Dissertations / Theses on the topic 'Orbital Collisions'

This thesis will present the effects of the orbital debris evolution in two key areas: the geosynchronous disposal orbit regime known as “graveyard” and the two geopotential wells found in 105◦ W and 75◦ E longitude bins. After developing a GEO specific orbit propagator for NASA Johnson Space Center’s Orbital Debris Of- fice, collisions were simulated throughout these regimes using a low velocity breakup model. This model considered the effects of perturbations particularly non-spherical Earth effects (specifically sectorial and zonal harmonics), lunar effects, third body effects and solar radiation pressure effects. The results show that CDPROP does well in simulating the presence of the Eastern and Western geopotential wells, as well as catching drifting GEO objects. It does not do as well in catching East-West trapped objects. Three collision test cases were then simulated in graveyard and the East and West geopotential wells.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics; and, (S.M. in Technology and Policy)--Massachusetts Institute of Technology, Engineering Systems Division, Technology and Policy Program, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 155-161).
Extravehicular Activity (EVA) spacesuits are a key enabling technology which allow astronauts to survive and work in the harsh environment of space. Of the entire spacesuit, the gloves may perhaps be considered the most difficult engineering design issue. A significant number of astronauts sustain hand and shoulder injuries during extravehicular activity (EVA) training and operations. In extreme cases these injuries lead to fingernail delamination (onycholysis) or rotator cuff tears and require medical or surgical intervention. In an effort to better understand the causal mechanisms of injury, a study consisting of modeling, statistical and experimental analyses was performed in section I of this thesis. A cursory musculoskeletal modeling tool was developed for use in comparing various spacesuit hard upper torso designs. The modeling effort focuses on optimizing comfort and range of motion of the shoulder joint within the suit. The statistical analysis investigated correlations between the anthropometrics of the hand and susceptibility to injury. A database of 192 male crewmembers' injury records and anthropometrics was sourced from NASA's Johnson Space Center. Hand circumference and width of the metacarpophalangeal (MCP) joint were found to be significantly associated with injuries by the Kruskal-Wallis test. Experimental testing was conducted to characterize skin blood flow and contact pressure inside the glove. This was done as part of NASA's effort to evaluate a hypothesis that fingernail delamination is caused by decreasing blood flow in the finger tips due to compression of the skin inside the extravehicular mobility unit (EMU) glove. The initial investigation consisted of a series of skin blood flow and contact pressure tests of the bare finger, and showed that blood flow decreased to approximately 60% of baseline value with increasing force, however, this occurred more rapidly for finger pads (4N) than for finger tips (ION). A gripping test of a pressure bulb using the bare hand was also performed at a moderate pressure of 13.33kPa (100mmHg) and at a high pressure of 26.66kPa (200mmHg), and showed that blood flow decreased 50% and 45%, respectively. Excessive hyperperfusion was observed for all tests following contact force or pressure, which may also contribute to the onset of delamination. Preliminary data from gripping tests inside the EMU glove in a hypobaric chamber at NASA's Johnson Space Center show that skin blood flow decreased by 45% and 40% when gripping at 3 moderate and high pressures, respectively. These tests show that finger skin blood flow is significantly altered by contact force/pressure, and that occlusion is more sensitive when it is applied to the finger pad than the finger tip. Our results indicate that the pressure on the finger pads required to articulate stiff gloves is more likely to impact blood flow than the pressure on the fingertips associated with tight or ill-fitting gloves. Improving the flexibility of the gloves will therefore not only benefit operational performance, but may also be an effective approach in reducing the incidence of finger injury. Space Policy Abstract EVA injury is only one of many dangers astronauts face in the extreme environment of space. Orbital debris presents a significant threat to astronaut safety and is a growing cause of concern. Since the dawn of satellites in the early 1950's, space debris from intentionally exploded spacecraft, dead satellites, and on-orbit collisions has significantly increased and currently outnumbers operational space hardware. Adding to this phenomenon, the advent of commercial spaceflight and the recent space activities in China and India to establish themselves as spacefairing nations are bound to accelerate the rate of space debris accumulating in low Earth orbit, thus, exacerbating the problem. The policies regulating orbital debris were drafted in the 1960s and 1970s and fail to effectively address the dynamic nature of the debris problem. These policies are not legally enforced under international law and implementation is entirely voluntary. Space debris is a relevant issue in international space cooperation. Unless regulated, some projections indicate space debris will reach a point of critical density, after which the debris will grow exponentially, as more fragments are generated by collisions than are removed by atmospheric drag. Space debris proliferation negatively impacts human spaceflight safety, presents a hazard to orbiting space assets, and may lead to portions of near-Earth orbit becoming inaccessible, thus limiting mission operations. The aim of this research effort was to review current international space policy, legislation and mitigation strategies in light of two recent orbital collision episodes. The first is the February 2009 collision between a defunct Russian Cosmos spacecraft and a commercial Iridium satellite. The second is China's display of technological prowess during the January 2007 intentional demolition of its inactive Fengyun-IC weather satellite using a SC-19 antisatellite (ASAT) missile. In each case the stakeholders, politics, policies, and consequences of the collision are analyzed. The results of this analysis as well as recommendations for alternative mitigation and regulatory strategies are presented.
by Roedolph A. Opperman.
S.M.in Technology and Policy
S.M.

Cette thèse présente une théorie non perturbative pour décrire les processus multi-électroniques intervenant au cours des collisions ion-atome. Le traitement choisi est semiclassique en ce sens que le mouvement relatif cible-projectile est décrit par des trajectoires classiques (mouvement rectiligne uniforme), tandis que la dynamique électronique est traitée quantiquement, en résolvant de manière non perturbative l’équation de Schrödinger dépendante du temps. Cette approche théorique a été codée au cours de la thèse dans une nouvelle version du code informatique à deux électrons actifs et mise en œuvre à l'étude de plusieurs systèmes de collision. Outre le développement long et complexe et les tests du code, les trois dernières années ont été spécialement consacrées à la compréhension de la physique d'événements spécifiques de diffusion de particules lourdes. Nous avons entrepris l’étude de trois types de systèmes de collision : par ordre d’apparition dans cette thèse, (i) collisions ion-ion faiblement chargé avec une extrême importance de la corrélation électronique (H+ - H-), (ii) collisions entre projectiles multiplement chargés et atome (C4+ - He) et (iii) collisions He+ - He avec un traitement très original prenant en compte des trois électrons dans la dynamique. Le choix de ces systèmes était guidé sur des systèmes benchmark pour lesquels des résultats expérimentaux et théoriques étaient disponibles, et présentant des questions ouvertes, liées par exemple à de forts désaccords entre les données existantes.Systématiquement, nous avons essayé de produire des résultats avec une convergence contrôlée permettant des interprétations physiques originales
This thesis presents a non perturbative theory to describe multi-electronic processes occurring in the course of ion-atom collisions. The treatment is semiclassical in that the relative target-projectile motion is described by classical straight-line constant velocity trajectories, while the electronic dynamics is treated quantum mechanically, by solving non perturbatively the time-dependent Schödinger equation. The treatment has been implemented in a new version of two-active-electron computer code. Besides the long and complex development and tests of the code, the last three years have been especially devoted to understanding of the physics of specific heavy particle scattering events. We have undertaken the study of three collision systems with various features: (i) low charge ion-ion collisions with an extreme importance of electronic correlation (H+ + H− collisions), (ii) multiply charged projectile-atom collisions (C4+ + He) and (iii) He+ + He collisions with the dynamical treatment of the three electrons. Our guideline was always to target systems for which experimental and theoretical results were available (at least in some energy domain), with still open questions, related, for example, to strong disagreement between the various data. We have tried as much as our computing resources and allowed it to produce results with controlled convergence. These investigations were carried out in a very wide, up to three decades, energy domain with same collision description (i.e. same basis sets), which brought continuity and coherence on the predictions and the interpretations of the results and of the underlying mechanisms giving rise to the processes considered

This thesis investigates the orbital debris evolution in the geosynchronous disposal orbit regime and within geosynchronous orbits effected by the geopotential wells. A propagator is developed for the accurate simulation of GEO specific orbits and the required perturbations are determined and described. Collisions are then simulated in the selected regimes using a low velocity breakup model derived from the NASA EVOLVE breakup model. The simulations described in this thesis consider a set of perturbations including the geopotential, solar and lunar gravity, and solar radiation pressure forces. This thesis is based on a prior paper and additionally seeks to address an issue in simulating East-West trapped objects. The results show that this propagator successfully simulates the presence of all wells and the East-West entrapment, and the required perturbations are outlined. Five collision test cases were simulated, one for each type of entrapment and an additional for the disposal orbit.

The main objective of this dissertation is the study of the ejection-collision (EC) orbits in the circular and planar Restricted Three Body Problem (RTBP from now on). In particular, we will focus on the analytical and numerical study of a very specific type of EC orbits, that we denote as n-EC orbits. An n-EC orbit is an orbit such that the particle ejects from one primary and reaches n times a relative maximum in the distance with respect to the primary from which it ejected before colliding with it. In this way, we will study numerically in depth this kind of orbits and we will show analytically that for a sufficiently large value of the Jacobi constant (for which we will give an expression in terms of the mass parameter and the value of n) there exist exactly four n-EC orbits with well-defined characteristics. These results generalize and improve the previous results for the particular case of n=1, and we will see that they can be easily extrapolated to the Hill problem. Besides, we will observe numerically that the evolution of these four original families of n-EC orbits present a very rich dynamics.It is well-known that the system that defines the motion of the particle is not well defined at the points where the primaries are located. For this reason, we have used two different techniques to regularize the collision, the McGehee regularization and the Levi-Civita regularization. Thus, in this dissertation we have analyzed the advantages and disadvantages of each regularization and the different methods that can be used to detect collisions. Since this dissertation will be mainly focused on values of the Jacobi constant greater than those associated to the equilibrium point L1, these two local regularizations will be enough. For less restrictive values of the Jacobi constant we will see that there exist other global regularizations or alternatively, we can simply work with local regularizations in a neighbourhood of each primary.On the other hand, from the numerical point of view we have analyzed the global behaviour of the ejection orbits in the RTBP. We have studied the relation between the family of Lyapunov periodic orbits around the equilibrium point L1 and the ejection orbits for values of the Jacobi constant such that the associated Hill regions only allow a bounded motion for these orbits. In particular, we have seen that a chaotic infinity of heteroclinic connections between one primary and the Lyapunov periodic orbits around the equilibrium point L1 are obtained. As a consequence a chaotic infinity of ejection-collision orbits is also derived. Besides, we will see that we can construct colour diagrams that allow to describe the global dynamics of the ejection orbits given a range of time. These colour diagrams provide a very precise understanding of the dynamics of these orbits.Finally, we have made a first exploration of the spatial case of the circular restricted three body problem (RTBP 3D). In this first approach we have not used the classical Kustaanheimo–Stiefel regularization, instead we have decided to use a 3D version of the McGehee regularization. This presents some problems that we have analyzed and addressed,
L'objectiu principal d'aquesta dissertació és l'estudi de les òrbites d'ejecció-col·lisió (EC) al problema restringit de tres cossos circular i pla (RTBP a partir d'ara). En particular, ens centrarem en l'estudi analític i numèric d'unes òrbites d'EC molt particulars, a les quals hem anomenat òrbites de n-EC. Aquestes òrbites de n-EC, són òrbites tal que la partícula ejecta d'un primari, assoleix n màxims en la distància respecte al primari del qual han ejectat per a continuació tornar a col·lisionar amb ell. D'aquesta forma numèricament estudiarem en profunditat aquest tipus d'òrbites i analíticament demostrarem que per un valor prou gran de la constant de Jacobi (per la qual donarem una expressió en termes del paràmetre de masses i el valor de n) existeixen exactament quatre òrbites de n-EC amb unes característiques ben determinades. Aquests resultats generalitzen i milloren els resultats previs pel cas particular de n=1, i veurem que es poden extrapolar fàcilment al problema de Hill. A més, numèricament veurem que l'evolució d'aquestes quatre famílies d'òrbites de n-EC originals presenta una dinàmica molt rica.És ben sabut, que el sistema que defineix el moviment de la partícula no està ben definit als punts on es troben situats els primaris. Per aquest motiu hem utilitzat dues tècniques de regularització de la col·lisió, la regularització de McGehee i la regularització de Levi-Civita. D'aquesta forma, en aquesta memòria hem analitzat els avantatges i els inconvenients de cada regularització, i els diferents mètodes que es poden utilitzar per detectar col·lisions. Com que gran part d'aquesta memòria es focalitzarà en valors de la constant de Jacobi més grans que l'associat al punt d'equilibri L1 aquestes dues regularitzacions de caràcter local seran suficients. Per valors menys restrictius de la constant de Jacobi veurem que existeixen altres regularitzacions de caràcter global o que simplement podem treballar amb regularitzacions locals a l'entorn de cada primari.Per altra banda, numèricament hem analitzat el comportament global de les òrbites d'ejecció al RTBP. Hem estudiat la relació entre la família de les òrbites periòdiques de Lyapunov al voltant del punt d'equilibri lineal L1 i les òrbites d'ejecció que es duu a terme al rang de valors de la constant de Jacobi tals que les regions de Hill associades només permeten un moviment fitat per a aquestes òrbites. En particular, hem vist que s'obté una infinitat caòtica de connexions heteroclíniques entre un primari i l'òrbita periòdica de Lyapunov al voltant del punt d'equilibri lineal L1. Com a conseqüència, també es deriva una infinitat caòtica d'òrbites d'ejecció-col·lisió. A més, veurem que podem construir uns diagrames de color que ens permeten descriure la dinàmica global de les òrbites d'ejecció donat un interval de temps. Aquests diagrames proporcionen una comprensió molt precisa de la dinàmica d'aquestes òrbites.Finalment, hem fet una primera exploració del cas espacial del problema restringit de tres cossos circular (RTBP 3D). En aquesta primera aproximació no hem utilitzat la clàssica regularització de Kustaanheimo-Stiefel i hem decidit utilitzar una versió 3D de la regularització de McGehee. Això presenta alguns problemes, que hem analitzat i abordat, però aquesta aproximació és suficient per obtenir un primer resultat numèric sobre òrbites de 1-EC i per il·lustrar la complexitat del cas 3D.
Matemàtica aplicada

Many satellites have an orbit of reference defined according to their mission. The satellites need therefore to navigate as close as possible to their reference orbit. However, due to external forces, the trajectory of a satellite is disturbed and actions need to be taken. For now, the trajectories of the satellites are monitored by the operations of satellites department which gives appropriate instructions of navigation to the satellites. These steps require a certain amount of time and involvement which could be used for other purposes. A solution could be to make the satellites autonomous. The satellites would take their own decisions depending on their trajectory. The navigation control would be therefore much more efficient, precise and quicker. Besides, the autonomous orbit control could be coupled with an avoidance collision risk management. The satellites would decide themselves if an avoidance maneuver needs to be considered. The alerts of collisions would be given by the ground segment. In order to advance in this progress, this internship enables to analyse the feasibility of the implementation of the two concepts by testing them on an experiments satellite. To do so, tests plans were defined, tests procedures were executed and post-treatment tools were developed for analysing the results of the tests. Critical computational cases were considered as well. The tests were executed in real operations conditions.
Många satelliter har en referensbana definierad enligt deras uppdrag. Satelliterna behöver därför navigera så nära deras referensbana som möjligt. På grund av externa krafter störs dock satellitbanan och åtgärder måste vidtas. För närvarande övervakas satellitbanorna av satellitavdelningar på marken vilka ger lämpliga instruktioner för navigering till satelliterna. Dessa steg kräver en tid och engagemang som skulle kunna användas för andra ändamål. En lösning är att göra satelliterna autonoma. Satelliterna skulle då kunna ta sina egna beslut beroende på deras bana. Navigeringskontrollen skulle därför vara mycket mer effektiv, exakt och snabbare. Dessutom kan den autonoma banregleringen kopplas till riskhantering för undvikande av kollision med rymdskrot och andra satelliter. Satelliterna skulle själva avgöra om en undvikande manöver måste övervägas. Varningar om kollisioner skulle ges av marksegmentet. För att gå vidare i denna utveckling analyserar detta arbete genomförbarheten av implementeringen av olika koncept för undanmanövrar genom att testa dem på en experimentsatellit. För att göra detta definierades testplaner, testprocedurer utfördes och efterbehandlingsverktyg utvecklades för analys av testresultaten. Kritiska beräkningsfall togs fram. Testerna utfördes under verkliga driftsförhållanden.

Vikram Sarabhai Space Centre,Trivandrum
In the space surrounding the earth there are two major regions where orbital debris causes concern. They are the Low Earth Orbits (LEO) up to about 2000 km, and Geosynchronous Orbits (GEO) at an altitude of around 36000 km. The impact of the debris accumulations are in principle the same in the two regions; nevertheless they require different approaches and solutions, due to the fact that the perturbations in the orbital decay due to atmospheric drag effects predominates in LEO, gravitational forces including earth’s oblateness and luni solar effects dominating in GEO are different in these two regions. In LEO it is generally known that the debris population dominates even the natural meteoroid population for object sizes 1 mm and larger. This thesis focuses the study mainly in the LEO region. Since the first satellite breakup in 1961 up to 01 January 2003 more than 180 spacecraft and rocket bodies have been known to fragment in orbit. The resulting debris fragments constitute nearly 40% of the 9000 or more of the presently tracked and catalogued objects by USSPACECOM. The catalogued fragment count does not include the much more numerous fragments, which are too small to be detected from ground. Hence in order to describe the trackable orbital debris environment, it is important to develop mathematical models to simulate the trackable fragments and later expand it to untrackable objects. Apart from the need to better characterize the orbital debris environment down to sub millimeter particles, there is also a pressing necessity of simulation tools able to model in a realistic way the long term evolution of space debris, to highlight areas, which require further investigations, and to study the actual mitigation effects of space policy measures. The present thesis has provided newer perspectives for five major issues in space debris modeling studies. The issues are (i) breakup modeling, (ii) environment modeling, (iii) evolution of the debris environment, (iv) collision probability analysis and (v) reentry prediction. The Chapter 1 briefly describes an overview of space debris environment and the issues associated with the growing space debris populations. A literature survey of important earlier work carried out regarding the above mentioned five issues are provided in the Chapter 2. The new contributions of the thesis commence from Chapter 3. The Chapter 3 proposes a new breakup model to simulate the creation of debris objects by explosion in LEO named “A Semi Stochastic Environment Modeling for Breakup in LEO” (ASSEMBLE). This model is based on a study of the characteristics of the fragments from on orbit breakups as provided in the TLE sets for the INDIAN PSLV-TES mission spent upper stage breakup. It turned out that based on the physical mechanisms in the breakup process the apogee, perigee heights (limited by the breakup altitude) closely fit suitable Laplace distributions and the eccentricity follows a lognormal distribution. The location parameters of these depend on the orbit of the parent body at the time of breakup and their scale parameters on the intensity of explosion. The distribution of the ballistic coefficient in the catalogue was also found to follow a lognormal distribution. These observations were used to arrive at the proper physical, aerodynamic, and orbital characteristics of the fragments. Subsequently it has been applied as an inverse problem to simulate and further validate it based on some more typical well known historical on orbit fragmentation events. All the simulated results compare quite well with the observations both at the time of breakup and at a later epoch. This model is called semi stochastic in nature since the size and mass characteristics have to be obtained from empirical relations and is capable of simulating the complete scenario of the breakup. A new stochastic environment model of the debris scenario in LEO that is simple and impressionistic in nature named SIMPLE is proposed in Chapter 4. Firstly among the orbital debris, the distribution of the orbital elements namely altitude, perigee height, eccentricity and the ballistic coefficient values for TLE sets of data in each of the years were analyzed to arrive at their characteristic probability distributions. It is observed that the altitude distribution for the number of fragments exhibits peaks and it turned out that such a feature can be best modeled with a tertiary mixture of Laplace distributions with eight parameters. It was noticed that no statistically significant variations could be observed for the parameters across the years. Hence it is concluded that the probability density function of the altitude distribution of the debris objects has some kind of equilibrium and it follows a three component mixture of Laplace distributions. For the eccentricity ‘e’ and the ballistic parameter ‘B’ values the present analysis showed that they could be acceptably quite well fitted by Lognormal distributions with two parameters. In the case of eccentricity also the describing parameter values do not vary much across the years. But for the parameters of the B distribution there is some trend across the years which perhaps may be attributed to causes such as decay effect, miniaturization of space systems and even the uncertainty in the measurement data of B. However in the absence of definitive cause that can be attributed for the variation across the years, it turns out to be best to have the most recent value as the model value. Lastly the same kind of analysis has also been carried out with respect to the various inclination bands. Here the orbital parameters are analyzed with respect to the inclination bands as is done in ORDEM (Kessler et al 1997, Liou et al 2001) for near circular orbits in LEO. The five inclination bands considered here are 0-36 deg (in ORDEM they consider 19-36 deg, and did not consider 0-19 deg), 36-61 deg, 61-73 deg, 73-91 deg and 91- 180 deg, and corresponding to each band, the altitude, eccentricity and B values were modeled. It is found that the third band shows the models with single Laplace distribution for altitude and Lognormal for eccentricity and B fit quite well. The altitude of other bands is modeled using tertiary mixture of Laplace distributions, with the ‘e’ and ‘B’ following once again a Lognormal distribution. The number of parameter values in SIMPLE is, in general, just 8 for each description of altitude or perigee distributions whereas in ORDEM96 it is more. The present SIMPLE model captures closely all the peak densities without losing the accuracy at other altitudes. The Chapter 5 treats the evolution of the debris objects generated by on orbit breakup. A novel innovative approach based on the propagation of an equivalent fragment in a three dimensional bin of semi major axis, eccentricity, and the ballistic coefficient (a, e, B) together with a constant gain Kalman filter technique is described in this chapter. This new approach propagates the number density in a bin of ‘a’ and ‘e’ rapidly and accurately without propagating each and every of the space debris objects in the above bin. It is able to assimilate the information from other breakups as well with the passage of time. Further this approach expands the scenario to provide suitable equivalent ballistic coefficient values for the conglomeration of the fragments in the various bins. The heart of the technique is to use a constant Kalman gain filter, which is optimal to track the dynamically evolving fragment scenario and further expand the scenario to provide time varying equivalent ballistic coefficients for the various bins. In the next chapter 6 a new approach for the collision probability assessment utilizing the closed form solution of Wiesel (1989) by the way of a three dimensional look up table, which takes only air drag effect and an exponential model of the atmosphere, is presented. This approach can serve as a reference collision probability assessment tool for LEO debris cloud environment. This approach takes into account the dynamical behavior of the debris objects propagation and the model utilizes a simple propagation for quick assessment of collision probability. This chapter also brings out a comparison of presently available collision probability assessment algorithms based on their complexities, application areas and sample space on which they operate. Further the quantitative assessment of the collision probability estimates between different presently available methods is carried out and the obtained collision probabilities are match qualitatively. The Chapter 7 utilizes once again the efficient and robust constant Kalman gain filter approach that is able to handle the many uncertain, variable, and complex features existing in the scenario to predict the reentry time of the risk objects. The constant gain obtained by using only a simple orbit propagator by considering drag alone is capable of handling the other modeling errors in a real life situation. A detailed validation of the approach was carried out based on a few recently reentered objects and comparison of the results with the predictions of other agencies during IADC reentry campaigns are also presented. The final Chapter 8 provides the conclusions based on the present work carried together with suggestions for future efforts needed in the study of space debris. Also the application of the techniques evolved in the present work to other areas such as atmospheric data assimilation and forecasting have also been suggested.

We exhibit multiple periodic, collision-based orbits of the Newtonian n-body problem. Many of these orbits feature regularizable collisions between the masses. We demonstrate existence of the periodic orbits after performing the appropriate regularization. Stability, including linear stability, for the orbits is then computed using a technique due to Roberts. We point out other interesting features of the orbits as appropriate. When applicable, the results are extended to a broader family of orbits with similar behavior.

Many topics in planetary studies demand an estimate of the collision probability of two objects moving on nearly Keplerian orbits. In the classic works of Opik and Wetherill, the collision probability was derived by linearizing the motion near the collision points, and there is now a vast amount of literature using their method. We present here a simpler and more physically motivated derivation for non-tangential collisions in Keplerian orbits, as well as for tangential collisions that were not previously considered. Our formulas have the added advantage of being manifestly symmetric in the parameters of the two colliding bodies. In common with the Opik-Wetherill treatments, we linearize the motion of the bodies in the vicinity of the point of orbit intersection (or near the points of minimum distance between the two orbits) and assume a uniform distribution of impact parameter within the collision radius. We point out that the linear approximation leads to singular results for the case of tangential encounters. We regularize this singularity by use of a parabolic approximation of the motion in the vicinity of a tangential encounter.

Cette thèse traite de l'évitement de collision entre un engin spatial opérationnel, appelé objet primaire, et un débris orbital, dit secondaire. Ces travaux concernent aussi bien la question de l'estimation du risque pour une paire d'objets sphériques que celle du calcul d'un plan de manoeuvres d'évitement pour le primaire. Pour ce qui est du premier point, sous certaines hypothèses, la probabilité de collision s'exprime comme l'intégrale d'une fonction gaussienne sur une boule euclidienne, en dimension deux ou trois. On en propose ici une nouvelle méthode de calcul, basée sur les théories de la transformée de Laplace et des fonctions holonomes. En ce qui concerne le calcul de manoeuvres de propulsion, différentes méthodes sont développées en fonction du modèle considéré. En toute généralité, le problème peut être formulé dans le cadre de l'optimisation sous contrainte probabiliste et s'avère difficile à résoudre. Dans le cas d'un mouvement considéré comme relatif rectiligne, l'approche par scénarios se prête bien au problème et permet d'obtenir des solutions admissibles. Concernant les rapprochements lents, une linéarisation de la dynamique des objets et un recouvrement polyédral de l'objet combiné sont à la base de la construction d'un problème de substitution. Deux approches sont proposées pour sa résolution : une première directe et une seconde par sélection du risque. Enfin, la question du calcul de manoeuvres de proximité en consommation optimale et temps fixé, sans contrainte d'évitement, est abordée. Par l'intermédiaire de la théorie du vecteur efficacité, la solution analytique est obtenue pour la partie hors-plan de la dynamique képlérienne linéarisée
This thesis is about collision avoidance for a pair of spherical orbiting objects. The primary object - the operational satellite - is active in the sense that it can use its thrusters to change its trajectory, while the secondary object is a space debris that cannot be controlled in any way. Onground radars or other means allow to foresee a conjunction involving an operational space craft,leading in the production of a collision alert. The latter contains statistical data on the position and velocity of the two objects, enabling for the construction of a probabilistic collision model.The work is divided in two parts : the computation of collision probabilities and the design of maneuvers to lower the collision risk. In the first part, two kinds of probabilities - that can be written as integrals of a Gaussian distribution over an Euclidean ball in 2 and 3 dimensions -are expanded in convergent power series with positive terms. It is done using the theories of Laplace transform and Definite functions. In the second part, the question of collision avoidance is formulated as a chance-constrained optimization problem. Depending on the collision model, namely short or long-term encounters, it is respectively tackled via the scenario approach or relaxed using polyhedral collision sets. For the latter, two methods are proposed. The first one directly tackles the joint chance constraints while the second uses another relaxation called risk selection to obtain a mixed-integer program. Additionaly, the solution to the problem of fixed-time fuel minimizing out-of-plane proximity maneuvers is derived. This optimal control problem is solved via the primer vector theory

Cette thèse généralise au problème spatial dans le cas lunaire les études sur diverses familles de mouvements quasi-périodiques dans le problème plan des trois corps. En tronquant au premier ordre non trivial le développement en puissances du rapport des demi grands axes de la fonction perturbatrice moyennée sur les angles rapides, on obtient un système complètement intégrable qui peut servir de première approximation pour le système initial. C'est le système quadrupolaire, découvert par Harrington. Dans un article classique, Lidov et Ziglin ont étudié la dynamique de ce système. Nous commençons par établir l'existence de solutions quasi-périodiques du problème spatial des trois corps en appliquant les théorèmes de KAM à ce système. Nous montrons ensuite l'existence de familles de solutions que nous appelons solutions quasi-périodiques de quasi-collision: ce sont des solutions le long desquelles deux des corps deviennent arbitrairement proches l'un de l'autre sans toutefois avoir de collision: la limite inférieure de leur distance est nulle alors que la limite supérieure est strictement positive. Ces solutions sont quasi-périodiques dans un système régularisé à un changement de temps près. Des solutions de ce type ont été mises en évidence tout d'abord dans le problème restreint plan circulaire par Chenciner et Llibre puis, dans le problème plan des trois corps par Féjoz. Nous prouvons l'existence d'une mesure positive de ces solutions dans le problème spatial des trois corps. L'existence de ce type de solutions avait été prédit par Marchai dont nous confirmons rigoureusement le résultat. La démonstration consiste en l'application d'un théorème KAM équivariant dans une régularisation du problème, ici celle de Kustaanheimo-Stiefel, et par la compréhension, suivant Féjoz, de la relation entre régularisation et moyennisation
This thesis generalizes to the spatial three-body problem in the lunar case some studies about several familles of quasiperiodic motions in the planar circular restricted three-body problem and in the planar three-body problem. As discovered by Harrington, if we develop the perturbing function of the system averaged over the fast angles in the powers of the ratio of the semi major axes, then the truncation at the first non-trivial order is integrable. This is the quadrupolar system. In a classical article, Lidov and Ziglin studied the dynamics of this system. We start by proving the existence of some quasi periodic solutions of the spatial three-body problem by applying KAM theorems to this system. We then prove the existence of a family of quasi-periodic almost-collision solutions: These are solutions along which two bodies become arbitrarily close to one another but never collide: the lower limit of their distance is zero but the upper limit is strictly positive. After a change of time, these solutions are quasi-periodic in a regularized system. Such solutions were first discovered in the planar circular restricted three-body problem by Chenciner and Llibre, and afterwards, in the planar three-body problem by Féjoz. We show the existence of a positive measure of such solutions in the spatial three-body problem, which confirms rigorously a prediction of Marchai. The proof goes through the application of an equivariant KAM theorem to a regularization of the problem, here the Kustaanheimo-Stiefel regularization, and, as in Féjoz's work, it requires understanding the relation between the regularization and averaging

We investigate the existence of a symmetric singular periodic brake orbit in the equal mass, fully symmetric planar four body problem. Using regularized coordinates, we remove the singularity of binary collision for each symmetric pair. We use topological and symmetry tools in our investigation.

Ce travail de thèse se veut être une contribution à l'estimation globale des risques de collisions dans l'environnement spatial de la Terre. Deux échelles de temps s'affrontent pour l'estimation de ces risques : le très court terme (quelques heures à quelques jours) où les évolutions notables de probabilité de collisions vont être dues à des événements de caractère catastrophique (collision entre satellites ou explosion), et le long voire le très long terme (où il s'agit d'évaluer l'évolution spatio-temporelle de la population de l'ensemble des débris spatiaux). Dans les deux cas, il s'agit d'évaluer la dangerosité d'une région de l'espace où évoluent des satellites opérationnels. L'assimilation de bases de données des objets en orbite autour de la Terre est fortement présente dans ce travail, tout comme des simulations pour les objets petits, nombreux, et donc non-observables. L'objectif suivi est d'étudier les caractéristiques statistiques générales de la population ainsi que celles d'une famille particulière née d'un événement ponctuel (de type fragmentation), tant par le biais d'outils usuels que novateurs, afin d'aboutir à une estimation des risques engendrés à court et long termes. Une méthode innovante est proposée, basée sur des outils de statistique spatiale utilisés en mathématiques appliquées dans des domaines variés mais jusque là autres que l’astrodynamique. Nous avons déterminé la répartition des débris spatiaux d'un point de vue statistique, en décrivant la dynamique d'agrégation ou de répulsion entre les objets, puis évalué l'influence des particules de petite taille sur la distribution des fragments. L'étude d'une fragmentation particulière et de la formation de son nuage de débris en orbite est également réalisée. Elle passe par la description des caractéristiques géométriques du nuage au cours du temps ainsi que par la déterminationdes temps de fermeture de ses différentes étapes de formation. Cette fragmentation est également utilisée pour déterminer l'influence des paramètres propres à l'explosion et à l'évolution des orbites sur la dispersion du nuage d'un point de vue statistique. Sur la base de l’ensemble de ces travaux, une série de critères nous permet finalement de tracer des voies vers une calibration d'un modèle de fragmentation complet par comparaison avec des données réelles issues d'observations
This PhD work is a contribution to the global estimation of collision risks in the Earth space environment. To estimate these risks, two time scales complement one another: over very short terms (from a few hours to a few days) the strongest changes of collision probabilities are likely to be due to catastrophic events (collision between satellites or explosions), whereas over long and even very long terms (decades or even centuries) the main goal is to assess the spatio-temporal evolution of a whole population of space debris. In both cases, this is the evaluation of the dangerousness of regions where active satellites evolve which is at stake.Throughout the discussion, we focuse on databases assimilation of on-orbit objects, as well as on simulations for small and (then) numerous objects objects that are unobservable. We follow the goal of characterizing the statistical distribution of the global population, as well as specific families generated after a punctual event (i.e: fragmentation). Some estimations of the incurred risks are provided over both short and long time scales. An innovative method is proposed to characterize the space debris distribution, that is rather commonly used in the fields of applied mathematique but not that frequently in astrodynamics: this method is based on spatial statistics to determine the space debris distribution from a statistical point of view. By defining the notions of aggregation and repulsion dynamics between objects, we have assessed the influence of small particles on the fragments distribution.The study of a real fragmentation and of the corresponding space debris cloud evolution is also conducted. The geometrical characteristics of the cloud over time are supplied as well as the estimation of the closure times corresponding to the different evolution phases of the cloud. This concrete example is also on the basis of a sensitivity analysis: by enlightening the influence of some parameters standing for the explosion and the orbit evolution parameterization, the spreading of the cloud is characterized from a statistical point of view.As a final step of this approach, some criteria are discussed to open a path through the calibration of a complete fragmentation model thanks to comparisons with real data coming from observations

Cette thèse généralise au problème spatial dans le cas lunaire les études sur diverses familles de mouvements quasi-périodiques dans le problème plan des trois corps. En tronquant au premier ordre non trivial le développement en puissances du rapport des demi grands axes de la fonction perturbatrice moyennée sur les angles rapides, on obtient un système complètement intégrable qui peut servir de première approximation pour le système initial. C'est le système quadripolaire, découvert par Harrington. Dans un article classique, Lidov et Ziglin ont étudié la dynamique de ce système. Nous commençons par établir l'existence de solutions quasi-périodiques du problème spatial des trois corps en appliquant les théorèmes de KAM à ce système. Nous montrons ensuite l'existence de familles de solutions que nous appelons solutions quasi-périodiques de quasi-collision : ce sont des solutions le long desquelles deux des corps deviennent arbitrairement proches l'un de l'autre sans toutefois avoir de collision : la limite inférieure de leur distance est nulle alors que la limite supérieure est strictement positive. Ces solutions sont quasi-périodiques dans un système régularisé à un changement de temps près. Des solutions de ce type ont été mises en évidence tout d'abord dans le problème restreint plan circulaire par Chenciner et Llibre puis, dans le problème plan des trois corps par Féjoz. Nous prouvons l'existence d'une mesure positive de ces solutions dans le problème spatial des trois corps. L'existence de ce type de solutions avait été prédit par Marchal dont nous confirmons rigoureusement le résultat. La démonstration consiste en l'application d'un théorème KAM équivariant dans une régularisation du problème, ici celle de Kustaanheimo-Stiefel, et par la compréhension, suivant Féjoz, de la relation entre régularisation et moyennisation.

Physics
Ph.D.
The quantum interference effects, such as the Autler-Townes (AT) effect and electromagnetically induced transparency (EIT) applied to molecular systems are the focus of this Dissertation in the context of high resolution molecular spectroscopy. We demonstrate that the AT effect can be used to manipulate the spin character of a spin-orbit coupled pair of molecular energy levels serving as a \textit{gateway} between the singlet and triplet electronic states. We demonstrate that the singlet-triplet mixing characters of the \textit{gateway} levels can be controlled by manipulating the coupling laser \textit{E} field amplitude. We observe experimentally the collisional population transfer between electronic states $G^1\Pi_g (v=12, J=21, f)$ and $1^3\Sigma _g^-(v=1, N=21, f)$ of $^7$Li$_2$. We obtain the Stern-Vollmer plot according to the vapor pressure dependence of collisional transfer rate. The triplet fluorescence from the mixed \textit{gateway} levels to the triplet $b^3\Pi_u(v'=1,J'=
Temple University--Theses

Calcul des géométries du points de sille et des barrières d'activation pour les réactions d'abstraction (HO::(2) + H->H::(2) + O::(2)) et d'approche concertée (HO::(2) + H->H::(2)O + O) pour la méthode SDCI à l'ordre d'une base DZ dans la région de valence, augmentée par des orbitales de polarisation de type D sur chaque atome O. Evaluation des paramètres cinétiques dans le cadre de la théorie de l'état de transition : énergies d'activation et constantes de vitesse. Faible probabilité du mécanisme de réaction concertée

I. Etude a haute resolution des spectres de fluorescence de **(128)te::(2), **(130)te::(2) et na::(2) et deduction de valeurs tres precises des constantes moleculaires; description des courbes de potentiels jusqu'a des niveaux vibrationnels eleves; mise en evidence d'une nouvelle transition laser en ir pour **(130)te::(2). Ii etude des perturbations de 11 niveaux vibrationnels de l'etat a**(1)sigma ::(u)**(+) par l'etat b**(3)pi ::(u) de na::(2); deduction des constantes moleculaires de ces etats et du parametre d'interaction spin-orbite

With the increasing number of satellites operating in orbit and the development of nanosatelliteconstellations, it has become more and more arduous for operators to keep track of every satellitestate, and perform corrective or avoidance manoeuvres. That is why CNES, the French space agency,is developing new algorithms, which aimed at making satellites more self-su cient. More especially,these algorithms are in charge of autonomous orbit control, collision risk calculations and satellitestatus monitoring. In this thesis, we present the architecture of these three algorithms and how theyinteract between them to deal with the autonomous control of a satellite. In addition, this paper studiestheir integration within the OPS-SAT nanosatellite, which is an in-orbit demonstrator developed bythe European Space Agency (ESA) and opened to worldwide experimenters. By analysing the dataused by the numerical propagators, the size of the input configuration files sent to the nanosatellitewas optimised. Thanks to this optimisation, the size of telecommands sent during each OPS-SATflyby above the ESOC ground station meets the requirements. Due to some issues encountered with the nanosatellite’s GPS, a solution was found to update thecurrent orbit on-board, and thus allow the proper algorithms’ operation. This thesis also introduceshow the tests were carried out in order to validate these algorithms, both on flat-sat and on the realsatellite. The results demonstrate that their integration on the OPS-SAT numerical environment issuccessful, meaning that the algorithms and their dependences are correctly packaged, sent and uploaded,and that they work as expected. Their execution time are of course longer due to the limitedcalculation capacity of the on-board computer, but are still compatible with real operations, except forthe collision risk computation, which can exceed the orbital period depending on the initial conditions.Finally, the thesis presents the process of real operations for one of the three algorithms developed byCNES, the di culties encountered and the solutions considered.
Med det ökande antalet satelliter i omloppsbana och utvecklingen av nanosatellitkonstellationer hardet blivit mer och mer krävande för operatörer att hålla reda på varje satellits tillstånd och utförakorrigerande eller undvikande manövrar. Det är därför som CNES, den franska rymdorganisationen,utvecklar nya algoritmer som syftar till att göra satelliter mer autonoma. Närmare bestämt ansvarardessa algoritmer för autonom omloppsbanereglering, kollisionsriskberäkningar och satellitstatusövervakning.I detta examensarbete presenterar vi arkitekturen för dessa tre algoritmer och hur de interagerarmellan sig för att hantera den autonoma styrningen av en satellit. Dessutom studeras deras integrationinom OPS-SAT-nanosatelliten, som är en demonstrator i omloppsbana som utvecklats av Europeiskarymdorganisationen (ESA) och öppnad för globala experiment. Genom att analysera de datasom används av de numeriska propagatorerna optimerades storleken på de ingångskonfigurationsfilersom skickades till nanosatelliten. Tack vare denna optimering uppfylls storlekskraven på telekommandonsom skickas under varje passage av OPS-SAT ovanför ESOC-markstationen. På grund av vissa problem med nanosatellitens GPS hittades en lösning för att uppdatera den aktuellaomloppsbanan ombord och därmed möjliggöra korrekt funktion av algoritmerna. Detta examensarbeteintroducerar också hur testerna genomfördes för att validera dessa algoritmer, både på en s.k. flat-satoch på den verkliga satelliten. Resultaten visar att deras integration i den numeriska miljön OPS-SATär framgångsrik, vilket innebär att algoritmerna och deras beroende är korrekt förpackade, skickade ochuppladdade och att de fungerar som förväntat. Deras exekveringstid är naturligtvis längre på grundav den inbyggda datorns begränsade beräkningskapacitet, men är fortfarande kompatibel med verkligaoperationer, förutom beräkningen av kollisionsrisk, som kan överstiga omloppsperioden beroende påde initiala förhållandena. Slutligen presenterar rapporten processen för verkliga operationer för en avde tre algoritmerna som utvecklats av CNES, svårigheterna och de lösningar som övervägs.

Le collisionneur SuperKEKB, dédié à l'expérience Belle II, prévoit une très haute luminosité, inégalée à ce jour. Son objectif est de fournir une luminosité instantanée de 8x10³⁵ cm⁻²s⁻¹ en mettant en collision des faisceaux minuscules au point d'interaction (IP) sur la base du schéma "nano-beam". Par conséquent, un excellent contrôle de l'orbite du faisceau à l’IP est nécessaire pour assurer un recouvrement géométrique optimal entre les deux faisceaux en collision, et ainsi maximiser la luminosité. Dans ce cadre, cette thèse présente le développement et l'implémentation d'un système de monitoring rapide de la luminosité de SuperKEKB basé sur des détecteurs en diamant sCVD. Pour atteindre une précision relative aussi élevée et couvrir une gamme dynamique de luminosité élevée, le processus de diffusion Bhabha radiatif à très petit angle est utilisé, dont la section efficace d’interaction est très importante et relativement bien connue. Des détecteurs diamant sCVD, dont le signal est rapide et qui ont une bonne tolérance au rayonnement, sont utilisés pour détecter les particules chargées dans les gerbes électromagnétiques induites par l’interaction entre les particules Bhabha diffusées et perdues dans le tube à vide du faisceau, et dans les autres matériaux, en particulier un radiateur, à des emplacements choisis spécialement en aval de l'IP, dans les deux anneaux LER et HER. Une simulation de bout en bout du système d'asservissement de l'orbite du faisceau à l'IP basé sur notre signal de luminosité rapide et précis a été réalisé, qui comprend: une estimation du signal du détecteur de diamant sCVD, basé sur des mesures de laboratoire à l'aide d'une source radioactive, la construction de séquences de signal représentative de SuperKEKB comprenant les bruits de fond à un seul faisceau et les particules diffusées par le processus Bhabha, un traitement du signal de luminosité, et la simulation de l'asservissement de l'orbite. Il a été possible de vérifier la faisabilité de ce système pour maintenir la très haute luminosité de SuperKEKB en présence des mouvements du sol et a de déterminer la précision relative du signal de luminosité rapide qu'il est possible d'obtenir toutes les 1 ms. Au cours des phases de mise en service de SuperKEKB, la phase 2 et le début de la phase 3, notre moniteur de luminosité rapide basé sur des détecteurs en diamant sCVD a été installé et utilisé avec succès. Les processus de perte de faisceau, principalement ceux provenant des processus de Bremsstrahlung et de Touschek, ont été étudiés en détail et, par rapport à la simulation, un bon accord a été trouvé. Lors de la mise en service de la collision, des signaux de luminosité intégrés toutes les secondes étaient fournis en continu pour le réglage des paramètres des faisceaux à l'IP. En outre, un signal de luminosité intégré toutes les 1 ms avec la précision relative attendue a également été fourni et utilisé comme entrée du système d'asservissement de l'orbite à l'IP, notamment pour des premiers tests conduits avec succès avec des décalages de faisceau horizontaux introduits volontairement. Davantage de tests de ce système d'asservissement sont attendus pour assurer son bon fonctionnement en continu à l'avenir. Cette thèse présente le développement et l’application d’un système de surveillance rapide de la luminosité basé sur les détecteurs de sCVD diamant de SuperKEKB
SuperKEKB is at the foremost frontier of high luminosity e⁺e⁻ colliders, dedicated to the Belle-II experiment. It aims to provide an instantaneous luminosity of 8x10³⁵ by involving extremely tiny beams colliding at the Interaction Point (IP) based on the "nano-beam scheme". Therefore, excellent control of its beam orbit at the IP is required to ensure the optimum geometrical overlap between the two colliding beams, and thereby maximize the luminosity. Besides, effective instrumentation to diagnose the behavior of the beam at the IP and possible beam interactions between bunches along the train are also quite essential during the long and rather difficult process of machine tuning towards the nominal beam parameters. This thesis presents the development and application of a fast luminosity monitoring system based on sCVD diamond detectors at SuperKEKB, including: (1),train integrated luminosity signals every 1 ms which will be used as input to the dithering orbit feedback system, its relative precision is expected to be better than 1% when luminosity reaches 10³⁴ (2), sensitive train integrated luminosity signals over a large luminosity dynamic range every 1 s which will be sent to the SuperKEKB control room as immediate observable for machine collision tuning, and (3) bunch integrated luminosity signals every 1 s with sufficient relative precision to monitor the collision performance for each single bunch. To achieve such high relative precision and cover a large luminosity dynamic range, the radiative Bhabha process events at vanishing scattering angle will be measured, whose interaction cross-section is quite large and reasonably well known. The sCVD diamond detectors, which have fast signal formation and good radiation tolerance, were used to detect the charged particles in the secondary showers induced by the interaction between the lost Bhabha scattered particles and the beam pipe and specific radiator materials at carefully chosen locations downstream of the IP in both the LER and HER. A start-to-end simulation was performed on the dithering orbit feedback system using fast, precise luminosity signal as input, which includes: sCVD diamond detector signal estimation based on laboratory measurements with a radioactive source, signal sequence construction at SuperKEKB including single beam backgrounds and Bhabha scattered particles, luminosity signal procession, dithering orbit feedback simulation. It enabled verifying the feasibility of this system to maintain very high luminosity in the presence of ground motion, in particular it determined the relative precision of the fast luminosity signal every 1 ms. Besides, the radiation damage of the sCVD diamond detectors in the LER was also estimated based on a FLUKA simulation and applying the NIEL hypothesis. During the Phase-2 and early Phase-3 commissioning periods of SuperKEKB, our fast luminosity monitor based on sCVD diamond detectors was installed and operated successfully. Single beam loss processes, mainly Bremsstrahlung and Touschek, were studied in detail and compared with the simulation, showing good agreement. During the collision commissioning, train and bunch integrated luminosity signals every 1 s were provided for machine tuning. e.g. the vertical beam sizes were determined with the vertical offset scan technique based on our luminosity signals, both the average and for the individual bunches, which is very important and useful for the collision and IP local optics tuning during the long and rather difficult process of SuperKEKB machine tuning towards the nominal beam parameters. Besides, a train integrated luminosity signal every 1 ms with the expected relative precision was also provided and used as input to the dithering orbit feedback system for its first successful tests with deliberately introduced horizontal beam-beam offsets. More tests on the dithering orbit feedback system are expected to ensure its future continuous operation

I. Etude des mécanismes de relaxation mis en jeu dans Cl2, Br2, I2 isolés en matrice, après excitation en UV proche ou lointain : émission structurée (transitions vibroniques) pour Cl2en UV proche et transitions électroniques avec interaction Rydberg-Valence en UV lointain; émission dans le visible pour Br2 et I2 quelle que soit l'énergie d'excitation; étude théorique des processus de relaxation. II. Observation d'ions moléculaires simplement ou doublement chargés, formés par échange de charge simple ou double étudié par spectrométrie de translation; analyse des règles de sélection : conservation du spin et observation des seuls états singlets pour Cl2, influence croissante du couplage spin-orbite lorsqu'on passe de Cl2, à Br2 puis I2.

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. The dynamics of plasma ions in the presence of large-amplitude electrostatic waves are investigated experimentally. The work was conducted in Caltech's Encore research tokamak. The toroidal plasma current excites coherent, poloidally propagating drift waves which stochastically heat ions in the poloidal plane. Ion distribution functions f (x, v ,t) are probed via Laser-Induced Fluorescence along three orthogonal velocity directions. Wave phase resolution is provided by the narrow laser pulse width and by a novel data-acquisition system which ensures synchronization between laser trigger and drift wave. Time-resolved measurements show a multi-step heating process during each wave period: (i) The wave electric field excites stochastic ion orbits in the poloidal [...] plane, resulting in [...] heating. (ii) ion-ion collisions impart energy to the toroidal [...] direction, raising [...] to relax the [...] temperature anisotropy. (iii) Hot ions with large gyroradius escape confinement, reaching the chamber wall and cooling the distribution. (iv) Cold ions from the plasma edge are convected back into the plasma (recycled), significantly replenishing the density depleted by orbit losses. The ion-ion collision period [...] is highly time-dependent due to intense ([...]50%) fluctuations in both n and T. The anisotropic temperature relaxation rate is found to be consistent with Fokker-Planck theory when the time-dependence of the collision period is properly taken into account. Thus, classical Fokker-Planck correctly describes the evolution of f (vil), despite the intrinsic single-particle stochasticity in the [...] direction. Evidence for ion recycling is given by observations of significantly non-Maxwellian (NM) ion velocity distributions near the plasma edge. These appear periodically, synchronous with the drift wave phase at which, simultaneously, ion fluid flow from the wall toward the plasma center peaks, ion density is a local minimum, and ion temperature is high. The appearance of NM features at this phase is consistent with the intantaneously low ion collision rate which allows non-equilibrium features to be long-lived. The observed NM distributions are bimodal and indicate the presence of a group of cold ions (0.4 eV) superimposed on a hot background plasma (8 eV) of roughly equal density.