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At least 379 records · Page 21

Neoclassical transport in strong gradient regions of large aspect ratio tokamaks

We present a new neoclassical transport model for large aspect ratio tokamaks where the gradient scale lengths are of the size of the ion poloidal gyroradius. Previous work on neoclassical transport across transport barriers assumed large density and potential gradients but a small temperature gradient, or neglected the gradient of the mean parallel flow. Using large aspect ratio and low collisionality expansions, we relax these restrictive assumptions. We define a new set of variables based on conserved quantities, which simplifies the drift kinetic equation whilst keeping strong gradients, and derive equations describing the transport of particles, parallel momentum and energy by ions in the banana regime. The poloidally varying parts of density and electric potential are included. Studying contributions from both passing and trapped particles, we show that the resulting transport is dominated by trapped particles. We find that a non-zero neoclassical particle flux requires parallel momentum input which could be provided through interaction with turbulence or impurities. We derive upper and lower bounds for the energy flux across a transport barrier in both temperature and density and present example profiles and fluxes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Long-Range Charge Transport Facilitated by Electron Delocalization in MoS 2 and Carbon Nanotube Heterostructures

Controlling charge transport at the interfaces of nanostructures is crucial for their successful use in optoelectronic and solar energy applications. Mixed-dimensional heterostructures based on single-walled carbon nanotubes (SWCNTs) and transition metal dichalcogenides (TMDCs) have demonstrated exceptionally long-lived charge-separated states. However, the factors that control the charge transport at these interfaces remain unclear. In this study, we directly image charge transport at the interfaces of single- and multilayered MoS 2 and (6,5) SWCNT heterostructures using transient absorption microscopy. We find that charge recombination becomes slower as the layer thickness of MoS 2 increases. This behavior can be explained by electron delocalization in multilayers and reduced orbital overlap with the SWCNTs, as suggested by nonadiabatic (NA) molecular dynamics (MD) simulations. Dipolar repulsion of interfacial excitons results in rapid density-dependent transport within the first 100 ps. Stronger repulsion and longer-range charge transport are observed in heterostructures with thicker MoS 2 layers, driven by electron delocalization and larger interfacial dipole moments. These findings are consistent with the results from NAMD simulations. Our results suggest that heterostructures with multilayer MoS 2 can facilitate long-lived charge separation and transport, which is promising for applications in photovoltaics and photocatalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Structure–Transport Properties Governing the Interplay in Humidity-Dependent Mixed Ionic and Electronic Conduction of Conjugated Polyelectrolytes

Polymeric mixed ionic-electronic conductors (MIECs) are of broad interest in the field of energy storage and conversion, opto-electronics, and bioelectronics. A class of polymeric MIECs are conjugated polyelectrolytes (CPEs), which possess a p-conjugated backbone imparting electronic transport characteristics along with side chains comprised of a pendant ionic group to allow for ionic transport. Here, our study focuses on the humidity-dependent structure-transport properties of poly[3-(potassium-n-alkanoate) thiophene-2,5-diyl] (P3KnT) CPEs with varied side-chain lengths of n = 4, 5, 6, and 7. UV-Vis spectroscopy along with electronic paramagnetic resonance (EPR) spectroscopy reveal the infiltration of water leads to a hydrated, self-doped state that allows for electronic transport. The resulting humidity-dependent ionic conductivity (σ i ) of the thin films shows a monotonic increase with relative humidity (RH) while electronic conductivity (σ e ) follows a nonmonotonic profile. The values of σ e continue to rise with increasing RH reaching a local maximum after which σ e begins to decrease. P3KnTs with higher n values demonstrate greater resiliency to increasing RH before suffering decrease in σ e . This drop in σ e is attributed to two factors. First, disruption of the locally-ordered π-stacked domains observed through in situ humidity-dependent grazing incidence wide angle X-ray scattering (GIWAXS) experiments can account for some of the decrease in σ e . A second and more dominant factor is attributed to the swelling of the amorphous domains where electronic transport pathways connecting ordered domains are impeded. P3K7T is most resilient to swelling (based on ellipsometry and water uptake measurements) where sufficient hydration allows for high σ i (1.0 × 10 -1 S/cm at 95% RH) while not substantially disrupting σ e (1.7 × 10 -2 S/cm at 85% RH and 8.0 × 10 -3 S/cm at 95% RH). Overall, our study highlights the complexity of balancing electronic and ionic transport in hydrated CPEs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Adaptive Multirate Mass Transfer (aMMT) Model: A New Approach to Upscale Regional‐Scale Transport Under Transient Flow Conditions

Abstract The long‐term evaluation of regional‐scale groundwater quality needs efficient upscaling methods for transient flow. Upscaling techniques, such as the Multirate Mass Transfer (MRMT) method with constant upscaling parameters, have been used for transport with steady‐state flow, yet the upscaling parameters (i.e., rate coefficients) may be time dependent. This study proposed and validated an adaptive MRMT (aMMT) method by allowing the mass transfer coefficients in MRMT to change with the flow field. Advective‐dispersive contaminant transport simulated in a 3‐D heterogeneous medium was used as a reference solution. Equivalent transport under homogeneous flow conditions was evaluated by applying the MRMT and aMMT models for upscaling. The relationship between mass transfer coefficients and flow rates was fitted under steady‐state flow driven by various hydraulic gradients. A power law relationship was obtained, which was then used to update the mass transfer coefficients in each stress period under transient flow conditions in the aMMT method. Results indicated that for advection‐dominated transport, both the MRMT and aMMT methods can upscale the anomalous transport dynamics affected by subgrid heterogeneity under transient flow conditions. Whereas for diffusion‐dominated systems, the MRMT model failed to capture the tails of tracer breakthrough curves after the boundary condition changed, but the results from the aMMT model were significantly improved. However, if the overall flow direction changed, both MRMT and aMMT failed to represent the breakthrough curve tail generated by the heterogeneous system. The results point toward a promising path for upscaling transport in complex aquifers with transient flow.

Guo, Zhilin↗

Connection Between Mass Flux Transport and Eddy Diffusivity in Convective Atmospheric Boundary Layers

Turbulence parameterizations for convective boundary layer in coarse-scale atmospheric models usually consider a combination of the eddy-diffusive transport and a non-local transport, typically in the form of a mass flux term, such as the widely adopted eddy-diffusivity mass-flux (EDMF) approach. These two types of turbulent transport are generally considered to be independent of each other. Using results from large-eddy simulations, here, we show that a Taylor series expansion of the updraft and downdraft mass-flux transport can be used to approximate the eddy-diffusivity transport in the atmospheric surface layer and the lower part of the mixed layer, connecting both eddy-diffusivity and mass-flux transport theories in convective conditions, which also quantifies departure from the Monin-Obukhov similarity (MOS) in the surface layer. This study provides a theoretical support for a unified EDMF parameterization applied to both the surface layer and mixed layer and highlights important correction required for surface models relying on MOS

54 ENVIRONMENTAL SCIENCES↗

Anomalous Transport in Three-Dimensional Discrete Fracture Networks: Interplay Between Aperture Heterogeneity and Injection Modes

In this work, we study how the interplay between fracture aperture heterogeneity and tracer injection mode controls fluid flow and tracer transport in three-dimensional (3D) discrete fracture networks (DFNs). The direct 3-D DFN simulations show that tracer injection mode has substantial effects on tracer spreading across all levels of aperture heterogeneity. The key controlling factor for effective transport is the initial Lagrangian velocity distribution, which is determined by the interplay between injection mode and aperture heterogeneity. The fundamental difference between initial Lagrangian velocity distribution and domain-scale Eulerian velocity distribution plays a vital role in determining anomalous transport. We effectively capture the observed anomalous transport using an upscaled transport model that incorporates initial velocity distribution, stationary velocity distribution, velocity correlation length, and average advective tortuosity. With the upscaled transport model, we accurately capture the evolution of Lagrangian velocity distribution and predict longitudinal spreading in 3-D DFN.

58 GEOSCIENCES↗

Revisiting AMOC Transport Estimates From Observations and Models

Abstract Reference level assumptions used to calculate the Atlantic meridional overturning circulation transports at the RAPID and Meridional Overturning Variability Experiment (MOVE) observing arrays are revisited in an eddying ocean model. Observational transport calculation methods are complemented by several alternative approaches. At RAPID, the model transports from the observational method and the model truth (based on the actual model velocities) agree well in their mean and variability. There are substantial differences among the transport estimates obtained with various methods at the MOVE site. These differences result from relatively large and time‐varying reference velocities at depth in the model, not supporting a level‐of‐no‐motion. The methods that account for these reference velocities properly at MOVE produce transports that are in good agreement with the model truth. In contrast with the observational estimates, the model transport trends at MOVE and RAPID largely agree with each other on pentadal to multi‐decadal time scales.

Danabasoglu, Gokhan↗

Regional and Temporal Variability of Atmospheric River Seasonality: Influences of Detection Algorithms and Moisture Transport Dynamics

Abstract Understanding the regional and temporal variability of atmospheric river (AR) seasonality is crucial for preparedness and mitigation of extreme events. While ARs were thought to peak in winter, recent research shows they exhibit region‐specific seasonality and are heavily influenced by the chosen detection algorithm. This study examines the link between the year‐to‐year consistency of peak‐AR activity to the presence of a dominant seasonal pattern, considering both location and algorithm choice. Regions are categorized by their temporal characteristics: consistent patterns (e.g., East Asia), patterns with occasional outliers (e.g., British Columbia coast), and regions lacking a clear dominant peak season (e.g., South Atlantic, parts of Australia). Hence, not all regions display a consistent seasonal cycle of AR activity. This study quantifies the extent to which a region experiences a dominant peak season of AR activity (or lacks one) and offers insights to enhance decision‐making in water management, natural hazard preparedness, and forecasting. Furthermore, given our finding that detection algorithms influence the peak season of AR activity, we also examine two diagnostic variables representative of moisture transport to corroborate our results. Integrated vapor transport, which captures meridional and zonal moisture transport, and Moist Wave Activity, representing moisture intrusions from lower to higher latitudes, are examined. Our analysis indicates that inconsistencies in the seasonal cycle of AR activity are not solely due to discrepancies in detection algorithms but also arise from changes in moisture transport. Plain Language Summary Atmospheric rivers (ARs) are critical weather phenomena that can cause extreme events like heavy rainfall and flooding. Understanding when and where ARs are most likely to occur throughout the year is essential for preparing and responding to these events. Traditionally, ARs were thought to peak in winter, but recent studies show this varies by region. Our study helps address the challenge decision‐makers face in anticipating and preparing for AR events by providing insights into the consistency of peak seasonal patterns across different areas. Some regions, like East Asia, and the British Columbia coast, show a consistent peak season, while others, like the South Atlantic and parts of Australia, have significant year‐to‐year variations, making it hard to identify a dominant season. To better understand these changes over time, the study also examines how moisture moves in the atmosphere, using Integrated Vapor Transport (which looks at moisture movement in various directions) and Moist Wave Activity (which tracks moisture shifts from lower to higher latitudes). The findings suggest that inconsistencies in AR patterns are due not only to detection methods but also due to changes in moisture transport. Key Points The peak season of atmospheric river activity can change depending on the year in some areas Interannual variations in the peak season can make identifying a dominant season challenging for some regions Frequent shifts in peak season across years reflect inconsistencies tied to detection algorithms and to underlying dynamics

Kamnani, Diya↗

Changing expression patterns of TonB-dependent transporters suggest shifts in polysaccharide consumption over the course of a spring phytoplankton bloom

Algal blooms produce large quantities of organic matter that is subsequently remineralised by bacterial heterotrophs. Polysaccharide is a primary component of algal biomass. It has been hypothesised that individual bacterial heterotrophic niches during algal blooms are in part determined by the available polysaccharide substrates present. Measurement of the expression of TonB-dependent transporters, often specific for polysaccharide uptake, might serve as a proxy for assessing bacterial polysaccharide consumption over time. To investigate this, we present here high-resolution metaproteomic and metagenomic datasets from bacterioplankton of the 2016 spring phytoplankton bloom at Helgoland island in the southern North Sea, and expression profiles of TonB-dependent transporters during the bloom, which demonstrate the importance of both the Gammaproteobacteria and the Bacteroidetes as degraders of algal polysaccharide. TonB-dependent transporters were the most highly expressed protein class, split approximately evenly between the Gammaproteobacteria and Bacteroidetes , and totalling on average 16.7% of all detected proteins during the bloom. About 93% of these were predicted to take up organic matter, and for about 12% of the TonB-dependent transporters, we predicted a specific target polysaccharide class. Most significantly, we observed a change in substrate specificities of the expressed transporters over time, which was not reflected in the corresponding metagenomic data. From this, we conclude that algal cell wall-related compounds containing fucose, mannose, and xylose were mostly utilised in later bloom stages, whereas glucose-based algal and bacterial storage molecules including laminarin, glycogen, and starch were used throughout. Quantification of transporters could therefore be key for understanding marine carbon cycling.

59 BASIC BIOLOGICAL SCIENCES↗

The structural basis of promiscuity in small multidrug resistance transporters

By providing broad resistance to environmental biocides, transporters from the small multidrug resistance (SMR) family drive the spread of multidrug resistance cassettes among bacterial populations. A fundamental understanding of substrate selectivity by SMR transporters is needed to identify the types of selective pressures that contribute to this process. Using solid-supported membrane electrophysiology, we find that promiscuous transport of hydrophobic substituted cations is a general feature of SMR transporters. To understand the molecular basis for promiscuity, we solved X-ray crystal structures of a SMR transporter Gdx-Clo in complex with substrates to a maximum resolution of 2.3 Å. These structures confirm the family’s extremely rare dual topology architecture and reveal a cleft between two helices that provides accommodation in the membrane for the hydrophobic substituents of transported drug-like cations.

59 BASIC BIOLOGICAL SCIENCES↗

Differences in water and vapor transport through angstrom-scale pores in atomically thin membranes

Abstract The transport of water through nanoscale capillaries/pores plays a prominent role in biology, ionic/molecular separations, water treatment and protective applications. However, the mechanisms of water and vapor transport through nanoscale confinements remain to be fully understood. Angstrom-scale pores (~2.8–6.6 Å) introduced into the atomically thin graphene lattice represent ideal model systems to probe water transport at the molecular-length scale with short pores (aspect ratio ~1–1.9) i.e., pore diameters approach the pore length (~3.4 Å) at the theoretical limit of material thickness. Here, we report on orders of magnitude differences (~80×) between transport of water vapor (~44.2–52.4 g m −2 day −1 Pa −1 ) and liquid water (0.6–2 g m −2 day −1 Pa −1 ) through nanopores (~2.8–6.6 Å in diameter) in monolayer graphene and rationalize this difference via a flow resistance model in which liquid water permeation occurs near the continuum regime whereas water vapor transport occurs in the free molecular flow regime. We demonstrate centimeter-scale atomically thin graphene membranes with up to an order of magnitude higher water vapor transport rate (~5.4–6.1 × 10 4 g m −2 day −1 ) than most commercially available ultra-breathable protective materials while effectively blocking even sub-nanometer (>0.66 nm) model ions/molecules.

36 MATERIALS SCIENCE↗

Spin transport of a doped Mott insulator in moiré heterostructures

Moiré superlattices of semiconducting transition metal dichalcogenide heterobilayers are model systems for investigating strongly correlated electronic phenomena. Specifically, WSe 2 /WS 2 moiré superlattices have emerged as a quantum simulator for the two-dimensional extended Hubbard model. Experimental studies of charge transport have revealed correlated Mott insulator and generalized Wigner crystal states, but spin transport of the moiré heterostructure has not yet been sufficiently explored. Here, we use spatially and temporally resolved circular dichroism spectroscopy to directly image the spin transport as a function of carrier doping and temperature in WSe 2 /WS 2 moiré heterostructures. We observe diffusive spin transport at all hole concentrations at 11 Kelvin — including the Mott insulator at one hole per moiré unit cell — where charge transport is strongly suppressed. At elevated temperatures the spin diffusion constant remains unchanged in the Mott insulator state, but it increases significantly at finite doping away from the Mott state. The doping- and temperature-dependent spin transport can be qualitatively understood using a t–J model, where spins can move via the hopping of spin-carrying charges and via the exchange interaction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Cooperative and inhibitory ion transport in functionalized angstrom-scale two-dimensional channels

Significant success has been achieved in fabricating angstrom-scale artificial solid ionic channels aiming to replicate the biological ion channels (BICs). Besides high selectivity, BICs also exhibit sophisticated ion gating and interplay. However, such behavior and functionality are seldomly recreated in the artificial counterparts due to the insufficient understanding of the molecular origin. Here we report cooperative and inhibitory ion transport in angstrom-scale acetate functionalized MoS 2 two-dimensional channels. For cooperative ion transport, the permeability of K + is doubled in the presence of only 1% Pb 2+ (versus K + by molarity), while the permeability of Pb 2+ is independent of K + . Molecular dynamics simulations reveal complex interplay among K + , Pb 2+ , and the anions in governing the cooperativity, such that Pb 2+ ions capture and slow down the anions via long-range interaction, which leads to the synchronization of anions with K + to transport as ion pairs with reduced interaction with the channel surface. For inhibitory ion transport, divalent Co 2+ (or Ba 2+ ) and Pb 2+ can replace each other in the confined channel and compete for the limited transport cross section. Our work reveals ion transport phenomena in extreme confinement and highlights the potential of manipulating ion interplay in confinement for achieving advanced functionalities.

Functionalized Angstrom↗

The putative transporter MtUMAMIT14 participates in nodule formation in Medicago truncatula

Transport systems are crucial in many plant processes, including plant–microbe interactions. Nodule formation and function in legumes involve the expression and regulation of multiple transport proteins, and many are still uncharacterized, particularly for nitrogen transport. Amino acids originating from the nitrogen-fixing process are an essential form of nitrogen for legumes. This work evaluates the role of MtN21 (henceforth MtUMAMIT14), a putative transport system from the MtN21/EamA-like/UMAMIT family, in nodule formation and nitrogen fixation in Medicago truncatula. To dissect this transporter’s role, we assessed the expression of MtUMAMIT14 using GUS staining, localized the corresponding protein in M. truncatula root and tobacco leaf cells, and investigated two independent MtUMAMIT14 mutant lines. Our results indicate that MtUMAMIT14 is localized in endosomal structures and is expressed in both the infection zone and interzone of nodules. Comparison of mutant and wild-type M. truncatula indicates MtUMAMIT14, the expression of which is dependent on the presence of NIN, DNF1, and DNF2, plays a role in nodule formation and nitrogen-fixation. While the function of the transporter is still unclear, our results connect root nodule nitrogen fixation in legumes with the UMAMIT family.

58 GEOSCIENCES↗

Chemical interaction and enhanced interfacial ion transport in a ceramic nanofiber–polymer composite electrolyte for all-solid-state lithium metal batteries

This article reports the synergy between ceramic nanofibers and a polymer, and the enhanced interfacial Li-ion transport along the nanofiber/polymer interface in a solid-state ceramic/polymer composite electrolyte, in which a three-dimensional (3D) electrospun aluminum-doped Li 0.33 La 0.557 TiO 3 (LLTO) nanofiber network is embedded in a polyvinylidene fluoride-hexafluoropropylene (PVDF-HFP) matrix. Strong chemical interaction occurs between the nanofibers and the polymer matrix. Addition of the ceramic nanofibers into the polymer matrix results in the dehydrofluorination of the PVDF chains, deprotonation of the –CH 2 moiety and amorphization of the polymer matrix. Solid-state nuclear magnetic resonance (NMR) spectra reveal that lithium ions transport via three pathways: (i) intra-polymer transport, (ii) intra-nanofiber transport, and (iii) interfacial polymer/nanofiber transport. In addition, lithium phosphate is coated on the LLTO nanofiber surface before the nanofibers are embedded into the polymer matrix. The presence of lithium phosphate at the LLTO/polymer interface further enhances the chemical interaction between the nanofibers and the polymer, which promotes the lithium ion transport along the polymer/nanofiber interface. This in turn improves the ionic conductivity and electrochemical cycling stability of the nanofiber/polymer composite. As a result, the flexible LLTO/Li 3 PO 4 /polymer composite electrolyte membrane exhibits an ionic conductivity of 5.1 × 10 -4 S cm -1 at room temperature and an electrochemical stability window of 5.0 V vs. Li/Li + . A symmetric Li|electrolyte|Li half-cell shows a low overpotential of 50 mV at a constant current density of 0.5 mA cm -2 for more than 800 h. In addition, a full cell is constructed by sandwiching the composite electrolyte between a lithium metal anode and a LiFePO 4 -based cathode. Such an all-solid-state lithium metal battery exhibits excellent cycling performance and rate capability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Potential-induced wetting and dewetting in pH-responsive block copolymer membranes for mass transport control

Wetting and dewetting behavior in channel-confined hydrophobic volumes is used in biological membranes to effect selective ion/molecular transport. Artificial biomimetic hydrophobic nanopores have been devised utilizing wetting and dewetting, however, tunable mass transport control utilizing multiple transport modes is required for applications such as controllable release/transport, water separation/purification and energy conversion. Here, we investigate the potential-induced wetting and dewetting behavior in a pH-responsive membrane composed of a polystyrene-b-poly(4-vinylpyridine) (PS-b-P4VP) block copolymer (BCP) when fabricated as a hierarchically-organized sandwich structure on a nanopore electrode array (NEA), i.e. BCP@NEA. At pH < pK a (P4VP) (pK a ~ 4.8), the BCP acts as an anion-exchange membrane due to the hydrophilic, protonated P4VP cylindrical nanodomains, but at pH > pK a (P4VP), the P4VP domains exhibit charge-neutral, hydrophobic and collapsed structures, blocking mass transport via the hydrophobic membrane. However, when originally prepared in a dewetted condition, mass transport in the BCP membrane may be switched on if sufficiently negative potentials are applied to the BCP@NEA architecture. When the hydrophobic BCP membrane is introduced on top of 2-electrode-embedded nanopore arrays, electrolyte solution in the nanopores is introduced, then isolated, by exploiting the potential-induced wetting and dewetting transitions in the BCP membrane. The potential-induced wetting/dewetting transition and the effect on cyclic voltammetry in the BCP@NEA structures is characterized as a function of the potential, pH and ionic strength. Additionally chronoamperometry and redox cycling experiments are used to further characterize the potential response. The multi-modal mass transport system proposed in this work will be useful for ultrasensitive sensing and single-molecule studies, which require long-time monitoring to explore reaction dynamics as well as molecular heterogeneity in nanoconfined volumes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Kinetic pathways of fast lithium transport in solid electrolyte interphases with discrete inorganic components

The transport of lithium ions in the solid electrolyte interphase (SEI) has been previously accepted to proceed in two steps: a fast pore diffusion through the outer, porous organic layer followed by a slow knock-off or vacancy diffusion in the inner, dense inorganic layer. The second step is believed to be the rate-limiting step during fast-charging. In this study, we have intentionally constructed a thicker SEI (SEI-rich) structure on the surface of monoclinic Nb 2 O 5 (H-Nb 2 O 5 ) by adding LiNO 3 into a conventional ethylene carbonate based electrolyte. The electrochemical performance of two electrodes, one SEI-rich and one with few SEI (SEI-lean), was found to be almost the same, including their fast-charging capability and cycling stability, despite the significant difference in their SEI structure. Importantly, analysis using cryogenic scanning/transmission electron microscopy showed the discrete decoration of individual inorganic particles (e.g., Li 2 O) and amorphous species (LiN x O y /organic components) over the surface of H-Nb 2 O 5 . These discrete inorganic particles are in contradiction to the formation of dense inner inorganic layer, which has been commonly postulated. Based on these findings, we propose a new mechanism for Li ion transport through the SEI: one-step pore diffusion, without the second step slow diffusion. This one-step pore diffusion process provides an extremely fast Li ion transport, and effectively removes the kinetic limitation of Li ion transport in the SEI for fast charging. Finally, these results strongly suggest that the influence of SEI structure on the transport kinetics of lithium ions is much less significant than previously accepted. These results offer a new understanding of possible lithium ion transport pathway within SEI and may have implications for the future designs of fast-charging battery materials.

25 ENERGY STORAGE↗

Mechanisms of energetic-particle transport in magnetically confined plasmas

Super-thermal ions and electrons occur in both space and fusion plasmas. Because these energetic particles (EP) have large velocities, EP orbits necessarily deviate substantially from magnetic surfaces. Orbits are described by conserved constants of motion that define topological boundaries for different orbit types. Electric and magnetic field perturbations produced by instabilities can disrupt particle orbits, causing the constants of motion to change. The statistics of the “kicks” associated with these perturbations determines the resulting cross field transport. A unifying theme of this tutorial is the importance of the perturbation’s phase at the particle’s position Θ = k • r – ωt, where k and ω are the wavevector and frequency of the perturbation, r is the EP position, and t is the time. A distinction is made between field perturbations that resonate with an aspect of the orbital motion and those that do not. Resonance occurs when the wave phase returns to its initial value in an integer multiple of an orbital period. Convective transport occurs when resonant particles experience an unvarying wave phase. Alternatively, multiple wave-particle resonances usually decorrelate the phase, resulting in diffusive transport. Large orbits increase the number of important resonances and can cause chaotic orbits even for relatively small amplitude waves. In contrast, in the case of non-resonant perturbations, orbital phase averaging reduces transport. Here, large field perturbations introduce additional effects, including nonlinear resonances at fractional values of the orbital motion. In summary, large orbits are a blessing and a curse: For non-resonant modes, orbit-averaging reduces transport but, for resonant transport, large orbits facilitate jumps across topological boundaries and enhance the number of important resonances.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗