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NASA NTRS2003

Preliminary Planar Formation: Flight Dynamics Near Sun-Earth L2 Point

NASA's Goddard Space Flight Center is planning a series of missions in the vicinity of the Sun-Earth L2 libration point. Some of these projects will involve a distributed space system of telescope spacecraft acting together as a single telescope for high-resolution. The individual telescopes will be configured in a plane, surrounding a hub, where the telescope plane can be aimed toward various astronomical targets of interest. In preparation for these missions, it is necessary to develop an improved understanding of the dynamical behavior of objects in a planar configuration near L2. The classical circular restricted three body problem is taken as the basis for the analysis. At first order, the motion of such a telescope relative to the hub is described by a system of linear second order differential equations. These equations are identical to the circular restricted problem's linear equations describing the hub motion about L2. Therefore, the fundamental frequencies, both parallel to and normal to the ecliptic plane, are the same for the relative telescope motion as for the hub motion. To maintain the telescope plane for the duration necessary for the planned observations, a halo-type orbit of the telescopes about the hub is investigated. By using a halo orbit, the individual telescopes remain in approximately the same plane over the observation duration. For such an orbit, the fundamental periods parallel to and normal to the ecliptic plane are forced to be the same by careful selection of the initial conditions in order to adjust the higher order forces. The relative amplitudes of the resulting oscillations are associated with the orientation of the telescope plane relative to the ecliptic. As in the circular restricted problem, initial conditions for the linearized equations must be selected so as not to excite the convergent or divergent linear modes. In a higher order analysis, the telescope relative motion equations include the effects of the position of the hub relative to L2. In this paper, the differential equations are developed through second order in the distance of the hub from the libration point. A modified Lindstedt-Poincad perturbation method is employed to construct the solution of these differential equations through that same order of magnitude. In the course of the solution process, relationships are determined between the initial conditions of the telescopes, selected in order to avoid resonance excitation. As the differential equations include the hub position, it is necessary to simultaneously develop the solution for the hub. As has been done in past analyses of the circular restricted problem, the hub position is written in a power series formulation in terms of its distance from L2. Then, in order to be included in the telescope equations, the hub solution is cast in terms of the nonlinear frequency of the relative telescope motion. In the course of the analysis, it is determined that the hub should also maintain a halo orbit - about L2. Additionally, relationships are formed between the initial conditions of the telescopes and the hub. These relationships may be used to associate sets of initial conditions with particular orientations of the telescope plane. The accuracy of the analytical solution is verified through various simulations and comparison to numerical integration of the differential equations. The results of the simulations are presented, along with a graphical representation of the relationships between the initial conditions of the telescopes and hub.

Segerman, Alan M.↗
NASA NTRS1994

Retrieval of sizes and total masses of particles in volcanic clouds using AVHRR bands 4 and 5

The advanced very high resolution radiometer (AVHRR) sensor on polar orbiting NOAA satellites can discriminate between volcanic clouds and meteorological clouds using two-band data in the thermal infrared. This paper is aimed at developing a retrieval of the particle sizes, optical depth, and total masses of particles from AVHRR two-band data of volcanic clouds. Radiative transfer calculations are used with a semi-transparent cloud model that is based on assumptions of spherical particle shape, a homogeneous underlying surface, and a simple thin cloud parallel to the surface. The model is applied to observed AVHRR data from a 13-hour old drifting cloud from the August 19, 1992, eruption of Crater Peak/Spurr Volcano, Alaska. The AVHRR data fit in the range of results calculated by the model, which supports its credibility. According to the model results, the average of effective particle radius in the test frame of this cloud is in the range of 2 to 2.5 micrometer, the optical depth at 12 micrometer is about 0.60 - 0.65. The total estimated mass of ash in the air amounts to 0.24 - 0.31 x 10(exp 6) tons, which is about 0.7-0.9% of the mass measured in the ashfall blanket. Sensitivity tests show that the mass estimate is more sensitive to the assumed ash size distribution than it is to the ash composition.

Wen, Shiming↗
NASA NTRS2020

Applying Orbital Multi-Angle Photopolarimetric Observations to Study Properties of Aerosols in the Earth's Atmosphere: Implications of Measurements in the 1.378 µm Spectral Channel to Retrieve Microphysical Characteristics and Composition of Stratospheric Aerosols

We analyze the possibilities of orbital photopolarimetric measurements to study properties of aerosols in the Earth's atmosphere. As an example, we consider the case when such measurements are performed within a narrow spectral channel centered at 1.378 µm that allows to retrieve microphysical characteristics of stratospheric aerosols separately from those of tropospheric aerosols. We consider the case of stratospheric aerosols caused by volcanic eruption, and adopt the model of the stratosphere in the form of a homogeneous plane-parallel layer composed of polydisperse spherical particles. We use numerically exact solutions of the vector radiative transfer equation to theoretically simulate measurements carried out at various numbers of scattering angles, including: (i) radiance measurements alone; (ii) polarization measurements alone; and (iii) radiance and polarization measurements together. The results of computations show that the simultaneous use of radiance and polarization measurements at a sufficiently large number of scattering angles enables one to retrieve the optical thickness, effective radius, and refractive index of aerosols with adequate accuracy. We demonstrate how the accuracy of the derived values of the optical parameters of aerosols depends on the accuracy of measurements of the intensity and polarization of the reflected light, optical thickness of aerosol layer itself, effective radius of aerosols, width of the particle size distribution, and number of viewing angles.

Aerosols↗
NASA NTRS1994

Effect of magnetic field geometry on the wave signature of the pickup of interstellar neutrals

By using the technique of Johnstone et al. (1991), the asymptotic wave spectrum induced by the pickup of interstellar ions in the heliosphere is derived. This approach is independent of quasi-linear theory. The asymptotic wave spectrum is calculated from the standard resonance condition by assuming that the asymptotic ion distribution is bispherical and by using conservation of energy. The calculation places no restriction on either the ratio of Alfven speed to solar wind flow speed or the particle pitch angle. Spectra for various geometries (relative orientations of the magnetic field and solar wind velocity) are calculated. Absolute upper limits to the expected wave enhancements are calculated. These upper limits are compared to the background fluctuation spectrum extrapolated from 0.87 AU, assuming a spectral index of -5/3 and radial dependences of -2 and -3. The heliocentric radial distances at which the peaks in the various geometry-dependent wave spectra are expected to be observable above the background are identified. Peaks due to pickup hydrogen at the proton gyrofrequency are found to be always stronger relative to the background in parallel than in perpendicular geometries. The parallel-geometry excitations consist only of sunward propagating waves. In perpendicular geometries a peak also occurs, this time near 0.1 of the proton gyrofrequency (corresponding to the peak calculated by Lee and Ip (1987)). However, the steep spectral dependence of the ambient wave field makes it unlikely that this peak will be observed inside 20 AU. A similar result holds for the case of pickup-helium induced excitation at the helium gyrofrequency. Inside 10 AU, peaks at these lower frequencies tend to be obscured by the steep frequency dependence (proportional to -5/3) of the ambient spectrum and then are only observable in parallel geometries.

Williams, L. L.↗
NASA NTRS1996

On the Sensitivity of Piezoceramics and Piezopolymers in Structural Integrity Monitoring of Large Trusses

An analytical assessment has been made of the reliability of using integrated microactuators and sensors in the form of piezoceramics and piezopolymers as joint integrity monitors in trussed systems. The concept is first implemented for a simple structure which consists of two truss members with a 45 deg lift angle joined at the apex. A piezoceramic patch (or piezopolymer film) bonded on the surface of one of the members at a location near the joint is used as a collocated actuator/sensor. The overall structural dynamic response under an excitation was modeled by finite element method. Different degrees of nodal constraints at the joints representing various degrees of joint integrity are employed. The resulting dynamic response showed distinct responses for varying joint stiffnesses. Parallel experimental work on a truss model using a multichannel data acquisition system and a digital signal analyzer confirms the results from analysis. We further studied the sensitivity of the micro-sensors to the behavior of joints of large arch truss structure. Results obtained for large trusses with many degrees of freedom indicate optimum locations of sensors for which the dynamic response signatures are distinct and distinguishable for relatively small changes in joint integrity and/or structural geometry. Computations based on finite element modeling show that locating the single actuator/sensor at the joint corresponding to the first loss of static stability appear optimal. Hence, static stability analysis of complex trusses can give us a good indication of the optimum placement of sensors for maximum response. This observation is important if few distributed sensors and actuators are available for placement in constructed facilities made from large trusses with many degrees of freedom. As an extension of this work a dynamic response signature identification technique to monitor in-service degradation of joints is under development for application to the monitoring of the integrity of adhesive joints in composite structures.

Abatan, A. O.↗
NASA NTRS1995

Growth and microtubule orientation of Zea mays roots subjected to osmotic stress

Previous work has shown that microtubule (MT) reorientation follows the onset of growth inhibition on the lower side of graviresponding roots, indicating that growth reduction can occur independently of MT reorientation. To test this observation further, we examined whether the reduction in growth in response to osmotic stress is correlated with MT reorientation. The distribution and rate of growth in maize roots exposed to 350 mOsm sorbitol and KCl or 5 mM Mes/Tris buffer were measured with a digitizer. After various times roots were processed for indirect immunofluorescence microscopy. Application of sorbitol or KCl had no effect on the organization of MTs in the apical 2 mm of the root but resulted in striking and different effects in the basal region of the root. Sorbitol treatment caused rapid appearance of oval to circular holes in the microtubular array that persisted for at least 9 h. Between 30 min and 4 h of submersion in KCl, MTs in cortical cells 4 mm and farther from the quiescent center began to reorient oblique to the longitudinal axis. After 9 h, the alignment of MTs had shifted to parallel to the root axis but MTs of the epidermal cells remained transverse. In KCl-treated roots MT reorientation appeared to follow a pattern of development similar to that in controls but without elongation. Our data provide additional evidence that MT reorientation is not the cause but a consequence of growth inhibition.

NASA Discipline Plant Biology↗
NASA NTRS1944

Comparative Results of Tests on Several Different Types of Nozzles

This paper presents the results of tests conducted to determine the effect of the constructional elements of a Laval nozzle on the velocity and pressure distribution and the magnitude of the reaction force of the jet. The effect was studied of the shapes of the entrance section of the nozzle and three types of divergent sections: namely, straight cone, conoidal with cylindrical and piece and diffuser obtained computationally by a graphical method due to Professor F. I. Frankle. The effect of the divergence angle of the nozzle on the jet reaction was also investigated. The results of the investigation showed that the shape of the generator of the inner surface of the entrance part of the nozzle essentially has no effect on the character of the flow and on the reaction. The nozzle that was obtained by graphical computation assured the possibility of obtaining a flow for which the velocity of all the gas particles is parallel to the axis of symmetry of the nozzle, the reaction being on the average 2 to 3 percent greater than for the usual conical nozzle under the same conditions, For the conical nozzle the maximum reaction was obtained for a cone angle of 25deg to 27deg. At the end of this paper a sample computation is given by the graphical method. The tests were started at the beginning of 1936 and this paper was written at the same time.

Kisenko, M. S.↗
NASA NTRS1992

Optimal routing and buffer allocation for a class of finite capacity queueing systems

The problem of routing jobs to K parallel queues with identical exponential servers and unequal finite buffer capacities is considered. Routing decisions are taken by a controller which has buffering space available to it and may delay routing of a customer to a queue. Using ideas from weak majorization, it is shown that the shorter nonfull queue delayed (SNQD) policy minimizes both the total number of customers in the system at any time and the number of customers that are rejected by that time. The SNQD policy always delays routing decisions as long as all servers are busy. Only when all the buffers at the controller are occupied is a customer routed to the queue with the shortest queue length that is not at capacity. Moreover, it is shown that, if a fixed number of buffers is to be distributed among the K queues, then the optimal allocation scheme is the one in which the difference between the maximum and minimum queue capacities is minimized, i.e., becomes either 0 or 1.

Towsley, Don↗
NASA NTRS1999

"Tools For Analysis and Visualization of Large Time- Varying CFD Data Sets"

During the four years of this grant (including the one year extension), we have explored many aspects of the visualization of large CFD (Computational Fluid Dynamics) datasets. These have included new direct volume rendering approaches, hierarchical methods, volume decimation, error metrics, parallelization, hardware texture mapping, and methods for analyzing and comparing images. First, we implemented an extremely general direct volume rendering approach that can be used to render rectilinear, curvilinear, or tetrahedral grids, including overlapping multiple zone grids, and time-varying grids. Next, we developed techniques for associating the sample data with a k-d tree, a simple hierarchial data model to approximate samples in the regions covered by each node of the tree, and an error metric for the accuracy of the model. We also explored a new method for determining the accuracy of approximate models based on the light field method described at ACM SIGGRAPH (Association for Computing Machinery Special Interest Group on Computer Graphics) '96. In our initial implementation, we automatically image the volume from 32 approximately evenly distributed positions on the surface of an enclosing tessellated sphere. We then calculate differences between these images under different conditions of volume approximation or decimation.

Wilhelms, Jane↗
NASA NTRS2003

Estimation of Instantaneous TOA Albedo at 670 nm over Ice Clouds from POLDER Multidirectional Measurements

An algorithm that determines the 670-nm top-of-atmosphere (TOA) albedo of ice clouds over ocean using Polarization and Directionality of the Earth's Reflectance ( POLDER) multidirectional measurements is developed. A plane-parallel layer of ice cloud with various optical thicknesses and light scattering phase functions is assumed. For simplicity, we use a double Henyey-Greenstein phase function to approximate the volume-averaged phase function of the ice clouds. A multidirectional reflectance best-fit match between theoretical and POLDER reflectances is used to infer effective cloud optical thickness, phase function and TOA albedo. Sensitivity tests show that while the method does not provide accurate independent retrievals of effective cloud optical depth and phase function, TOA albedo retrievals are accurate to within similar to 3% for both a single layer of ice clouds or a multilayer system of ice clouds and water clouds. When the method is applied to POLDER measurements and retrieved albedos are compared with albedos based on empirical angular distribution models (ADMs), zonal albedo differences are generally smaller than similar to 3%. When albedos are compared with those on the POLDER-I ERB and Cloud product, the differences can reach similar to 15% at small solar zenith angles.

Sun, W.↗
NASA NTRS2012

An Empirical Temperature Variance Source Model in Heated Jets

An acoustic analogy approach is implemented that models the sources of jet noise in heated jets. The equivalent sources of turbulent mixing noise are recognized as the differences between the fluctuating and Favre-averaged Reynolds stresses and enthalpy fluxes. While in a conventional acoustic analogy only Reynolds stress components are scrutinized for their noise generation properties, it is now accepted that a comprehensive source model should include the additional entropy source term. Following Goldstein s generalized acoustic analogy, the set of Euler equations are divided into two sets of equations that govern a non-radiating base flow plus its residual components. When the base flow is considered as a locally parallel mean flow, the residual equations may be rearranged to form an inhomogeneous third-order wave equation. A general solution is written subsequently using a Green s function method while all non-linear terms are treated as the equivalent sources of aerodynamic sound and are modeled accordingly. In a previous study, a specialized Reynolds-averaged Navier-Stokes (RANS) solver was implemented to compute the variance of thermal fluctuations that determine the enthalpy flux source strength. The main objective here is to present an empirical model capable of providing a reasonable estimate of the stagnation temperature variance in a jet. Such a model is parameterized as a function of the mean stagnation temperature gradient in the jet, and is evaluated using commonly available RANS solvers. The ensuing thermal source distribution is compared with measurements as well as computational result from a dedicated RANS solver that employs an enthalpy variance and dissipation rate model. Turbulent mixing noise predictions are presented for a wide range of jet temperature ratios from 1.0 to 3.20.

Khavaran, Abbas↗
NASA NTRS1987

Correlation between calmodulin activity and gravitropic sensitivity in primary roots of maize

Recent evidence indicates a role for calcium and calmodulin in the gravitropic response of primary roots of maize (Zea mays, L.). We examined this possibility by testing the relationship between calmodulin activity and gravitropic sensitivity in roots of the maize cultivars Merit and B73 x Missouri 17. Roots of the Merit cultivar require light to the gravitropically competent. The gravitropic response of the Missouri cultivar is independent of light. The occurrence of calmodulin in primary roots of these maize cultivars was tested by affinity gel chromatography followed by sodium dodecyl sulfate-polyacrylamide gel electrophoresis with bovine brain calmodulin as standard. The distribution of calmodulin activity was measured using both the phosphodiesterase and NAD kinase assays for calmodulin. These assays were performed on whole tissue segments, crude extracts, and purified extracts. In light-grown seedlings of the Merit cultivar or in either dark- or light-grown seedlings of the Missouri cultivar, calmodulin activity per millimeter of root tissue was about 4-fold higher in the apical millimeter than in the subtending 3 millimeters. Calmodulin activity was very low in the apical millimeter of roots of dark-grown (gravitropically nonresponsive) seedlings of the Merit cultivar. Upon illumination, the calmodulin activity in the apical millimeter increased to a level comparable to that of light-grown seedlings and the roots became gravitropically competent. The time course of the development of gravitropic sensitivity following illumination paralleled the time course of the increase in calmodulin activity in the apical millimeter of the root. The results are consistent with the suggestion that calmodulin plays an important role in the gravitropic response of roots.

NASA Program Space Biology↗
NASA NTRS2021

Analysis of simultaneous aerosol and ocean glint retrieval using multi-angle observations

Since early 2000, NASA's Multi-angle Imaging SpectroRadiometer (MISR) instrument has been performing remote sensing retrievals of aerosol optical properties from the polar-orbiting Terra spacecraft. A noteworthy aspect of MISR observations over the ocean is that, for much of the Earth, some of the multi-angle views have contributions from solar reflection by the ocean surface (glint, or glitter), while others do not. Aerosol retrieval algorithms often discard these glint-influenced observations because they can overwhelm the signal and are difficult to predict without knowledge of the (wind-speed-driven) ocean surface roughness. However, theoretical studies have shown that multi-angle observations of a location at geometries with and without reflected sun glint can be a rich source of information, sufficient to support simultaneous retrieval of both the aerosol state and the wind speed at the ocean surface. We are in the early stages of creating such an algorithm. In this paper, we describe our assessment of the appropriate level of parameterization for simultaneous aerosol and ocean surface property retrievals using sun glint. For this purpose, we use generalized nonlinear retrieval analysis (GENRA), an information content assessment (ICA) technique employing Bayesian inference, and simulations from the Ahmad–Fraser iterative radiative transfer code. We find that four parameters are suitable: aerosol optical depth (τ), particle size distribution (expressed as the fine mode fraction f of small particles in a bimodal size distribution), surface wind speed (w), and relative humidity (r, to define the aerosol water content and complex refractive index). None of these parameters define ocean optical properties, as we found that the aerosol state could be retrieved with the nine MISR near-infrared views alone, where the ocean body is strongly absorbing in the open ocean. We also found that retrieval capability varies with observation geometry and that as τ increases so does the ability to determine aerosol intensive optical properties (r and f, while it decreases for w). Increases in w decrease the ability to determine the true value of that parameter but have minimal impact on retrieval of aerosol properties. We explored the benefit of excluding the two most extreme MISR view angles for which radiative transfer with the plane-parallel approximation is less certain, but we found no advantage in doing so. Finally, the impact of treating wind speed as a scalar parameter, rather than as a two-parameter directional wind, was tested. While the simpler scalar model does contribute to overall aerosol uncertainty, it is not sufficiently large to justify the addition of another dimension to parameter space. An algorithm designed upon these principles is in development. It will be used to perform an atmospheric correction with MISR for coincident ocean color (OC) observations by the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument, also on the NASA Terra spacecraft. Unlike MISR, MODIS is a single-view-angle instrument, but it has a more complete set of spectral channels ideal for determination of optical ocean properties. The atmospheric correction of MODIS OC data can therefore benefit from MISR aerosol retrievals. Furthermore, higher-spatial-resolution data from coincident MISR observations may also improve glint screening.

Kirk Knobelspiesse↗
NASA NTRS1998

Effects of Planetary Speed Reduction Ratio on Mean Service Life

Planetary gear transmissions are compact speed reductions which use parallel-load paths to transmit high power. The range of possible reduction ratios is bounded from below and above by limits on the relative size of the planet gears. For a single plane planetary transmission, the speed-reduction ratio must be greater than two for planet gears to exist. As the ratio increase, so does the size of the planets relative to the sizes of the sun and ring. Which ratio is best for a planetary reduction can be resolved by studying a series of optimal designs. In this series, each design is obtained by maximizing the service life for a spur-gear planetary with a fixed size, speed reduction ratio, input speed, power and materials. The planetary gear reduction service life is modeled as a function of the two-parameter Weibull distributed service lives of the ball bearings and spur gears in the reduction. Planet-bearing life strongly influences the optimal reduction lives which point to an optimal planetary reduction ratio in the neighborhood of four to five.

Savage, M.↗
NASA NTRS1994

The streaming-trapped ion interface in the equatorial inner magnetosphere

Spacecraft measurements of core ions on L=4-7 field-lines typically show trapped ion distributions near the magnetic equator, and frequently indicate field-aligned ion streams at higher latitudes. The nature of the transition between them may indicate both the microphysics of hot-cold plasma interactions and overall consequences for core plasma evolution. We have undertaken a statistical analysis and characterization of this interface and its relation to the equatorial region of the inner magnetosphere. In this analysis, we have characterized such features as the equatorial ion flux anisotropy, the penetration of field-aligned ionospheric streams into the equatorial region, the scale of the transition into trapped ion populations, and the transition latitude. We found that most transition latitudes occur within 13 deg of the equator. The typical values of equatorial ion anisotropies are consistent with bi-Maxwellian temperature ratios of T(sub perpendicular)/T(sub parallel) in the range of 3-5. The latitudinal scales for the edges of the trapped ion populations display a rather strong peak in the 2-3 deg range. We also found that there is a trend for the penetration ratio, the anisotropy half width, and the transition scale length to decrease with a higher equatorial ion anisotropy. We may interpret these features in terms of Liouville mapping of equatorially trapped ions and the reflection of the incoming ionospheric ion streams from the equatorial potential peaks associated with such trapped ions.

Lin, J.↗
NASA NTRS1986

Further work on sodium montmorillonite as catalyst for the polymerization of activated amino acids

When the polycondensation of amino acid acylates was catalyzed with Na-montmorillonite, the polypeptides were consistently found to exhibit a distribution of discrete molecular weights, for as yet undiscovered reasons. One possible explanation was connected to the stepwise mode of monomer addition. New experiments have eliminated this possibility, so that there is the general assumption that this discreteness is the result of a preference of shorter oligomers to add to others of the same length, a feature that could be attributed to some structure of the platelet aggregates of the montmorillonite. The production of optical stereoisomers is anticipated when D,L-amino acids are polymerized on montmorillonite. Having used an optically active surface, the essence of the results lies not only in the occurrence of optically active oligomers and polymers, but also in the fact that the latter exhibit the same molecular weight characteristics as the D,L-polymers. Preparatory to work contemplated on a parallel synthesis of amino acid and nucleotide oligomers, studies were continued on the co-adsorption of amino acids, nucleotides, and amino acid-nucleotides on montmorillonite.

Eirich, F. R.↗
NASA NTRS1998

Effects of Planetary Speed-Reduction Ratio on Mean Service Life

Planetary-gear transmissions are compact speed reductions which use parallel-load paths to transmit high power. The range of possible reduction ratios is bounded from below and above by limits on the relative size of the planet gears. For a single-plane planetary transmission, the speed-reduction ratio must be greater than two for planet gears to exist. As the ratio increases, so does the size of the planets relative to the sizes of the sun and ring. Which ratio is best for a planetary reduction can be resolved by studying a series of optimal designs. In this series, each design is obtained by maximizing the service life for a spur-gear planetary with a fixed size, speed-reduction ratio, input speed, power and materials. The planetary-gear reduction service life is modeled as a function of the two-parameter Weibull distributed service lives of the ball bearings and spur gears in the reduction. Planet-bearing life strongly influences the optimal reduction lives which point to an optimal planetary reduction ratio in the neighborhood of four to five.

Savage, M.↗
NASA NTRS2019

Continuous Electrode Inertial Electrostatic Confinement Fusion

The NIAC Phase I project on Inertial Electrostatic Confinement was a continuation of early stage research that was funded by an NSTRF. The student on the project, Andrew Chap, was funded by the NSTRF from Fall 2013 through the Summer of 2017, and then was funded on the NIAC through the completion of his PhD. A significant amount of work targeting the plasma confinement physics was the focus of his NSTRF, and over the course of that effort he developed a number of analyses and computational tools that leveraged GPU parallelization. A detailed discussion of these models can be found in his dissertation, which has been included as Appendix D in this report. As a requirement for the NSTRF, Andrew's full dissertation was submitted at the end of the program.Having developed the computational tools, a substantial amount of simulation and analyses leveraging those tools were conducted during the Fall of 2017, under the auspices of the NIAC funded research. Much of this work targeted optimization of the confinement fields, investigating their structure and the possible advantages of having them be time-varying. The results of these simulations can also be found in Appendix D.One of the main results from this research is that the density of ions electrostatically confined within the system can indeed be increased by several orders of magnitude by optimizing the radial potential distribution, and by dynamically varying these fields to maintain compressed ion bunches. An electron population can also be confined within the core by a static radial cusped magnetic field,which helps to support a greater ion density within the core. The issue with the confinement mechanism is that as the ion densities are increased toward fusion-relevant levels, the electrostatic forces generated by the confined electron population become so great that the ions are no longer energetic enough to leave the device core. As their excursions into the outer channels are diminished, the mechanism that is used to maintain their non-thermal velocity distributions becomes ineffective, and eventually the ions become fully confined within the core, where they thermalize. A possible fix to the problem comes by discarding the active ion control (a main pillar of the concept)but retaining the structure of the permanent magnet confinement of the electron population. Such cusped field confinement has been the focus of other IEC approaches (e.g. Polywell), but the high transparency of the permanent magnet structure lends itself to better ion extraction and power conversion (a second pillar of the concept). The question then becomes whether any influence on the ion evolution within the core can be achieved to slow the thermalization of the ions. Such approaches have been studied in highly idealized analytic models, but face major criticisms within the literature. While this is a possible path forward, the uncertainty in the approach did not warrant committing NIAC Phase II resources to investigating the concept at this time.

Sedwick, Raymond↗