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NASA NTRSDate not supplied

Variational Coupled Loads Analysis using the Hybrid Parametric Variation Method

Time-domain coupled loads analysis (CLA)is used to determine the response of a launch vehicle and payload system to transient forces, such as liftoff, engine ignitions and shutdowns, jettison events, and atmospheric flight loads, such as buffet. CLA, using Hurty/Craig-Bampton (HCB)component models, is the accepted method for the establishment of design-level loads for launch systems. However, uncertainty in the component models flows into uncertainty in predicted system results. Uncertainty in the structural responses during launch is a significant concern because small variations in launch vehicle and payload mode shapes and their interactions can result in significant variations in system loads. Uncertainty quantification (UQ)is used to determine statistical bounds on prediction accuracy based on model uncertainty. In this paper uncertainty is treated at the HCB component-model level. In an effort to account for model uncertainties and statistically bound their effect on CLA predictions, this work combines CLA with UQ in a process termed variational coupled loads analysis (VCLA). The modeling of uncertainty using a parametric approach, in which input parameters are represented by random variables, is common, but its major drawback is the resulting uncertainty is limited to the form of the nominal model. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. Model-form uncertainty can be represented using a nonparametric approach based on random matrix theory (RMT). In this work, UQ is performed using the hybrid parametric variation (HPV)method, which combines parametric with nonparametric uncertainty at the HCB component model level. The HPV method requires the selection of dispersion values for the HCB fixed-interface (FI)eigenvalues, and the HCB mass and stiffness matrices. The dispersions are based upon component test-analysis modal correlation results. During VCLA, random component models are assembled into an ensemble of random systems using a Monte Carlo (MC)approach. CLA is applied to each of the ensemble members to produce an ensemble of system-level responses for statistical analysis. The proposed methodology is demonstrated through its application to a buffet loads analysis of NASA’s Space Launch System (SLS)during the transonic regime fifty seconds after liftoff. Core stage (CS)section shears and moments are recovered, and statistics are computed.

Uncertainty Quantification↗
NASA NTRSDate not supplied

SLS Integrated Modal Test Uncertainty Quantification using the Hybrid Parametric Variation Method

Uncertainty in structural loading during launch is a significant concern in the development of spacecraft and launch vehicles. Small variations in launch vehicle and payload mode shapes and their interaction can result in significant variation in system loads. In many cases involving large aerospace systems it is difficult, not economical, or impossible to perform a system modal test. However, it is still vital to obtain test results that can be compared with analytical predictions to validate models. Instead, the “Building Block Approach” is used in which system components are tested individually. Component models are correlated and updated to agree as best they can with test results. The Space Launch System consists of a number of components that are assembled into a launch vehicle. Finite element models of the components are developed, reduced to Hurty/Craig-Bampton models and assembled to represent different phases of flight. The only opportunity to obtain modal test data from an assembled Space Launch System will be during the Integrated Modal Test. There is always uncertainty in every model, which flows into uncertainty in predicted system results. Uncertainty Quantification is used to determine statistical bounds on prediction accuracy based on model uncertainty. For the Space Launch System, model uncertainty is at the Hurty/Craig-Bampton component level. Uncertainty in the Hurty/Craig-Bampton components is quantified using the hybrid parametric variation approach that combines parametric and nonparametric uncertainty. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. This type of uncertainty cannot be represented by variations infinite element model input parameters and thus cannot be included in a parametric approach. However, model-form uncertainty can be modeled using a nonparametric approach based on random matrix theory. The hybrid parametric variation method requires the selection of dispersion values for the Hurty/Craig-Bampton fixed-interface eigenvalues, and the Hurty/Craig-Bampton stiffness matrices. Component test/analysis frequency error is used to identify the fixed-interface eigenvalue dispersions, while test/analysis cross-orthogonality is used to identify stiffness dispersion values. The hybrid parametric variation uncertainty quantification approach is applied to the Space Launch System Integrated Modal Test configuration. Monte Carlo analysis is performed, and statistics are determined for modal correlation metrics, frequency response from Integrated Modal Test shakers to selected accelerometers, as well as other metrics for determining how well target modes are excited and identified. If the predicted uncertainty envelopes future Integrated Modal Test results, then there will be increased confidence in the utility of the component-based hybrid parametric variation uncertainty quantification approach.

Uncertainty Quantification↗
NASA NTRS2022

Uncertainty Models for the Hybrid Parametric Variation Method of Uncertainty Quantification; Analysis

There is some level of uncertainty in every finite element model (FEM), which flows to a level of uncertainty in predicted results. The purpose of uncertainty quantification (UQ) is to provide statistical bounds on prediction accuracy based on model uncertainty. This is distinct from model updating, which attempts to modify models to improve their accuracy. UQ does not improve the accuracy of models, but accepts that the models are inherently inaccurate and attempts to quantify the impact of that inaccuracy on predicted results. Previously, an alternate method for UQ, called the Hybrid Parametric Variation (HPV) method, was applied to Space Launch System (SLS) Hurty/Craig-Bampton (HCB) components to predict system-level statistics for launch vehicle attitude control transfer functions and core stage section loads due to buffet. The HPV method combines a parametric variation of the HCB fixed-interface (FI) modal frequencies with a nonparametric variation (NPV) method that randomly varies the HCB mass and stiffness matrices as Wishart random matrix distributions using random matrix theory (RMT). Alternatively, the most common method for modeling uncertainty in the structural dynamics community is a parametric approach, which varies physical parameters in the model. However, there are several disadvantages associated with the parametric method. Determining a reduced set of parameters that have a significant impact on the system response can be time consuming, and the selected parameter probability distributions are rarely reliably known. Therefore, in practice, the parameters are surrogates for the actual errors, and the link to parameter uncertainty is unknown. Another major drawback is that the uncertainty that can be represented is limited to the form of the nominal FEM. It is the experience of the authors that based on numerous aerospace programs, almost all FEM errors are in form rather than parameter values. This hypothesis is supported by the observation of the authors that it is almost never possible to ‘tune’ a FEM to match modal test results by only modifying model parameters. Model-form uncertainty cannot be directly represented by FEM input parameters nor included in a parametric approach. However, model-form uncertainty can be modeled using RMT, where a probability distribution is developed for the matrix ensemble of interest. The major advantage of the NPV method is that it covers errors in model form. The HPV method anchors uncertainty at the HCB component level to component modal test results by matching the HCB and test modes based on mode descriptions or other methods, and then applying differing levels of frequency variation. The specific variations depend on the confidence to which a component FEM has been validated through modal testing. The NPV method is layered on the frequency variation to match modal test self-orthogonality and cross-orthogonality (XO) results. Once the component uncertainty models are identified, they are assembled, and the uncertainty is propagated to the system level using a Monte Carlo (MC) analysis approach that generates statistics for system-level predictions This provides a UQ method that can be traced to test data, which can be updated as additional data and improved correlated models become available. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The second example is an application to a component that is design specific to the SLS. Based on this work and other assessments, the HPV method provides another tool to the toolset used for complex system UQ analysis. From experience gathered to date using the HPV method, additional design specific applications must be investigated to provide further confidence in the validity of the HPV method of UQ analysis.

Uncertainty quantification↗
NASA NTRSDate not supplied

Probability Bounds Analysis Applied to Multi-Purpose Crew Vehicle Nonlinearity

The Multi-Purpose Crew Vehicle (MPCV) Program Orion vehicle finite element model (FEM) was updated based on a modal test performed by Lockheed Martin. Due to nonlinearity observed in the test results, linear low force level (LL) and high force level (HL) FEMs were developed for use during various Space Launch System (SLS) flight regimes depending on expected forcing levels. Uncertainty models were derived for the combined MPCV and MPCV Stage Adaptor LL and HL Hurty/Craig-Bampton (HCB) components based on the MPCV structural test article Configuration 4 modal test-analysis correlation results. Subsequently, system-level uncertainty quantification analyses were performed using both models for various SLS flight configurations to determine the impact of the nonlinearity on important system metrics. The system metrics included both transfer functions associated with attitude control and dynamic loads associated with aerodynamic buffeting during ascent. In each case, an independent Monte Carlo (MC) analysis was performed, and no attempt was made to combine the results. The Hybrid Parametric Variation (HPV) method was used to develop the LL and HL MPCV HCB uncertainty models. The HPV method provides both parametric and non-parametric components of uncertainty. The non-parametric uncertainty accounts for the difference in model-form between the linearized analytical model and the corresponding linearized component test results in the form of mode shapes and frequencies at that force level. This linear model-form uncertainty is implemented in the HPV method using random matrix theory. However, the HPV uncertainty models developed for the linear LL and HL MPCV components do not account for the nonlinearity in the MPCV. With respect to the linearized models, this nonlinearity is also an uncertainty in model form, but in this case, it must be treated independently as an epistemic uncertainty. It represents a lack of knowledge, in contrast to an aleatory uncertainty due to the randomness of a variable. In the case of an epistemic variable, the true value is unknown, only the interval within which it lies is known. Epistemic uncertainty can be reduced with increased knowledge, while in general, aleatory uncertainty cannot. This work combines the epistemic uncertainty due to the MPCV nonlinearity with the parametric and non-parametric uncertainty within the HPV method using a second order propagation approach. The LL and HL test data is augmented with surrogate test data derived from a nonlinear MPCV representation. The impact of the MPCV nonlinearity on system response statistics is determined using a series of cumulative distribution functions in the form of a horsetail plot, or p-box. This results in an interval of probabilities for a specific response value, or an interval of response values at a specific probability.

Daniel C Kammer↗
NASA NTRS2022

NASA Engineering and Safety Center Technical Bulletin No. 22-04: Uncertainty Quantification of Reduced Order Structural Dynamic Models

Uncertainty quantification (UQ) provides statistical bounds on prediction accuracy based on finite element model (FEM) uncertainty. An alternate method for UQ, called the Hybrid Parametric Variation (HPV) combines a parametric variation of the Hurty/Craig-Bampton (HCB) fixed-interface (FI) modal frequencies with a nonparametric variation (NPV) method. This provides a UQ method that can be traced to test data, which can be updated as additional data and improved correlated models become available.

Uncertainty Quantification↗
NASA NTRS2024

Sizing and Performance Analysis of a MW-Class Electrified Aircraft Propulsion (EAP) System for a Parallel Hybrid Turboprop Concept

Aircraft electrification has emerged as a pivotal research and development focus in the 21st century, gaining international momentum as a strategic approach to curtail fuel consumption and emissions in the civil aviation sector. Through the Electrified Powertrain Flight Demonstration (EPFD) project, NASA is collaborating with industry partners to develop and demonstrate Megawatt (MW) class Electrified Aircraft Propulsion (EAP) systems using regional turboprops, as well as single-aisle commercial transports. With the rapid emergence of novel EAP concepts, current efforts are focused on developing the capabilities to evaluate the impacts of electrification on vehicle-level performance. This requires parametric modeling at the conceptual design stage, using uncertainty propagation techniques to account for the high variability in EAP system architecture. This paper details an integrated approach to parametric sizing of multi-MW EAP systems in a large turboprop freighter concept with a parallel hybrid configuration. The primary goal is to assess vehicle-level performance sensitivities, such as range and fuel burn reduction, to variations in electrical system component-level performance metrics, including specific power, efficiency, and energy density, based on near-term EAP technology levels.

electrified aircraft propulsion↗
NASA NTRS1992

Application of composite materials to impact-insensitive munitions

An approach is outlined for developing bullet-impact-insensitive munitions based on composite materials that provide rapid venting of the rocket-motor case. Impact experiments are conducted with test specimens of hybrid laminates of graphite/epoxy and epoxy reinforcing with woven glass fibers. The dynamic strain response and initial impact force are measured with strain gauges, and perforation damage is examined in the plates. The results show that impact damage can be designed by means of parametric variations of the fiber, matrix, and ply orientations. It is suggested that rocket-motor cases can be designed with composite materials to provide rapid venting during the failure mode. The experimental ballistic testing performed provides data that can be used comparatively with analytical data on composite materials.

Neradka, Vincent F.↗
NASA NTRSDate not supplied

Sizing and Performance Analysis of a MegaWatt-Class Electrified Aircraft Propulsion (EAP) System for a Parallel Hybrid Turboprop Concept

Aircraft electrification has emerged as a pivotal research and development focus in the 21st century, gaining international momentum as a strategic approach to curtail fuel consumption and emissions in the civil aviation sector. Under the Electrified Powertrain Flight Demonstration (EPFD) project, NASA and industry partners are raising the technical readiness, addressing integration challenges and gathering data for future standards and regulations for demonstrate Megawatt (MW) class Electrified Aircraft Propulsion (EAP) systems which can be utilized on regional turboprop or single aisle transports. With the rapid emergence of novel EAP concepts, risk reduction efforts are focused on developing the capabilities to evaluate the impacts of electrification at the conceptual design level where high variability in the EAP system architecture must be accounted for. This paper details an integrated, approach to parametric sizing of multi-MW EAP systems with the primary goal of assessing vehicle-level performance sensitivities to variations in electrical system component-level performance metrics. The focus of this work is to investigate the degree to which EAP component parameters such as specific power, efficiency, and energy density impact range and overall fuel savings.

EAP↗
NASA NTRSDate not supplied

Sizing and Performance Analysis of a MW-Class Electrified Aircraft Propulsion (Eap) System for A Parallel Hybrid Turboprop Concept

Aircraft electrification has emerged as a pivotal research and development focus in the 21st century, gaining international momentum as a strategic approach to curtail fuel consumption and emissions in the civil aviation sector. Under the Electrified Powertrain Flight Demonstration (EPFD) project, NASA and industry partners are raising the technical readiness, addressing integration challenges and gathering data for future standards and regulations for demonstrate Megawatt (MW) class Electrified Aircraft Propulsion (EAP) systems which can be utilized on regional turboprop or single aisle transports. With the rapid emergence of novel EAP concepts, risk reduction efforts are focused on developing the capabilities to evaluate the impacts of electrification at the conceptual design level where high variability in the EAP system architecture must be accounted for. This paper details an integrated, approach to parametric sizing of multi-MW EAP systems with the primary goal of assessing vehicle-level performance sensitivities to variations in electrical system component-level performance metrics. The focus of this work is to investigate the degree to which EAP component parameters such as specific power, efficiency, and energy density impact range and overall fuel savings.

EAP↗
NASA NTRS1985

Formation and detection of high latitude ionospheric irregularities

Measurements of Total Electron Content (TEC) and airglow variations show that large scale plasma patches appearing in the high-latitude ionsophere have irregular structures evidenced by the satellite phase and amplitude scintillations. Whistler waves, intense quasi-DC electric field, and atmospheric gravity waves can become potential sources of various plamsa instabilities. The role of thermal effects in generating ionospheric irregularities by these sources is discussed. Meter-scale irregularities in the ionospheric E and F regions can be excited parametrically with lower hybrid waves by intense whistler waves. Ohmic dissipation of Pedersen current in the electron gas is able to create ionospheric F region irregularities in plasma blobs or plasma patches (i.e., high ambient plasma density environment) with broad scale lengths ranging from tens of meters to a few kilometers. Through the neutral-charged particle collisions, gravity waves can excite large-scale (less than tens of kilometers) ionospheric irregularities simultaneously with forced ion acoustic modes in the E region. The large-scale ionospheric density fluctuations produced in the E region can extend subsequently alogn the earth's magnetic field to the F region and the topside ionospheric regions. These mechanisms characterized by various thermal effects can contribute additively with other processes to the formation of ionospheric irregularities in the high latitude region.

Lee, M. C.↗
NASA NTRS2010

Summary of the Fourth AIAA CFD Drag Prediction Workshop

Results from the Fourth AIAA Drag Prediction Workshop (DPW-IV) are summarized. The workshop focused on the prediction of both absolute and differential drag levels for wing-body and wing-body-horizontal-tail configurations that are representative of transonic transport air- craft. Numerical calculations are performed using industry-relevant test cases that include lift- specific flight conditions, trimmed drag polars, downwash variations, dragrises and Reynolds- number effects. Drag, lift and pitching moment predictions from numerous Reynolds-Averaged Navier-Stokes computational fluid dynamics methods are presented. Solutions are performed on structured, unstructured and hybrid grid systems. The structured-grid sets include point- matched multi-block meshes and over-set grid systems. The unstructured and hybrid grid sets are comprised of tetrahedral, pyramid, prismatic, and hexahedral elements. Effort is made to provide a high-quality and parametrically consistent family of grids for each grid type about each configuration under study. The wing-body-horizontal families are comprised of a coarse, medium and fine grid; an optional extra-fine grid augments several of the grid families. These mesh sequences are utilized to determine asymptotic grid-convergence characteristics of the solution sets, and to estimate grid-converged absolute drag levels of the wing-body-horizontal configuration using Richardson extrapolation.

Vassberg, John C.↗
NASA NTRS2016

Ice-Accretion Test Results for Three Large-Scale Swept-Wing Models in the NASA Icing Research Tunnel

Icing simulation tools and computational fluid dynamics codes are reaching levels of maturity such that they are being proposed by manufacturers for use in certification of aircraft for flight in icing conditions with increasingly less reliance on natural-icing flight testing and icing-wind-tunnel testing. Sufficient high-quality data to evaluate the performance of these tools is not currently available. The objective of this work was to generate a database of ice-accretion geometry that can be used for development and validation of icing simulation tools as well as for aerodynamic testing. Three large-scale swept wing models were built and tested at the NASA Glenn Icing Research Tunnel (IRT). The models represented the Inboard (20 percent semispan), Midspan (64 percent semispan) and Outboard stations (83 percent semispan) of a wing based upon a 65 percent scale version of the Common Research Model (CRM). The IRT models utilized a hybrid design that maintained the full-scale leading-edge geometry with a truncated afterbody and flap. The models were instrumented with surface pressure taps in order to acquire sufficient aerodynamic data to verify the hybrid model design capability to simulate the full-scale wing section. A series of ice-accretion tests were conducted over a range of total temperatures from -23.8 to -1.4 C with all other conditions held constant. The results showed the changing ice-accretion morphology from rime ice at the colder temperatures to highly 3-D scallop ice in the range of -11.2 to -6.3 C. Warmer temperatures generated highly 3-D ice accretion with glaze ice characteristics. The results indicated that the general scallop ice morphology was similar for all three models. Icing results were documented for limited parametric variations in angle of attack, drop size and cloud liquid-water content (LWC). The effect of velocity on ice accretion was documented for the Midspan and Outboard models for a limited number of test cases. The data suggest that there are morphological characteristics of glaze and scallop ice accretion on these swept-wing models that are dependent upon the velocity. This work has resulted in a large database of ice-accretion geometry on large-scale, swept-wing models.

Wing Aerodynamics↗
NASA NTRS2016

Ice-Accretion Test Results for Three Large-Scale Swept-Wing Models in the NASA Icing Research Tunnel

Icing simulation tools and computational fluid dynamics codes are reaching levels of maturity such that they are being proposed by manufacturers for use in certification of aircraft for flight in icing conditions with increasingly less reliance on natural-icing flight testing and icing-wind-tunnel testing. Sufficient high-quality data to evaluate the performance of these tools is not currently available. The objective of this work was to generate a database of ice-accretion geometry that can be used for development and validation of icing simulation tools as well as for aerodynamic testing. Three large-scale swept wing models were built and tested at the NASA Glenn Icing Research Tunnel (IRT). The models represented the Inboard (20% semispan), Midspan (64% semispan) and Outboard stations (83% semispan) of a wing based upon a 65% scale version of the Common Research Model (CRM). The IRT models utilized a hybrid design that maintained the full-scale leading-edge geometry with a truncated afterbody and flap. The models were instrumented with surface pressure taps in order to acquire sufficient aerodynamic data to verify the hybrid model design capability to simulate the full-scale wing section. A series of ice-accretion tests were conducted over a range of total temperatures from -23.8 deg C to -1.4 deg C with all other conditions held constant. The results showed the changing ice-accretion morphology from rime ice at the colder temperatures to highly 3-D scallop ice in the range of -11.2 deg C to -6.3 deg C. Warmer temperatures generated highly 3-D ice accretion with glaze ice characteristics. The results indicated that the general scallop ice morphology was similar for all three models. Icing results were documented for limited parametric variations in angle of attack, drop size and cloud liquid-water content (LWC). The effect of velocity on ice accretion was documented for the Midspan and Outboard models for a limited number of test cases. The data suggest that there are morphological characteristics of glaze and scallop ice accretion on these swept-wing models that are dependent upon the velocity. This work has resulted in a large database of ice-accretion geometry on large-scale, swept-wing models.

Wind-Tunnel Tests↗
NASA NTRS1998

A 2-D Interface Element for Coupled Analysis of Independently Modeled 3-D Finite Element Subdomains

Over the past few years, the development of the interface technology has provided an analysis framework for embedding detailed finite element models within finite element models which are less refined. This development has enabled the use of cascading substructure domains without the constraint of coincident nodes along substructure boundaries. The approach used for the interface element is based on an alternate variational principle often used in deriving hybrid finite elements. The resulting system of equations exhibits a high degree of sparsity but gives rise to a non-positive definite system which causes difficulties with many of the equation solvers in general-purpose finite element codes. Hence the global system of equations is generally solved using, a decomposition procedure with pivoting. The research reported to-date for the interface element includes the one-dimensional line interface element and two-dimensional surface interface element. Several large-scale simulations, including geometrically nonlinear problems, have been reported using the one-dimensional interface element technology; however, only limited applications are available for the surface interface element. In the applications reported to-date, the geometry of the interfaced domains exactly match each other even though the spatial discretization within each domain may be different. As such, the spatial modeling of each domain, the interface elements and the assembled system is still laborious. The present research is focused on developing a rapid modeling procedure based on a parametric interface representation of independently defined subdomains which are also independently discretized.

Kandil, Osama A.↗
NASA NTRSDate not supplied

Hybrid NEP-Chemical Vehicle and Propulsion Technology Study for Crewed Mars Missions

Nuclear Electric Propulsion (NEP) is a suite of technologies with the potential to enable crewed opposition-class missions to Mars. Each subsystem comprising an NEP system has multiple technology options that present tradeoffs in vehicle sizing and technology development risk. Multiple vehicle concepts have been studied in the past and are currently being studied at NASA. Three models have been developed to illustrate the impact of key technology parameters on overall sizing for a crewed Mars transportation vehicle. Vehicle mass required to close the mission as a function of NEP system alpha (kWe/kg) and specific impulse (Isp) is estimated with a detailed trajectory model. A power system mass model estimates alpha as a function of power and radiator mass assumption. A power conversion system thermodynamic model predicts the radiator area required to close a Brayton cycle power conversion system. Combined with the architecture mass required for mission closure, the radiator area and alpha model provide insight into how technology development may impact the mission. Our focus is on parametric sweeps of the whole design space rather than any particular point design. Results from the mission model comparing electric propulsion technology (Hall, Ion, Magnetoplasmadynamic) and both 2039 and 2042 opposition-class mission launch windows are included. The results of the study illustrate the technology parameters that can result in mission closure and illustrate where the architecture is sensitive to variations in technology performance or requirements.

Matthew Duchek↗
NASA NTRS1990

Ion Beam Heating in the Auroral Zone

Recent satellite observations at high altitudes (greater than 5000 km) in the auroral zone have shown the existence of hybrid or bimodal ion beam distributions that are evidence of both parallel and perpendicular ion acceleration. Acceleration parallel to the magnetic field is most likely due to quasi-static electric fields (double layers) which can create outflowing ion beams; since ions of different mass will have different drift speeds due to this acceleration, a plasma configuration unstable to the ion-ion two-stream acoustic mode develops. When the net drift velocity (U) between the two ion species is greater than the sound speed (C(sub 0)), the ion-ion instability has maximum growth at oblique wave propagation. To study the nonlinear effects of the ion-ion instability in terms of plasma heating, a numerical simulation parametric study has been performed. It was found that the parallel acceleration that forms the ion beams occurs on a time scale faster than ion- ion wave growth at low drifts; thus ion-ion wave growth is expected to occur primarily for higher drift speeds (U greater than C(sub 0)) which results in strong oblique heating of the ions (both hydrogen and oxygen) forming elevated ion conics (sometimes called 'bowl' distributions). Also, strong parallel electron heating in the direction of the ion beams can occur, and electrons near the top of the acceleration region may attain a net upward drift along with the elevated ion conics. Variation of the oxygen density greatly affects the ion heating due to the ion-ion instability; as the oxygen density decreases, oxygen heating increases, in agreement with observations (Collin et al., 1987). Ion-ion electrostatic wave properties and the plasma heating that results over a wide range of auroral zone parameters are included.

Schriver, David↗