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NASA NTRS2015

Active Collision Avoidance for Planetary Landers

The use of automotive radar systems are being evaluated for collision avoidance in planetary landers. Our focus is to develop a low-cost, light-weight collision avoidance system that overcomes the drawbacks identified with optical-based systems. We also seek to complement the Autonomous Landing and Hazard Avoidance Technology system by providing mission planners an alternative system that can be used on low-cost, small robotic missions and in close approach. Our approach takes advantage of how electromagnetic radiation interacts with solids. As the wavelength increases, the sensitivity of the radiation to isolated solids of a specific particle size decreases. Thus, rocket exhaust-blown dust particles, which have major significance in visible wavelengths, have much less significance at radar wavelengths.

Rickman, Doug↗

DOE OSTI2025

Disoriented isospin condensates in heavy-ion collisions

Anomalous neutral to charged kaon correlations measured by the ALICE collaboration have defied usual explanations. We propose that the large fluctuations could arise because of a disoriented isospin condensate where there is an imbalance between up and down condensates at the time kaons hadronize. This could happen in heavy-ion collisions when the quark condensate re-forms as the system cools and the approximate chiral symmetry of QCD is broken. Within the linear sigma model, we show that the energy cost of forming a disoriented isospin condensate is small making it very plausible.

Kapusta, Joseph [University of Minnesota, Minneapo↗

DOE OSTI2024

GX: a GPU-native gyrokinetic turbulence code for tokamak and stellarator design

GX is a code designed to solve the nonlinear gyrokinetic system for low-frequency turbulence in magnetized plasmas, particularly tokamaks and stellarators. In GX, our primary motivation and target is a fast gyrokinetic solver that can be used for fusion reactor design and optimization along with wide-ranging physics exploration. Here, this has led to several code and algorithm design decisions, specifically chosen to prioritize time to solution. First, we have used a discretization algorithm that is pseudospectral in the entire phase space, including a Laguerre–Hermite pseudospectral formulation of velocity space, which allows for smooth interpolation between coarse gyrofluid-like resolutions and finer conventional gyrokinetic resolutions and efficient evaluation of a model collision operator. Additionally, we have built GX to natively target graphics processors (GPUs), which are among the fastest computational platforms available today. Finally, we have taken advantage of the reactor-relevant limit of small $\rho _*$ by using the radially local flux-tube approach. In this paper we present details about the gyrokinetic system and the numerical algorithms used in GX to solve the system. We then present several numerical benchmarks against established gyrokinetic codes in both tokamak and stellarator magnetic geometries to verify that GX correctly simulates gyrokinetic turbulence in the small $\rho _*$. Moreover, we show that the convergence properties of the Laguerre–Hermite spectral velocity formulation are quite favourable for nonlinear problems of interest. Coupled with GPU acceleration, which we also investigate with scaling studies, this enables GX to be able to produce useful turbulence simulations in minutes on one (or a few) GPUs and higher fidelity results in a few hours using several GPUs. GX is open-source software that is ready for fusion reactor design studies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2012

Collisional Histories of Comets and Trojan Asteroids: Diopside, Magnesite, and Fayalite Impact Studies

Comets and asteroids have weathered dynamic histories, as evidenced by their rough surfaces. The Nice model describes a violent reshuffling of small bodies during the Late Heavy Bombardment, with collisions acting to grind these planetesimals away. This creates an additional source of impact material that can re-work the surfaces of the larger bodies over the lifetime of the solar system. Here, we investigate the possibility that signatures due to impacts (e.g. from micrometeoroids or meteoroids) could be detected in their spectra, and how that can be explained by the physical manifestation of shock in the crystalline structure of minerals. All impact experiments were conducted in the Johnson Space Center Experimental Impact Laboratory using the vertical gun. Impact speeds ranged from approx.2.0 km/s to approx.2.8 km/s. All experiments were conducted at room temperature. Minerals found in comets and asteroids were chosen as targets, including diopside (MgCaSi2O6, monoclinic pyroxene), magnesite (MgCO3, carbonate), and fayalite (FeSiO4, olivine). Impacted samples were analyzed using a Fourier Transform Infrared Spectrometer (FTIR) and a Transmission Electron Microscope (TEM). Absorbance features in the 8-13 m spectral region demonstrate relative amplitude changes as well as wavelength shifts. Corresponding TEM images exhibit planar shock dislocations in the crystalline structure, attributed to deformation at high strain and low temperatures. Elongating or shortening the axes of the crystalline structure of forsterite (Mg2SiO4, olivine) using a discrete dipole approximation model (Lindsay et al., submitted) yields changes in spectral features similar to those observed in our impacted laboratory minerals.

Lederer, S. M.↗

DOE OSTI2022

Hybrid time–frequency domain dual-probe coherent anti-Stokes Raman scattering for simultaneous temperature and pressure measurements in compressible flows via spectral fitting

We demonstrate a hybrid time–frequency spectroscopic method for simultaneous temperature/pressure measurements in nonreacting compressible flows with known gas composition. Hybrid femtosecond–picosecond, pure-rotational coherent anti-Stokes Raman scattering (CARS), with two independent, time-delayed probe pulses, is deployed for single-laser-shot measurements of temperature and pressure profiles along an ∼ <#comment/> 5 -mm line. The theory of dual-probe CARS is presented, along with a discussion of the iterative fitting of experimental spectra. Temperature is obtained from spectra acquired with an early, near-collision-free probe time delay ( τ <#comment/> 1 = 0 p s ) and pressure from spectra obtained at probe delays of τ <#comment/> 2 = 150 − <#comment/> 1000 p s , where collisions significantly impact the spectral profile. Unique solutions for temperature and pressure are obtained by iteratively fitting the two spectra to account for small collisional effects observed for the near zero probe delay spectrum. A dual-probe pure-rotational CARS system, in a 1D line-imaging configuration, is developed to demonstrate effectively the simultaneous temperature and pressure profiles recorded along the axial centerline of a highly underexpanded jet. The underexpanded air jet permits evaluation of this hybrid time–frequency domain approach for temperature and pressure measurements across a wide range of low-temperature–low-pressure conditions of interest in supersonic ground-test facilities. Single-laser-shot measurement precisions in both quantities and pressure measurement accuracy are systematically evaluated in the quiet zone upstream of the Mach disk. Precise thermometry approaching 1%−2% is observed in regions of high CARS signal-to-noise ratios. Pressure measurements are optimized at probe time delays where the ratio of the late probe delay to the Raman lifetime exceeds four ( τ <#comment/> 2 / τ <#comment/> R > <#comment/> 4 ). The impact of low-temperature Raman linewidths on CARS pressure measurements is evaluated, and comparisons of CARS pressures obtained with our recent low-temperature pure-rotational Raman linewidth data and extrapolated high-temperature Q -branch linewidths are presented. Considering all measurements with τ <#comment/> 2 / τ <#comment/> R ≥ <#comment/> 4.0 , measured pressures were on average 7.9% of the computed isentropic values with average shot-to-shot deviations representing a combination of instrument noise and fluid fluctuations of 5.0%.

Retter, Jonathan E.↗

NASA NTRS1976

Post-Newtonian gravitational radiation from orbiting point masses

General formulas are derived which describe the gravitational radiation at large distances from a system of bodies whose sizes are small compared with their separations. The calculation is carried out through post-Newtonian order within general relativity. More explicit formulas are derived for two-body systems, and detailed results are presented for circular orbits, gravitational bremsstrahlung, and head-on collisions.

Wagoner, R. V.↗

NASA NTRS1999

External Pulsed Plasma Propulsion and Its Potential for the Near Future

This paper examines External Pulsed Plasma Propulsion (EPPP), a propulsion concept that derives its thrust from plasma waves generated from a series of small, supercritical fission/fusion pulses behind an object in space. For spacecraft applications, a momentum transfer mechanism translates the intense plasma wave energy into a vehicle acceleration that is tolerable to the rest of the spacecraft and its crew. This propulsion concept offers extremely high performance in terms of both specific impulse (Isp) and thrust-to-weight ratio, something that other concepts based on available technology cannot do, The political concerns that suspended work on this type of system (i.e. termination of Project ORION) may now not be as insurmountable as they were in 1965. The appeal of EPPP stems from its relatively low cost and reusability, fast interplanetary transit times, safety and reliability, and independence from major technological breakthroughs. In fact, a first generation EPPP system based on modern-day technology (i.e., GABRIEL - an evolutionary framework- of EPPP concepts) may very well be the only form of propulsion that could realistically be developed to perform ambitious human exploration beyond Mars in the 21st century. It could also provide the most effective approach for deterrence against collision between earth and small planetary objects - a growing concern over recent years.

Bonometti, J. A.↗

DOE OSTI2020

Deep learning to generate in silico chemical property libraries and candidate molecules for small molecule identification in complex samples

Comprehensive and unambiguous identification of small molecules in complex samples will revolutionize our understanding of the role of metabolites in biological systems. Existing and emerging technologies have enabled measurement of chemical properties of molecules in complex mixtures and, in concert, are sensitive enough to resolve even stereoisomers. Despite these experimental advances, small molecule identification is inhibited by (i) chemical reference libraries (e.g. mass spectra, collision cross section, and other measurable property libraries) representing <1% of known molecules, limiting the number of possible identifications, and (ii) the lack of a method to generate candidate matches directly from experimental features (i.e. without a library). To this end, we developed a variational autoencoder (VAE) to learn a continuous numerical, or latent, representation of molecular structure to expand reference libraries for small molecule identification. We extended the VAE to include a chemical property decoder, trained as a multitask network, in order to shape the latent representation such that it assembles according to desired chemical properties. The approach is unique in its application to metabolomics and small molecule identification, with its focus on properties that can be obtained from experimental measurements (m/z, CCS) paired with its training paradigm, which involved a cascade of transfer learning iterations. First, molecular representation is learned from a large dataset of structures with m/z labels. Next, in silico property values are used to continue training, as experimental property data is limited. Finally, the network is further refined by being trained with the experimental data. This allows the network to learn as much as possible at each stage, enabling success with progressively smaller datasets without overfitting. Once trained, the network can be used to predict chemical properties directly from structure, as well as generate candidate structures with desired chemical properties. Our approach is orders of magnitude faster than first-principles simulation for CCS property prediction. Additionally, the ability to generate novel molecules along manifolds, defined by chemical property analogues, positions DarkChem as highly useful in a number of application areas, including metabolomics and small molecule identification, drug discovery and design, chemical forensics, and beyond.

Colby, Sean M.↗

DOE OSTI2024

Modeling stochastic fluctuations in relativistic kinetic theory

Using the information current, we develop a Lorentz-covariant framework for modeling equilibrium fluctuations in relativistic kinetic theory in the grand-canonical ensemble. The resulting stochastic theory is proven to be causal and covariantly stable, and its predictions do not depend on the choice of spacetime foliation used to define the grand-canonical probabilities. As expected, in a box containing N > 5 particles, Boltzmann’s molecular chaos postulate is broken with (almost exact) probability N -1/2 , leading to a breakdown of the Boltzmann equation in small systems. Here, we also verify that, in ultrarelativistic gases, transient hydrodynamics already accounts for at least 80% of the equilibrium fluctuations of the stress-energy tensor at a given time. Finally, we compute the correlators at nonequal times for two selected collision kernels: that of a chemically active diluted solution, and that of ultrarelativistic scalar particles self-interacting via a quartic potential. For the former, we compute the density-density correlators analytically in real space, and dehydrodynamization of the stochastic theory is proven to occur whenever the mean free path diverges at high energy.

Astronomy & Astrophysics↗

NASA NTRS1987

Collisional dynamics of perturbed particle disks in the solar system

Investigations of the collisional evolution of particulate disks subject to the gravitational perturbation of a more massive particle orbiting within the disk are underway. Both numerical N-body simulations using a novel collision algorithm and analytical kinetic theory are being employed to extend our understanding of perturbed disks in planetary rings and during the formation of the solar system. Particular problems proposed for investigation are: (1) The development and testing of general criteria for a small moonlet to clear a gap and produce observable morphological features in planetary rings; (2) The development of detailed models of collisional damping of the wavy edges observed on the Encke division of Saturn's A ring; and (3) The determination of the extent of runaway growth of the few largest planetesimals during the early stages of planetary accretion.

Roberts, W. W.↗

NASA NTRS2004

Buffer Gas Experiments in Mercury (Hg+) Ion Clock

We describe the results of the frequency shifts measured from various buffer gases that might be used as a buffer gas to increase the loading efficiency and cooling of ions trapped in a small mercury ion clock. The small mass, volume and power requirement of space clock precludes the use of turbo pumps. Hence, a hermetically sealed vacuum system, incorporating a suitable getter material with a fixed amount of inert buffer gas may be a practical alternative to the groundbased system. The collision shifts of 40,507,347.996xx Hz clock transition for helium, neon and argon buffer gases were measured in the ambient earth magnetic field. In addition to the above non-getterable inert gases we also measured the frequency shifts due to getterable, molecular hydrogen and nitrogen gases which may be used as buffer gases when incorporated with a miniature ion pump. We also examined the frequency shift due to the low methane gas partial pressure in a fixed higher pressure neon buffer gas environment. Methane gas interacted with mercury ions in a peculiar way as to preserve the ion number but to relax the population difference in the two hyperfine clock states and thereby reducing the clock resonance signal. The same population relaxation was also observed for other molecular buffer gases (N H ,) but at much reduced rate.

mercury ion clock↗

NASA NTRS2018

USA Space Debris Environment, Operations, and Research Updates

Space Missions in 2017 Earth Satellite Population Collision Avoidance Maneuvers Post mission Disposal of U.S.A. Spacecraft Space Situational Awareness (SSA) and the Space Debris Sensor (SDS) A total of 86 space launches placed more than 400 spacecraft into Earth orbits during 2017, following the trend of increase over the past decade NASA has established conjunction assessment processes for its human spaceflight and uncrewed spacecraft to avoid accidental collisions with objects tracked by the U.S. Space Surveillance Network - NASA also assists other U.S. government spacecraft owners with conjunction assessments and subsequent maneuvers The ISS has conducted 25 debris collision avoidance maneuvers since 1999 - None in 2016-2017, but an ISS visiting vehicle had one collision avoidance maneuver in 2017 During 2017 NASA executed or assisted in the execution of 21 collision avoidance maneuvers by uncrewed spacecraft - Four maneuvers were conducted to avoid debris from Fengyun-1C - Two maneuvers were conducted to avoid debris from the collision of Cosmos 2251 and Iridium 33 - One maneuver was conducted to avoid the ISS NASA has established conjunction assessment processes for its human spaceflight and uncrewed spacecraft to avoid accidental collisions with objects tracked by the U.S. Space Surveillance Network - NASA also assists other U.S. government spacecraft owners with conjunction assessments and subsequent maneuvers The ISS has conducted 25 debris collision avoidance maneuvers since 1999 - None in 2016-2017, but an ISS visiting vehicle had one collision avoidance maneuver in 2017 During 2017 NASA executed or assisted in the execution of 21 collision avoidance maneuvers by uncrewed spacecraft - Four maneuvers were conducted to avoid debris from Fengyun-1C - Two maneuvers were conducted to avoid debris from the collision of Cosmos 2251 and Iridium 33 The 2014-15 NASA Engineering and Safety Center (NESC) study on the micrometeoroid and orbital debris (MMOD) assessment for the Joint Polar Satellite System (JPSS) provided the following findings - Millimeter-sized orbital debris pose the highest penetration risk to most operational spacecraft in LEO - The most effective means to collect direct measurement data on millimetersized debris above 600 km altitude is to conduct in situ measurements - There is currently no in situ data on such small debris above 600 km altitude Since the orbital debris population follows a power-law size distribution, there are many more millimeter-sized debris than the large tracked objects - Current conjunction assessments and collision avoidance maneuvers against the tracked objects (which are typically 10 cm and larger) only address a small fraction (<1%) of the mission-ending risk from orbital debris To address the millimeter-sized debris data gap above 600 km, NASA has recently developed an innovative in situ measurement instrument - the Space Debris Sensor (SDS) - One maneuver was conducted to avoid the ISS

Liou, J.-C.↗

DOE OSTI2024

Effect of causality constraints on Bayesian analyses of heavy-ion collisions

There have long been questions about the limits to the validity of relativistic fluid dynamics and whether it is being used outside its regime of validity in modern simulations of relativistic heavy-ion collisions. An important new tool for answering this question is a causality analysis in the nonlinear regime—if the solutions of the evolution equations do not respect relativistic causality, then they are not a faithful representation of the underlying relativistic theory (in this case, quantum chromodynamics). Using this nonlinear criterion, it has recently been shown that hydrodynamics is indeed being used outside its regime of validity in simulations, at least sometimes. Here we explore the phenomenological implications, particularly the quantitative effects of demanding limits on acausality in modern Bayesian parameter estimation. We find that, while typically only a small fraction of the system's energy is initially in an acausal regime, placing strict limits on the allowed energy fraction significantly changes the preferred properties of the initial condition, which in turn alters the extracted medium properties such as bulk viscosity, where large values are no longer favored. Furthermore, these findings highlight the importance of developing better theoretical descriptions of the early-time, out-of-equilibrium dynamics of relativistic heavy-ion collisions.

Bayesian methods↗

NASA NTRS2019

Airborne Radar for sUAS Sense and Avoid

A primary challenge for the safe integration of small UAS operations into the National Airspace System (NAS) is traffic deconfliction, both from manned and unmanned aircraft. The UAS Traffic Management (UTM) project being conducted at the National Aeronautics and Space Administration (NASA) considers a layered approach to separation provision, ranging from segregation of operations through airspace volumes (geofences) to autonomous sense and avoid (SAA) technologies for higher risk, densely occupied airspace. Cooperative SAA systems, such as Automatic Dependent Surveillance-Broadcast (ADS-B) and/or vehicle-to-vehicle communication systems provide significant additional risk mitigation but they fail to adequately mitigate collision risks for non-cooperative (non-transponder equipped) airborne aircraft. The RAAVIN (Radar on Autonomous Aircraft to Verify ICAROUS Navigation) flight test being conducted by NASA and the Mid-Atlantic Aviation Partnership (MAAP) was designed to investigate the applicability and performance of a prototype, commercially available sUAS radar to detect and track non-cooperative airborne traffic, both manned and unmanned. The radar selected for this research was a Frequency Modulated Continuous Wave (FMCW) radar with 120 degree azimuth and 80 degree elevation field of view operating at 24.55GHz center frequency with a 200 MHz bandwidth. The radar transmits 2 watts of power thru a Metamaterial Electronically Scanning Array antenna in horizontal polarization. When the radar is transmitting, personnel must be at least 1 meter away from the active array to limit nonionizing radiation exposure. The radar physical dimensions are 18.7cm by 12.1cm by 4.1cm and it weighs less than 820 grams making it well suited for installation on small UASs. The onboard, SAA capability, known as ICAROUS, (Independent Configurable Architecture for Reliable Operations of Unmanned Systems), developed by NASA to support sUAS operations, will provide autonomous guidance using the traffic radar tracks from the onboard radar. The RAAVIN set of studies will be conducted in three phases. The first phase included outdoor, ground-based radar evaluations performed at the Virginia Tech’s Kentland Farm testing range in Blacksburg, VA. The test was designed to measure how well the radar could detect and track a small UAS flying in the radar’s field of view. The radar was used to monitor 5 test flights consisting of outbound, inbound and crossing routes at different ranges and altitudes. The UAS flown during the ground test was the Inspire 2, a quad copter weighing less than 4250 grams (10 pounds) at maximum payload. The radar was set up to scan and track targets over its full azimuthal field of view from 0 to 40 degrees in elevation. The radar was configured to eliminate tracks generated from any targets located beyond 2000 meters from the radar and moving at velocities under 1.45 meters per second. For subsequent phases of the study the radar will be integrated with a sUAS platform to evaluate its performance in flight for SAA applications ranging from sUAS to manned GA aircraft detections and tracking. Preliminary data analysis from the first outdoor ground tests showed the radar performed well at tracking the vehicle as it flew outbound and repeatedly maintained a track out to 1000 meters (maximum 1387 meters) until the vehicle slowed to a stop to reverse direction to fly inbound. As the Inspire flew inbound tracks from beyond 800 meters, a reacquisition time delay was consistently observed between when the Inspire exceeds a speed of 1.45 meters per second and when the radar indicated an inbound target was present and maintained its track. The time delay varied between 6 seconds to over 37 seconds for the inbound flights examined, and typically resulted in about a 200 meter closure distance before the Inspire track was maintained. The radar performed well at both acquiring and tracking the vehicle as it flew crossing routes out past 400 meters across the azimuthal field of view. The radar and ICAROUS software will be integrated and flown on a BFD-1400-SE8-E UAS during the next phase of the RAAVIN project. The main goal at the conclusion of this effort is to determine if this radar technology can reliably support minimum requirements for SAA applications of sUAS. In particular, the study will measure the range of vehicle detections, lateral and vertical angular errors, false and missed/late detections, and estimated distance at closest point of approach after an avoidance maneuver is executed. This last metric is directly impacted by sensor performance and indicates its suitability for the task.

Szatkowski, George N.↗

NASA NTRS1983

Cloud-particle galactic gas dynamics and star formation

Galactic gas dynamics, spiral structure, and star formation are discussed in relation to N-body computational studies based on a cloud-particle model of the interstellar medium. On the small scale, the interstellar medium is seen as cloud-dominated and supernova-perturbed. It is noted that the cloud-particle model simulates cloud-cloud collisions, the formation of stellar associations, and supernova explosions as dominant local processes. On the large scale, in response to a spiral galactic gravitational field, global density waves and galactic shocks develop having large-scale characteristics similar to those found in continuum gas dynamical studies. Both the system of gas clouds and the system of young stellar associations forming from the clouds figure in the global spiral structure. However, with the attributes of neither assuming a continuum of gas (as in continuum gas dynamical studies) or requiring a prescribed equation of state (such as the isothermal condition), the cloud-particle picture retains much of the detail lost in earlier work. By detail is meant the small-scale features and structures so important in understanding the local, turbulent state of the interstellar medium as well as the degree of raggedness often seen to be superposed on the global spiral structure.

Roberts, W. W., Jr.↗

NASA NTRS1992

Proportional proximity sensing for telerobots using Coherent Laser Radar

The ability of a telerobotic manipulator to operate in confined spaces while avoiding unwanted collisions is enhanced by the accurate sensing of its proximate environment. To achieve the fidelity required for precise manipulator control, a proportional proximity sensor system with a sufficiently large measurement envelope is required. Current proximity sensors provide a binary indication of the presence of obstacles within a small envelope with coarse or no proportional measurement of their location. A proportional proximity sensor system configured as a Frequency Modulated Continuous Wave (FMCW) Coherent Laser Radar (CLR) using a semiconductor laser as the energy source is described and analyzed. The source and reflected energies mix coherently to generate a radio frequency (RF) signal whose frequency is proportional to the range. The system is tested for accuracy, range, depth of range, speed, and sensitivity and the results are presented. Techniques to derive orientation information and an application to telerobotic control are also described.

Vazquez, Sixto L.↗

NASA NTRS2010

First Earth-Based Detection of a Superbolide on Jupiter

Cosmic collisions can planets cause detectable optical flashes that range from terrestrial shooting stars to bright fireballs. On 2010 June 3 a bolide in Jupiter's atmosphere was simultaneously observed from the Earth by two amateur astronomers observing Jupiter in red and blue wavelengths, The bolide appeared as a flash of 2 s duration in video recording data of the planet. The analysis of the light carve of the observations results in an estimated energy of the impact of (0.9-4,0) x 10(exp 15) J which corresponds to a colliding body of 8-13 m diameter assuming a mean density of 2 g/cu cm. Images acquired a few days later by the Hubble Space Telescope and other large ground-based facilities did not show any signature of aerosol debris, temperature, or chemical composition anomaly, confirming that the body was small and destroyed in Jupiter's upper atmosphere. Several collisions of this size may happen on Jupiter on a yearly basis. A systematic study of the impact rate and size of these bolides can enable an empirical determination. of the flux of meteoroids in Jupiter with implications for the populations of small bodies in the outer solar system and may allow a better quantification of the threat of impacting bodies to Earth. The serendipitous recording of this optical flash opens a new window in the observation of Jupiter with small telescopes.

Hueso, R.↗

NASA NTRS1972

Kinetic theory of a two-dimensional magnetized plasma. II - Balescu-Lenard limit.

The kinetic theory of a two-dimensional one-species plasma in a uniform dc magnetic field is investigated in the small plasma parameter limit. The plasma consists of charged rods interacting through the logarithmic Coulomb potential. Vahala and Montgomery earlier (1971) derived a Fokker-Planck equation for this system, but it contained a divergent integral, which had to be cut off on physical grounds. This cutoff is compared to the standard cutoff introduced in the two-dimensional unmagnetized Fokker-Planck equation. In the small plasma parameter limit, it is shown that the Balescu-Lenard collision term is zero in the long time average limit if only two-body interactions are considered. The energy transfer from a test particle to an equilibrium plasma is discussed and is also shown to be zero in the long time average limit. This supports the unexpected result of zero Balescu-Lenard collision term.

Vahala, G.↗