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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Evolution of attached and detached slabs and their associated mantle dynamics

Over the two years of the NASA grant, this project has produced a significant amount of research results related to the plate subduction process and the surface crustal deformation at convergent boundaries (i.e., above subduction zones). While some research objectives are completely accomplished, other research tasks remain active and continue to be investigated at present. A steady state analytic thermal model for subducting slabs was used to examine the torques acting on a descending slab. It is found that gravitational torque vanishes when a slab is dipping either vertically or horizontally, unlike previous studies indicating that the magnitude of gravitational torque decreases as dip angle increases. Subsequently, a new time-dependent, analytic thermal model for a subducting slab was developed. The new model enables us to study transient phenomena associated with plate subduction analytically. On the basis of this model, the nature of slab dip angles was evaluated. Slab dip angles are found to be transient features. As they penetrate into the mantle and increase their lengths, the associated gravitational torque also increases resulting in a downward pulling of the slab to the steeper dip angle. This is especially true once a slab penetrates the olivine-spinel phase boundary at about 400 km depth. However, if the phase transformation does not follow the equilibrium condition, the gravitational torque may have a different behavior. This problem was investigated. Except for fast descending slabs, non-equilibrium phase transformation can only slow down the transient increase of slab dip angles discussed earlier. Its effect is not sufficiently strong to reverse the downward pulling for most of the slabs. However, when slabs subducting at 10 cm/yr or faster, a sufficient amount of metastable olivine can exist beneath 400 km. Because of its low density compared with the surrounding spinel, an upward buoyancy is produced resulting in an upward bending of the slab and possibly an upward rotation of the slab such that smaller dip angles are formed. Seismic studies of the Japanese Slab seem to support this interpretation. The development of oroclinal geometries at convergent boundaries was also examined to study plate obduction which is an important ingredient to the initiation of plate subduction. Although the study suggests that surface features are better modeled by block models, the large scale deformation can be adequately studied by viscous models. Such a model is now under development to complete our original objective to study the initiation of plate subduction. Finally, a three-dimensional, finite element, spherical convective model is developed to study dynamic plate subductions. The model development is now complete and it is being tested to ensure its proper operation. The model is able to generate convection results with a viscosity contrast of about 100. Our research continues to push the viscosity contrast to a level that is appropriate for a subducting slab.

Hsui, Albert T.↗
NASA NTRS1992

SAR observations of the Gulf Stream during SWADE

The Surface Wave Dynamics Experiment (SWADE) has gathered SAR observations of the Gulf Stream that show a change in ocean surface brightness; this may be due to the effects of a change in air-sea temperature difference across the observed edge, where the boundary is defined by warm, quickly flowing Gulf Stream water and cooler, relatively stationary shelf water. The two images discussed indicate the possibility of deepening understanding of Gulf Stream front dynamics by using the abundant spatial data of SAR imagery, in conjunction with more conventional (point-like) data on hydrography and currents.

Vachon, Paris W.↗
DOE OSTI2022

The role of breakup and coalescence in fine-scale bubble-induced turbulence. I. Dynamics

We study the effect of bubble breakup and coalescence on fine-scale dynamics of bubbly turbulent flows using direct numerical simulations. We perform two different simulations of dilute bubbly flows of void fraction 0.5%: one with bubbles breaking up and coalescing and the other without these physical processes. The volume of the fluid method is used for simulating bubbles undergoing breakup and coalescence while the bubbles are treated as rigid spheres in the immersed boundary method simulation. The energy spectrum in both types of simulation, consistent with previous studies, exhibits a -3 slope. We follow a single infinitesimal fluid element as it evolves to understand velocity gradient dynamics using conditional mean trajectories. We note finite-time divergence when the fluid element evolves under the action of inertial and pressure dynamics. The inertial, pressure, and viscous velocity gradient dynamics, when considered individually, produce the same results for bubble-induced turbulence (BIT) as with the classical homogeneous isotropic turbulence (HIT). Yet when the overall velocity gradient dynamics is considered, BIT results in non-cyclic trajectories moving toward stable node and unstable saddle while classical HIT shows cyclic behavior in their trajectories that move toward the origin. Interestingly, both the volume of fluid and immersed boundary simulations produce similar results. Therefore, there are two main takeaways from this research. First, new velocity gradient models are needed for BIT as their velocity gradients behavior is entirely different from the HIT. Second, we can neglect the bubble topology, breakup, and coalescence while studying or modeling the fine-scale dynamics of BIT.

42 ENGINEERING↗
NASA NTRS2011

Assessing Uncertainties in Boundary Layer Transition Predictions for HIFiRE-1 at Non-zero Angles of Attack

Boundary layer stability was analyzed for the HIFiRE-1 flight vehicle geometry for ground tests conducted at the CUBRC LENS I hypersonic shock test facility and the Langley Research Center (LaRC) 20- inch Mach 6 Tunnel. Boundary layer stability results were compared to transition onset location obtained from discrete heat transfer measurements from thin film gauges during the CUBRC test and spatially continuous heat transfer measurements from thermal phosphor paint data during the LaRC test. The focus of this analysis was on conditions at non-zero angles of attack as stability analysis has already been performed at zero degrees angle of attack. Also, the transition onset data obtained during flight testing was at nonzero angles of attack, so this analysis could be expanded in the future to include the results of the flight test data. Stability analysis was performed using the 2D parabolized stability software suite STABL (Stability and Transition Analysis for Hypersonic Boundary Layers) developed at the University of Minnesota and the mean flow solutions were computed using the DPLR finite volume Navier-Stokes computational fluid dynamics (CFD) solver. A center line slice of the 3D mean flow solution was used for the stability analysis to incorporate the angle of attack effects while still taking advantage of the 2D STABL software suite. The N-factors at transition onset and the value of Re(sub theta)/M(sub e), commonly used to predict boundary layer transition onset, were compared for all conditions analyzed. Ground test data was analyzed at Mach 7.2 and Mach 6.0 and angles of attack of 1deg, 3deg and 5deg. At these conditions, the flow was found to be second mode dominant for the HIFiRE-1 slender cone geometry. On the leeward side of the vehicle, a strong trend of transition onset location with angle of attack was observed as the boundary layer on the leeward side of the vehicle developed inflection points at streamwise positions on the vehicle that correlated to angle of attack. Inflection points are a strong instability mechanism that lead to rapid breakdown and transition to turbulence. The transition onset location on the windward side of the vehicle displayed no trend with angle of attack or freestream Reynolds number and transition was observed farther down the vehicle than observed on the leeward side of the vehicle. In analysis of both windward and leeward sides of the vehicle, use of the N factor methodology to develop trends to predict boundary layer transition onset showed improvements over the Re(sub theta)/M(sub e) empirical correlation methodology. Stronger correlations and less scatter in the data were observed when using the N factor method for these cases.

Marek, Lindsay C.↗
NASA NTRS2003

Lidar Measurements of Wind, Moisture and Boundary Layer Evolution in a Dryline During IHOP2002

Variability in the convective boundary layer moisture, wind and temperature fields and their importance in the forecasting and understanding of storms have been discussed in the literature. These variations have been reported in relation to frontal zones, stationary boundaries and during horizontal convective rolls. While all three vary substantially in the convective boundary layer, moisture poses a particular challenge. Moisture or water vapor concentration (expressed as a mass mixing ratio, g/kg), is conserved in all meteorological processes except condensation and evaporation. The water vapor mixing ratio often remains distinct across an air -mass boundary even when the temperature difference is indistinct. These properties make it an ideal choice in visualizing and understanding many of the atmosphere's dynamic features. However, it also presents a unique measurement challenge because water vapor content can vary by more than three orders of magnitude in the troposphere. Characterization of the 3D-distribution of water vapor is also difficult as water vapor observations can suffer from large sampling errors and substantial variability both in the vertical and horizontal. This study presents groundbased measurements of wind, boundary layer structure and water vapor mixing ratio measurements observed by three co-located lidars. This presentation will focus on the evolution and variability of moisture and wind in the boundary layer during a dry line event that occurred on 22 May 2002. These data sets and analyses are unique in that they combine simultaneous measurements of wind, moisture and CBL structure to study the detailed thermal variability in and around clear air updrafts during a dryline event. It will quantify the variation caused by, in and around buoyant plumes and across a dryline. The data presented here were collected in the panhandle of Oklahoma as part of the International BO Project (IHOP-2002), a field experiment that took place over the Southern Great Plains (SGP) of the United States from 13 May to 30 June 2002. The chief goal of IHOP-2002 is to improve characterization of the four-dimensional (4-D) distribution of water vapor and its application to improving the understanding and prediction of convection

Demoz, Belay↗
NASA NTRS1948

Theoretical Analysis of Stationary Potential Flows and Boundary Layers at High Speed

The present report consists of two parts. The first part deals with the two-dimensional stationary flow in the presence of local supersonic zones. A numerical method of integration of the equation of gas dynamics is developed. Proceeding from solutions at great distance from the body the flow pattern is calculated step by step. Accordingly the related body form is obtained at the end of the calculation. The second part treats the relationship between the displacement thickness of laminar and turbulent boundary layers and the pressure distribution at high speeds. The stability of the boundary layer is investigated, resulting in basic differences in the behavior of subsonic and supersonic flows. Lastly, the decisive importance of the boundary layer for the pressure distribution, particularly for thin profiles, is demonstrated.

Oswaititsch, K.↗
NASA NTRS1982

Data use investigation for the magnetic field satellite (MAGSAT) mission: Geomagnetic field forecasting and fluid dynamics of the core

MAGSAT data were used to construct a variety of spherical harmonic models of the main geomagnetic field emanating from Earth's liquid core at poch 1980. These models were used to: (1) accurately determine the radius of Earth's core by a magnetic method, (2) calculate estimates, of the long-term ange of variation of geomagnetic Gauss coefficients; (3) establish a preferred truncation level for current spherical harmonic models of the main geomagnetic field from the core; (4) evaluate a method for taking account of electrical conduction in the mantle when the magnetic field is downward continued to the core-mantle boundary; and (5) establish that upwelling and downwelling of fluid motion at the top of the core is probably detectable, observationally. A fluid dynamics forecast model was not produced because of insufficient data.

Benton, E. R.↗
NASA NTRS2002

Lidar Measurements of Wind, Moisture, and Boundary Layer Evolution in a Dry Line during 1HOP 2002

Variability in the convective boundary layer moisture, wind and temperature fields and their importance in the forecasting and understanding of storms have been discussed in the literature. These . variations have been reported in relation to frontal zones, stationary boundaries and during horizontal convective rolls. While all three vary substantially in the convective boundary layer, moisture poses a particular challenge. Moisture or water vapor concentration (expressed as a mass mixing ratio, g/kg), is conserved in all meteorological processes except condensation and evaporation. The water vapor mixing ratio often remains distinct across an air-mass boundary even when the temperature difference is indistinct. These properties make it an ideal choice in visualizing and understanding many of the atmosphere's dynamic features. However, it also presents a unique measurement challenge because water vapor content can vary by more than three orders of magnitude in the troposphere. Characterization of the 3D-distribution of water vapor is also difficult as water vapor observations can suffer from large sampling errors and substantial variability both in the vertical and horizontal. This study presents ground-based measurements of wind, boundary layer structure and water vapor mixing ratio measurements observed by three co-located lidars. This presentation will focus on the evolution and variability of moisture and wind in the boundary layer during a dry line event that occurred on 22 May 2002. These data sets and analyses are unique in that they combine simultaneous measurements of wind, moisture and CBL structure to study the detailed thermal variability in and around clear air updrafts during a dryline event. It will quantify the variation caused by, in and around buoyant plumes and across a dryline. The data presented here were collected in the panhandle of Oklahoma as part of the International H2O Project (MOP-2002), a field experiment that took place over the Southern Great Plains (SGP) of the United States from 13 May to 30 June 2002. The chief goal of MOP-2002 is to improve characterization of the four-dimensional (4-D) distribution of water vapor and its application to improving the understanding and prediction of convection

Demoz, Belay↗
NASA NTRS2009

Numerical Study of Outlet Boundary Conditions for Unsteady Turbulent Internal Flows Using the NCC

This paper presents the results of studies on the outlet boundary conditions for turbulent internal flow simulations. Several outlet boundary conditions have been investigated by applying the National Combustion Code (NCC) to the configuration of a LM6000 single injector flame tube. First of all, very large eddy simulations (VLES) have been performed using the partially resolved numerical simulation (PRNS) approach, in which both the nonlinear and linear dynamic subscale models were employed. Secondly, unsteady Reynolds averaged Navier- Stokes (URANS) simulations have also been performed for the same configuration to investigate the effects of different outlet boundary conditions in the context of URANS. Thirdly, the possible role of the initial condition is inspected by using three different initial flow fields for both the PRNS/VLES simulation and the URANS simulation. The same grid is used for all the simulations and the number of mesh element is about 0.5 million. The main purpose of this study is to examine the long-time behavior of the solution as determined by the imposed outlet boundary conditions. For a particular simulation to be considered as successful under the given initial and boundary conditions, the solution must be sustainable in a physically meaningful manner over a sufficiently long period of time. The commonly used outlet boundary condition for steady Reynolds averaged Navier-Stokes (RANS) simulation is a fixed pressure at the outlet with all the other dependent variables being extrapolated from the interior. The results of the present study suggest that this is also workable for the URANS simulation of the LM6000 injector flame tube. However, it does not work for the PRNS/VLES simulation due to the unphysical reflections of the pressure disturbances at the outlet boundary. This undesirable situation can be practically alleviated by applying a simple unsteady convection equation for the pressure disturbances at the outlet boundary. The numerical results presented in this paper suggest that this unsteady convection of pressure disturbances at the outlet works very well for all the unsteady simulations (both PRNS/VLES and URANS) of the LM6000 single injector flame tube.

Liu, Nan-Suey↗
NASA NTRS2024

Pliocene Model Intercomparison Project Phase 3 (PlioMIP3) – Science Plan and Experimental Design

The Pliocene Model Intercomparison Project (PlioMIP) was initiated in 2008. Over two phases PlioMIP has helped co-ordinate the experimental design and publication strategy of the community, which has included an increasing number of climate models and modelling groups from around the world. It has engaged with palaeoenvironmental scientists to foster new data synthesis supporting the construction of new model boundary conditions, as well as to facilitate new data-model comparisons. The work has advanced our understanding of Pliocene climates and environments, enhanced our knowledge regarding the ability of complex climate and Earth System models to accurately simulate climate change, and helped to refine our estimates of how sensitive the climate system is to forcing conditions. In this community protocol paper, we outline the scientific plan for PlioMIP Phase 3 (PlioMIP3). This plan provides the required guidance to participating modelling groups from around the world to successfully set up and perform PlioMIP3 climate model experiments. The project is open to new participants from the scientific community (both from the climate modelling and geosciences communities). In PlioMIP3, we retain the PlioMIP2 Core experiments (Eoi 400 , E 280 ) and extend the Core requirements to include either an experiment focussed on the Early Pliocene or an alternative Late Pliocene simulation (or both). These additions (a) allow a comparison of Early and Late Pliocene warm intervals and help build research connections and synergy with the MioMIP (Miocene Model Intercomparison Project - also known as DeepMIP-Miocene) and PlioMioVAR projects (Pliocene-Miocene Variability Working Group), and (b) create an alternative time slice simulation for 3.205 Ma (MIS KM5c) through removal of some of the largest palaeogeographic differences introduced between PlioMIP1 and 2 resulting in minimal land-sea mask variations from the modern. In addition, we present ten optional experiments designed to enhance our assessment of climate sensitivity and to explore the uncertainty in greenhouse gas-related forcing. For the first time, we introduce orbital sensitivity experiments into the science plan, as well as simulations incorporating dynamic vegetation-climate feedbacks and an experiment designed to examine the potential significance of East Antarctic Ice Sheet boundary condition uncertainty. These changes enhance palaeo-to-future scientific connections and enable an exploration of the significance of palaeogeographic uncertainties on climate simulations.

Climate modelling↗
DOE OSTI2022

Development of a creep model informed by lower-length scale simulations to simulate creep in doped UO 2

Using molecular dynamics, we predict information at the atomistic scale used to develop a mechanistic UO 2 creep model for use in higher length-scale fuel performance codes. The ultimate objective of the model is to better describe the grain size dependence and therefore impact of doping on creep rates in UO 2 . In a previous NEAMS milestone, we found that Nabarro-Herring (bulk diffusional) creep was too low to capture the experimentally observed creep rates in standard UO 2 . Moreover, in that milestone, other mechanisms were explored, such as Coble (grain boundary) creep and dislocation climb, with each mechanism exhibiting different grain size dependencies. Again, these were orders of magnitude too low to describe the experimental creep rates. In this work, we address the previous assumptions made for the Coble creep mechanism by investigating the diffusivity of various defects at grain boundaries in UO 2 and, critically, to determine if enhanced grain boundary diffusivity allows the model to better reproduce experimental results. The diffusivity as a function of temperature for different concentrations of uranium vacancies and interstitials for bulk UO 2 have also been examined using cluster dynamics. Furthermore, using a concentration dependent segregation model, the concentration of defects at the grain boundary were predicted. This atomistic data was then input into the various creep mechanisms and the creep rates compared to the empirical MATPRO correlation (used in BISON) and experiment.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

ExaWind: Predictive Wind Energy Simulations

This presentation describes the ExaWind project and the team's progress in creating a suite of performance-portable codes designed for predictive simulations of wind farms on next-generation exascale-class supercomputers. Such simulations will require the resolution of scales spanning many orders of magnitude, from blade boundary layers to wind farm flow structures. In the U.S., the first exascale systems will be GPU accelerated, and different GPU manufacturers have been chosen for the different systems. At the heart of the ExaWind software is a hybrid-solver approach based on the codes Nalu-Wind and AMR-Wind, which are computational fluid dynamics solvers for the incompressible Navier-Stokes equations. Nalu-Wind is an unstructured-grid code used to resolve wind turbine geometry and blade boundary layers, whereas AMR-Wind is a structured-grid background solver for atmospheric turbulent flow and turbine wake propagation. The models are coupled with overset meshes and global linear systems are approximated through a loose-coupling algorithm. Results will include validation-quality high-fidelity simulations and strong/weak scaling results from the Summit supercomputer.

49 EE - Wind and Water Power Program - Wind (EE-4W↗
DOE OSTI2023

Fuel-air mixing in motored CFR engine at research octane number (RON) relevant condition

This paper presents a three-dimensional (3-D) computational fluid dynamics (CFD) study of a motored cooperative fuel research (CFR) engine at research octane number (RON) relevant condition. The boundary conditions for 3-D simulations were generated with a one-dimensional GT-Power model. For the first time in literature, a carburetor was added to a virtual CFR engine model with 3-D CFD. Therefore, the proposed setup can simulate the fuel and thermal stratifications inside the engine cylinder with realistic detail. The transient simulations in this work were performed within the Reynolds-averaged Navier-Stokes (RANS) framework with a Realizable k-ε turbulence model. Major conclusions from the present work are: (1) The in-cylinder flow of the CFR engine is swirl-dominated due to the existence of the intake valve shroud. (2) There is a significant amount of liquid droplets entering the cylinder during the intake stroke. The maximum instantaneous amount of liquid for 50% PRF 87 (containing 87% iso-octane and 13% n-heptane (v/v)) and 50% ethanol mixture is indicated to be around 26% of total injected fuel mass. (3) The heat of vaporization (HoV) of the fuel is responsible for creating both temperature and charge stratification inside the cylinder.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2022

Single- and two-particle finite size effects in interacting lattice systems

Simulations of extended quantum systems are typically performed by extrapolating results of a sequence of finite-system-size simulations to the thermodynamic limit. In the quantum Monte Carlo community, twist-averaging was pioneered as an efficient strategy to eliminate one-body finite size effects. In the dynamical mean field community, cluster generalizations of the dynamical mean field theory were formulated to study systems with nonlocal correlations. In this work, we put the twist-averaging and the dynamical cluster approximation variant of the dynamical mean field theory onto equal footing, discuss commonalities and differences, and compare results from both techniques to the standard periodic boundary technique. At the example of Hubbard-type models with local, short-range and Yukawa-like longer range interactions we show that all methods converge to the same limit, but that the convergence speed differs in practice. We show that embedding theories are an effective tool for managing both one-body and two-body finite size effects, in particular if interactions are averaged over twist angles.

36 MATERIALS SCIENCE↗
NASA NTRS2004

Study of Near-Surface Models in Large-Eddy Simulations of a Neutrally Stratified Atmospheric Boundary Layer

Large-eddy simulation (LES) is a widely used technique in armospheric modeling research. In LES, large, unsteady, three dimensional structures are resolved and small structures that are not resolved on the computational grid are modeled. A filtering operation is applied to distinguish between resolved and unresolved scales. We present two near-surface models that have found use in atmospheric modeling. We also suggest a simpler eddy viscosity model that adopts Prandtl's mixing length model (Prandtl 1925) in the vicinity of the surface and blends with the dynamic Smagotinsky model (Germano et al, 1991) away from the surface. We evaluate the performance of these surface models by simulating a neutraly stratified atmospheric boundary layer.

Senocak, I.↗
NASA NTRS2021

Comparison of chemical lateral boundary conditions for air quality predictions over the contiguous United States during pollutant intrusion events

The National Air Quality Forecast Capability (NAQFC) operated in U.S.’s National Oceanic and Atmospheric Administration (NOAA) provides the operational forecast guidance for ozone and fine particulate matters with aerodynamic diameters less than 2.5μm (PM2.5) over the contiguous 48 U.S. states (CONUS) using the Community Multi-scale Air Quality (CMAQ) model. The existing NAQFC uses climatological chemical lateral boundary conditions ( CLBCs), which cannot capture pollutant intrusion events originating outside of the model domain. In this study, we developed a model framework to use dynamic CLBCs from the Goddard Earth Observing System Model, version 5 (GEOS) to drive NAQFC. A mapping of the GEOS chemical species to the CMAQ’s Carbon Bond 5 (CB05)-Aero6 species was developed. The utilization of the GEOS dynamic CLBCs in NAQFC showed the best overall performance in simulating the surface observations during the Saharan dust intrusion and Canadian wildfire events in summer 2015.The simulated PM2.5 was improved from 0.18 to 0.37 and the mean bias was reduced from -6.74 μg/m3 to -2.96 μg/m3 over CONUS. Although the effect of CLBCs on the PM2.5 correlation was mainly near the inflow boundary, its impact on the background concentrations reached further inside the domain. The CLBCs could affect background ozone concentrations through the inflows of ozone itself and its precursors, such as CO. It was further found that the aerosol optical thickness (AOT) from satellite retrievals correlated well with the column CO and elemental carbon from GEOS. The satellite-derived AOT CLBCs generally improved the model performance for the wildfire intrusion events during a summer 2018 case study, and demonstrated how satellite observations of atmospheric composition could be used as an alternative method to capture the air quality effects of intrusions when the global model CLBCs, such as GEOS CLBCs, are not available.

Community Multi-scale Air Quality (CMAQ) model↗
DOE OSTI2026

Trigonometric continuous-variable gates and hybrid quantum simulations of the sine-Gordon model

Hybrid qubit-qumode quantum computing platforms provide a natural setting for simulating interacting bosonic quantum field theories. However, existing continuous-variable gate constructions rely predominantly on polynomial functions of canonical quadratures. In this work, we introduce a complementary universality paradigm based on trigonometric continuous-variable gates, which enable a Fourier-like representation of bosonic operators and are particularly well suited for periodic and non-perturbative interactions. We present an ancilla-based framework for implementing trigonometric gates with arguments given by arbitrary Hermitian functions of qumode quadratures. The protocol yields unitary gates deterministically, and non-unitary gates through probabilistic post-selection. As a concrete application, we develop a hybrid qubit-qumode quantum simulation of the lattice sine-Gordon model. Using these gates, we prepare ground states via quantum imaginary-time evolution, simulate real-time dynamics, compute time-dependent vertex two-point correlation functions, and extract quantum kink profiles under topological boundary conditions. Our results demonstrate that trigonometric continuous-variable gates provide a physically natural framework for simulating interacting field theories on near-term hybrid quantum hardware, while establishing a parallel route to universality beyond polynomial gate constructions. We expect that the trigonometric gates introduced here to find broader applications, including quantum simulations of condensed matter systems, quantum chemistry, and biological models.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Bounce-averaged theory in arbitrary multi-well plasmas: solution domains and the graph structure of their connections

Bounce-averaged theories provide a framework for simulating relatively slow processes, such as collisional transport and quasilinear diffusion, by averaging these processes over the fast periodic motions of a particle on a closed orbit. This procedure dramatically increases the characteristic time scale and reduces the dimensionality of the modelled system. The natural coordinates for such calculations are the constants of motion (COM) of the fast particle motion, which by definition do not change during an orbit. However, for sufficiently complicated fields – particularly in the presence of local maxima of the electric potential and magnetic field – the COM are not sufficient to specify the particle trajectory. In such cases, multiple domains in COM space must be used to solve the problem, with boundary conditions enforced between the domains to ensure continuity and particle conservation. Previously, these domains have been imposed by hand, or by recognising local maxima in the fields, limiting the flexibility of bounce-averaged simulations. Here, we present a general set of conditions for identifying consistent domains and the boundary condition connections between the domains, allowing the application of bounce-averaged theories in arbitrarily complicated and dynamically evolving electromagnetic field geometries. We also show how the connections between the domains can be represented by a directed graph, which can help to succinctly represent the trajectory bifurcation structure.

fusion plasma↗