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Multiple interaction points in ghost collisions

The Ghost Collider makes use of unique “ghost” bunches, which are electrically neutral combinations of electrons and positrons within the same RF bucket, eliminates the beam-beam effects typically present at the interaction point (IP) in conventional colliders. This allows for the novel possibility of placing multiple interaction regions in series, achieving additive luminosity without introducing significant disruption. However, to get higher luminosity, the beta functions at the IP reaches millimeter scale, which in turn adds significant chromatic contribution to the collider. Correcting these chromatic effects is essential to maintain beam stability and ensure high luminosity during collider operation. By carefully adjusting the phase advance between two IRs that are placed in series, it becomes possible to cancel chromaticity globally, enabling stable collider operation while preserving high luminosity. In this paper we discuss the design of such IR/IRs to be used in a ghost collider.

Accelerator Physics

A Multi-Sensor Approach for Measuring Bird and Bat Collisions with Offshore Wind Turbines (Final Technical Report)

Collision of birds and bats with wind turbines is a conservation concern for both land-based and offshore wind projects. The fatality rates of birds and bats at land-based turbines are well documented. The measurement strategies on land focus on finding carcasses following collision, estimating the number of carcasses missed through searcher efficiency, carcass persistence trials and carcass fall distributions, and modeling statistically robust fatality rates. Few technologies have been developed to monitor offshore bird and bat collisions, and many that have been developed focused on detecting collisions with large birds. The few studies that have attempted to document collisions at offshore turbines do not account for smaller bodied animals or for collisions that might be missed, which prevents the calculation of statistically robust fatality rates. The overall goal of this report, A Multi-Sensor Approach for Measuring Bird and Bat Collisions with Offshore Wind Turbines (Project), was to develop an effective multi-sensor system for quantifying bird and bat collision rates, specifically for offshore wind facilities. The Project goal and resulting automated collision detection system was achieved through two major technological advancements: 1) refining The Netherlands Organisation for Applied Scientific Research’s (TNO’s) existing WT-Bird® vibration sensing system, that had successfully detected large bird collisions during daytime, to allow for improved detection of smaller birds and bats during both daytime and nighttime hours and 2) improving image processing systems and developing and integrating machine learning algorithms to automatically detect and classify small and large bird and bat collisions with offshore turbines. This final technical report (FTR) summarizes Methods , Results , Conclusions , and Lessons Learned during each of the five Tasks identified for this research and development effort. This FTR includes summaries of the following: Task 1. Initial Engineering Tests to Improve WT-Bird® Task 2. Installation of WT‐Bird® on a Utility-scale Turbine at the National Wind Technology Center – National Renewable Energy Laboratory Task 3. Field Tests and Refinement of the Object Detection System Task 4. Validation of WT-Bird® on a Land-based Turbine Task 5. Preparation for the Implementation of WT-Bird® on an Offshore Turbine. This research and development effort documented successful improvement of the WT Bird® collision detection system to detect small birds and bats, and WT-Bird® is the first collision detection system to validate results compared to land-based post-construction monitoring. The collision trials provide estimates of missed targets that can be used to estimate fatality rates, a significant improvement relative to other offshore collision monitoring systems. Advances were made in developing an edge-processing solution to reduce data storage requirements, which is important if the system is deployed for long periods of time at offshore turbines. The improved WT-Bird® system also provides an important option for wind operators on land or offshore who need to document specific details about when collisions occur, particularly efforts to further research on bat impact minimization, or when standard fatality searches are impractical (e.g. offshore) or inadequate (e.g. challenging locations on land).

17 WIND ENERGY

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

Cooperative Collision Avoidance Step 1 - Technology Demonstration Flight Test Report. Revision 1

The National Aeronautics and Space Administration (NASA) Access 5 Project Office sponsored a cooperative collision avoidance flight demonstration program for unmanned aircraft systems (UAS). This flight test was accomplished between September 21st and September 27th 2005 from the Mojave Airport, Mojave, California. The objective of these flights was to collect data for the Access 5 Cooperative Collision Avoidance (CCA) Work Package simulation effort, i.e., to gather data under select conditions to allow validation of the CCA simulation. Subsequent simulation to be verified were: Demonstrate the ability to detect cooperative traffic and provide situational awareness to the ROA pilot; Demonstrate the ability to track the detected cooperative traffic and provide position information to the ROA pilot; Demonstrate the ability to determine collision potential with detected cooperative traffic and provide notification to the ROA pilot; Demonstrate that the CCA subsystem provides information in sufficient time for the ROA pilot to initiate an evasive maneuver to avoid collision; Demonstrate an evasive maneuver that avoids collision with the threat aircraft; and lastly, Demonstrate the ability to assess the adequacy of the maneuver and determine that the collision potential has been avoided. The Scaled Composites, LLC Proteus Optionally Piloted Vehicle (OPV) was chosen as the test platform. Proteus was manned by two on-board pilots but was also capable of being controlled from an Air Vehicle Control Station (AVCS) located on the ground. For this demonstration, Proteus was equipped with cooperative collision sensors and the required hardware and software to place the data on the downlink. Prior to the flight phase, a detailed set of flight test scenarios were developed to address the flight test objectives. Two cooperative collision avoidance sensors were utilized for detecting aircraft in the evaluation: Traffic Alert and Collision Avoidance System-II (TCAS-II) and Automatic Dependent Surveillance Broadcast (ADS-B). A single intruder aircraft was used during all the flight testing, a NASA Gulfstream III (G-III). During the course of the testing, six geometrically different near-collision scenarios were evaluated. These six scenarios were each tested using various combinations of sensors and collision avoidance software. Of the 54 planned test points 49 were accomplished successfully. Proteus flew a total of 21.5 hours during the testing and the G-III flew 19.8 hours. The testing fully achieved all flight test objectives. The Flight IPT performed an analysis to determine the accuracy of the simulation model used to predict the location of the host aircraft downstream during an avoidance maneuver. The data collected by this flight program was delivered to the Access 5 Cooperative Collision Avoidance (CCA) Work Package Team who was responsible for reporting on their analysis of this flight data.

Trongale, Nicholas A.

Space-time evolution of particle emission in p–Pb collisions at $\sqrt{{s}_{\text{NN}}} = 5.02$ TeV with 3D kaon femtoscopy

The measurement of three-dimensional femtoscopic correlations between identical charged kaons (K ± K ± ) produced in p–Pb collisions at center-of-mass energy per nucleon pair $\sqrt{{s}_{\text{NN}}}=5.02$ TeV with ALICE at the LHC is presented for the first time. This measurement, supplementary to those in pp and Pb–Pb collisions, allows understanding the particle-production mechanisms at different charged-particle multiplicities and provides information on the dynamics of the source of particles created in p–Pb collisions, for which a general consensus does not yet exist. It is shown that the measured source sizes increase with charged-particle multiplicity and decrease with increasing pair transverse momentum. These trends for K ± K ± are similar to the ones observed earlier in identical charged-pion and ${\text{K}}_{\text{s}}^{0}{\text{K}}_{\text{s}}^{0}$ correlations in Pb–Pb collisions at various energies and in π ± π ± correlations in p–Pb collisions at $\sqrt{{s}_{\text{NN}}}=5.02$ TeV. At comparable multiplicity, the source sizes measured in p–Pb collisions agree within uncertainties with those observed in pp collisions, and there is an indication that they are smaller than those observed in Pb–Pb collisions. The obtained results are also compared with predictions from the hadronic interaction model EPOS 3, which tends to underestimate the source size for the most central collisions and agrees with the data for semicentral and peripheral events. Furthermore, the time of maximal emission for kaons is extracted. It turns out to be comparable with the value obtained in highly peripheral Pb–Pb collisions at the same energy, indicating that the kaon emission evolution is similar to that in p–Pb collisions.

Heavy Ion Experiments

Algorithm Plans Collision-Free Path for Robotic Manipulator

An algorithm has been developed to enable a computer aboard a robot to autonomously plan the path of the manipulator arm of the robot to avoid collisions between the arm and any obstacle, which could be another part of the robot or an external object in the vicinity of the robot. In simplified terms, the algorithm generates trial path segments and tests each segment for potential collisions in an iterative process that ends when a sequence of collision-free segments reaches from the starting point to the destination. The main advantage of this algorithm, relative to prior such algorithms, is computational efficiency: the algorithm is designed to make minimal demands upon the limited computational resources available aboard a robot. This path-planning algorithm utilizes a modified version of the collision-detection method described in "Improved Collision-Detection Method for Robotic Manipulator" (NPO-30356), NASA Tech Briefs, Vol. 27, No. 3 (June 2003), page 72. The method involves utilization of mathematical models of the robot constructed prior to operation and similar models of external objects constructed automatically from sensory data acquired during operation. This method incorporates a previously developed method, known in the art as the method of oriented bounding boxes (OBBs), in which an object is represented approximately, for computational purposes, by a box that encloses its outer boundary. Because many parts of a robotic manipulator are cylindrical, the OBB method has been extended in this method to enable the approximate representation of cylindrical parts by use of octagonal or other multiple-OBB assemblies denoted oriented bounding prisms (OBPs). A multiresolution OBB/OBP representation of the robot and its manipulator arm and a multiresolution OBB representation of external objects (including terrain) are constructed and used in a process in which collisions at successively finer resolutions are detected through computational detection of overlaps between the corresponding OBB and OBP models. For computational efficiency, the process is started at the coarsest resolution and stopped as soon as possible, preferably before reaching the finest resolution. At the coarsest resolution, there is a single OBB enclosing all relevant external objects and a single OBB enclosing the entire robot. At the next finer level of resolution, the coarsest-resolution OBB is divided into two OBBs, and so forth. If no collision is detected at the coarsest resolution, then there is no need for further computation to detect collisions. If a collision is detected at the coarsest resolution, then tests for collisions are performed at the next finer level of resolution. This process is continued to successively finer resolutions until either no more collisions are detected or the finest resolution is reached.

Backes, Paul

Assessment and Validation of Collision "Consequence" Method of Assessing Orbital Regime Risk Posed by Potential Satellite Conjunctions

Collision risk management theory requires a thorough assessment of both the likelihood and consequence of potential collision events. Satellite conjunction risk assessment has produced a highly-developed theory for assessing the likelihood of collision but neglects to account for the consequences of a given collision. While any collision may compromise the operational survival of a spacecraft, the amount of debris produced by the potential collision, and therefore the degree to which the orbital corridor may be compromised, can vary greatly among satellite conjunctions. Previous studies leveraged work on satellite collision modeling to develop a method to estimate whether a particular collision is likely to produce a relatively large or relatively small amount of resultant debris. The approximation of the number of debris pieces is dependent on a mass estimation process for the secondary objects utilizing the radar cross section of said object. This study examines the validity of the mass estimation process and establishes uncertainty bounds on the secondary object mass, which will be used to best approximate the possible consequences of a potential collision. This process is then applied to a large set of historical conjunctions to assess the frequency at which possible collisions may significantly augment the orbital debris environment in operational spacecraft.

Collision Consequence

Ridge-trench collision in Archean and Post-Archean crustal growth: Evidence from southern Chile

The growth of continental crust at convergent plate margins involves both continuous and episodic processes. Ridge-trench collision is one episodic process that can cause significant magmatic and tectonic effects on convergent plate margins. Because the sites of ridge collision (ridge-trench triple junctions) generally migrate along convergent plate boundaries, the effects of ridge collision will be highly diachronous in Andean-type orogenic belts and may not be adequately recognized in the geologic record. The Chile margin triple junction (CMTJ, 46 deg S), where the actively spreading Chile rise is colliding with the sediment-filled Peru-Chile trench, is geometrically and kinematically the simplest modern example of ridge collision. The south Chile margin illustrates the importance of the ridge-collision tectonic setting in crustal evolution at convergent margins. Similarities between ridge-collision features in southern Chile and features of Archean greenstone belts raise the question of the importance of ridge collision in Archean crustal growth. Archean plate tectonic processes were probably different than today; these differences may have affected the nature and importance of ridge collision during Archean crustal growth. In conclusion, it is suggested that smaller plates, greater ridge length, and/or faster spreading all point to the likelihood that ridge collision played a greater role in crustal growth and development of the greenstone-granite terranes during the Archean. However, the effects of modern ridge collision, and the processes involved, are not well enough known to develop specific models for the Archean ridge collison.

Nelson, E. P.

Electronic excitation of ground state atoms by collision with heavy gas particles

Most of the important chemical reactions which occur in the very high temperature air produced around space vehicles as they enter the atmosphere were investigated both experimentally and theoretically, to some extent at least. One remaining reaction about which little is known, and which could be quite important at the extremely high temperatures that will be produced by the class of space vehicles now contemplated - such as the AOTV - is the excitation of bound electron states due to collisions between heavy gas particles. Rates of electronic excitation due to free electron collisions are known to be very rapid, but because these collisions quickly equilibrate the free and bound electron energy, the approach to full equilibrium with the heavy particle kinetic energy will depend primarily on the much slower process of bound electron excitation in heavy particle collisions and the subsequent rapid transfer to free electron energy. This may be the dominant mechanism leading to full equilibrium in the gas once the dissociation process has depleted the molecular states so the transfer between molecular vibrational energy and free electron energy is no longer available as a channel for equilibration of free electron and heavy particle kinetic energies. Two mechanisms seem probable in electronic excitation by heavy particle impact. One of these is the collision excitation and deexcitation of higher electronic states which are Rydberg like. A report, entitled 'Semi-Classical Theory of Electronic Excitation Rates', was submitted previously. This presented analytic expressions for the transition probabilities, assuming that the interaction potential is an exponential repulsion with a perturbation ripple due to the dipole-induced dipole effect in the case of neutral-neutral collisions, and to the ion-dipole interaction in the case of ion-neutral collisions. However the above may be, there is little doubt that excitation of ground state species by collision occurs at the point where the initial and final potentials cross, or at least come very close. Therefore, this mechanism would be applicable to the case where a gas is initially at very low temperature suddenly subjected to high energy heavy particle bombardment. This situation would model the measurement of excitation cross section by molecular beam techniques, for example. The purpose is to report values of cross sections and rate coefficients for collision excitation of ground state atoms estimated with the Landau-Zener transition theory and to compare results with measurement of excitation cross sections for a beam of Hydrogen atoms impacting Argon atom targets. Some very dubious approximations are used, and the comparison with measurement is found less than ideal, but results are at least consistent within order of magnitude. The same model is then applied to the case of N-N atom collisions, even though the approximations then become even more doubtful. Still the rate coefficients obtained are at least plausible in both magnitude and functional form, and as far as I am aware these are the only estimates available for such rate coefficients.

Hansen, C. Frederick

NASA Lewis Launch Collision Probability Model Developed and Analyzed

There are nearly 10,000 tracked objects orbiting the earth. These objects encompass manned objects, active and decommissioned satellites, spent rocket bodies, and debris. They range from a few centimeters across to the size of the MIR space station. Anytime a new satellite is launched, the launch vehicle with its payload attached passes through an area of space in which these objects orbit. Although the population density of these objects is low, there always is a small but finite probability of collision between the launch vehicle and one or more of these space objects. Even though the probability of collision is very low, for some payloads even this small risk is unacceptable. To mitigate the small risk of collision associated with launching at an arbitrary time within the daily launch window, NASA performs a prelaunch mission assurance Collision Avoidance Analysis (or COLA). For the COLA of the Cassini spacecraft, the NASA Lewis Research Center conducted an in-house development and analysis of a model for launch collision probability. The model allows a minimum clearance criteria to be used with the COLA analysis to ensure an acceptably low probability of collision. If, for any given liftoff time, the nominal launch vehicle trajectory would pass a space object with less than the minimum required clearance, launch would not be attempted at that time. The model assumes that the nominal positions of the orbiting objects and of the launch vehicle can be predicted as a function of time, and therefore, that any tracked object that comes within close proximity of the launch vehicle can be identified. For any such pair, these nominal positions can be used to calculate a nominal miss distance. The actual miss distances may differ substantially from the nominal miss distance, due, in part, to the statistical uncertainty of the knowledge of the objects positions. The model further assumes that these position uncertainties can be described with position covariance matrices. With these, and some additional simplifying assumptions, a closed-form solution for the probability of collision is obtained. This solution provides clear insights into how each of the independent parameters affects the probability of collision. It shows that for a given maximum probability of collision and prior knowledge of the objects position uncertainties and sizes, only knowledge of the nominal closest approach distance is required to make the launch/no launch decision. The model was completed and used for the mission assurance COLA analysis for the Cassini spacecraft, which was launched on a Titan IV/Centaur rocket on October 15, 1997. Although the model was specifically developed for the Cassini mission, it is clearly applicable for other launches as well. The effect of COLA closures on the launch window is shown. The bar represents the entire 140-min launch window on October 15, 1997; the blackened areas represent the loss of launch opportunities due to the potential for a collision with an orbiting object.

Bollenbacher, Gary

Measurement of inclusive $J/ψ$ production in Au+Au collisions at $\sqrt{s_{\textrm{NN}}}$ = 54.4 GeV at STAR

This article presents measurements of inclusive J/ψ production at midrapidity (|y| < 1.0) in Au+Au collisions at $\sqrt{s_{\textrm{NN}}}$ = 54.4 GeV with the STAR detector at the Relativistic Heavy Ion Collider. A suppression of the J/ψ yield, quantified using the nuclear modification factors (R AA , R CP ), is observed with respect to the scaled production p + p in collisions. The dependence of R AA on collision centrality and J/ψ transverse momentum is measured with improved precision compared to previous measurements at 39 and 62.4 GeV, while the centrality dependence of R CP is measured and compared to the same results at 39, 62.4, and 200 GeV. In central collisions, no significant collision energy dependence of R AA is found within uncertainties for collision energies between 17.3 and 200 GeV. Two transport model calculations that include dissociation and regeneration contributions are consistent with the experimental results within uncertainties. Although no significant collision energy dependence of the J/ψ suppression in high energy heavy-ion collisions up to $\sqrt{s_{\textrm{NN}}}$ = 200 GeV is observed within uncertainties, the newly measured results at 54.4 GeV Au+Au collisions provide additional constraints on theoretical calculations of the hot medium evolution and cold nuclear matter effects.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Production of neutron-rich heavy nuclei in deep-inelastic 208 Pb + 208 Pb collisions within the stochastic mean-field theory

In deep-inelastic collisions of heavy nuclei, reaction products with a wide range of mass and charge are produced. Such collisions been considered as a possible way to produce superheavy nuclei, as an alternative to fusion reactions. To provide reliable theoretical predictions, it is desired to develop microscopic approaches that correctly and accurately describe nucleon transfer processes in dissipative collisions of heavy nuclei. The purpose of the present work is (1) to investigate the mechanism of nucleon transfers in dissipative collisions of two heavy nuclei, and (2) to explore possible pathways to produce neutron-rich heavy nuclei, through detailed theoretical analyses of fluctuations and correlations in nucleon transfers in 208 Pb + 208 Pb reactions. Three-dimensional time-dependent Hartree-Fock (TDHF) calculations are performed for the collisions of 208 Pb + 208 Pb at 𝐸 c.m. = 832, 936, and 1040 MeV, using the Skyrme SLy4d energy density functional. To calculate fluctuations and correlations in nucleon transfers, we employ the stochastic mean-field (SMF) theory, and the results are compared with another theoretical framework currently available, the time-dependent random phase approximation (TDRPA). Primary and secondary production cross sections are calculated with the SMF theory combined with a statistical model, GEMINI ++ . Using information of nucleon flow across a neck of colliding nuclei in TDHF calculations, we solve quantal diffusion equations for fluctuations and correlations in nucleon transfers based on the SMF theory. From the SMF calculations, we obtain the time evolution of diffusion coefficients as well as fluctuations and correlations in nucleon transfers for a range of initial orbital angular momenta. We compare the results of the SMF calculations with those of TDRPA, showing that TDRPA tends to predict substantially larger fluctuations and correlations in strongly damped collisions of heavy nuclei, which exhibit complex initial angular momentum dependence, while the SMF results provide almost constant (stable) values. Using the obtained fluctuations and correlations, we calculate primary and secondary production cross sections for the 208 Pb + 208 Pb collisions. From the results, we find that both lighter and heavier reaction products as compared to 208 Pb are produced for a wide region in the 𝑁−𝑍 plane as primary products, thanks to the quantal diffusion mechanism in the dissipative collisions. However, we show that cross sections for production of heavy nuclei with 𝑍 ≳ 90 or 𝑁 ≳ 135 are washed out due to secondary particle evaporation and/or fission processes. On the other hand, we find that there remain sizable cross sections for production of neutron-rich nuclei along 𝑁 = 126 with 𝑍< 82, even after secondary disintegration processes. We demonstrate that the secondary production cross sections depend weakly on incident energies, but lower (higher) energy is slightly preferred for production of nuclei with smaller (larger) atomic numbers as compared to 𝑍 = 82. Here, based on the microscopic SMF calculations, it has been shown that deep-inelastic collisions of heavy nuclei, such as 208 Pb + 208 Pb examined in this study, can be a promising means to produce neutron-rich heavy nuclei along 𝑁=126. Discrepancies between the SMF and TDRPA approaches are left unsolved for future investigations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Collision-free motion of two robot arms in a common workspace

Collision-free motion of two robot arms in a common workspace is investigated. A collision-free motion is obtained by detecting collisions along the preplanned trajectories using a sphere model for the wrist of each robot and then modifying the paths and/or trajectories of one or both robots to avoid the collision. Detecting and avoiding collisions are based on the premise that: preplanned trajectories of the robots follow a straight line; collisions are restricted to between the wrists of the two robots (which corresponds to the upper three links of PUMA manipulators); and collisions never occur between the beginning points or end points on the straight line paths. The collision detection algorithm is described and some approaches to collision avoidance are discussed.

Basta, Robert A.

Pseudorapidity distributions of charged hadrons in lead-lead collisions at $\sqrt{S_{NN}}$ = 5.36 TeV

The pseudorapidity (η) distributions of charged hadrons are measured using data collected at the highest ever nucleon-nucleon center-of-mass energy of $\sqrt{S_{NN}}$ = 5.36 TeV for collisions of lead-lead ions. The data were recorded by the CMS experiment at the LHC in 2022 and correspond to an integrated luminosity of 0.30 ± 0.03 μb -1 . Using the CMS silicon pixel detector, the yields of primary charged hadrons produced in the range |η| < 2.6 are reported. The evolution of the midrapidity particle density as a function of collision centrality is also reported. In the 5% most central collisions, the charged-hadron η density in the range |η| < 0.5 is found to be 2032 ± 91(syst), with negligible statistical uncertainty. This result is consistent with an extrapolation from nucleus-nucleus collision data at lower center-of-mass energies. Comparisons are made to various Monte Carlo event generators and to previous measurements of lead-lead and xenon-xenon collisions at similar collision energies. These new data detail the dependence of particle production on the collision energy, initial collision geometry, and the size of the colliding nuclei.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Enhanced Collisional Losses from a Magnetic Mirror Using the Lenard-Bernstein Collision Operator

Collisions are crucial in governing particle and energy transport in plasmas confined in a magnetic mirror trap. Modern gyrokinetic codes model transport in magnetic mirrors, but some utilize approximate model collision operators. This study focuses on a Pastukhov-style method of images calculation of particle and energy confinement times using a Lenard-Bernstein model collision operator. Prior work on parallel particle and energy balances used a different Fokker-Planck plasma collision operator. The method must be extended in non-trivial ways to study the Lenard-Bernstein operator. To assess the effectiveness of our approach, we compare our results with a modern finite element solver. Our findings reveal that the particle confinement time scales like a exp( a 2 ) using the Lenard-Bernstein operator, in contrast to the more accurate scaling that the Coulomb collision operator would yield a 2 exp( a 2 ), where a 2 is approximately proportional to the ambipolar potential. We propose that codes solving for collisional losses in magnetic mirrors utilizing the Lenard-Bernstein or Dougherty collision operator scale their collision frequency of any electrostatically confined species. This study illuminates the collision operator’s intricate role in the Pastukhov-style method of images calculation of collisional confinement.

fusion plasma

Inverse Mapping of the Collision Kernel and Wall Flux Scaling in a Tall Convection‐Cloud Chamber Using Local Sensors and Knowledge‐Informed Deep Learning

Droplet collision–coalescence is a crucial process in cloud physics, but accurately representing this process under different dynamical conditions remains challenging. A proposed future convective‐cloud chamber aims to investigate this key process, but the method for observing it remains unclear, even though it is theoretically established that collision‐coalescence will occur. This study serves as a proof‐of‐concept demonstration of how knowledge‐informed deep learning, combined with measurement data from local sensors in the chamber, can be used to estimate the collision kernels, which determine how the droplet size distribution evolves during collision‐coalescence. In addition to estimating the collision kernel, we also address wall fluxes, another uncertain but important process that acts as a source of heat and moisture in the chamber. Ensemble runs of large‐eddy simulations are conducted by scaling the wall fluxes and the collision kernel, while the measured flow and cloud properties are used as inputs for a neural network. Results indicate that this approach successfully maps the scaling of wall fluxes and the collision kernel with biases of approximately 1% or less relative to the range of the target data. This proof‐of‐concept lays the groundwork for future applications; when the real measurements are available, real sensor data combined with the trained model presented in this work will enable estimation of the actual wall fluxes and collision kernel.

cloud chamber

Development of a Nonlinear Probability of Collision Tool for the Earth Observing System

The Earth Observing System (EOS) spacecraft Terra, Aqua, and Aura fly in constellation with several other spacecraft in 705-kilometer mean altitude sun-synchronous orbits. All three spacecraft are operated by the Earth Science Mission Operations (ESMO) Project at Goddard Space Flight Center (GSFC). In 2004, the ESMO project began assessing the probability of collision of the EOS spacecraft with other space objects. In addition to conjunctions with high relative velocities, the collision assessment method for the EOS spacecraft must address conjunctions with low relative velocities during potential collisions between constellation members. Probability of Collision algorithms that are based on assumptions of high relative velocities and linear relative trajectories are not suitable for these situations; therefore an algorithm for handling the nonlinear relative trajectories was developed. This paper describes this algorithm and presents results from its validation for operational use. The probability of collision is typically calculated by integrating a Gaussian probability distribution over the volume swept out by a sphere representing the size of the space objects involved in the conjunction. This sphere is defined as the Hard Body Radius. With the assumption of linear relative trajectories, this volume is a cylinder, which translates into simple limits of integration for the probability calculation. For the case of nonlinear relative trajectories, the volume becomes a complex geometry. However, with an appropriate choice of coordinate systems, the new algorithm breaks down the complex geometry into a series of simple cylinders that have simple limits of integration. This nonlinear algorithm will be discussed in detail in the paper. The nonlinear Probability of Collision algorithm was first verified by showing that, when used in high relative velocity cases, it yields similar answers to existing high relative velocity linear relative trajectory algorithms. The comparison with the existing high velocity/linear theory will also be used to determine at what relative velocity the analysis should use the new nonlinear theory in place of the existing linear theory. The nonlinear algorithm was also compared to a known exact solution for the probability of collision between two objects when the relative motion is strictly circular and the error covariance is spherically symmetric. Figure I shows preliminary results from this comparison by plotting the probabilities calculated from the new algorithm and those from the exact solution versus the Hard Body Radius to Covariance ratio. These results show about 5% error when the Hard Body Radius is equal to one half the spherical covariance magnitude. The algorithm was then combined with a high fidelity orbit state and error covariance propagator into a useful tool for analyzing low relative velocity nonlinear relative trajectories. The high fidelity propagator is capable of using atmospheric drag, central body gravitational, solar radiation, and third body forces to provide accurate prediction of the relative trajectories and covariance evolution. The covariance propagator also includes a process noise model to ensure realistic evolutions of the error covariance. This paper will describe the integration of the nonlinear probability algorithm and the propagators into a useful collision assessment tool. Finally, a hypothetical case study involving a low relative velocity conjunction between members of the Earth Observation System constellation will be presented.

McKinley, David P.