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At least 271 records · Page 15

Supersonic Aerodynamic Characteristics of a Low-Drag Aircraft Configuration having an Arrow Wing of Aspect Ratio 1.86 and a Body of Fineness Ratio 20

A free-flight rocket-propelled-model investigation was conducted at Mach numbers of 1.2 to 1.9 to determine the longitudinal and lateral aero-dynamic characteristics of a low-drag aircraft configuration. The model consisted of an aspect-ratio -1.86 arrow wing with 67.5 deg. leading-edge sweep and NACA 65A004 airfoil section and a triangular vertical tail with 60 deg. sweep and NACA 65A003 section in combination with a body of fineness ratio 20. Aerodynamic data in pitch, yaw, and roll were obtained from transient motions induced by small pulse rockets firing at intervals in the pitch and yaw directions. From the results of this brief aerodynamic investigation, it is observed that very slender body shapes can provide increased volumetric capacity with little or no increase in zero-lift drag and that body fineness ratios of the order of 20 should be considered in the design of long-range supersonic aircraft. The zero-lift drag and the drag-due-to-lift parameter of the test configuration varied linearly with Mach number. The maximum lift-drag ratio was 7.0 at a Mach number of 1.25 and decreased slightly to a value of 6.6 at a Mach number of 1.81. The optimum lift coefficient, normal-force-curve slope, lateral-force-curve slope, static stability in pitch and yaw, time to damp to one-half amplitude in pitch and yaw, the sum of the rotary damping derivatives in pitch and also in yaw, and the static rolling derivatives all decreased with an increase in Mach number. Values of certain rolling derivatives were obtained by application of the least-squares method to the differential equation of rolling motion. A comparison of the experimental and calculated total rolling-moment-coefficient variation during transient oscillations of the model indicated good agreement when the damping-in-roll contribution was included with the static rolling-moment terms.

Gillespie, Warren, Jr.↗

Major Constituents Analysis for the Vehicle Cabin Atmosphere Monitor

Vehicle Cabin Atmosphere Monitor (VCAM) can provide a means for monitoring the air within enclosed environments such as the International Space Station, the Crew Exploration Vehicle (CEV), a Lunar habitat, or another vehicle traveling to Mars. The software processes a sum total spectra (counts vs. mass channel) with the intention of computing abundance ratios for N2, O2, CO2, Ar2, and H2O. A brute-force powerset expansion compares a library of expected mass lines with those found within the data. Least squares error is combined with a penalty term for using small peaks.

Mandrake, Lukas↗

Exponential Approximations Using Fourier Series Partial Sums

The problem of accurately reconstructing a piece-wise smooth, 2(pi)-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. It is conjectured that the locations of the singularities are approximated to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is approximated to within O(N(sup -M-l+k), as N approaches infinity, and the method is robust. These estimates are then used with a class of singular basis functions, which have certain 'built-in' singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M approaches infinity. The technique is illustrated with several examples.

Banerjee, Nana S.↗

Energetics of RHESSI X-Class Flares

The thermal and nonthermal energies of several X-class flares seen with the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) will be presented. The same techniques described by Emslie et al. (JGR, 109, A10104, 2004) are used to take the RHESSI imaging spectroscopic observations and compute the energies in the thermal plasma and in the nonthermal electrons as a function of time throughout the flares. Radiative and conductive cooling rates are estimated and total thermal and nonthermal energies are computed for each flare. Typically, the energy in nonthermal electrons integrated up to the time of peak soft X-ray emission is equal to or exceeds the energy in the thermal plasma at that time. This suggests that energy must have been converted into a form not visible with RHESSI and that the total energy released by the flares may be significantly greater than the sum of energies calculated from the RHESSI observations alone. This conclusion is supported by the high radiative energy seen with SORCE during the impulsive phase of the 28 October 2003 flare. The peak increase in total solar irradiance of 270 mW per square meters measured with SORCE was over two orders of magnitude higher than the peak soft X-ray flux seen with GOES or RHESSI. The implications of this new observation as compared to the energetics derived from the X-ray observations of that flare will be discussed along with the energetics analysis of most of the other X- class flares in October/November 2003.

Dennis, Brian R.↗

Sampling Size Optimization for Bioburden Density Estimation in Planetary Protection

Planetary protection (PP) is a discipline that focuses on minimizing the biological contamination of spacecraft to ensure compliance with international policy. Precise estimation of bioburden - the total number of microbes in or on spacecraft hardware – and the bioburden density are of utmost importance for PP. Such estimation is the way concordance with requirements is demonstrated, and it is critical for quantifying the potential risk of inadvertently contaminating other planetary bodies. Although a suite of molecular techniques have been used to thoroughly characterize and profile the microbiome of various cleanroom environments and spacecraft, the gold standard remains the physical enumeration of microbes via culturing of samples directly taken from spacecraft and associated surfaces. However, due to technical, budgetary, and programmatic constraints, only a manageable portion (around 10%) of the entire spacecraft surface is directly sampled with cotton swabs or wipes. To generate the bioburden current best estimate (CBE) for components not directly verifiable, the accepted approach is to apply a NASA-defined bioburden estimate based on the components’ manufacturing or assembly environment. This approach utilizes a prespecified bioburden density estimation that applies a maximum value across the total surface area of the specified component. For hardware components that underwent similar assembly processes, an implied bioburden is adopted for all components, based on a direct verification of a representative component within the same lot. Once all components have a CBE, the bioburden estimates are generated. In previous publication [ 1], we have shown that statistical risks quantifying the accuracy of the estimates for sampled, prespecified, and implied components can be derived and ranked. For mean squared error (MSE) function, the risks are available analytically and hence a cost function can be obtained to optimize the risks with respect to the sampling area and sampling cost. Since the sampling area and sampling cost are two complimentary variables, their sum will have a well-defined minimum. This paper presents the multivariate optimization of the integrated risk of an empirical Bayes estimator to determine the optimal sampling schedule for a given number of components. It is assumed that given a number of components, N, the bioburden density for each component can either be sampled, implied, or prespecified. The multivariate optimization searches through different options to sample, imply or prespecify the bioburden density for a component, and account for the component’s surface area and cost of sampling. The idea of the optimization is based on the observation that the statistical risk of using an estimator is a monotonically decreasing function of the sampled area. The larger the sampled area, the lower the risk of using the estimator as the estimator becomes more and more accurate as the sampling area increases. On the other hand, the cost of sampling is monotonically increasing as the sampled surface grows. This makes the risk and total cost of sampling complimentary variables which can be counterbalanced to achieve an optimal overall value with respect to the sampled surface. In this paper, the integrated risk has been used to quantify the accuracy of the estimator. This risk has been selected because it depends on neither the true value of the parameter nor on the collected data. The cost of each sample was also available to obtain the total cost of sampling of N components. The paper will present the results based on computer-simulated data as well as the data collected during the InSight mission. The computer-simulated data have N components with randomly generated total areas and each component assigned to one of the three categories according to the method of estimating of bioburden density: sampled, implied, or prespecified. The cost of sampling is also available. The cost of sampling is estimated based on a cost model provided by the planetary protection group at JPL. For this paper, the overall cost was assumed to be a linear function of exposure. The optimization process finds the allocation of the components to the three categories that minimizes the tradeoff between integrated risk and total cost. For the InSight data, a set of components is selected representing all three categories, and optimization is performed to determine if the performed allocation was optimal or if a better allocation could have been obtained. To the best of our knowledge, this work is the first attempt not only perform an accurate estimation of bioburden density but also do it in an optimal way.

97 - MATHEMATICS AND COMPUTING↗

Search for pair production of heavy particles decaying to a top quark and a gluon in the lepton+jets final state in proton–proton collisions at $\sqrt{s}=13\,\text {Te}\hspace{-.08em}\text {V}$

A search is presented for the pair production of new heavy resonances, each decaying into a top quark (t) or antiquark and a gluon (g). The analysis uses data recorded with the CMS detector from proton–proton collisions at a center-of-mass energy of 13 TeV at the LHC, corresponding to an integrated luminosity of 138 fb -1 . Events with one muon or electron, multiple jets, and missing transverse momentum are selected. After using a deep neural network to enrich the data sample with signal-like events, distributions in the scalar sum of the transverse momenta of all reconstructed objects are analyzed in the search for a signal. No significant deviations from the standard model prediction are found. Upper limits at 95% confidence level are set on the product of cross section and branching fraction squared for the pair production of excited top quarks in the t* → tg decay channel. The upper limits range from 120 to 0.8 fb for a t* with spin-1/2 and from 15 to 1.0 fb for a t* with spin-3/2. These correspond to mass exclusion limits up to 1050 and 1700 GeV for spin-1/2 and spin-3/2 t* particles, respectively. These are the most stringent limits to date on the existence of t* → tg resonances.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Applying the System Complexity Metric (SCM)

A fundamental cause of difficulty in larger engineering projects is their inherent complexity. An impression of complexity occurs if a system is simply difficult to understand, so that there is no obvious mental model that correctly predicts its behavior. Higher complexity is usually associated with higher cost and higher failure rate. Complexity is indicated by a system having more and diverse components, multiple interactions and feedback loops, transients and dynamic behavior, and often the emergence of unanticipated failure modes. Identifying and removing these signs of complexity should reduce complexity and improve performance. Here we limit complexity measurement to the number of components and their interactions. A System Complexity Metric (SCM) is defined as equal to the sum of the number of parts in a system, N, plus the sum of the one-way interconnections between them, I. SCM = N + I. The SCM is easily determined by direct inspection of system block diagrams. Previous work found that life support system cost was directly proportional to SCM and that failure rate increased faster than SCM squared. SCM can be used to compare systems or to guide their redesign to reduce cost and failure rate. Carbon dioxide removal systems will be analyzed using SCM, cost, and failure rate.

Harry W Jones↗

Origins of Clustering of Metalate–Extractant Complexes in Liquid–Liquid Extraction

Effective and energy-efficient separation of precious and rare metals is very important for a variety of advanced technologies. Liquid-liquid extraction (LLE) is a relatively less energy intensive separation technique, widely used in separation of lanthanides, actinides, and platinum group metals (PGMs). In LLE, the distribution of an ion between an aqueous phase and an organic phase is determined by enthalpic (coordination interactions) and entropic (fluid reorganization) contributions. The molecular scale details of these contributions are not well understood. Preferential extraction of an ion from the aqueous phase is usually correlated with the resulting fluid organization in the organic phase, as the longer-range organization increases with metal loading. However, it is difficult to determine the extent to which organic phase fluid organization causes, or is caused by, metal loading. In this study, we demonstrate that two systems with the same metal loading may impart very different organic phase organizations and investigate the underlying molecular scale mechanism. Small-angle X-ray scattering shows that the structure of a quaternary ammonium extractant solution in toluene is affected differently by the extraction of two metalates (octahedral PtCl 6 2- and square-planar PtCl 6 2- ), although both are completely transferred into the organic phase. The aggregates formed by the metalate-extractant complexes (approximated as reverse micelles) exhibit a more long-range order (clustering) with PtCl 6 2- compared to that with PtCl 6 2- . Vibrational sum frequency generation spectroscopy and complementary atomistic molecular dynamics simulations on model Langmuir monolayers indicate that the two metalates affect the interfacial hydration structures differently. Furthermore, the interfacial hydration is correlated with water extraction into the organic phase. Overall, these results support a strong relationship between the organic phase organizational structure and the different local hydration present within the aggregates of metalate-extractant complexes, which is independent of metalate concentration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Simulation of ocean SAR images via phase history generation

A method for simulating an ocean synthetic-aperture radar (SAR) image is illustrated for a simple internal wave current pattern. The method calculates both the amplitude image and the radar signal history. The simulation model used consists of six stages. In the first stage, the full wave spectrum in two spatial coordinates is calculated from the wind speed and direction using the action spectral density equation. In the second stage, the pixel size is selected and used as the basis for dividing the spectrum into large and small scale motions. Realizations for the large-scale ocean surface height and velocity are then calculated. In the third stage, the sensor wavelength and geometry are used to calculate the small scale statistics (radar cross section, coherence time, root-mean square (RMS), radial velocity and RMS slope). In the fourth stage, an autoregressive method is used to generate a realization of the surface reflectivity history that is consistent with the radial velocity and the radial velocity variance. In the fifth stage, the signal history is generated by summing the reflectivities at the proper times with the appropriate antenna weighting function for the SAR. As a consequence of this process, speckle is automatically included in the signal. In the final stage, the SAR image can be created by using any of the traditional ways to process the signal history, including variable focusing and multilook processing.

Bennett, John R.↗

Implementation of equivalent domain integral method in the two-dimensional analysis of mixed mode problems

An equivalent domain integral (EDI) method for calculating J-intergrals for two-dimensional cracked elastic bodies is presented. The details of the method and its implementation are presented for isoparametric elements. The total and product integrals consist of the sum of an area of domain integral and line integrals on the crack faces. The line integrals vanish only when the crack faces are traction free and the loading is either pure mode 1 or pure mode 2 or a combination of both with only the square-root singular term in the stress field. The EDI method gave accurate values of the J-integrals for two mode I and two mixed mode problems. Numerical studies showed that domains consisting of one layer of elements are sufficient to obtain accurate J-integral values. Two procedures for separating the individual modes from the domain integrals are presented. The procedure that uses the symmetric and antisymmetric components of the stress and displacement fields to calculate the individual modes gave accurate values of the integrals for all problems analyzed. The EDI method when applied to a problem of an interface crack in two different materials showed that the mode 1 and mode 2 components are domain dependent while the total integral is not. This behavior is caused by the presence of the oscillatory part of the singularity in bimaterial crack problems. The EDI method, thus, shows behavior similar to the virtual crack closure method for bimaterial problems.

Raju, I. S.↗

Location and thermal evolution of the pseudogap due to spin fluctuations

We study pseudogap behavior in a metal near a spin density wave (SDW) instability due to thermal magnetic fluctuations. We consider the t–t' Hubbard model on a square lattice at a finite doping, at intermediate coupling strength, and analyze the thermal evolution of the electron spectral function between a SDW ordered state at low temperatures and a normal Fermi liquid at high temperatures. We argue that for proper description of the pseudogap one needs to sum up infinite series of diagrams for both the fermionic self-energy and the SDW order parameter in the SDW state or the magnetic correlation length in the paramagnetic state. We use the eikonal approach to sum up an infinite series of diagrammatic contributions from thermal fluctuations. Earlier studies found that in the SDW state the spectral function A k (ω) of a hot fermion at a finite T is exponentially small below the energy scale Δ(T), which scales with SDW order and vanishes at the ordering temperature T N , and has a hump at a larger frequency Δ PG , comparable to the zero-temperature SDW gap Δ(T = 0). We argue that the hump, which we associate with the pseudogap, survives in some T range above T N . We show that this range is split by regions of strong and weak pseudogap behavior. In the first region, Δ PG is weakly temperature dependent, despite the fact that it comes from thermal fluctuations. Such a behavior has been seen in numerical studies of the Hubbard model. We show that to obtain it one needs to go beyond the one-loop approximation and sum up the infinite series of diagrams. In the second regime, Δ PG decreases with increasing T and eventually vanishes. Here, we further argue that a magnetic pseudogap at a finite T emerges only if the ground state is magnetically ordered. We present the phase diagram and apply the results to high-T c cuprates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Detection of False Data Injection Attacks in Battery Stacks Using Input Noise-Aware Nonlinear State Estimation and Cumulative Sum Algorithms

Grid-scale battery energy storage systems (BESSs) are vulnerable to false data injection attacks (FDIAs), which could be used to disrupt state of charge (SoC) estimation. Inaccurate SoC estimation has negative impacts on system availability, reliability, safety, and the cost of operation. In this article a combination of a Cumulative Sum (CUSUM) algorithm and an improved input noise-aware extended Kalman filter (INAEKF) is proposed for the detection and identification of FDIAs in the voltage and current sensors of a battery stack. The series-connected stack is represented by equivalent circuit models, the SoC is modeled with a charge reservoir model and the states are estimated using the INAEKF. Further, the root mean squared error of the states’ estimation by the modified INAEKF was found to be superior to the traditional EKF. By employing the INAEKF, this article addresses the research gap that many state estimators make asymmetrical assumptions about the noise corrupting the system. Additionally, the INAEKF estimates the input allowing for the identification of FDIA, which many alternative methods are unable to achieve. The proposed algorithm was able to detect attacks in the voltage and current sensors in 99.16% of test cases, with no false positives. Utilizing the INAEKF compared to the standard EKF allowed for the identification of FDIA in the input of the system in 98.43% of test cases.

25 ENERGY STORAGE↗

Uniform-density Bose-Einstein condensates of the Gross-Pitaevskii equation found by solving the inverse problem for the confining potential

Here, in this work, we consider a “reverse-engineering” approach to construct confining potentials that support exact, constant density kovaton solutions to the classical Gross-Pitaevskii equation (GPE) also known as the nonlinear Schr¨odinger equation (NLSE). In the one-dimensional case, the exact solution is the sum of stationary kink and anti-kink solutions, i.e. a kovaton, and in the overlapping region, the density is constant. In higher dimensions, the exact solutions are generalizations of this wave function. In the absence of self-interactions, the confining potential is similar to a smoothed out finite square well with minima also at the edges. When self-interactions are added, a term proportional to ±gψ*ψ gets added to the confining potential and ±gM, where M is the norm, gets added to the total energy. In the realm of stability analysis, we find (linearly) stable solutions in the case with repulsive self-interactions which also are stable to self-similar deformations. For attractive interactions, however, the minima at the edges of the potential get deeper and a barrier in the center forms as we increase the norm. This leads to instabilities at a critical value of M (related to the number of particles in the BEC). Comparing the stability criteria from Derrick’s theorem and Bogoliubov-de Gennes analysis stability results, we find that both predict stability for repulsive self-interactions and instability at a critical mass M for attractive interactions. However, the numerical analysis gives a much lower critical mass. The numerical analysis shows further that the initial instabilities violate the symmetry x → -x assumed by Derrick’s theorem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Global Precipitation at One-Degree Daily Resolution From Multi-Satellite Observations

The One-Degree Daily (1DD) technique is described for producing globally complete daily estimates of precipitation on a 1 deg x 1 deg lat/long grid from currently available observational data. Where possible (40 deg N-40 deg S), the Threshold-Matched Precipitation Index (TMPI) provides precipitation estimates in which the 3-hourly infrared brightness temperatures (IR T(sub b)) are thresholded and all "cold" pixels are given a single precipitation rate. This approach is an adaptation of the Geostationary Operational Environmental Satellite (GOES) Precipitation Index (GPI), but for the TMPI the IR Tb threshold and conditional rain rate are set locally by month from Special Sensor Microwave/Imager (SSM/I)-based precipitation frequency and the Global Precipitation Climatology Project (GPCP) satellite-gauge (SG) combined monthly precipitation estimate, respectively. At higher latitudes the 1DD features a rescaled daily Television Infrared Observation Satellite (TIROS) Operational Vertical Sounder (TOVS) precipitation. The frequency of rain days in the TOVS is scaled down to match that in the TMPI at the data boundaries, and the resulting non-zero TOVS values are scaled locally to sum to the SG (which is a globally complete monthly product). The time series of the daily 1DD global images shows good continuity in time and across the data boundaries. Various examples are shown to illustrate uses. Validation for individual grid -box values shows a very high root-mean-square error but, it improves quickly when users perform time/space averaging according to their own requirements.

Huffman, George J.↗

Thermal iron ions in high speed solar wind streams. II - Temperatures and bulk velocities

Mitchel and Roelof (1980) reported the detection of iron in high speed solar wind flows using the small, but finite sensitivity of solid state detectors to Fe ions in the low energy (50-200 keV protons) L1 channel of the NOAA/JHU energetic particle experiment (EPE). In the current investigation, the EPE response is modeled to a convected Maxwellian to obtain the thermal velocity, flow angle, and bulk velocity of the iron distribution. It is assumed that the iron bulk flow velocity can be represented as a vector sum of the hydrogen bulk velocity and an interplanetary magnetic field (IMF) aligned velocity increment. It is found that the velocity increment is smaller than the local Alfven speed in magnitude, and that the iron thermal velocity is comparable with or greater than the proton thermal velocity, with the 'thermal' velocity defined as the square root of 2kT/m.

Mitchell, D. G.↗

Ab Initio Calculations of Water Line Strengths

We report on the determination of a high quality ab initiu potential energy surface (PES) and dipole moment function for water. This PES is empirically adjusted to improve the agreement between the computed line positions and those from the HITRAN 92 data base with J less than 6 for H2O. The changes in the PES are small, nonetheless including an estimate of core (oxygen 1s) electron correlation greatly improves the agreement with experiment. Using this adjusted PES, we can match 30,092 of the 30,117 transitions in the HITRAN 96 data base for H2O with theoretical lines. The 10,25,50,75, and 90 percentiles of the difference between the calculated and tabulated line positions are -0.11, -0.04, -0.01, 0.02, and 0.07 l/cm. Non-adiabatic effects are not explicitly included. About 3% of the tabulated line positions appear to be incorrect. Similar agreement using this adjusted PES is obtained for the oxygen 17 and oxygen 18 isotopes. For HDO, the agreement is not as good, with root-mean-square error of 0.25 l/cm for lines with J less than 6. This error is reduced to 0.02 l/cm by including a small asymmetric correction to the PES, which is parameterized by simultaneously fitting to HDO md D2O data. Scaling this correction by mass factors yields good results for T2O and HTO. The intensities summed over vibrational bands are usually in good agreement between the calculations and the tabulated results, but individual lines strengths can differ greatly. A high temperature list consisting of 307,721,352 lines is generated for H2O using our PES and dipole moment function.

Schwenke, David W.↗

High Angular Resolution Gravitational Wave Astronomy

Since the very beginning of astronomy the location of objects on the sky has been a fundamental observational quantity that has been taken for granted. While precise two dimensional positional information is easy to obtain for observations in the electromagnetic spectrum, the positional accuracy of current and near future gravitational wave detectors is limited to between tens and hundreds of square degrees, which makes it extremely challenging to identify the host galaxies of gravitational wave events or to detect any electromagnetic counterparts. Gravitational wave observations provide information on source properties that is complementary to the information in any associated electromagnetic emission. Observing systems with multiple messengers thus has scientific potential much greater than the sum of its parts. A gravitational wave detector with higher angular resolution would significantly increase the prospects for finding the hosts of gravitational wave sources and triggering a multi-messenger follow-up campaign. An observatory with arcminute precision or better could be realised within the Voyage 2050 programme by creating a large baseline interferometer array in space and would have transformative scientific potential. Precise positional information of standard sirens would enable precision measurements of cosmological parameters and offer new insights on structure formation; a high angular resolution gravitational wave observatory would allow the detection of a stochastic background and resolution of the anisotropies within it; it would also allow the study of accretion processes around black holes; and it would have tremendous potential for tests of modified gravity and the discovery of physics beyond the Standard Model.

Gravitational waves↗

Plume Characterization of a One-Millipound Solid Teflon Pulsed Plasma Thruster, Phase 2

Measurements of the pulsed plasma thruster (PPT) plume upstream mass flux were made in the Molecular Sink (MOLSINK) vacuum facility in order to minimize the plume-tank wall reflected mass flux. Using specially designed collimators on 4 rows of Quartz Crystal Microbalanced (QCMs) mounted on a support extending radially away from the plume axis, measurements were made of the mass flux originating in a thin slice of the PPT primary plume at an arbitrary dip angle with respect to the thruster axis. The measured and analytically corrected mass flux from particles reflected from the MOLSINK walls was substracted from the collimated QCM measurements to improve their accuracy. These data were then analytically summed over dip angle to estimate the total plume backflow upstream of the thruster nozzle. The results indicate that the PPT backflow is of order 10 to the minus 10th power g/square cm/pulse in the region from 38 to 86 cm from the PPT axis in the nozzle exit plane. This flux drops with the square of the radial distance from the PPT axis and is comparable to the backflow of an 8 cm ion thruster, which has performance characteristics similar to those of the PPT.

Rudolph, L. K.↗