Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “collision operators”

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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2017

Earth Observing System (EOS) Aqua & Aura Space Weather Effects on Operational Collision Avoidance

This presentation will describe recent EOS Aqua and Aura operational collision avoidance experience during periods of solar and geomagnetic storm activity. It will highlight challenges faced by the operations team during short-notice, high-risk predicted close approaches. The presentation will highlight the evolution of the operational collision avoidance process for the EOS Aqua and Aura missions. The presentation will highlight operational challenges that have occurred, process improvements that have been implemented and identify potential future challenges.

Operational collision avoidance↗
NASA NTRS2017

Earth Observing System (EOS) Aqua and Aura Space Weather Effects on Operational Collision Avoidance

This presentation will describe recent EOS Aqua and Aura operational collision avoidance experience during periods of solar and geomagnetic storm activity. It will highlight challenges faced by the operations team during short-notice, high-risk predicted close approaches. The presentation will highlight the evolution of the operational collision avoidance process for the EOS Aqua and Aura missions. The presentation will highlight operational challenges that have occurred, process improvements that have been implemented and identify potential future challenges.

Guit, Bill↗
NASA NTRS2015

Operational Collision Avoidance

This presentation will describe the early days of the EOS Aqua and Aura operational collision avoidance process. It will highlight EOS debris avoidance maneuvers, EOS high interest event statistic and A-Train systematic conjunctions and conclude with future challenges. This is related to earlier e-DAA (tracking number 21692) that an abstract was submitted to a different conference. Eric Moyer, ESMO Deputy Project Manager has reviewed and approved this presentation on May 6, 2015

collision avoidance↗
NASA NTRS1979

Velocity Fourier transform solution of a model collision operator

A simpler technique than those introduced by Lenard and Bernstein (1958), and Dougherty (1964) is employed to obtain the perturbed species density from a specified kinetic equation for a plasma in a given uniform magnetic field. The technique is a generalization of the velocity-Fourier transform method employed by Karpman (1967) for B sub 0 identical to zero, and relies on the fact that in transform space the model collision operator, used to obtain the kinetic equation for waves in a magnetized plasma, contains only first derivatives. The technique is illustrated by evaluating the perturbed density of an arbitrary species.

Catto, P. J.↗
NASA NTRS2012

Kinetic Description of Ionospheric Outflows Based on the Exact Form of Fokker-Planck Collision Operator: Electrons

We present the results of a finite difference implementation of the kinetic Fokker-Planck model with an exact form of the nonlinear collisional operator, The model is time dependent and three-dimensional; one spatial dimension and two in velocity space. The spatial dimension is aligned with the local magnetic field, and the velocity space is defined by the magnitude of the velocity and the cosine of pitch angle. An important new feature of model, the concept of integration along the particle trajectories, is discussed in detail. Integration along the trajectories combined with the operator time splitting technique results in a solution scheme which accurately accounts for both the fast convection of the particles along the magnetic field lines and relatively slow collisional process. We present several tests of the model's performance and also discuss simulation results of the evolution of the plasma distribution for realistic conditions in Earth's plasmasphere under different scenarios.

Khazanov, George V.↗
NASA NTRS1987

Collision detection for spacecraft proximity operations

Collision Detection for Spacecraft Proximity Operations This thesis describes the development of a new collision detection algorithm to be used when two spacecraft are operating in the same vicinity. The two spacecraft are modelled as unions of convex polyhedra, where the polyhedron resulting from the union may be either convex or nonconvex. The relative motion of the two spacecraft is assumed to be such that one vehicle is moving with constant linear and angular velocity with respect to the other. The algorithm determines if a collision is possible and, if so, predicts the time when the collision will take place. The theoretical basis for the new collision detection algorithm is the C-function formulation of the configuration space approach recently introduced by researchers in robotics. Three different types of C-functions are defined that model the contacts between the vertices, edges, and faces of the polyhedra representing the two spacecraft. These C-functions are used to formulate three "collision" conditions. The first of these conditions limits the points representing potential collisions to the zeros of the C-functions. The new algorithm is fundamentally a search for the smallest zero of any C-function that satisfies the second and third collision conditions. The C-functions are shown to be transcendental functions of time for the assumed trajectory of the moving spacecraft. The zeros of these functions cannot be expressed in dosed form. Therefore, numerical search procedures are developed to find aLl of the zeros of a C-function in specified bounded intervals of time. These bounded intervals of time are found by examining the second and third collision conditions. The capabilities of the new algorithm are demonstrated for several example cases. These include examples of collisions determined by zeros of each of the three different types of C-functions. In addition to predicting the time of first contact of the polyhedra, the algorithm identifies the features of the two polyhedra that are touching at this time. The new collision detection algorithm is the first such algorithm that is capable of solving the collision detection problem exactly for the case where the moving object has constant linear and angular velocities. This is a significant improvement on previous collision detection algorithms described in the literature. In particular, the ability to handle constant angular velocity represents a more realistic type of rotational motion than those which have been used in other algorithms.

Robin M Vaughan↗
NASA NTRS1983

Thermal electron heating rate: A derivation

The thermal electron heating rate is an important heat source term in the ionospheric electron energy balance equation, representing heating by photoelectrons or by precipitating higher energy electrons. A formula for the thermal electron heating rate is derived from the kinetic equation using the electron-electron collision operator as given by the unified theory of Kihara and Aono. This collision operator includes collective interactions to produce a finite collision operator with an exact Coulomb logarithm term. The derived heating rate O(e) is the sum of three terms, O(e) = O(p) + S + O(int), which are respectively: (1) primary electron production term giving the heating from newly created electrons that have not yet suffered collisions with the ambient electrons; (2) a heating term evaluated on the energy surface m(e)/2 = E(T) at the transition between Maxwellian and tail electrons at E(T); and (3) the integral term representing heating of Maxwellian electrons by energetic tail electrons at energies ET. Published ionospheric electron temperature studies used only the integral term O(int) with differing lower integration limits. Use of the incomplete heating rate could lead to erroneous conclusions regarding electron heat balance, since O(e) is greater than O(int) by as much as a factor of two.

Hoegy, W. R.↗
NASA NTRS1984

Thermal electron heating rate - A derivation

The thermal electron heating rate is an important heat source term in the ionospheric electron energy balance equation, representing heating by photoelectrons or by precipitating higher energy electrons. A formula for the thermal electron heating rate is derived from the kinetic equation using the electron-electron collision operator as given by the unified theory of Kihara and Aono. This collision operator includes collective interactions to produce a finite collision operator with an exact Coulomb logarithm term. The derived heating rate O(e) is the sum of three terms, O(e) = O(P) + S + O(int), which are respectively: (1) primary electron production term giving the heating from newly created electrons that have not yet suffered collisions with the ambient electrons; (2) a heating term evaluated on the energy surface m(e)/2 = E(T) at the transition between Maxwellian and tail electrons at E(T); and (3) the integral term representing heating of Maxwellian electrons by eneegetic tail electrons at energies ET. Published ionospheric electron temperature studies used only the integral term O(int) with differing lower integration limits. Use of the incomplete heating rate could lead to erroneous conclusions regarding electron heat balance, since O(e) is greater than O(int) by as much as a factor of two. Previously announced in STAR as N84-15941

Hoegy, W. R.↗
NASA NTRS1972

Shock-wave structure using nonlinear model Boltzmann equations.

The structure of strong plane shock waves in a perfect monatomic gas was studied using four nonlinear models of the Boltzmann equation. The models involved the use of a simplified collision operator with velocity-independent collision frequency, in place of the complicated Boltzmann collision operator. The models employed were the BGK and ellipsoidal models developed by earlier authors, and the polynomial and trimodal gain function models developed during the work. An exact set of moment equations was derived for the density, velocity, temperature, viscous stress, and heat flux within the shock. This set was reduced to a pair of coupled nonlinear integral equations and solved using specially adapted numerical techniques. A new and simple Gauss-Seidel iteration was developed during the work and found to be as efficient as the best earlier iteration methods.

Segal, B. M.↗
NASA NTRS1976

A strictly Markovian expansion for plasma turbulence theory

The collision operator that appears in the equation of motion for a particle distribution function that was averaged over an ensemble of random Hamiltonians is non-Markovian. It is non-Markovian in that it involves a propagated integral over the past history of the ensemble averaged distribution function. All formal expansions of this nonlinear collision operator to date preserve this non-Markovian character term by term yielding an integro-differential equation that must be converted to a diffusion equation by an additional approximation. An expansion is derived for the collision operator that is strictly Markovian to any finite order and yields a diffusion equation as the lowest nontrivial order. The validity of this expansion is seen to be the same as that of the standard quasilinear expansion.

Jones, F. C.↗
NASA NTRS1978

A strictly Markovian expansion for plasma turbulence theory

The collision operator that appears in the equation of motion for a particle distribution function that has been averaged over an ensemble of random Hamiltonians is non-Markovian. It is non-Markovian in that it involves a propagated integral over the past history of the ensemble averaged distribution function. All formal expansions of this nonlinear collision operator to date preserve this non-Markovian character term by term yielding an integro-differential equation that must be converted to a diffusion equation by an additional approximation. In this note we derive an expansion of the collision operator that is strictly Markovian to any finite order and yields a diffusion equation as the lowest non-trivial order. The validity of this expansion is seen to be the same as that of the standard quasi-linear expansion.

Jones, F. C.↗
NASA NTRS2007

Mars Reconnaissance Orbiter Aerobraking Daily Operations and Collision Avoidance

The Mars Reconnaissance Orbiter reached Mars on March 10, 2006 and performed a Mars orbit insertion maneuver of 1 km/s to enter into a large elliptical orbit. Three weeks later, aerobraking operations began and lasted about five months. Aerobraking utilized the atmospheric drag to reduce the large elliptical orbit into a smaller, near circular orbit. At the time of MRO aerobraking, there were three other operational spacecraft orbiting Mars and the navigation team had to minimize the possibility of a collision. This paper describes the daily operations of the MRO navigation team during this time as well as the collision avoidance strategy development and implementation.

Long, Stacia M.↗
NASA NTRS2013

Discrete Kinetic Eigenmode Spectra of Electron Plasma Oscillations in Weakly Collisional Plasma: A Numerical Study

It has been demonstrated that in the presence of weak collisions, described by the Lenard-Bernstein collision operator, the Landau-damped solutions become true eigenmodes of the system and constitute a complete set. We present numerical results from an Eulerian Vlasov code that incorporates the Lenard-Bernstein collision operator. The effect of the collisions on the numerical recursion phenomenon seen in Vlasov codes is discussed. The code is benchmarked against exact linear eigenmode solutions in the presence of weak collisions, and a spectrum of Landau-damped solutions is determined within the limits of numerical resolution. Tests of the orthogonality and the completeness relation are presented.

Kinetic Eigenmode Spectra↗
NASA NTRS1979

A theory of local and global processes which affect solar wind electrons. I - The origin of typical 1 AU velocity distribution functions - Steady state theory

A kinetic theory for the velocity distribution of solar wind electrons which illustrates the global and local properties of the solar wind expansion is proposed. By means of the Boltzmann equation with the Krook collision operator accounting for Coulomb collisions, it is found that Coulomb collisions determine the population and shape of the electron distribution function in both the thermal and suprathermal energy regimes. For suprathermal electrons, the cumulative effects of Coulomb interactions are shown to take place on the scale of the heliosphere itself, whereas the Coulomb interactions of thermal electrons occur on a local scale near the point of observation (1 AU). The bifurcation of the electron distribution between thermal and suprathermal electrons is localized to the deep solar corona (1 to 10 solar radii).

Scudder, J. D.↗