Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “component model”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 937 records · Page 52
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

The eROSITA Final Equatorial-Depth Survey (eFEDS): The AGN catalog and its X-ray spectral properties

The eROSITA Final Equatorial Depth Survey (eFEDS), observed with eROSITA ahead of its planned 4-yr all-sky survey, is the largest contiguous-field X-ray survey at present. It yielded a large sample of X-ray sources with very rich multiband photometric and spectroscopic coverage. We present here the eFEDS active galactic nuclei (AGN) catalog and the eROSITA X-ray spectral properties of the eFEDS sources. Using a Bayesian method, we performed a systematic X-ray spectral analysis for all the eFEDS sources. We adopted multiple spectral models, including single-component power-law or hot-plasma models and double-component models of a power law plus soft excess. We investigated the capacity of eROSITA X-ray spectra for constraining AGN spectral shapes through a detailed analysis of the posterior parameter probability distribution functions. Hierarchical Bayesian modeling was used to recover the spectral parameter distribution of the sample. The source fluxes and luminosities were measured from the posterior of the spectral fitting. The eFEDS AGN catalog (22 079 sources) comprises ~80% of the eFEDS point sources. Despite a large number of faint sources, our spectral fitting provides reasonable measurements of spectral shapes and intrinsic luminosities for a majority of the sources. Because of sample selection bias, this AGN catalog is dominated by X-ray unobscured sources, with an obscured (logN H > 21.5) fraction of 8%; the power-law emission of the hot corona is also relatively soft, with a typical slope of 2.0. For type-I AGN, the X-ray emission is well correlated with the UV emission with the usual anticorrelation between the X-ray to UV spectral slope α OX and the UV luminosity. The X-ray spectral properties measured with various models are presented for all the eFEDS sources.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1994

Nonequilibrium radiation and chemistry models for aerocapture vehicle flowfields

The primary accomplishments of the project were as follows: (1) From an overall standpoint, the primary accomplishment of this research was the development of a complete gasdynamic-radiatively coupled nonequilibrium viscous shock layer solution method for axisymmetric blunt bodies. This method can be used for rapid engineering modeling of nonequilibrium re-entry flowfields over a wide range of conditions. (2) Another significant accomplishment was the development of an air radiation model that included local thermodynamic nonequilibrium (LTNE) phenomena. (3) As part of this research, three electron-electronic energy models were developed. The first was a quasi-equilibrium electron (QEE) model which determined an effective free electron temperature and assumed that the electronic states were in equilibrium with the free electrons. The second was a quasi-equilibrium electron-electronic (QEEE) model which computed an effective electron-electronic temperature. The third model was a full electron-electronic (FEE) differential equation model which included convective, collisional, viscous, conductive, vibrational coupling, and chemical effects on electron-electronic energy. (4) Since vibration-dissociation coupling phenomena as well as vibrational thermal nonequilibrium phenomena are important in the nonequilibrium zone behind a shock front, a vibrational energy and vibration-dissociation coupling model was developed and included in the flowfield model. This model was a modified coupled vibrational dissociation vibrational (MCVDV) model and also included electron-vibrational coupling. (5) Another accomplishment of the project was the usage of the developed models to investigate radiative heating. (6) A multi-component diffusion model which properly models the multi-component nature of diffusion in complex gas mixtures such as air, was developed and incorporated into the blunt body model. (7) A model was developed to predict the magnitude and characteristics of the shock wave precursor ahead of vehicles entering the Earth's atmosphere. (8) Since considerable data exists for radiating nonequilibrium flow behind normal shock waves, a normal shock wave version of the blunt body code was developed. (9) By comparing predictions from the models and codes with available normal shock data and the flight data of Fire II, it is believed that the developed flowfield and nonequilibrium radiation models have been essentially validated for engineering applications.

Carlson, Leland A.↗
DOE OSTI2026

A System-Level Cost Modeling Framework for Design for Remanufacturing: A Case Study of an Agricultural Machine Transmission

Remanufacturing offers significant environmental and economic benefits by restoring end-of-life products to as-new conditions. Although extensive research has been conducted on the topic, the adoption of remanufacturing practices remains limited across various industries. A primary barrier to broader implementation is the substantial upfront investment required, which necessitates reliable cost modeling to justify potential future savings. Most existing models treat components independently and ignore inter-component dependencies. We develop a probabilistic, system-level cost modeling framework that integrates reliability, reusability, and a dependency matrix to capture cascading effects across components over multiple life cycles. Our model identifies those critical components that maximize remanufacturing benefits across a product's many lives. A toy example and an industry case study (John Deere PowrQuad transmission subassembly) illustrate how design alternatives affect cumulative cost. Using a Monte Carlo simulation (MCS) to perform life cycle cost analysis on the system with different design changes, we show the normalized average cost savings after three remanufacturing cycles. Accounting for dependencies meaningfully alters cost projections and ignoring them underestimates accumulated cost by up to 20% in our examples. Furthermore, the results of our study confirm that accounting for component interdependencies is necessary to produce cost estimates that meet industry standards.

Life Cycle Analysis and Design↗
DOE OSTI2025

E3SM‐GCAM: A Synchronously Coupled Human Component in the E3SM Earth System Model Enables Novel Human‐Earth Feedback Research

Abstract Modeling human‐environment feedbacks is critical for assessing the effectiveness of climate change mitigation and adaptation strategies under a changing climate. The Energy Exascale Earth System Model (E3SM) now includes a human component, with the Global Change Analysis Model (GCAM) at its core, that is synchronously coupled with the land and atmosphere components through the E3SM coupling software. Terrestrial productivity is passed from E3SM to GCAM to make climate‐responsive land use and CO 2 emission projections for the next 5‐year period, which are interpolated and passed to E3SM annually. Key variables affected by the incorporation of these feedbacks include land use/cover change, crop prices, terrestrial carbon, local surface temperature, and climate extremes. Regional differences are more pronounced than global differences because the effects are driven primarily by differences in land use. This novel system enables a new type of scenario development and provides a powerful modeling framework that facilitates the addition of other feedbacks between these models. This system has the potential to explore how human responses to climate change impacts in a variety of sectors, including heating/cooling energy demand, water management, and energy production, may alter emissions trajectories and Earth system changes. Plain Language Summary Earth system models help us understand how humans are changing the climate. Currently, these models do not include human systems, so predetermined greenhouse gas, aerosol, and land use change data are input to these models. These data do not reflect human responses to changes projected by Earth system models. We have added a human component to an Earth system model to represent human responses to environmental change and calculate corresponding greenhouse gas and land use change data instead of using predetermined data. Including this human component changes projections of land use, land carbon storage, and regional climate. Key Points We have incorporated a novel, advanceable human component in an Earth system model to simulate human‐Earth feedbacks Including terrestrial productivity feedbacks from the Earth to the human systems affects land change, crop prices, carbon, and climate Regional effects of including terrestrial productivity feedbacks are greater than global effects because land change is the main driver

E3SM↗
DOE OSTI2020

Uncertainty quantification of an empirical shell-model interaction using principal component analysis

Recent investigations have emphasized the importance of uncertainty quantification (UQ) in nuclear theory. Here, we carry out UQ for configuration-interaction shell-model calculations in the 1$\textit{s}$–0$\textit{d}$ valence space, investigating the sensitivity of observables to perturbations in the 66 parameters (matrix elements) of a high-quality empirical interaction. The large parameter space makes computing the corresponding Hessian numerically costly, so we compare a cost-effective approximation, using the Feynman-Hellmann theorem, to the full Hessian and find it works well. Diagonalizing the Hessian yields the principal components of the interaction: linear combinations of parameters ordered by sensitivity. This approximately decoupled distribution of parameters facilitates theoretical uncertainty propagation onto structure observables: electromagnetic transitions, Gamow-Teller decays, and dark matter-nucleus scattering matrix elements.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1995

Probabilistic material strength degradation model for Inconel 718 components subjected to high temperature, high-cycle and low-cycle mechanical fatigue, creep and thermal fatigue effects

This report presents the results of both the fifth and sixth year effort of a research program conducted for NASA-LeRC by The University of Texas at San Antonio (UTSA). The research included on-going development of methodology for a probabilistic material strength degradation model. The probabilistic model, in the form of a postulated randomized multifactor equation, provides for quantification of uncertainty in the lifetime material strength of aerospace propulsion system components subjected to a number of diverse random effects. This model is embodied in the computer program entitled PROMISS, which can include up to eighteen different effects. Presently, the model includes five effects that typically reduce lifetime strength: high temperature, high-cycle mechanical fatigue, low-cycle mechanical fatigue, creep and thermal fatigue. Statistical analysis was conducted on experimental Inconel 718 data obtained from the open literature. This analysis provided regression parameters for use as the model's empirical material constants, thus calibrating the model specifically for Inconel 718. Model calibration was carried out for five variables, namely, high temperature, high-cycle and low-cycle mechanical fatigue, creep and thermal fatigue. Methodology to estimate standard deviations of these material constants for input into the probabilistic material strength model was developed. Using an updated version of PROMISS, entitled PROMISS93, a sensitivity study for the combined effects of high-cycle mechanical fatigue, creep and thermal fatigue was performed. Then using the current version of PROMISS, entitled PROMISS94, a second sensitivity study including the effect of low-cycle mechanical fatigue, as well as, the three previous effects was performed. Results, in the form of cumulative distribution functions, illustrated the sensitivity of lifetime strength to any current value of an effect. In addition, verification studies comparing a combination of high-cycle mechanical fatigue and high temperature effects by model to the combination by experiment were conducted. Thus, for Inconel 718, the basic model assumption of independence between effects was evaluated. Results from this limited verification study strongly supported this assumption.

Bast, Callie C.↗
NASA NTRS2004

Turbofan Engine Simulated in a Graphical Simulation Environment

Recently, there has been an increase in the development of intelligent engine technology with advanced active component control. The computer engine models used in these control studies are component-level models (CLM), models that link individual component models of state space and nonlinear algebraic equations, written in a computer language such as Fortran. The difficulty faced in performing control studies on Fortran-based models is that Fortran is not supported with control design and analysis tools, so there is no means for implementing real-time control. It is desirable to have a simulation environment that is straightforward, has modular graphical components, and allows easy access to health, control, and engine parameters through a graphical user interface. Such a tool should also provide the ability to convert a control design into real-time code, helping to make it an extremely powerful tool in control and diagnostic system development. Simulation time management is shown: Mach number versus time, power level angle versus time, altitude versus time, ambient temperature change versus time, afterburner fuel flow versus time, controller and actuator dynamics, collect initial conditions, CAD output, and component-level model: CLM sensor, CAD input, and model output. The Controls and Dynamics Technologies Branch at the NASA Glenn Research Center has developed and demonstrated a flexible, generic turbofan engine simulation platform that can meet these objectives, known as the Modular Aero-Propulsion System Simulation (MAPSS). MAPSS is a Simulink-based implementation of a Fortran-based, modern high pressure ratio, dual-spool, low-bypass, military-type variable-cycle engine with a digital controller. Simulink (The Mathworks, Natick, MA) is a computer-aided control design and simulation package allows the graphical representation of dynamic systems in a block diagram form. MAPSS is a nonlinear, non-real-time system composed of controller and actuator dynamics (CAD) and component-level model (CLM) modules. The controller in the CAD module emulates the functionality of a digital controller, which has a typical update rate of 50 Hz. The CLM module simulates the dynamics of the engine components and uses an update rate of 2500 Hz, which is needed to iterate to balance mass and energy among system components. The actuators in the CAD module use the same sampling rate as those in the CLM. Two graphs of normalized spool speed versus time in seconds and one graph of normalized average metal temperature versus time in seconds is shown. MAPSS was validated via open-loop and closed-loop comparisons with the Fortran simulation. The preceding plots show the normalized results of a closed-loop comparison looking at three states of the model: low-pressure spool speed, high-pressure spool speed, and the average metal temperature measured from the combustor to the high-pressure turbine. In steady state, the error between the simulations is less than 1 percent. During a transient, the difference between the simulations is due to a correction in MAPSS that prevents the gas flow in the bypass duct inlet from flowing forward instead of toward the aft end, which occurs in the Fortran simulation. A comparison between MAPSS and the Fortran model of the bypass duct inlet flow for power lever angles greater than 35 degrees is shown.

Parker, Khary I.↗
NASA NTRS1993

A COMPACT model reduction methodology for articulated, multi-flexible bodies structures

To simulate the dynamical motion of articulated, multiflexible body structures, one can use multibody simulation packages such as DISCOS. To this end, one need appropriate reduced-order models for all the flexible components involved. The component modes projection and assembly model reduction methodology is one way to construct these reduced-order component models. However, the generated reduced-order system models typically contain high frequency extraneous modes. The presence of high frequency extraneous modes in a reduced-order system model forces us to use a small stepsize in the numerical integration of that model, resulting in an increase in the elapsed time of the integration process. To eliminate these high-frequency modes, we first identify and discard the component modes that 'contributed' to the generations of these modes. A sensitivity analysis is then used to determine how the remaining component modes should be perturbed in order to still closely capture the selected system modes. The effectiveness of the proposed methodology has been successfully verified using a finite-element model of the Galileo spacecraft.

Lee, Allan Y.↗
DOE OSTI2020

Exploring Hydrologic Model Process Connectivity at the Continental Scale Through an Information Theory Approach

Exploring water fluxes between hydrological model (HM) components is essential to assess and improve model realism. Many classical metrics for HM diagnosis rely solely on streamflow and hence provide limited insights into model performance across processes. This study applies an information theory measure known as “transfer entropy” (TE) to systematically quantify the transfer of information among major HM components. To test and demonstrate the benefits of TE, we use the Framework for Understanding Structural Errors (FUSE) model to mimic and compare four commonly used HM structures, VIC, PRMS, SACRAMENTO, and TOPMODEL, across 671 catchments spanning a variety of hydrologic regimes in the conterminous United States. We explore connections between HM components and catchment landscape characteristics (e.g., climate, topography, soil, and vegetation) and characterize their nonlinear associations using distance correlation and Spearman correlation coefficients. Our results indicate that while the information transferred from precipitation to runoff is similar across model structures (likely as a result of calibration), the information transferred among other components can vary significantly from a FUSE structure to another. We find that aridity, precipitation duration and frequency, snow fraction, mean elevation, forest area, and leaf area index are often significantly associated with TE between the main HM components. Here, we propose that the presence of meaningful nonlinear associations can be used to diagnose process representation in HMs. Our results highlight the necessity to enhance the conventional streamflow-only calibration approach for a more realistic representation of water dynamics in the models.

large-sample hydrology↗
NASA NTRS1982

Stellar model chromospheres. XIII - M dwarf stars

Single-component, homogeneous model chromospheres that are consistent with high-resolution profiles of the Ca II K line calibrated in surface flux units for three dMe and 2 dM stars observed at quiescent times are constructed. The models reveal several systematic trends. Large values of the ratio of T(min) to T(eff) are derived, indicating a large amount of nonradiative heating present in the upper photospheres of M dwarf stars. It is also found that the lower chromospheric temperature gradient is similar for all the M dwarf stars. Since for the models here the chromospheric K line emission strength is most sensitive to the total amount of chromospheric material present within the approximate temperature range T(min)-6000 K, increasing the emission strength is not simply due to increasing chromospheric temperature gradients. It is also found that both the electron density and electron temperature at one thermalization length in the K line below the top of the chromospheres are greater in the dMe stars than in the dM stars. The M dwarf models here have microturbulent velocities between 1 and 2 km/sec, which are much smaller than for solar chromosphere models.

Giampapa, M. S.↗
NASA NTRS2012

The Fast Evolution of SN 2010bh Associated with XRF 100316D

The first observational evidence of a connection between supernovae (SNe) and gamma-ray bursts (GRBs) was found about a decade ago. Since then, only half a dozen spectroscopically confirmed associations have been discovered and XRF 1003160 associated with the type-Ic SN 20lObh is among the latest. Aims. We constrain the progenitor radius, the host-galaxy extinction, and the physical parameters of the explosion of XRF l00316D/SN 20lObh at z 0.059. We study the SN brightness and colours in the context of GRB-SNe. Methods. We began observations with the Gamma-Ray burst Optical and Near-infrared Detector (GROND) 12 hours after the GRB trigger and continued until 80 days after the burst. GROND provided excellent photometric data in six filter bands covering a wavelength range from approximately 350 to 1800 nm, significantly expanding the pre-existing data set for this event. Combining GROND and Swift data, the early broad-band spectral energy distribution (SED) is modelled with a blackbody and afterglow component attenuated by dust and gas absorption. The temperature and radius evolution of the thermal component are analysed and combined with earlier measurements available from the literature. Templates of SN 1998bw are fitted to the SN itself to directly compare the lightcurve properties. Finally, a two-component parametrized model is fitted to the quasi-bolometric light curve. which delivers physical parameters of the explosion. Results. The best-fit models to the broad-band SEDs imply moderate reddening along the line of sight through the host galaxy (A(sub v.host = 1.2 +/- 0.1 mag). Furthermore, the parameters of the blackbody component reveal a cooling envelope at an apparent initial radius of 7 x 10(exp 11) cm, which is compatible with a dense wind surrounding a Wolf-Rayet star. A multicolor comparison shows that SN 2010bh is 60 - 70% as bright as SN 1998bw. Reaching maximum brightness at 8 - 9 days after the burst in the blue bands, SN 20lObh proves to be the most rapidly evolving GRB-SNe to date. Modelling of the quasi-bolometric light curve yields M(sub Ni) = 0.21 +/- 0.03 solar M and M(sub ej) = 2.6 +/- 0.2 solar M, typical of values within the GRB-SN population. The kinetic energy is E(sub k) = (2.4 +/- 0.7) x 10(exp 52) erg, which is making this SN the second most energetic GRB-SN after SN 1998bw. Conclusions. This supernova has one of the earliest peaks ever recorded and thereafter fades more rapidly than other GRB-SNe, hypernovae, or typical type-Ic SNe. This could be explained by a thin envelope expanding at very high velocities, which is therefore unable to retain the gamma-rays that would prolong the duration of the SN event.

Olivares E., F.↗
NASA NTRS2002

Method for distributed object communications based on dynamically acquired and assembled software components

A method for acquiring and assembling software components at execution time into a client program, where the components may be acquired from remote networked servers is disclosed. The acquired components are assembled according to knowledge represented within one or more acquired mediating components. A mediating component implements knowledge of an object model. A mediating component uses its implemented object model knowledge, acquired component class information and polymorphism to assemble components into an interacting program at execution time. The interactions or abstract relationships between components in the object model may be implemented by the mediating component as direct invocations or indirect events or software bus exchanges. The acquired components may establish communications with remote servers. The acquired components may also present a user interface representing data to be exchanged with the remote servers. The mediating components may be assembled into layers, allowing arbitrarily complex programs to be constructed at execution time.

Sundermier, Amy↗
NASA NTRS1989

Application of cyclic damage accumulation life prediction model to high temperature components

A high temperature, low cycle fatigue life prediction method was developed. This method, Cyclic Damage Accumulation (CDA), was developed for use in predicting the crack initiation lifetime of gas turbine engine materials, but it can be applied to other materials as well. The method is designed to account for the effects on creep-fatigue life of complex loading such as thermomechanical fatigue, hold periods, waveshapes, mean stresses, multiaxiality, cumulative damage, coatings, and environmental attack. Several features of this model were developed to make it practical for application to actual component analysis, such as the ability to handle nonisothermal loading (including TMF), arbitrary cycle paths, and multiple damage modes. The CDA life prediction model was derived from extensive specimen tests conducted on cast nickel-base superalloy B1900 + Hf. These included both monotonic tests (tensile and creep) and strain-controlled fatigue experiments (uniaxial, biaxial, TMF, mixed creep-fatigue, and controlled mean stress). Additional specimen tests were conducted on wrought INCO 718 to verify the applicability of the final CDA model to other high-temperature alloys. The model will be available to potential users in the near future in the form of a FORTRAN-77 computer program.

Nelson, Richard S.↗
NASA NTRS1996

Application of the k-epsilon-v(exp 2) model to multi-component airfoils

Flow computations around two-element and three-element configurations are presented and compared to detailed experimental measurements. The k-epsilon-v(exp 2)(bar) model has been applied and the ability of the model to capture streamline curvature effects, wake-boundary layer confluence, and laminar/turbulent transition is discussed. The numerical results are compared to experimental datasets that include mean quantities (velocity and pressure coefficient) and turbulent quantities (Reynolds normal and shear stresses).

Iaccarino, G.↗
DOE OSTI2021

Efficient kinetic thermal inverse modeling for organic material decomposition

The prevalent use of organic materials in manufacturing is a fire safety concern, and motivates the need for predictive thermal decomposition models. A critical component of predictive modeling is numerical inference of kinetic parameters from bench scale data. Currently, an active area of computational pyrolysis research focuses on identifying efficient, robust methods for optimization. This paper demonstrates that kinetic parameter calibration problems can successfully be solved using classical gradient-based optimization. We explore calibration examples that exhibit characteristics of concern: high nonlinearity, high dimensionality, complicated schemes, overlapping reactions, noisy data, and poor initial guesses. The examples demonstrate that a simple, non-invasive change to the problem formulation can simultaneously avoid local minima, avoid computation of derivative matrices, achieve a computational efficiency speedup of 10x, and make optimization robust to perturbations of parameter components. Techniques from the mathematical optimization and inverse problem communities are employed. By re-examining gradient-based algorithms, we highlight opportunities to develop kinetic parameter calibration methods that should outperform current methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2013

Uncertainty Quantification in Remaining Useful Life of Aerospace Components using State Space Models and Inverse FORM

This paper investigates the use of the inverse first-order reliability method (inverse- FORM) to quantify the uncertainty in the remaining useful life (RUL) of aerospace components. The prediction of remaining useful life is an integral part of system health prognosis, and directly helps in online health monitoring and decision-making. However, the prediction of remaining useful life is affected by several sources of uncertainty, and therefore it is necessary to quantify the uncertainty in the remaining useful life prediction. While system parameter uncertainty and physical variability can be easily included in inverse-FORM, this paper extends the methodology to include: (1) future loading uncertainty, (2) process noise; and (3) uncertainty in the state estimate. The inverse-FORM method has been used in this paper to (1) quickly obtain probability bounds on the remaining useful life prediction; and (2) calculate the entire probability distribution of remaining useful life prediction, and the results are verified against Monte Carlo sampling. The proposed methodology is illustrated using a numerical example.

Sankararaman, Shankar↗
DOE OSTI2020

A Novel Approach to Modeling Biomass Pyrolysis in a Fluidized Bed Reactor

A novel approach to simulating biomass pyrolysis in a fluidized bed of mostly inert material is presented. The bed is assumed to be externally heated, although simulation of autothermal operation with partial oxidation of the products is a future objective. Combining pyrolysis reaction kinetics developed by the CRECK Modeling Group and a previously published component properties model, material and energy balances are closed by tracking the residence time of biomass particles without regard for their exact spatial distribution. The model is used to simulate a pilot-scale fluidized bed pyrolysis process being developed at Iowa State University, and model predictions are compared with experimental results for red oak and corn stover feedstocks. The results are in general agreement, with the model typically predicting more noncondensable gas and less low-boiling liquid products. The differences are ascribed to the limitations of the kinetics model. This model provides a rigorous energy balance for fluidized bed pyrolysis processes that can be incorporated into commercial flowsheet models with the capacity for future addition of partial oxidation reactions and implementation of improved kinetics models.

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

Friction in a strongly magnetized neutral plasma

A charged projectile generates an electrostatic wake as it moves through a background plasma. This wake normally gives rise to a drag force that acts antiparallel to the velocity vector of the projectile, and is commonly referred to as the stopping power. A recent theory predicted that an additional component of the friction force that is perpendicular to both the projectile velocity and the Lorentz force arises when a plasma is strongly magnetized. We extend the previous analysis of this transverse friction force, which was based on the one-component plasma model, to treat a two-component charge-neutral electron-ion plasma. The direction and magnitude of the transverse force is found to depend on the projectile speed relative to the electron and ion thermal velocities, and to change sign three times. For projectile speeds below a certain threshold, the transverse force is dominated by collisions with ions, while above this threshold, only electron collisions contribute. Here, the average trajectory of the projectile is significantly altered by the transverse force as it slows.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗