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DOE OSTI2021

Impact of particle loading and phase coupling on gas–solid flow dynamics: A case study of a two-phase, gas–solid flow in an annular pipe

The present study is devoted to a two-phase, gas–solid flow in an annular pipe (hollow cylinder) at an elevated pressure of 15 bars and moderate Reynolds number of circa 6000. The influence of the particle loading, the interaction between the phases, and turbulence dispersion on the flow dynamics is systematically studied by means of computational fluid dynamics simulations, employing the Ansys FLUENT commercial package. The cases with a particle volumetric fraction of 1.2% are referred to as “high particle loading,” and those with 0.13% are denoted as “low particle loading.” The following cases are investigated: (1) pure gas flow; (2) low particle loading two-phase flow with one-way coupling and with turbulence dispersion; (3) low particle loading two-phase flow with two-way coupling but without turbulence dispersion; (4) low particle loading two-phase flow with two-way coupling and with turbulence dispersion; (5) high particle loading two-phase flow with one-way coupling and with turbulence dispersion; (6) high particle loading two-phase flow with two-way coupling but without turbulence dispersion; and (7) high particle loading two-phase flow with two-way coupling and with turbulence dispersion. Additionally, the boundary layer is found to grow without fluctuations of the turbulent kinetic energy (TKE) for cases 1, 2, and 5. For case 4, the TKE fluctuations have been identified, although they appear to be less substantial than those in cases 6 and 7. The authors attribute the semi-chaotic nature of the TKE fluctuations to the particle loading and two-way coupling. In addition, the onset and development of the flow instability have been observed at a random axial distance in cases 4, 6, and 7. Such instability is also attributed to the two-way coupling with turbulence dispersion in the flow. It is concluded that the particle loading, one-way, or two-way coupling between the phases, and the turbulence dispersion models significantly influence the development of the flow dynamics with the same inlet and boundary conditions. Consequently, it is not a trivial question, which result a user should trust. The present computational results inspire to perform verification as well as experimental validation of the simulations, so the simulation results can subsequently be used with confidence for design analysis.

42 ENGINEERING↗

DOE OSTI2022

Solid organic-coated ammonium sulfate particles at high relative humidity in the summertime Arctic atmosphere

The ability of atmospheric aerosols to impact climate through water uptake and cloud formation is fundamentally determined by the size, composition, and phase (liquid, semisolid, or solid) of individual particles. Particle phase is dependent on atmospheric conditions (relative humidity and temperature) and chemical composition and, importantly, solid particles can inhibit the uptake of water and other trace gases, even under humid conditions. Particles composed primarily of ammonium sulfate are presumed to be liquid at the relative humidities (67 to 98%) and temperatures (–2 to 4 °C) of the summertime Arctic. Under these atmospheric conditions, we report the observation of solid organic-coated ammonium sulfate particles representing 30% of particles, by number, in a key size range (<0.2 µm) for cloud activation within marine air masses from the Arctic Ocean at Utqiagvik, AK. The composition and size of the observed particles are consistent with recent Arctic modeling and observational results showing new particle formation and growth from dimethylsulfide oxidation to form sulfuric acid, reaction with ammonia, and condensation of marine biogenic sulfate and highly oxygenated organic molecules. Aqueous sulfate particles typically undergo efflorescence and solidify at relative humidities of less than 34%. Therefore, the observed solid phase is hypothesized to occur from contact efflorescence during collision of a newly formed Aitken mode sulfate particle with an organic-coated ammonium sulfate particle. With declining sea ice in the warming Arctic, this particle source is expected to increase with increasing open water and marine biogenic emissions.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Near-field radiative heat transfer between irregularly shaped dielectric particles modeled with the discrete system Green's function method

Near-field radiative heat transfer (NFRHT) between irregularly shaped dielectric particles made of SiO 2 and morphology characterized by Gaussian random spheres is studied. Particles are modeled using the discrete system Green's function (DSGF) approach, which is a volume integral numerical method based on fluctuational electrodynamics. This method is applicable to finite, three-dimensional objects, and all system interactions are defined independent of thermal excitation by a generalized system Green's function. The DSGF method is deemed suitable to model NFRHT between irregularly shaped particles after verification against the analytical solution for chains of two and three SiO 2 spheres. The NFRHT results reveal that geometric irregularity in particles leads to a reduction of the total conductance from that of comparable perfect spheres at vacuum separation distances smaller than the particle size, a regime in which NFRHT is a surface phenomenon. At vacuum separation distances larger than the particle size, NFRHT becomes a volumetric process, and the total conductance between irregularly shaped particles converges to that of comparable perfect spheres. Spectral analysis reveals, however, that particle irregularity leads to damping and broadening of resonances at all separation distances, thereby highlighting the importance of the DSGF method for spectral engineering in the near field. The reduced spectral coherence when particle size is larger than the vacuum separation distance is attributed to coupling of surface phonon-polaritons within the randomly generated, distorted particle features. For particle size smaller than the vacuum separation distance, resonance broadening and damping are linked with the multiple localized surface phonon modes supported by the composite spherical harmonic morphologies of the Gaussian random spheres. In conclusion, this paper has direct implications for thermal management of packed particle systems, with applications in radiative property control, electronics, energy conversion, and nanomanufacturing.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Dynamics of Magnus-dominated particle clusters, collisions, pinning, and ratchets

Motivated by the recent work in skyrmions and active chiral matter systems, we examine pairs and small clusters of repulsively interacting point particles in the limit where the dynamics is dominated by the Magnus force. We find that particles with the same Magnus force can form stable pairs, triples, and higher ordered clusters or exhibit chaotic motion. For mixtures of particles with opposite Magnus force, particle pairs can combine to form translating dipoles. Under an applied drive, particles with the same Magnus force translate; however, particles with different or opposite Magnus force exhibit a drive-dependent decoupling transition. When the particles interact with a repulsive obstacle, they can form localized orbits with depinning or unwinding transitions under an applied drive. We examine the interaction of these particles with clusters or lines of obstacles and find that the particles can become trapped in orbits that encircle multiple obstacles. Under an ac drive, we observe a series of ratchet effects, including ratchet reversals, for particles interacting with a line of obstacles due to the formation of commensurate orbits. Lastly, in assemblies of particles with mixed Magnus forces of the same sign, we find that the particles with the largest Magnus force become localized in the center of the cluster, while for mixtures with opposite Magnus forces, the motion is dominated by transient local pairs or clusters, where the translating pairs can be regarded as a form of active matter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

LARGE PARTICLE SEPARATION FROM NON-NEWTONIAN SLURRIES USING BUMP ARRAYS

Here we evaluate the performance of bump arrays to separate large particles from non-Newtonian slurries with Bingham and Cross rheology. Bump arrays in deterministic lateral displacement devices separate large particles from small particles using arrays of staggered posts. Large particles, defined as those with radii larger than the distance between the edge of a post and the stagnation streamline from the next downstream post, must bump toward one side of the device, whereas particles smaller than this distance slalom from entrance to exit. Although these devices have been used to separate a wide variety of large particles from blood cells to sand, partition of large particles from non-Newtonian fluids remains unexplored. Yet, an important set of modestly concentrated slurries, including Hanford nuclear waste, displays non-Newtonian rheology. Here we evaluate the influence of non-Newtonian rheology on the large-small particle size cutoff in bump arrays using a model that explores the influence of yield stresses, ratios of zero and infinite shear viscosities, and Cross’s exponent under strictly laminar well-developed conditions. Surprisingly, we find that viscosity ratios and Cross’s exponent make no significant difference on the particle cutoffs between large particles that bump and small particles that slalom around the posts from entrance to exit. In contrast, we find that yield stresses do significantly affect the size cutoff. As the yield stress increases, the velocity profiles become more plug like lowering the size cutoff. For nuclear waste separations where removing large particles is a priority, increasing yield stresses is conservative.

slurry, solids removal, deterministic later displa↗

DOE OSTI2022

Experimental Results for Large Particle Separation from Non-Newtonian Slurries Using Tapered Bump Arrays

Lateral displacement arrays are useful for separating particles such as blood cells and sand from carrier fluids. These arrays consist of staggered posts, which allow smaller particles to follow streamlines and larger particles to flow around the posts and migrate to one side. This migration increases the particle concentration in one direction and depletes the particle concentration in the other direction allowing particle separation to occur. Experiments were conducted to separate large particles in non-Newtonian yield stress slurries using tapered bump arrays. The non-Newtonian slurry used was composed of a bentonite kaolin blend with the inclusion of larger diameter particles. These experiments were conducted to evaluate the performance of particle separation using a tapered array of staggered posts as configured in a bump array for non-Newtonian yield stress slurries, an application that has not been explored experimentally. A theory for large particle separation was developed for slurries that exhibit Bingham or Cross rheology. The results of these experiments are described. This information could be applied in industrial settings such as separation of particles from nuclear waste slurries including those to be processed at the Hanford site, where removing large particles from waste streams is important to processing.

slurry, solids removal, deterministic lateral disp↗

DOE OSTI2023

Comparing Experimental Results for Large Particle Separation from Non-Newtonian Slurries Using Full and Tapered Bump Arrays

To separate particles from carrier fluids arrays of staggered posts inserted into the flow stream can be employed. The smaller particles follow the flow stream while the larger particles move laterally to one side. During flow, the concentration of particulate increases in one direction and decreases in the other crosswise direction. This technique separates the particles from the carrier fluid. Experiments using a slurry with non-Newtonian rheology were conducted to evaluate large particle separation from the non-Newtonian carrier fluid using bump arrays. The bentonite kaolin clay slurry with non-Newtonian rheology was spiked with large diameter inert glass particles. Experiments with flow through lateral displacement arrays evaluated the performance of particle separation using two array configurations: a full array with all posts and a tapered array with posts removed in a triangular portion of the array past the rows of anticipated particle of separation. The posts are staggered posts to promote particle segregation to one side of the flow channel. Using this type of array for removing particles from non-Newtonian yield stress slurries is novel and we present unique results. In this paper, the performance of full and tapered arrays are compared. These results have many industrial applications including removing particles from slurries of nuclear waste. Large particle removal is an important step in waste processing.

slurry, solids removal, deterministic lateral disp↗

DOE OSTI2020

High-Temperature Particle Heat Exchanger for sCO2 Power Cycles [Award 30342]

This report describes the design, development, and testing of a prototype 100 kWt particle-to-supercritical CO 2 (sCO2) heat exchanger. An analytic hierarchy process was implemented to compare and evaluate alternative heat-exchanger designs (fluidized bed, shell-and-plate moving packed bed, and shell-and-tube moving packed bed) that could meet the high pressure (≥ 20 MPa) and high temperature (≥ 700 °C) operational requirements associated with sCO2 power cycles. Cost, heat-transfer coefficient, structural reliability, manufacturability, parasitics and heat losses, scalability, compatibility, erosion and corrosion, transient operation, and inspection ease were considered in the evaluation. A 100 kWt shell-and-plate design was selected for construction and integration with Sandia’s falling particle receiver system that heats the particles using concentrated sunlight. Sandia worked with industry to design and construct the moving packed-bed shell-and-plate heat exchanger. Tests were performed to evaluate its performance using both electrical heating and concentrated sunlight to heat the particles. Overall heat transfer coefficients at off-design conditions (reduced operating temperatures and only three stainless steel banks in the counter-crossflow heat exchanger) were measured to be approximately ~25 - 70 W/m 2 -K, significantly lower than simulated values of >100 W/m 2 -K. Tests using the falling particle receiver to heat the particles with concentrated sunlight yielded overall heat transfer coefficients of ~35 – 80 W/m 2 -K with four banks (including a nickel-alloy bank above the three stainless steel banks). The overall heat transfer coefficient was observed to decrease with increasing particle inlet temperatures, which contrasted the results of simulations that showed an increase in heat transfer coefficient with temperature due to increased effective particle-bed thermal conductivity from radiation. The likely cause of the discrepancy was particle-flow maldistributions and funnel flow within the heat exchanger caused by internal ledges and cross-bracing, which could have been exacerbated by increased particle-wall friction at higher temperatures. Additional heat loss at higher temperatures may also contribute to a lower overall heat-transfer coefficient. Design challenges including pressure drop, particle and sCO2 flow maldistribution, and reduced heat transfer coefficient are discussed with approaches for mitigation in future designs. Lessons learned regarding instrumentation, performance characterization, and operation of particle components and sCO2 flow loops are also discussed. Finally, a 200 MWt commercial-scale shell-and-plate heat-exchanger design based on the concepts investigated in this report is proposed.

14 SOLAR ENERGY↗

DOE OSTI2023

A numerical investigation of coal particle modeling for the inlet section of a pressurized oxy-combustion burner

Concerns over climate change have led to numerous efforts to develop low-carbon technologies, and pressurized oxy-combustion (POC) is a promising candidate to reduce carbon emissions in the power industry. Designing an effective burner for such technologies is vital for the development of these and other coal combustion technologies. Because of the high pressure, the volume fraction of coal particles at the fuel inlet of the pressurized oxy-combustor burner is close to or even higher than the maximum limit for commercial CFD codes (e.g., ANSYS FLUENT). At these high particle volume fractions, the interactions among particles, fluid flow and wall need to be re-evaluated. The present computational work is a first step in a systematic analysis of the influence of various parameters, like method of particle release, release location, and particle size, in a pilot-scale POC combustor, developed at Washington University in St. Louis (WUSTL). In the POC process, pulverized coal is burned under elevated pressure in an O2-CO2 environment. Specifically, a 15-bar, 100 kWth, POC combustor is modeled employing Ansys FLUENT commercial sodtware using the Reynolds-Averaged Navier-Stokes (RANS) approach. It is revealed that for this pilot-scale, pressurized burner, velocity profiles in the near-wall region exhibit some anomalies. In order to investigate the influence of particle loading in the near-wall region, particle release location was investigated. The numerical simulations incorporate the coupling between the turbulent flow and the particles. A sensitivity investigation of particle release location found that by tuning the release location, the velocity profile can be consistent with the pure gas flow velocity profile. More importantly, the particle releasing location also affects flame stability. Particle size was also found to have a significant impact on particle trajectory, flame stability and temperature. Finally, Large Eddy Simulations (LES) were performed and compared with the results from two-dimensional RANS.

Li, Lei↗

DOE OSTI2024

Proton Acceleration in Low- β Magnetic Reconnection with Energetic Particle Feedback

Magnetic reconnection regions in space and astrophysics are known as active particle acceleration sites. There is ample evidence showing that energetic particles can take a substantial amount of converted energy during magnetic reconnection. However, there has been a lack of studies understanding the backreaction of energetic particles at magnetohydrodynamical scales in magnetic reconnection. To address this, we have developed a new computational method to explore the feedback by nonthermal energetic particles. This approach considers the backreaction from these energetic particles by incorporating their pressure into magnetohydrodynamics (MHD) equations. The pressure of the energetic particles is evaluated from their distribution evolved through Parker's transport equation, solved using stochastic differential equations (SDEs), so we coin the name MHD-SDE. Applying this method to low-β magnetic reconnection simulations, we find that reconnection is capable of accelerating a large fraction of energetic particles that contain a substantial amount of energy. When the feedback from these particles is included, their pressure suppresses the compression structures generated by magnetic reconnection, thereby mediating particle energization. Consequently, the feedback from energetic particles results in a steeper power-law energy spectrum. These findings suggest that feedback from nonthermal energetic particles plays a crucial role in magnetic reconnection and particle acceleration.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Measurement report: The Fifth International Workshop on Ice Nucleation phase 1 (FIN-01): intercomparison of single-particle mass spectrometers

Knowledge of the chemical composition and mixing state of aerosols at a single-particle level is critical for gaining insights into atmospheric processes. One common tool to make these measurements is single-particle mass spectrometry. There remains a need to compare the performance of different single-particle mass spectrometers (SPMSs). An intercomparison of SPMSs was conducted at the Aerosol Interaction and Dynamics in the Atmosphere (AIDA) chamber at the Karlsruhe Institute of Technology (KIT) in November 2014, as part of the first phase of the Fifth International Workshop on Ice Nucleation (FIN-01). In this paper we compare size distributions and mass spectra of atmospherically relevant particle types measured by five SPMSs. These include different minerals, desert and soil dusts, soot, bioaerosol (Snomax; protein granule), secondary organic aerosol (SOA), and SOA-coated mineral particles. Most SPMSs reported similar vacuum aerodynamic diameter (d va ) within typical instrumental ranges from ~100–200 nm (lower limit) to ~2–3 µm (upper limit). In general, all SPMSs exhibited a wide dynamic range (up to ~10 3 ) and high signal-to-noise ratio (up to ~10 4 ) in mass spectra. Common spectral features with small diversities in mass spectra were found with high average Pearson's correlation coefficients, i.e., for average positive spectra r avg-pos =0.74 ± 0.12 and average negative spectra r avg-neg =0.67 ± 0.22. We found that instrument-specific detection efficiency (DE) was more dependent on particle size than particle type, and particle identification favored the use of bipolar, rather than monopolar, instruments. Particle classification from “blind experiments” showed that all instruments differentiated SOA, soot, and soil dust and detected subtle changes in the particle internal mixing but had difficulties differentiating among specific mineral types and dusts. This study helps to further understand the capabilities and limitations of the single-particle mass spectrometry technique in general and the specific performance of the instrument in characterizing atmospheric aerosol particles.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

System and method for controlling metal oxide gel particle size

Metal oxide gel particles, may be prepared with a desired particle size, by preparing a low-temperature aqueous metal nitrate solution containing hexamethylene tetramine as a feed solution; and causing the feed solution to flow through a first tube and exit the first tube as a first stream at a first flow rate, so as to contact a high-temperature nonaqueous drive fluid. The drive fluid flows through a second tube at a second flow rate. Shear between the first stream and the drive fluid breaks the first stream into particles of the metal nitrate solution, and decomposition of hexamethylene tetramine converts metal nitrate solution particles into metal oxide gel particles. A metal oxide gel particle size is measured optically, using a sensor device directed at a flow of metal oxide gel particles within the stream of drive fluid. The sensor device measures transmission of light absorbed by either the metal oxide gel particles or the drive fluid, so that transmission of light through the drive fluid changes for a period of time as a metal oxide gel particle passes the optical sensor. If a measured particle size is not about equal to a desired particle size, the particle size may be corrected by adjusting a ratio of the first flow rate to a total flow rate, where the total flow rate is the sum of the first and second flow rates.

Linneen, Nicholas N.↗

DOE OSTI2023

System and method for controlling metal oxide gel particle size

Linneen, Nicholas↗

DOE OSTI2024

Multimodal 3D quantification of particle stimulated nucleation in industrially manufactured aluminium AA5182 sheet

Particle stimulated nucleation is a dominant recrystallisation mechanism observed in many industrially relevant aluminium alloys during thermomechanical processing. Here, in this work, we quantify particle stimulated nucleation in 3D in an aluminium AA5182 alloy sheet cold-rolled to 75% thickness reduction. Second phase particles and nuclei are mapped in the same sample volume by conventional laboratory absorption X-ray tomography and synchrotron X-ray Laue micro-diffraction. The large second phase particles are classified as Fe- and Mg-rich phases. It is found that 84% of the nuclei are particle stimulated and 40% of the particles stimulate nucleation. The critical particle diameter is found to be 4 μm. Deviatoric elastic strains are derived from micro-diffraction data and it is found that elastic strains are present in the recrystallised nuclei. The effects of the different particle types, particle clustering, particle size and aspect ratio as well as strain inheritance are discussed. This work provides a full 3D quantification of particle stimulated nucleation behaviour in AA5182 alloy sheet deformed to high strain.

Deviatoric strain↗

DOE OSTI2022

Frictional Contacts Between Individual Woody Biomass Particles under Wet and Dry Conditions

Friction between wood particles can be a critical property when designing processing equipment for creating cellulosic biofuels and similar natural products. Also, as wood processing is likely to occur year-round, understanding the friction between wet as well as dry wood particles can help design and model equipment, such as screw feeders. Here, a tribo-rheometry method was developed using a commercial rheometer that measured the torque required to rotate two contacting millimeter-scale wood chip particles. First, a range of normal forces were used to find the limits of the experimental method. Torque values were measured for seven pairs of wood chip particles at 1 N normal force under both dry and wet conditions, at both ambient conditions and in a humidity-controlled chamber. The torque required to rotate the wet particles was consistently higher than that of the dry particles, although differences were not quite statistically significant when measurements were performed at ambient conditions. Using humidity control resulted in torque values for wet particles of 1900 uNm and 900 uNm for dry particles. Finally, the friction coefficient was calculated as 0.23 for wet particles and 0.11 for dry particles when humidity was controlled. These frictions coefficients agreed with values for wood reported in the literature. Overall, controlling humidity is strongly recommended to quantify the range of friction for particles that uptake water, including granular systems from biomass to food to powders.

biomass↗

DOE OSTI2023

Size-Resolved Elemental Composition of Respiratory Particles in Three Healthy Subjects

The chemical composition of respiratory particles is of interest because the viability of any viruses and bacteria in the particles has been shown to depend on this factor. Here, using computer controlled scanning electron microscopy/energy dispersive X-ray spectroscopy (CCSEM/EDX), we analyzed the size-resolved chemical composition of greater than 35,000 individual respiratory particles collected from three healthy human subjects, quantitatively at nanometer-scale spatial resolution. The desiccated particles ranged in size from 0.05 to 4.4 μm, and the mode of the size distribution was approximately 0.1 μm. Particles were heterogeneous in composition, with approximately 42% of them containing a carbon atomic percentage greater than 95% and approximately 53% of them containing a Na + P + K + Cl percentage greater than 5%. Based on the particles’ elemental composition, we classified them into five categories: 48%–56% of the total number were carbonaceous, mostly organic; 40%–50% Na-rich salt; 0.3%–0.5% P-rich salt; 0.1–0.8% K-rich salt; and 1%–2.5% mixed salt. The number ratio of Na-rich salt particles to carbonaceous particles increased with increasing particle size; particles larger than approximately 2 μm were dominated by Na-rich salt. Size-dependent differences in the chemical composition of respiratory particles may have important implications for the efficiency of airborne transmission of respiratory pathogens.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2022

Turbulent Flux Measurements of the Near‐Surface and Residual‐Layer Small Particle Events

Abstract According to recent field studies, almost half of the New Particle Formation (NPF) events occur aloft, in a residual layer, near the top of the boundary layer. Therefore, measurements of the meteorological parameters, precursor gas concentrations, and aerosol loadings conducted at the ground level are often not representative of the conditions where the NPFs take place. This paper presents new measurements obtained during the Turbulent Flux Measurements of the Residual Layer Nucleation Particles, conducted at the Southern Great Plains research site. Vertical turbulent fluxes of 3–10 nm‐sized particles were measured using a sonic anemometer and two condensation particle counters with nominal cutoff diameters of 3 nm and 10 nm mounted at the top of the 10‐m telescoping tower. Aerosol number size distribution (5–300 nm) was determined through the ground‐based Scanning Mobility Particle Sizers. The size selected (15–50 nm) particle hygroscopicity was derived with the Humidified Tandem Differential Mobility Analyzer. The ground level observations were supplemented by vertically‐resolved measurements of horizontal and vertical wind speeds and aerosol backscatter. The data analysis suggests that (a) turbulent flux measurements of 3–10 nm particles can distinguish between near‐surface and residual‐layer small particle events; (b) sub‐50 nm particles had a hygroscopicity value of 0.2, suggesting that organic compounds dominate atmospheric nanoparticle chemical composition at the site; and (c) current methodologies are inadequate for estimating the dry deposition velocity of sub‐10 nm particles because it is not feasible to measure particle concentration very near the surface, in the diffusion sublayer.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Numerical investigation of alpha particle confinement under the perturbation of neoclassical tearing modes and toroidal field ripple in CFETR

The confinement of alpha particles in burning plasma is a key issue in fusion reactor design, including particle interaction with instabilities. Here, we include two topics: the effect of neoclassical tearing modes (NTMs) and toroidal field ripple on alpha particle loss, and the assessment of particle redistribution under an NTM with a reduced model. We consider Chinese fusion engineering test reactor parameters, the alpha particle distribution given by TRANSP/NUBEAM and the NTM perturbation function given by the initial value code TM1. We show that the synergistic effect of the NTM and ripple is negligible; the particle loss fraction does not change with increasing NTM amplitude. Only passing particles are affected by the mode particle resonance, producing profile flattening but no increased loss because only trapped particles are influenced by ripple. To study alpha particle profile flattening, the work adopts an innovative method of phase vector rotation to determine regions of good and broken Kolmogorov–Arnold–Moser surfaces and equilibrates the particle density according to local stochasticity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗