical laser light into > 1 KeV x-rays, a record conversion efficiency of 20 %. Critical to the realization of the proposed experiments was the generation of ultrafast laser pulses with ultra-high contrast that can deposit the energy deep into the nanowire arrays before the nanowires explode to create a continuous plasma. Supporting the proposed experiments was the recent demonstration at Colorado State University of a Petawatt-class laser that emits 30 fs pulses at high repetition rates. The experiments combined this unique laser tool with a variety of tailored nanowire arrays fabricated in house and with an extensive suite of diagnostics. The experiments were accompanied by 3-dimensional particle-in-cell simulations and detailed atomic physics simulations with transient kinetics and radiation transport. The proposed research allowed us to continue training Ph.D students and post-docs with broad experience in HEDP Science.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Evaluation Of Glass Density to Support the Estimation of Fissile Mass Loadings in Sludge Batch 10 Glasses

Per a directive from the Department of Energy Savannah River Operations Office (DOE-SR) in 2008, the fissile mass loading concentration must remain below 897 g/m 3 in each high-level waste (HLW) glass canister produced by the Defense Waste Processing Facility (DWPF). To support Sludge Batch 5 (SB5) processing, the Savannah River National Laboratory (SRNL) developed a technical basis that facilitates the evaluation of fissile mass loading of the glass product. The calculation is based on the iron (Fe) concentration in the glass as determined by measurements from the Slurry Mix Evaporator acceptability analysis as well as the glass density. In April 2022, a subsequent DOE-SR directive increased the fissile mass loading limit to 2500 g/m 3 beginning with Sludge Batch 11. Thus, the 897 g/m 3 limit still applies to Sludge Batch 10 (SB10) processing. For SB5 through initial Sludge Batch 9 (SB9) processing prior to coupled operation with the Salt Waste Processing Facility (SWPF), SRNL provided DWPF a bounding glass density value that was based on a statistical evaluation of density measurements. To eliminate the need for experimental work, a composition-based density model for HLW glasses was developed at SRNL in 2019. The objective of this report is to present the bounding glass density determined with the composition-based density model for SB10 sludge-only (SO) and coupled processing.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2016

INFERRING GRAVITATIONAL POTENTIALS FROM MASS DENSITIES IN CLUSTER-SIZED HALOS

We use N-body simulations to quantify how the escape velocity in cluster-sized halos maps to the gravitational potential in a ΛCDM universe. Using spherical density-potential pairs and the Poisson equation, we find that the matter density inferred gravitational potential profile predicts the escape velocity profile to within a few percent accuracy for group and cluster-sized halos (10{sup 13}<M{sub 200}<10{sup 15} M {sub ⊙}, with respect to the critical density). The accuracy holds from just outside the core to beyond the virial radius. We show the importance of explicitly incorporating a cosmological constant when inferring the potential from the Poisson equation. We consider three density models and find that the Einasto and Gamma profiles provide a better joint estimate of the density and potential profiles than the Navarro, Frenk, and White profile, which fails to accurately represent the escape velocity. For individual halos, the 1σ scatter between the measured escape velocity and the density-inferred potential profile is small (<5%). Finally, while the sub-halos show 15% biases in their representation of the particle velocity dispersion profile, the sub-halo escape velocity profile matches the dark matter escape velocity profile to high accuracy with no evidence of velocity bias outside 0.4r {sub 200}.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Density jumps near the virial radius of galaxy clusters

Recent simulations have indicated that the dark matter halos of galaxy clusters should feature steep density jumps near the virial radius. Since the member galaxies are expected to follow similar collisionless dynamics as the dark matter, the galaxy density profile should show such a feature as well. We examine the potential of current data sets to test this prediction by selecting cluster members for a sample of 56 low-redshift (0.1<z<0.3) galaxy clusters, constructing their projected number density profiles, and fitting them with two profiles, one with a steep density jump and one without. Additionally, we investigate the presence of a jump using a non-parametric spline approach. We find that some of these clusters show strong evidence for a model with a density jump, with the strength of the signal increasing with the inclusion of spectroscopic cluster member identification. We discuss avenues for further analysis of the density jump with future data sets, particularly with the inclusion of additional spectroscopy of cluster outskirts.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

WEIBEL INSTABILITY DRIVEN BY SPATIALLY ANISOTROPIC DENSITY STRUCTURES

Observations of afterglows of gamma-ray bursts (GRBs) suggest that post-shock magnetic fields are strongly amplified to about 100 times the shock-compressed value. The Weibel instability appears to play an important role in generating the magnetic field. However, recent simulations of collisionless shocks in homogeneous plasmas show that the magnetic field generated by the Weibel instability rapidly decays. There must be some density fluctuations in interstellar and circumstellar media. The density fluctuations are anisotropically compressed in the downstream region of relativistic shocks. In this paper, we study the Weibel instability in electron–positron plasmas with spatially anisotropic density distributions by means of two-dimensional particle-in-cell simulations. We find that large magnetic fields are maintained for a longer time by the Weibel instability driven by spatially anisotropic density structure. Particles anisotropically escape from the high density region, so that a temperature anisotropy is generated and the Weibel instability becomes unstable. Our simulation results suggest that the Weibel instability driven by an anisotropic density structure can generate sufficiently large magnetic fields and they can cover sufficiently large regions to explain the afterglow emission of GRBs.

79 ASTRONOMY AND ASTROPHYSICS↗