Search NASA⌕ Search

SEARCH · Search NASA

Results for “Hall propulsion system”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9

Advanced Electric Propulsion for Space Solar Power Satellites

The sun tower concept of collecting solar energy in space and beaming it down for commercial use will require very affordable in-space as well as earth-to-orbit transportation. Advanced electric propulsion using a 200 kW power and propulsion system added to the sun tower nodes can provide a factor of two reduction in the required number of launch vehicles when compared to in-space cryogenic chemical systems. In addition, the total time required to launch and deliver the complete sun tower system is of the same order of magnitude using high power electric propulsion or cryogenic chemical propulsion: around one year. Advanced electric propulsion can also be used to minimize the stationkeeping propulsion system mass for this unique space platform. 50 to 100 kW class Hall, ion, magnetoplasmadynamic, and pulsed inductive thrusters are compared. High power Hall thruster technology provides the best mix of launches saved and shortest ground to Geosynchronous Earth Orbital Environment (GEO) delivery time of all the systems, including chemical. More detailed studies comparing launch vehicle costs, transfer operations costs, and propulsion system costs and complexities must be made to down-select a technology. The concept of adding electric propulsion to the sun tower nodes was compared to a concept using re-useable electric propulsion tugs for Low Earth Orbital Environment (LEO) to GEO transfer. While the tug concept would reduce the total number of required propulsion systems, more launchers and notably longer LEO to GEO and complete sun tower ground to GEO times would be required. The tugs would also need more complex, longer life propulsion systems and the ability to dock with sun tower nodes.

Oleson, Steve↗

Status of Propulsion Technology Development Under the NASA In-Space Propulsion Technology Program

Since 2001, the In-Space Propulsion Technology (ISPT) program has been developing and delivering in-space propulsion technologies for NASA's Science Mission Directorate (SMD). These in-space propulsion technologies are applicable, and potentially enabling for future NASA Discovery, New Frontiers, Flagship and sample return missions currently under consideration. The ISPT program is currently developing technology in three areas that include Propulsion System Technologies, Entry Vehicle Technologies, and Systems/Mission Analysis. ISPT's propulsion technologies include: 1) the 0.6-7 kW NASA's Evolutionary Xenon Thruster (NEXT) gridded ion propulsion system; 2) a 0.3-3.9kW Halleffect electric propulsion (HEP) system for low cost and sample return missions; 3) the Xenon Flow Control Module (XFCM); 4) ultra-lightweight propellant tank technologies (ULTT); and 5) propulsion technologies for a Mars Ascent Vehicle (MAV). The NEXT Long Duration Test (LDT) recently exceeded 50,000 hours of operation and 900 kg throughput, corresponding to 34.8 MN-s of total impulse delivered. The HEP system is composed of the High Voltage Hall Accelerator (HIVHAC) thruster, a power processing unit (PPU), and the XFCM. NEXT and the HIVHAC are throttle-able electric propulsion systems for planetary science missions. The XFCM and ULTT are two component technologies which being developed with nearer-term flight infusion in mind. Several of the ISPT technologies are related to sample return missions needs: MAV propulsion and electric propulsion. And finally, one focus of the Systems/Mission Analysis area is developing tools that aid the application or operation of these technologies on wide variety of mission concepts. This paper provides a brief overview of the ISPT program, describing the development status and technology infusion readiness.

systems analysis↗

SmallSat missions enabled by paired low-thrust hybrid rocket and low-power long-life Hall thruster

The capabilities of a SmallSat-class spacecraft targeting the outer solar system and using a combined chemical and electric propulsion system are explored. The development of compact hybrid rockets has enabled high-thrust engines to be packaged tightly enough to fit on cubesat and SmallSat spacecraft. These hybrid rockets provide 10’s-100 N of thrust depending on the propellant load & >300 s of specific impulse and have been demonstrated in both ambient and vacuum environments. Advancements in low-power long-life Hall thruster technologies have provided the potential for significantly greater propellant throughputs, enabling their use as a primary propulsion element on interplanetary spacecraft. In a recent characterization test campaign, the MaSMi-DM Hall thruster demonstrated power throttling from 150 – 1000 W with >1500 s of specific impulse available at >500 W and >40% total thrust efficiency available at >300 W; peak values of 1940 s and 53% were observed. A notional low-mass spacecraft employing a combined hybrid rocket and low-power electric propulsion system was designed and used for mission concept analysis targeting the outer solar system. Using an imposed wet mass limit of 400 kg, mission trajectories to Saturn and Uranus were generated. Orbit capture with >40% of the launch mass was shown to be possible at either target, with mission transfer times of 7.5 years and 13.5 years for Saturn and Uranus, respectively. Significant follow-on mission activities near Saturn (e.g. to Titan & Enceladus) were also possible by carrying extra propellant mass while remaining under the total wet mass limit.

Karp, Ashley C.↗

NASA's In-Space Propulsion Technology Project Overview, Near-term Products and Mission Applicability

The In-Space Propulsion Technology (ISPT) Project, funded by NASA's Science Mission Directorate (SMD), is continuing to invest in propulsion technologies that will enable or enhance NASA robotic science missions. This overview provides development status, near-term mission benefits, applicability, and availability of in-space propulsion technologies in the areas of aerocapture, electric propulsion, advanced chemical thrusters, and systems analysis tools. Aerocapture investments improved (1) guidance, navigation, and control models of blunt-body rigid aeroshells, 2) atmospheric models for Earth, Titan, Mars and Venus, and 3) models for aerothermal effects. Investments in electric propulsion technologies focused on completing NASA s Evolutionary Xenon Thruster (NEXT) ion propulsion system, a 0.6-7 kW throttle-able gridded ion system. The project is also concluding its High Voltage Hall Accelerator (HiVHAC) mid-term product specifically designed for a low-cost electric propulsion option. The primary chemical propulsion investment is on the high-temperature Advanced Material Bipropellant Rocket (AMBR) engine providing higher performance for lower cost. The project is also delivering products to assist technology infusion and quantify mission applicability and benefits through mission analysis and tools. In-space propulsion technologies are applicable, and potentially enabling for flagship destinations currently under evaluation, as well as having broad applicability to future Discovery and New Frontiers mission solicitations.

Dankanich, John↗

The Iodine Satellite (iSat) Propellant Feed System - Design and Demonstration

CUBESATS are relatively new spacecraft platforms that are typically deployed from a launch vehicle as a secondary payload, providing low-cost access to space for a wide range of end-users. These satellites are comprised of building blocks having dimensions of 10x10x10 cm3 and a mass of 1.33 kg (a 1-U size). While providing low-cost access to space, a major operational limitation is the lack of a propulsion system that can fit within a CubeSat and is capable of executing high Delta V maneuvers. This makes it difficult to use CubeSats on missions requiring certain types of maneuvers (i.e. formation flying, spacecraft rendezvous). Work has been performed investigating the use of iodine as a propellant for Hall-effect thrusters (HETs) that could subsequently be used to provide a high specific impulse path to CubeSat propulsion. One of the systems under development to support such a technology is the propellant feed system, which must be capable of storing solid iodine propellant, applying heat to sublime the stored solid into the vapor phase, and then control the flow of low-pressure gaseous iodine to both the thruster and cathode. In a test conducted in 2016, a first-generation iodine propellant feed system was integrated with a cathode and Hall thruster. While this test had to be terminated, the feed system in this first test was able to support both cathode and integrated cathode and thruster operation prior to the termination of the test. In the present paper, we describe work performed since that initial integrated test. The effort uses lessons learned from the previous integrated test, retiring risk associated with the iodine propellant feed system, answering open design-space questions, and demonstrating iodine flow control in an integrated system. The work is undertaken at both the component level and then at the integrated subsystem level to systematically improve the feed system design, improving the hardware fidelity so the appearance and operation of the system are as flight-like as possible. At the component level, the work focuses on the propellant tank, the feed system tubing, the valves used to control the flow to the cathode and thruster, and the heaters that maintain the temperature of the flowpaths and keep iodine from redepositing and clogging the system. Work on the propellant reservoir focuses on fabricating a tank that matches the geometry of the flight design, which allows for the identification of flight tank fabrication issues that may arise and permits thermal testing of a tank possessing the same size and thermal mass as the flight design, which can be used to anchor thermal modeling of the component. This is critical for finalizing the tank heater power requirements that feed into the heater design. All metallic materials in the feed system are hastelloy or Inconel, as these materials are resistant to chemical attack by the highly-reactive iodine vapor. The tubing in the iodine feed system must possess ports to permit a neutral gas purge of the system that clear impurities after iodine is loaded into the propellant tank. A procedure is discussed whereby these ports are crimped and sealed after the purge process is completed so as to not re-expose the iodine system to air. The valves are a critical component for control of the flow to the thruster and the cathode. Significant effort has gone into upgrading the materials of the valves to make them more resistant to chemical attack and into developing an understanding of the use of these valves during the startup and operation of the cathode and thruster. The heaters that line the entire feed system are designed to draw minimal power from the power processing unit (PPU) while still having the capacity to maintain all the feed system components at the temperatures required to discourage iodine deposition inside components downstream of the propellant tank exit. The heaters possess two separate resistive traces, giving the design redundancy should a failure occur in the primary heater circuit of one of the heater zones. The task of operating a feed system in conjunction with a thruster and cathode is undertaken in a series of sub-steps. The system is first assembled and operated on xenon gas, using the valves for cathode startup and thruster control based on measurement of the discharge current. After startup and control on xenon are demonstrated, the thruster will be transitioned to iodine operation, demonstrating thruster startup and feed system control while using a xenon-fed cathode. Finally, the last step is to integrate an iodine-compatible cathode with the system, demonstrate autonomous cathode start-up with open-loop control and thruster start-up with closed-loop control for multiple cycles.

Polzin, Kurt A.↗

The NASA In-Space Propulsion Technology Project, Products, and Mission Applicability

The In-Space Propulsion Technology (ISPT) Project, funded by NASA s Science Mission Directorate (SMD), is continuing to invest in propulsion technologies that will enable or enhance NASA robotic science missions. This overview provides development status, near-term mission benefits, applicability, and availability of in-space propulsion technologies in the areas of aerocapture, electric propulsion, advanced chemical thrusters, and systems analysis tools. Aerocapture investments improved: guidance, navigation, and control models of blunt-body rigid aeroshells; atmospheric models for Earth, Titan, Mars, and Venus; and models for aerothermal effects. Investments in electric propulsion technologies focused on completing NASA s Evolutionary Xenon Thruster (NEXT) ion propulsion system, a 0.6 to 7 kW throttle-able gridded ion system. The project is also concluding its High Voltage Hall Accelerator (HiVHAC) mid-term product specifically designed for a low-cost electric propulsion option. The primary chemical propulsion investment is on the high-temperature Advanced Material Bipropellant Rocket (AMBR) engine providing higher performance for lower cost. The project is also delivering products to assist technology infusion and quantify mission applicability and benefits through mission analysis and tools. In-space propulsion technologies are applicable, and potentially enabling for flagship destinations currently under evaluation, as well as having broad applicability to future Discovery and New Frontiers mission solicitations.

Anderson, David J.↗

1000 Hours of Testing Completed on 10-kW Hall Thruster

Between the months of April and August 2000, a 10-kW Hall effect thruster, designated T- 220, was subjected to a 1000-hr life test evaluation. Hall effect thrusters are propulsion devices that electrostatically accelerate xenon ions to produce thrust. Hall effect propulsion has been in development for many years, and low-power devices (1.35 kW) have been used in space for satellite orbit maintenance. The T-220, shown in the photo, produces sufficient thrust to enable efficient orbital transfers, saving hundreds of kilograms in propellant over conventional chemical propulsion systems. This test is the longest operation ever achieved on a high-power Hall thruster (greater than 4.5 kW) and is a key milestone leading to the use of this technology for future NASA, commercial, and military missions.

Mason, Lee S.↗

Stirling Technology Development at NASA GRC

The Department of Energy, Stirling Technology Company (STC), and NASA Glenn Research Center (NASA Glenn) are developing a free-piston Stirling convertor for a high efficiency Stirling Radioisotope Generator (SRG) for NASA Space Science missions. The SRG is being developed for multimission use, including providing electric power for unmanned Mars rovers and deep space missions. NASA Glenn is conducting an in-house technology project to assist in developing the convertor for space qualification and mission implementation. Recent testing of 55-We Technology Demonstration Convertors (TDCs) built by STC includes mapping of a second pair of TDCs, single TDC testing, and TDC electromagnetic interference and electromagnetic compatibility characterization on a nonmagnetic test stand. Launch environment tests of a single TDC without its pressure vessel to better understand the convertor internal structural dynamics and of dual-opposed TDCs with several engineering mounting structures with different natural frequencies have recently been completed. A preliminary life assessment has been completed for the TDC heater head, and creep testing of the IN718 material to be used for the flight convertors is underway. Long-term magnet aging tests are continuing to characterize any potential aging in the strength or demagnetization resistance of the magnets used in the linear alternator (LA). Evaluations are now beginning on key organic materials used in the LA and piston/rod surface coatings. NASA Glenn is also conducting finite element analyses for the LA, in part to look at the demagnetization margin on the permanent magnets. The world's first known integrated test of a dynamic power system with electric propulsion was achieved at NASA Glenn when a Hall-effect thruster was successfully operated with a free-piston Stirling power source. Cleveland State University is developing a multidimensional Stirling computational fluid dynamics code to significantly improve Stirling loss predictions and assist in identifying convertor areas for further improvements. This paper will update the status and results for these efforts.

Thieme, Lanny G.↗

Stirling Technology Development at NASA GRC

The Department of Energy, Stirling Technology Company (STC), and NASA Glenn Research Center (NASA Glenn) are developing a free-piston Stirling convertor for a high-efficiency Stirling Radioisotope Generator (SRG) for NASA Space Science missions. The SRG is being developed for multimission use, including providing electric power for unmanned Mars rovers and deep space missions. NASA Glenn is conducting an in-house technology project to assist in developing the convertor for space qualification and mission implementation. Recent testing, of 55-We Technology Demonstration Convertors (TDC's) built by STC includes mapping, of a second pair of TDC's, single TDC testing, and TDC electromagnetic interference and electromagnetic compatibility characterization on a nonmagnetic test stand. Launch environment tests of a single TDC without its pressure vessel to better understand the convertor internal structural dynamics and of dual-opposed TDC's with several engineering mounting structures with different natural frequencies have recently been completed. A preliminary life assessment has been completed for the TDC heater head, and creep testing of the IN718 material to be used for the flight convertors is underway. Long-term magnet aging tests are continuing to characterize any potential aging in the strength or demagnetization resistance of the magnets used in the linear alternator (LA). Evaluations are now beginning on key organic materials used in the LA and piston/rod surface coatings. NASA Glenn is also conducting finite element analyses for the LA, in part to look at the demagnetization margin on the permanent magnets. The world's first known integrated test of a dynamic power system with electric propulsion was achieved at NASA Glenn when a Hall-effect thruster was successfully operated with a free-piston Stirling power source. Cleveland State University is developing a multidimensional Stirling computational fluid dynamics code to significantly improve Stirling loss predictions and assist in identifying convertor areas for further improvements. This paper will update the status and results for these efforts.

Thieme, Lanny G.↗

13kW Advanced Electric Propulsion Flight System Development and Qualification

The next phase of robotic and human deep space exploration missions requires high performance, high power solar electric propulsion systems for large-scale science missions and cargo transportation. Aerojet Rocketdyne's Advanced Electric Propulsion System (AEPS) program is completing development and qualification of a 13kW flight EP system to support NASA exploration. The first use of the AEPS is planned for the NASA Power & Propulsion Element, which is the first element of NASA's cis-lunar Gateway. The flight AEPS system includes a magnetically shielded long-life Hall thruster, power processing unit (PPU), and xenon flow controller (XFC). The Hall thruster, originally developed and demonstrated by NASA's Glenn Research Center and the Jet Propulsion Laboratory, operates at input powers up to 13.3kW while providing a specific impulse over 2600s at an input voltage of 600V. The power processor is designed to accommodate an input voltage range of 95 to 140V, consistent with operation beyond the orbit of Mars. The integrated system is continuously throttleable between 3 and 13.3kW. The program has completed testing of the Technology Development Units and is progressing into the Engineering Development Unit test phase and the final design phase to Critical Design Review (CDR). This paper will present the high power AEPS system capabilities, overall program and design status and the latest test results for the 13kW flight system development as well as the plans for the development and qualification effort of the EP string.

in-space propulsion↗

13kW Advanced Electric Propulsion Flight System Development and Qualification

The next phase of robotic and human deep space exploration missions requires high performance, high power solar electric propulsion systems for large-scale science missions and cargo transportation. Aerojet Rocketdyne's Advanced Electric Propulsion System (AEPS) program is completing development and qualification of a 13kW flight EP system to support NASA exploration. The first use of the AEPS is planned for the NASA Power & Propulsion Element, which is the first element of NASA's cis-lunar Gateway. The flight AEPS system includes a magnetically shielded long-life Hall thruster, power processing unit (PPU), and xenon flow controller (XFC). The Hall thruster, originally developed and demonstrated by NASA's Glenn Research Center and the Jet Propulsion Laboratory, operates at input powers up to 13.3kW while providing a specific impulse over 2600s at an input voltage of 600V. The power processor is designed to accommodate an input voltage range of 95 to 140V, consistent with operation beyond the orbit of Mars. The integrated system is continuously throttleable between 3 and 13.3kW. The program has completed testing of the Technology Development Units and is progressing into the Engineering Development Unit test phase and the final design phase to Critical Design Review (CDR). This paper will present the high power AEPS system capabilities, overall program and design status and the latest test results for the 13kW flight system development as well as the plans for the development and qualification effort of the EP string.

in-space propulsion↗

The Ion Propulsion System for the Solar Electric Propulsion Technology Demonstration Mission

The Asteroid Redirect Robotic Mission is a candidate Solar Electric Propulsion Technology Demonstration Mission whose main objectives are to develop and demonstrate a high-power solar electric propulsion capability for the Agency and return an asteroidal mass for rendezvous and characterization in a companion human-crewed mission. The ion propulsion system must be capable of operating over an 8-year time period and processing up to 10,000 kg of xenon propellant. This high-power solar electric propulsion capability, or an extensible derivative of it, has been identified as a critical part of an affordable, beyond-low-Earth-orbit, manned-exploration architecture. Under the NASA Space Technology Mission Directorate the critical electric propulsion and solar array technologies are being developed. The ion propulsion system being co-developed by the NASA Glenn Research Center and the Jet Propulsion Laboratory for the Asteroid Redirect Vehicle is based on the NASA-developed 12.5 kW Hall Effect Rocket with Magnetic Shielding (HERMeS0 thruster and power processing technologies. This paper presents the conceptual design for the ion propulsion system, the status of the NASA in-house thruster and power processing activity, and an update on flight hardware.

Electric Propulsion↗

SUbsonic Single Aft eNgine (SUSAN) Power/Propulsion System Control Architecture Updates

The development of hybrid-electric propulsion technology for transport aircraft presents opportunities for new designs that can reduce fuel consumption and greenhouse gas emissions from commercial aviation and improve on safety and reliability when compared to modern aircraft. The SUbsonic Single Aft eNgine (SUSAN) Electrofan is a conceptual design for a transport aircraft with a series/parallel partial hybrid-electric propulsion system that is being developed by NASA as a reference design for a regional transport aircraft with a high degree of electrification. The SUSAN concept incorporates multiple tightly coupled power, propulsion, and flight control systems that introduce new challenges to the control design process, requiring a hierarchical and more coordinated control architecture. This paper summarizes updates to the SUSAN Power/Propulsion System (PPS) model and control architecture made in preparation for planned flight simulator and hardware-in-the-loop testing at NASA Glenn Research Center (GRC). These updates include a new electrical power system (EPS) model based on the NASA-developed Electrical Modeling and Thermal Analysis Toolbox (EMTAT), and a new PPS control architecture that improves the operational flexibility and responsiveness of the propulsion system. The performance of the upgraded control system is also demonstrated and discussed.

SUSAN↗

SUbsonic Single Aft eNgine (SUSAN) Power/Propulsion System Control Architecture Updates

The development of hybrid-electric propulsion technology for transport aircraft presents opportunities for new designs that can reduce fuel consumption and greenhouse gas emissions from commercial aviation and improve on safety and reliability when compared to modern aircraft. The SUbsonic Single Aft eNgine (SUSAN) Electrofan is a conceptual design for a transport aircraft with a series/parallel partial hybrid-electric propulsion system that is being developed by NASA as a reference design for a regional transport aircraft with a high degree of electrification. The SUSAN concept incorporates multiple tightly coupled power, propulsion, and flight control systems that introduce new challenges to the control design process, requiring a hierarchical and more coordinated control architecture. This paper summarizes updates to the SUSAN Power/Propulsion System (PPS) model and control architecture made in preparation for planned flight simulator and hardware-in-the-loop testing at NASA Glenn Research Center (GRC). These updates include a new electrical power system (EPS) model based on the NASA-developed Electrical Modeling and Thermal Analysis Toolbox (EMTAT), and a new PPS control architecture that improves the operational flexibility and responsiveness of the propulsion system. The performance of the upgraded control system is also demonstrated and discussed.

SUSAN↗

Spacecraft Impacts with Advanced Power and Electric Propulsion

A study was performed to assess the benefits of advanced power and electric propulsion systems for various space missions. Advanced power technologies that were considered included multiband gap and thin-film solar arrays, lithium batteries, and flywheels. Electric propulsion options included Hall effect thrusters and Ion thrusters. Several mission case studies were selected as representative of future applications for advanced power and propulsion systems. These included a low altitude Earth science satellite, a LEO communications constellation, a GEO military surveillance satellite, and a Mercury planetary mission. The study process entailed identification of overall mission performance using state-of-the-art power and propulsion technology, enhancements made possible with either power or electric propulsion advances individually, and the collective benefits realized when advanced power and electric propulsion are combined. Impacts to the overall spacecraft included increased payload, longer operational life, expanded operations and launch vehicle class step-downs.

Mason, Lee S.↗

Update on the Nested Hall Thruster Subsystem for the NextSTEP XR-100 Program

Under the NextSTEP program led by Aerojet Rocketdyne in collaboration with NASA Glenn Research Center the University of Michigan, and the Jet Propulsion Laboratory, the XR-100 100 kW Electric Propulsion system is being developed to Technology Readiness Level (TRL) 5. As part of this program, the X3, a Nested Hall Thruster (NHT) designed to operate at powers up to 200kW, is being further developed through parallel modeling and experimental efforts with the ultimate goal of supporting a 100kW-100hr system test in the final year of the NextSTEP program. Recent developments for the X3 subsystem are presented including a summary of testing and modeling results and design updates in anticipation of a risk reduction test scheduled for the summer of 2018.

Jorns, Benjamin A.↗

Update on the Nested Hall Thruster Subsystem for the NextSTEP XR-100 Program

Under the NextSTEP program led by Aerojet Rocketdyne in collaboration with NASA Glenn Research Center the University of Michigan, and the Jet Propulsion Laboratory, the XR-100 100 kW Electric Propulsion system is being developed to Technology Readiness Level (TRL) 5. As part of this program, the X3, a Nested Hall Thruster (NHT) designed to operate at powers up to 200kW, is being further developed through parallel modeling and experimental efforts with the ultimate goal of supporting a 100kW-100hr system test in the final year of the NextSTEP program. Recent developments for the X3 subsystem are presented including a summary of testing and modeling results and design updates in anticipation of a risk reduction test scheduled for the summer of 2018.

Jorns, Benjamin A.↗

Propulsion Technology Assessment: Science and Enabling Technologies to Explore the Interstellar Medium

The Advanced Concepts Office at NASA’s George C. Marshall Space Flight Center conducted a study to assess what low-thrust advanced propulsion system candidates, existing and near term, could deliver a small, Voyager-like satellite to our solar system’s heliopause, approximately 100 AU from the sun, within 10 years. The advanced propulsion system trade study consisted of three candidates, including a Magnetically Shielded Miniature Hall thruster, a solar sail and an electric sail. A second analysis was conducted to determine which solid rocket motor kick stage(s) would be required to provide additional thrust at various points in the trajectory, assuming a characteristic energy capability provided by a Space Launch System Block 1B vehicle architecture carrying an 8.4 meter payload fairing. Two trajectory profiles were considered, including an escape trajectory using a Jupiter gravity assist and an escape trajectory first performing a Jupiter gravity assist followed by an Oberth maneuver around the sun and an optional Saturn gravity assist. Results indicated that if the Technology Readiness Level of an electric sail could be increased in time, this technology could not only enable a satellite to reach 100 AU in 10 years but it could potentially do so in even less time.

Hopkins, Randall C.↗