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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Reduced diffusion and enhanced retention of multiple radionuclides from pore structure characterization of barrier materials for enhanced repository performance

Fluid flow and chemical transport in porous media are the macroscopic consequences of pore structure, which integrates geometry (e.g., pore size and surface area, pore-size distribution) and topology (e.g., pore connectivity). Low-permeability geological media whose pores are poorly interconnected will exhibit the characteristics of anomalous diffusion and sample size-dependent effective porosity, which will strongly impact long-term net diffusion and retention of radionuclides in geological repository settings involving different host rocks and barrier materials. A suite of innovative and complementary experimental approaches is utilized to study the microscopic pore structure and macroscopic fluid flow & chemical transport for a range of host rocks and barrier materials, in addition to standard clay minerals and reference rocks. With a particular focus on quantifying the presence and magnitude of “isolated” pores for a reduced effective porosity in low-permeability geomedia, the integrated methodologies for basic properties and pore structure characterization of these geomedia include X-ray diffraction, thin section petrography, grain size distribution, water immersion porosimetry after vacuum-pulling for full saturation, mercury intrusion porosimetry, nitrogen physisorption, scanning electron microscopy, X-ray computed tomography, and (ultra-)small angle neutron (X-ray) scattering. In addition, custom-designed gas diffusion, tracer recipe involving a range of anionic and cationic chemicals with subsequent analyses by laser ablation and inductively coupled plasma-mass spectrometry, along with batch sorption, column transport, and imbibition tests were conducted for coupled effects of pore structure and chemical retention/transport. From the perspectives of pore structure in conjunction with multiple and complementary approaches to examining a range of sample sizes under different observational scales, we find that the poor pore connectivity is prevalent in low-permeability media (mudstone and crystalline rock) that is related to geological processes (e.g., compaction, diagenesis and thermal maturation). For example, the deep and organic matter-rich mudstones have a much smaller effective porosity than the total porosity (as a result of poor pore connectivity) and associated diffusion coefficient, and the effective porosity & diffusion coefficients are also dependent upon the sample sizes used in the measurement. Similarly, most of the pore space in the shallow mudstone is also controlled by pore-throat diameters in the 5-50 nm range of intergranular pore types from its fine-grained nature, but with an overall good pore connectivity. However, the nm-sized pore space (physically pore-network architecture) and strong sorption capacities (chemical retention from clay minerals) of both shallow and deep mudstones lead to the synergistic retention of cationic radionuclides and their utilities as effective host rocks and barrier materials. Our unique approaches of studying how the micro-scale pore structure affect macro-scale fluid flow, diffusion & retention, and chemical transport produce improved mechanistic understanding, and realistic quantification, of diffusion and retention of typical radionuclides in a range of generic host rocks and barrier materials (clay/shale, salt, crystalline rock, and tuff), with the overall results leading to scientifically-based understanding of enhanced isolation (from both diffusion and retention) of radionuclides and improved confidence on the long-term performance of geological repository to store high-level radioactive wastes. In addition to the training of 25 undergraduates, graduates, and postdocs of UTA, the scientists (organizations) involved in performing this work (e.g., discussion, sample sharing, and operation of SANS and SAXS instruments) include Ed Matteo, Yifeng Wang, and Kristopher Kuhlman (Sandia National Laboratories), Jens Birkholzer, Liange Zheng, Tim Kneafsey, and Sharon Borglin (Lawrence Berkeley National Laboratory), Mavrik Zavarin (Lawrence Livermore National Laboratory), Yukio Tachi and Yuta Fukatsu (Japan Atomic Energy Agency), Mieke de Craen (Euridice, Belgium), Markus Bleuel (NIST), Wei-Ren Chen, Gergely Nagy, Changwoo Do, William Heller, Larry Anovitz, and Kenneth Littrell (ORNL), as well as Jan Illvsky, Ivan Kuzmenko, Ju-Sang Park and Jon Almers (ANL). Key deliverables include a total of 13 peer-reviewed journal articles (nine published and three under review), 23 presentations at scientific conferences (AAPG, AAPG Southwest Section, AGU, Asian Clay Conference, GSA, GSA South-Central Section, IHLRWM, InterPore, International Conference on Chemistry and Migration Behavior of Actinides and Fission Products in the Geosphere, International Conference on Coupled Processes in Fractured Geological Media: Observation, Modeling and Application), and academic institutions (UTA, New Mexico State University; University of Poitiers, France; University of Helsinki, Finland; Uppsala University, Sweden; Istanbul Technical University, Turkey) and other organizations (Andra, France; Posiva Oy, Finland).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Co-ion specific effect on sodium halides sorption and transport in a cross-linked poly(p-styrene sulfonate-co-divinylbenzene) for membrane applications

Here, sodium halide sorption and transport in a cation exchange membrane based on cross-linked poly(p-styrene sulfonate-co-divinylbenzene) (CR61) were investigated experimentally and theoretically. At fixed co-ion valence, sodium halide partitioning between aqueous electrolyte solutions and ion exchange polymers is only minimally sensitive to co-ion chemical identity. NaCl, NaF and NaI exhibit similar solubility coefficients in CR61, which agrees reasonably well with predictions of the Donnan-Manning model, especially at high external salt concentrations. Ion activity coefficients in the membrane were evaluated and ion sorption thermodynamics were investigated. Ion diffusion coefficients in CR61 were predicted using a recently developed framework based on the Manning diffusion model, which accounts for electrostatic effects on ion diffusion, and the Mackie-Meares model, which accounts for tortuosity/area effects on ion diffusion in swollen polymers. Model predictions agree reasonably well with the experimental data, especially at high external salt concentrations. The observed decrease in salt diffusion coefficients in CR61 relative to values in aqueous solutions is due primarily to tortuosity/area effects. Salt diffusion coefficients correlate with co-ion hydrated radius and membrane water content. Finally, salt permeability coefficients predicted using the solution-diffusion model exhibit good agreement with experimental data, especially at external salt concentration greater than 0.1 mol/L.

42 ENGINEERING↗
DOE OSTI2022

Understanding the effect of irradiation and silicon carbide microstructure on silver diffusion in TRISO particles

The silicon carbide (SiC) layer in tristructural isotropic (TRISO) fuel particles serves as a barrier to prevent the escape of fission from the fuel kernel. The release of silver (Ag) is a concern due to the long half-life of the 110mAg isotope. In this study, a combination of atomistic and phase-field methods focuses on quantifying the effect of irradiation and SiC microstructure on Ag diffusion. Atomistic calculations provide the Ag diffusivity in SiC bulk and GBs, also providing an estimate of the effect of irradiation defects on Ag diffusivity in bulk SiC. These lower length scale efforts are leveraged to develop a mesoscale effective Ag diffusion coefficient (Deff) in SiC. Deff is defined as a function of temperature, microstructure variables, and fluence. Deff is implemented in the fuel performance code Bison to predict Ag release from AGR-1 and AGR-2 TRISO fuel particles. We hereby quantify the impact of SiC grain size and irradiation on Ag release and improve Bison's predictions.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Characteristics and mathematical modeling of apple slice drying in an electrohydrodynamic system with a needle‐plate electrode

Abstract The drying of apple slices in an electrohydrodynamic (EHD) system with a needle‐plate electrode was characterized and mathematically modeled at voltages of 30, 40, and 50 kV and with distances between needles of 5, 6, and 7 cm. The results showed that the drying rate, effective water diffusion coefficient, and rehydration ratio of the apple slices, and specific energy consumption of drying, all increased with increasing voltage. Initially, there was a period when the drying rate was approximately constant in the low‐voltage EHD, but not in the high voltage conditions. At the same voltage, the drying rate was highest when the distance between needles was 6 cm. The voltage and distance between needles had a significant ( p < .05) interactive effect on the effective water diffusion coefficient and specific energy consumption, but not on the rehydration ratio. General mathematical models for drying can be used to represent the drying behavior of apple slices. The Midilli and Kucuk model and the Logarithmic model had the best fits, with correlation coefficients of 0.998803 and 0.998267, respectively. Predictive functions for the moisture ratio of apple slices based on voltage and distance between needles were established and verified. The results indicated that the Logarithmic model could more accurately predict the moisture ratio of apple slices dried using the EHD method. Practical Applications As a new drying technology, electrohydrodynamic (EHD) drying has unequaled advantages. According to the results, using the appropriate voltage and distance between needles improves not only drying efficiency, but also the rehydration ratio of apple slices, which reflects the quality of dried products. The Logarithmic model can accurately predict the EHD drying behavior of apple slices, which is of great significance in optimizing actual production.

Li, Bowen↗
DOE OSTI2023

Evolving radon diffusion through earthen barriers at uranium waste disposal sites

Field measurements of Rn-222 fluxes from the tops and bottoms of compacted clay radon barriers were used to calculate effective Rn diffusion coefficients (D Rn ) at four uranium waste disposal sites in the western United States to assess cover performance after more than 20 years of service. Values of D Rn ranged from 7.4 × 10 -7 to 6.0 × 10 -9 m 2 /s, averaging 1.42 × 10 -7 . Water saturation (S W ) from soil cores indicated that there was relatively little control of D Rn by S W , especially at higher moisture levels, in contrast to estimates from most steady-state diffusion models. Further, this is attributed to preferential pathways intrinsic to construction of the barriers or to natural process that have developed over time including desiccation cracks, root channels, and insect burrows in the engineered earthen barriers. A modification to some models in which fast and slow pathway D Rn values are partitioned appears to give a good representation of the data; 4% of the fast pathway was needed to fit the data regression. For locations with high S w and highest D Rn (and fluxes) at each site, the proportion of fast pathway ranged from 1.7% to 34%, but for many locations with lower fluxes, little if any fast pathway was needed.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2024

Multiscale, mechanistic modeling of irradiation-enhanced silver diffusion in TRISO particles

Tristructural isotropic (TRISO) particles are under consideration for use in several proposed advanced nuclear reactor concepts. The silicon carbide (SiC) layer in TRISO acts as a barrier to prevent the release of the fission products. However, despite remarkable retention, silver (Ag) release has been observed from intact particles, which requires investigation since the Ag isotope ( 110m Ag) has a long half-life. Previous work focused on developing a multiscale, mechanistic model for Ag diffusion accounting for temperature and microstructure effect and has been successfully validated. In this work, we expand the previous model to account for irradiation-enhanced Ag diffusivity in SiC and improve its accuracy over a wider grain size and temperature ranges relevant for advanced reactor conditions. A temperature, grain size, and flux dependent diffusivity is therefore derived using the mesoscale code MARMOT and implemented in the fuel performance code BISON. The irradiation-enhanced Ag diffusivity in SiC is compared against experimental data and validated using BISON against Ag release measurements from the Advanced Gas Reactor Fuel Development and Qualification Program (AGR-1 and AGR-2). Herein, we quantify the impact of SiC grain size, irradiation, and temperature on Ag release. In agreement with previous studies, we find accounting for SiC grain size improves agreement between BISON predictions and experimental observations for most cases. In conclusion, we also find that accounting for irradiation improves agreement for cases where Ag release was underestimated, but the impact was less significant than accounting for microstructure.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Polyelectrolyte Surface Diffusion in a Nanoslit Geometry

The surface diffusion of poly-l-lysine (PLL) in a planar nanoslit was studied using convex lens-induced confinement (CLiC) single-molecule tracking microscopy. Here, three surface chemistries were employed to understand the interplay of electrostatic and short-range interactions: an amine-functionalized silica surface, an oligo(ethylene oxide) (OEG)-modified surface, and a 1:1 mixture of the two ligands. Effective surface diffusion coefficients increased rapidly with slit height until saturating for slit heights <30 nm. While diffusion at a semi-infinite interface was significantly faster for OEG surfaces, the diffusion coefficient increased most rapidly with slit height for amine-functionalized surfaces, resulting in surface diffusion within very thin slits being nearly independent of surface chemistry. Intermittent random walks were simulated within a planar slit geometry, using experimentally measured parameters obtained from diffusion at a single interface to account for the characteristic short-range interactions between PLL and each surface chemistry, and were in good agreement with experimental measurements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Structure and dynamics of hydrodynamically interacting finite-size Brownian particles in a spherical cavity: Spheres and cylinders

The structure and dynamics of confined suspensions of particles of arbitrary shape are of interest in multiple disciplines from biology to engineering. Theoretical studies are often limited by the complexity of long-range particle-particle and particle-wall forces, including many-body fluctuating hydrodynamic interactions. Here, we report a computational study on the diffusion of spherical and cylindrical particles confined in a spherical cavity. We rely on an immersed-boundary general geometry Ewald-like method to capture lubrication and long-range hydrodynamics and include appropriate non-slip conditions at the confining walls. A Chebyshev polynomial approximation is used to satisfy the fluctuation-dissipation theorem for the Brownian suspension. We explore how lubrication, long-range hydrodynamics, particle volume fraction, and shape affect the equilibrium structure and the diffusion of the particles. It is found that once the particle volume fraction is greater than 10%, the particles start to form layered aggregates that greatly influence particle dynamics. Hydrodynamic interactions strongly influence the particle diffusion by inducing spatially dependent short-time diffusion coefficients, stronger wall effects on the particle diffusion toward the walls, and a sub-diffusive regime-caused by crowding-in the long-time particle mobility. The level of asymmetry of the cylindrical particles considered here is enough to induce an orientational order in the layered structure, decreasing the diffusion rate and facilitating a transition to the crowded mobility regime at low particle concentrations. Our results offer fundamental insights into the diffusion and distribution of globular and fibrillar proteins inside cells.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Diffusion–convection model of runaway electrons due to large magnetohydrodynamic perturbations in post-thermal quench plasmas

Systematic test particle tracing simulations for runaway electrons (REs) are performed for six post-thermal quench equilibria from DIII-D and ITER, where large scale, kink-like n = 1 (n is the toroidal mode number) magnetohydrodynamic (MHD) instabilities are found. The modeled particle guiding center orbits allow extraction of the effective diffusion–convection coefficients of REs in the presence of large three-dimensional (3D) perturbations up to 10% of the equilibrium toroidal field. With a fixed spatial distribution of the field perturbation, the RE transport coefficients along the plasma radial coordinate track reasonably well with the surface-averaged perturbation level. A substantial variation in the value of the transport coefficients—by three orders of magnitude in most cases, however, occurs with varying launching location of REs along the plasma radius. Large 3D perturbations almost always lead to comparable diffusion and convection processes, meaning that diffusion alone is insufficient to describe the particle motion. At lower (but still high) level of perturbation, the RE convection is found to be dominant over diffusion. A similar observation is made when the perturbation is too strong. In the presence of large perturbation, the dependence of the RE transport on the particle energy is sensitive to the spatial distribution of the perturbation. Based on numerically obtained RE transport coefficients, an analytic fitting model is proposed to quantify the particle diffusion and convection processes due to large MHD events in post-thermal quench plasmas. The model is shown to reasonably well reproduce the direct test particle tracing results for the RE loss fraction and can, thus, be useful for incorporating into other kinetic RE codes in order to simulate the RE beam evolution in the presence of large 3D perturbations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Analysis of Silver Release from Furnace-Tested TRISO Particles

High temperature testing of intact TRISO particles previously irradiated in the AGR-5/6/7 experiment was performed in the Furnace for Irradiated TRISO Testing (FITT) to directly confirm diffusive release of silver and europium from intact TRISO particles. Testing was conducted from 1,100–1,600°C for exposure times up to 100 h to directly confirm silver through layer release below safety testing temperatures. The FITT analysis showed highest levels of silver release at 1,300–1,400°C which confirms athermal release behaviors previous observed in step-wise and transient safety tests. Additionally, release was non-uniform with some particles releasing a majority of their inventory while others did not appear to release silver under identical testing conditions, which was consistent with historic observations. An assessment of the effective silver diffusion coefficient in the SiC layer was conducted and indicated maximum values in the 1,300–1,400°C range. The magnitude of the calculated diffusion coefficients also exceeded currently accepted diffusion coefficients. The release behavior of europium from intact particles was also analyzed in FITT for at 1,450–1,550°C for 500 h to 750 h. Direct confirmation of europium release below safety testing temperatures was confirmed absent contributions from matrix release. The analysis indicated europium release follows a general Arrhenius behavior and suggests general uniform release and indicates irradiation conditions influence observed release response. Calculated diffusion kinetics agree well with historic experiments.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Larger than uncorrelated vacancy diffusion contributions in chemically disordered crystalline materials

Arising from a variational approach to compute diffusion coefficients, we introduce “superkinetic kinosons”, which are contributions to the diffusion flux of mobile defects and atomic species by single jump mechanisms that can exceed their uncorrelated values. In vacancy-mediated diffusion in crystalline random and high entropy materials, these contributions primarily arise from intermittent jumps of slow moving atoms that remove the vacancy out of correlation traps and enable a quantification of such effects on the diffusion coefficients. They can be significant contributors to diffusion, even when faster moving atoms have infinite percolation networks. Furthermore, their existence and importance provide fundamental insights about underlying aspects of vacancy diffusion such as formation of localized correlation traps and deviation of vacancy diffusion from percolation behavior.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Diffusion of cesium in oxidized and unoxidized IG-110 nuclear graphite

Time-release diffusion measurements of cesium have been conducted over the temperature range 1073 K – 1973 K on oxidized and unoxidized IG-110 graphite. Four cesium concentrations were tested to investigate the concentration dependence of the diffusion coefficient. Two levels of oxidation were tested and compared to unoxidized concentration-matched sets to explore the effects of graphite oxidation. Here, the results demonstrate that cesium diffusion coefficient in unoxidized IG-110 graphite is independent of concentration within the range 34 – 163 µg Cs/g graphite . Above this, the effective cesium diffusion coefficient changes with concentration. The diffusion coefficient was increased by a factor of 2–12 in the oxidized set with 7.8% mass loss. These results can be used to aid predictive modeling of cesium diffusion in HTGR cores.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Measurement of the longitudinal diffusion of ionization electrons in the MicroBooNE detector

Accurate knowledge of electron transport properties is vital to understanding the information provided by liquid argon time projection chambers (LArTPCs). Ionization electron drift-lifetime, local electric field distortions caused by positive ion accumulation, and electron diffusion can all significantly impact the measured signal waveforms. This paper presents a measurement of the effective longitudinal electron diffusion coefficient, D L , in MicroBooNE at the nominal electric field strength of 273.9 V/cm. Historically, this measurement has been made in LArTPC prototype detectors. This represents the first measurement in a large-scale (85 tonne active volume) LArTPC operating in a neutrino beam. This is the largest dataset ever used for this measurement. Using a sample of ~70,000 through-going cosmic ray muon tracks tagged with MicroBooNE's cosmic ray tagger system, we measure D L = 3.74 +0.28 -0.29 cm 2 /s.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Enhanced Diffusive Transport in Fluctuating Porous Media

Mass transport within porous structures is a ubiquitous process in biological, geological, and technological systems. Despite the importance of these phenomena, there is no comprehensive theory that describes the complex and diverse transport behavior within porous environments. While the porous matrix itself is generally considered a static and passive participant, many porous environments are in fact dynamic, with fluctuating walls, pores that open and close, and dynamically changing cross-links. While diffusion has been measured in fluctuating structures, notably in model biological systems, it is rarely possible to isolate the effect of fluctuations because of the absence of control experiments involving an identical static counterpart, and it is generally impossible to observe the dynamics of the structure. In this paper, we present a direct comparison of the diffusion of nanoparticles of various sizes within a trackable, fluctuating porous matrix and a geometrically equivalent static matrix, in conditions spanning a range of regimes from obstructed to highly confined. The experimental system comprised a close-packed layer of colloidal spheres that were either immobilized to a planar surface or allowed to fluctuate locally, within the space defined by their nearest neighbors. Interestingly, the effective long-time diffusion coefficient was approximately 35–65% greater in the fluctuating porous matrix than in the static one (depending on the size of the nanoparticle probes), regardless of the geometric regime. This was explained by considering the enhancing effects of matrix fluctuations on the short-time diffusion coefficient and cooperative “gate-opening” motions of matrix particles and nanoparticle probes.

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

Mutual Diffusion Coefficients of Na 2 SO 4 at C = 0.02989 mol·dm -3 and 298.15 K by Using Rayleigh Interferometry with Free Diffusion Boundary Conditions: Experimental Test of the Effect of the C 3/2 Concentration Dependence of Refractive Index at Low Concentration

Rayleigh interferometry is one of the most precise and accurate methods for the experimental determination of the mutual diffusion coefficients of both electrolytes and non-electrolytes in liquid solutions. For binary solutions at moderate and high concentrations where the concentration dependences of both diffusion coefficient and refractive index can be assumed to be linear or almost linear and the concentration difference ΔC between a pair of solutions undergoing free diffusion is not large compared to their average concentration, and by using proper combinations of the interference fringe positions as they vary with time, under these conditions diffusion coefficients are obtained that are independent of the size of ΔC. However, this situation becomes more complicated at low concentrations for electrolyte solutions where the concentration dependences of both the diffusion coefficient and refractive index are non-linear, with C 1/2 dependence for the diffusion coefficient and C 3/2 dependence for the refractive index. As a test of these effects on calculated mutual diffusion of electrolyte solutions at low concentrations as measured by Rayleigh interferometry, apparent mutual diffusion coefficients D v,a (volume-fixed reference frame) were measured for fixed average concentrations C=(0.02989 ± 0.00001) mol·dm –3 of Na 2 SO 4 (aq) at 298.15 K while varying ΔC/C from 0.66673 to 2, a threefold variation. The dependence of the diffusion coefficient on ΔC/C was found to be linear, yielding D v = 1.041 6 × 10 –9 m 2 ·s –1 for an infinitely small concentration difference between the diffusing solutions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

The Effect of Proton Conductivity of Fe–N–C–Based Cathode on PEM Fuel cell Performance

A model–based impedance spectroscopy is used to determine proton conductivity, oxygen transport parameter, double layer capacitance and oxygen reduction reaction (ORR) Tafel slope in the Fe–N–C cathode catalyst layer (CCL) of a PEM fuel cell. Experimental spectra of two cells differing by the membrane thickness only are processed using a physics–based model for PEMFC impedance. The spectra have been measured in the range of current densities from 25 to 800 mA cm -2 . The ORR Tafel slope of both the cells shows almost linear growth with the current density. In one of the cells, the CCL proton conductivity σp strongly decays at the current density of 100 mA cm -2 ; this decay is accompanied by the step growth of the double layer capacitance. Other minor variations of proton conductivity and double layer capacitance with the cell current occur also in a counterphase; presumed origin of this effect is discussed. The oxygen diffusion coefficient in the cathode exhibits explosive growth with the cell current. We attribute this effect to formation of temperature and pressure gradients in the CCL due to strongly non–uniform distribution of ORR rate in the electrode.

25 ENERGY STORAGE↗
DOE OSTI2022

Quasilinear theory for inhomogeneous plasma

Here, this paper presents quasilinear theory (QLT) for a classical plasma interacting with inhomogeneous turbulence. The particle Hamiltonian is kept general; for example, relativistic, electromagnetic and gravitational effects are subsumed. A Fokker–Planck equation for the dressed ‘oscillation-centre’ distribution is derived from the Klimontovich equation and captures quasilinear diffusion, interaction with the background fields and ponderomotive effects simultaneously. The local diffusion coefficient is manifestly positive-semidefinite. Waves are allowed to be off-shell (i.e. not constrained by a dispersion relation), and a collision integral of the Balescu–Lenard type emerges in a form that is not restricted to any particular Hamiltonian. This operator conserves particles, momentum and energy, and it also satisfies the H -theorem, as usual. As a spin-off, a general expression for the spectrum of microscopic fluctuations is derived. For on-shell waves, which satisfy a quasilinear wave-kinetic equation, the theory conserves the momentum and energy of the wave–plasma system. The action of non-resonant waves is also conserved, unlike in the standard version of QLT. Dewar's oscillation-centre QLT of electrostatic turbulence is proven formally as a particular case and given a concise formulation. Also discussed as examples are relativistic electromagnetic and gravitational interactions, and QLT for gravitational waves is proposed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗