Princeton Satellite Systems Fusion-Enabled Pluto Orbiter and Lander Phase I Final Report Award Title: Fusion-Enabled Pluto Orbiter and Lander Report Type: Phase I Final Report Principal Investigator: Ms. Stephanie Thomas Period of Performance: May 13, 2016 through May 12, 2017 Institution: Princeton Satellite Systems, Inc. 6 Market St. Suite 926 Plainsboro, NJ 08536 Award Number: NNX16AK28G The Pluto orbiter mission proposed here is credible and exciting. The benefits to this and all outer-planet and interstellar-probe missions are difficult to overstate. The enabling technology, Direct Fusion Drive, is a unique fusion engine concept based on the Princeton Field-Reversed Configuration (PFRC) fusion reactor under development at the Princeton Plasma Physics Laboratory. The truly game-changing levels of thrust and power in a modestly sized package could integrate with our current launch infrastructure while radically expanding the science capability of these missions. During this Phase I effort, we made great strides in modeling the engine efficiency, thrust, and specific impulse and analyzing feasible trajectories. Based on 2D fluid modeling of the fusion reactor’s outer stratum, its scrape-off-layer (SOL), we estimate achieving 2.5 to 5 N of thrust for each megawatt of fusion power, reaching a specific impulse, Isp, of about 10,000 s. Supporting this model are particle-in-cell calculations of energy transfer from the fusion products to the SOL electrons. Subsequently, this energy is transferred to the ions as they expand through the magnetic nozzle and beyond. Our point solution for the Pluto mission now delivers 1000 kg of payload to Pluto orbit in 3.75 years using 7.5 N constant thrust. This could potentially be achieved with a single 1 MW engine. The departure spiral from Earth orbit and insertion spiral to Pluto orbit require only a small portion of the total delta-V. Departing from low Earth orbit reduces mission cost while increasing available mission mass. The payload includes a lander, which utilizes a standard green propellant engine for the landing sequence. The lander has about 4 square meters of solar panels mounted on a gimbal that allows it to track the orbiter, which beams 30 to 50 kW of power using a 1080 nm laser. Optical communication provides dramatically high data rates back to Earth. Our mass modeling investigations revealed that if current high-temperature superconductors are utilized at liquid nitrogen temperatures, they drive the mass of the engine, partly because of the shielding required to maintain their critical temperature. Second generation materials are thinner but the superconductor is a very thin layer deposited on a substrate with additional layers of metallic classing. Tremendous research is being performed on a variety of these superconducting materials, and new irradiation data is now available. This raises the possibility of operating near-future “high-temperature” superconductors at a moderately low temperature to dramatically reduce the amount of shielding required. At the same time, a first generation space engine may require low-temperature superconductors, which are higher TRL and have been designed for space coils before (AMS-02 experiment for the ISS). We performed detailed analysis of the startup system and thermal conversion system components. The ideal working fluid was determined to be a blend of Helium and Xenon. No significant problems were identified with these subsystems. For the RF system, we conceived of a new, more efficient design using state-of-the-art switch amplifiers, which have the potential for 100% efficiency. This report presents details of our engine and trajectory analyses, mass modeling efforts, and updated vehicle designs. Table of contents 1 Introduction - 8 2 Methods and Assumptions - 9 2.1 Work Plan - 9 2.2 Princeton Field-Reversed Configuration (PFRC) Reactor - 10 2.3 Modeling Tools - 11 2.3.1 Plasma Software Packages - 11 2.3.2 Spacecraft Control Toolbox: Fusion Propulsion Module - 12 3 Results - 12 3.1 Mass Model - 12 3.1.1 Thermal Conversion - 13 3.1.2 Startup Subsystem - 19 3.1.3 RF Subsystem - 21 3.1.4 Radiators - 22 3.1.5 Superconducting Coils - 23 3.2 Shielding Design - 26 3.3 Thrust Augmentation - 29 3.4 Optimal Pluto Trajectory - 34 3.4.1 Lambert Impulsive Trajectory - 34 3.4.2 Straight Line Trajectory - 35 3.4.3 Pluto Insertion - 38 3.4.4 Earth departure - 39 3.4.5 Planar Optimal Trajectories - 42 3.5 Updated System Design - 45 3.5.1 Engine Modeling - 45 3.5.2 Engine Layout - 51 3.5.3 Vehicle Design - 53 3.5.4 Lander Design - 54 4 Conclusions - 57 5 Bibliography - 58 6 Acronyms - 58 Appendix A. PFRC Technical Description - 59 A.1 PFRC Overview - 59 A.2 The Field-Reversed Configuration - 61 A.3 PFRC Fusion Reactions - 62 A.4 RMF Heating Method - 63 A.5 Reduction of Neutrons - 64 A.6 Radiation Losses - 64 A.7 Thrust Augmentation - 65 A.8 Development Plan - 66 A.9 PFRC Summary - 68 The Pluto orbiter mission proposed here is credible and exciting. The benefits to this and all robotic outer planet or manned interplanetary missions are difficult to overstate. The enabling technology, Direct Fusion Drive, is a unique fusion engine concept based on the Princeton Field-Reversed Configuration (PFRC) fusion reactor under development at the Princeton Plasma Physics Laboratory. The truly game-changing levels of thrust and power in a modestly sized package could integrate with our current launch infrastructure while radically expanding the science capability of these missions. Figure 1 shows an artistic rendition of the space reactor, with key components labeled. The mission context we have proposed is delivery of a Pluto orbiter with a lander. Direct Fusion Drive (DFD) provides high thrust to allow for reasonable transit times to Pluto while delivering substantial mass to orbit: 1000 kg delivered in under four years using 5-10 N thrust. Since DFD provides power as well as propulsion in one integrated device, it will also provide as much as 2 MW of power to the payloads upon arrival. This enables high-bandwidth communication, powering of the lander from orbit, and radically expanded options for instrument design. The data acquired by New Horizons' recent Pluto flyby are just a tiny fraction of the scientific data that could be generated from an orbiter and lander. To date our work on the space applications and balance-of-plant has been entirely funded by internal research and development. Our work has included preliminary analysis of a variety of space missions, from outer planets missions to asteroid deflection to interstellar missions, but funding levels have precluded detailed subsystems analysis. Our computations show that the predicted thrust level can accomplish the mission and that no other plausible technology can deliver such significant mass and power-producing capability to Pluto orbit with a flight duration of just a few years and relatively low development and launch costs. We would like to acknowledge the contributions of Dr. Sam Cohen, Co-I at PPPL; Mr. Michael Paluszek and Gary Pajer of PSS; Eric Hinterman, Matt Daigger, and Charlotte Sun, PSS interns; Charles Swanson, Eugene Evans and Peter Jandovitz, PPPL graduate students; Nick McGreivy, PPPL intern; and Tom Rognlien, LLNL. The artist who did the rendering was S. Shalumov. 2.1 Work Plan In this Phase I study, we proposed to analyze the Pluto mission concept using new models of the predicted DFD engine characteristics. The goal is to determine the feasibility of the preliminary trajectory concept by applying limits on the thrust steering and range of throttle. The throttling of the thrust and specific impulse will affect the efficiency. We subcontracted to Princeton Plasma Physics Laboratory for part of this investigation. The subtasks are: 1. Analyze all subsystems and produce an improved mass model 2. Analyze shielding requirements on a component level and produce an improved shielding design and neutron radiation mitigation strategy 3. Analyze the thrust augmentation system and produce a model of efficiency vs. thrust (subcontract to Princeton Plasma Physic Lab) 4. Using the new mass and thrust models generate an optimal Pluto mission trajectory 5. Revisit the system design and produce a new spacecraft model Figure 2 shows a block diagram of the system components. The blocks that we are studying in this Phase I project are shaded light blue. In Phase I we have not performed any analysis of the superconducting coil cooling subsystem, but have focused on the heat engine, startup system, and the RF generator. Approximately 550 hours were allocated to PSS staff for the modeling and system analysis and 80 hours for PPPL's Dr. Cohen to develop a model of the thrust augmentation system that evaluates engine efficiency, thrust, and specific impulse. 2.2 Princeton Field-Reversed Configuration (PFRC) Reactor The Direct Fusion Drive concept is an extension of ongoing fusion research at Princeton Plasma Physics Laboratory dating to 2002. Princeton Field-Reversed Configuration machines (PFRC) employ a unique radio frequency (RF) heating method invented by Dr. Samuel Cohen. Studies of electron heating with this method have surpassed theoretical predictions and experiments to measure ion heating in the second-generation machine are ongoing. A full-sized PFRC is perfectly suited to use as a rocket engine for two reasons: one, the configuration results in a radical reduction of neutron production compared to other D3-He approaches; two, the reactor features an axial flow of cool plasma to absorb the energy of the fusion products. Adding propellant to this flow results in a variable thrust, variable specific impulse exhaust through a magnetic nozzle. We call this process thrust augmentation of the reactor. Approximately 35% of the fusion power goes to thrust, 30% to electric power, 25% lost to heat, and 10% is recirculated for the RF heating. The current one-quarter-scale machine, the PFRC-2 with a plasma radius to 7 cm (see Figure 3), is designed to demonstrate electron and ion heating. At an applied RF heating power of about 20 kW, electron heating to temperatures Te > 300 eV has been demonstrated, see Figure 4. Ion heating studies will follow, once Te > 1 keV has been achieved. Pulse lengths of 300 ms have been reached. The main axial-field water-cooled magnets, in conjunction with eight high-temperature superconducting internal flux conservers can produce a central internal field of 1.2 kG. (An operational PFRC would have a field of 70 kG). The RF heating system has been upgraded to 200 kW. Additional diagnostics have been added, a notable one being a soft X-ray pulse-height spectrometer with an spectral range of 0.25-10 keV, an energy resolution of 9% at 525 eV and 1% at 5.9 keV, and a count rate capability to in excess of 10^6/s. Probes are used to measure SOL properties. 2.3 Modeling Tools 2.3.1 Plasma Software Packages There are four main software packages that have been used to analyze the PFRC configuration and operation: 1. LSP - This is a 3-D electromagnetic particle-in-cell code for Large Scale Plasma simulations. This is commercial software owned by Orbital/ATK and run under a PPPL license. This code has been used to study FRC formation by RMF, RMF penetration, plasma heating, and fast-ion slowing down in cool magnetized plasmas. It requires significant supercomputer time, typically 10^5 cpu-hrs per run. 2. UEDGE - This 2-D multi-species fluid code predicts electron and ion temperatures based on a specified magnetic configuration and plasma, neutral gas, and power input. Lawrence Livermore National Lab staff wrote and maintain this code. 3. RMF - This Hamiltonian code, authored by Alan Glasser, models single-particle heating in 3-D with specified magnetic fields, e.g., FRCs and RMF. 4. ATTILA – a comprehensive radiation transport environment. This code is used to model radiation effects in ITER, including neutron transport, activation, and defect generation. ATTILA was used in prior work to generate shielding thicknesses based on certain neutron power and acceptable neutron fluences. UEDGE was used during the course of this study to generate new simulation results for thrust and specific impulse as a function of input power and gas flow rate. RMF and LSP have been used in prior work to build the theoretical foundation of PFRC operation including detachment in the terminating magnetic nozzle. For more details see Appendix A which has a detailed technical description of the PFRC. 2.3.2 Spacecraft Control Toolbox: Fusion Propulsion Module This software packaged was initially developed using internal research and development funds. It includes the following tools: • plasma physics utilities • fusion reactions including the power released by each species and cross-sections • Bremsstrahlung and synchrotron radiation models • magnet sizing using Virial and shell methods • power conversion system sizing (L. S. Mason 2003) • tools for sizing shielding and cryogenic cooling systems • point reactor designs (Santarius 1998) • rectilinear mission planning During this Phase I, we added additional plasma models from the 2016 NRL Plasma Formulary, as well as additional fusion cross-section models. (Hively 1982) 3.1 Mass Model The goal of this task was to develop detailed tables of the mass and power numbers for a complete DFD system as to better estimate the specific power of the technology. Previous estimates have used mass scaling laws, such as for a gas turbine. We want to move away from scaling laws and size the individual components in the heat exchanger, RF system, and radiators, as well as the support structure for the coils. We also began analysis of layout options and developed an initial layout in a CAD package. 3.1.1 Thermal Conversion A Rankine cycle was eliminated from consideration because it has a lower technological maturity and higher operational complexity than the other two. In spaceflight applications, reducing complexity is an important design parameter. The reason that a Brayton cycle was chosen over a Stirling cycle is because of its projected operational efficiency. For low-power, nuclear-based space plants, Stirling engines offer a significantly lower system mass than Brayton engines. However, at power levels greater than 20 kW, Brayton engines begin to become more efficient in terms of mass-to-power-output levels (L. Mason 2002). As this spacecraft is operating in the MW range, a Brayton cycle is the clear choice. Figure 5 shows a basic Brayton cycle with a recuperator. The components of a Brayton Cycle are: 1. Compressor 1 - a low pressure compressor 2. Intercooler - cools the gas before entering the next compressor stage. It cools by passing the gas over the radiator, which rejects heat to space. 3. Compressor 2 - a high pressure compressor 4. Recuperator - a primary heat exchanger that heats gas coming from the compressor prior to heat addition by the external source. This increases efficiency by raising the temperature seen at the turbine. However, if the external source already heats the working fluid to the turbine blade limit of 1589 K, a recuperator may not be needed. 5. Heat source - heat from the fusion engine is transferred into the cooling loops that house the working fluid via radiation. 6. Turbine 1 - a low pressure turbine 7. Turbine 2 - a high pressure turbine 8. Generator - converts turbine work output into electrical energy for use by the rest of the spacecraft 9. Precooler - transfers heat to the radiators in order to cool the working fluid down to an acceptable level to be fed into the first compressor 10. Radiator - rejects waste heat to space The turbine and compressor can have any number of stages: only two are shown here. Notice in the figure that the compressors are connected with a shaft to Turbine 1, which is how they receive their power. Similarly, the generator is connected to Turbine 2, which is how the electrical energy for the spacecraft is generated. Excluding preheaters in-between turbine stages, this list contains all of the possible components in a closed loop Brayton cycle. However, it is likely that not every component will be used in the actual system. In Figure 5, the working fluid first enters Compressor 1. The compressor is driven by Turbine 1, though it will need power at the start of the cycle from elsewhere. This will come from the D2/O2 combustion that also powers the start-up of the Heater. The fluid’s pressure and temperature increase as it passes through Compressor 1. In order to maximize efficiency of subsequent compressors, the fluid will be cooled before entering each one. After exiting the last compressor, it may be passed through a Recuperator in order to be pre-heated. This depends on the mission’s operating parameters and the power dissipation of the Heater. After the Recuperator, the working fluid will pass into cooling coils that loop around the nuclear reactor. At this point, the working fluid will be heated to very high temperatures - around 1500 K - through radiation absorption. This hot fluid will then be passed through a series of turbines in order to generate power. The compressors will be directly driven by turbines, and the turbines that remain at the end of the series will be used to drive an electricity-producing generator. After passing out of the turbines, the gas will have cooled but will still be relatively hot. It also will have dropped to roughly the same pressure as the inlet stream to Compressor 1. The gas may pass through a Recuperator to further cool it before being passed into the pre-cooler heat exchanger to bring it down to its original temperature. This is how the Brayton cycle works: fluid is compressed, heated, passed through turbines to generate power, and then cooled. Whereas jet engines employ open-loop Brayton cycles using air as the working fluid, all space applications must employ the closed-loop version to contain the working fluid. Two MATLAB codes, one with and one without a recuperator, have been developed to accurately model a non-ideal closed-loop Brayton Cycle. The scripts take an inlet pressure, inlet temperature, and desired pressure ratio as inputs, and calculate pressure, temperature, flow rate, cycle efficiency, and work for each step as outputs. Adjustable parameters in the scripts are as follows: 1. Baseline pressure 2. Baseline temperature 3. Pressure ratio 4. Compressor efficiency 5. Turbine efficiency 6. Recuperator effectiveness 7. Working fluid specific heat ratio 8. Working fluid specific heat 9. Working fluid molecular weight Figure 6 shows sample output for a pressure ratio of 2. The temperature and pressure are noted for each stage. The efficiency is only 20% without the recuperator. Figure 7 shows MATLAB output for the Brayton cycle with a recuperator (Thermal Efficiency: 65.59%, Flowrate: 42.9266 kg/s, Turbine Work Output: 7.4613 MW, Compressor Work Input: 2.3448 MW, Net Work: 5.1165 MW). Several working fluid options have been considered for Brayton Cycles with similar applications to this proposal. Monatomic working fluids of interest include Helium (He), Argon (Ar), and Xenon (Xe). All are noble gases and are thus stable and non-reactive. Diatomic working fluids include Nitrogen (N2) and Hydrogen (H2). Carbon Dioxide (CO2) has been considered as a polyatomic working fluid. Finally, gas mixtures are often considered, including He-Ar and He-Xe. For this concept, a 70/30 mole fraction mixture of helium and xenon was chosen to be the working fluid. There are a number of reasons why this mixture is advantageous over pure helium or hydrogen: • The higher molecular weight of the mixture increases both the turbine and compressor efficiencies. Because of its higher molecular weight, Xenon has a lower value of beta, which is derived from its value of (1 – specific heat ratio) . A lower value of beta means that an increase in pressure drop will correspond to a lower change in temperature. Higher pressure drops and smaller temperature changes are ideal. Thus, by utilizing a working fluid with a higher molecular weight, the increase in turbine and compressor efficiencies can increase the overall system efficiency up to 50% [Wright et al., 2002]. • The molecular weight of the mixture (42.2g/mol) is closer to that of air (28.8g/mol) than pure helium (4g/mol), making it easier to design and test the turbines and compressors. • Higher molecular weight working fluids allow the design of turbines of better performance. • Lower kinematic viscosities result in higher power generation efficiencies [?]. Xenon significantly lowers the kinematic viscosity of the working fluid compared to that of a pure helium system. • The mixture has been found to reduce the turbine exit impeller-root stress by up to 50% [Klann, 1968]. This increases the lifetime of the system. One downside to increasing the molecular weight by adding Xenon into the working fluid is that the heat capacity and thermal conductivity decrease. However, the gains in efficiencies and ease of testing outweigh the decrease in thermal control. Figure 8 shows a schematic layout of the Brayton cycle components relative to the DFD main engine, to help in determining the length of the pipes required between the components. Note the lengths given, which assume that the main engine is 4 m long and 1 m in diameter. There needs to be an intercooler (IC) between each compressor stage (C1, C2, …) This results in a total cycle pipe length of 15 m. Table 1. Brayton Engine Design Parameters - Working fluid: 70/30 molar fraction He-Xe - Input heat: 350 kW - Max fluid temperature: 1589 K - Compressor stages: 6 - Pressure ratio: Up to 30 - Pipe material: Stainless steel Table 2 gives estimates for the component masses. The generator mass is based on existing electric vehicle motors, which produce about 150 kW in about 80 kg. The turbine and compressor masses are scaled using GE90 jet engine which uses the same pressure ratio, temperature, and ceramic blade material as our system. The piping assumes 18 cm diameter stainless pipes with a wall thickness of 0.2 cm. Table 2. Brayton Engine Component Mass Estimates - Turbines and Compressors: 30 kg - Piping (stainless steel): 130 kg - Generator: 80 kg - SUBTOTAL: 240 kg 3.1.2 Startup Subsystem Our startup concept uses combustion of the available deuterium in an auxiliary power unit (APU), which can start up the fusion engine. An oxygen tank is required. An optional electrolysis unit can then recuperate the oxygen for future restarts. The heat from the APU is converted to electricity using the same thermal conversion system as the main engine. 1 kg Hydrogen produces 120 MJ/kg of energy when combusted with 8 kg of oxygen. Deuterium has double the atomic mass of hydrogen, so twice as much is required, and 2 kg of deuterium produces approximately the same energy. The engine is started up at partial power in electricity generation mode and this power replaces the power from the combustion as the engines return to full power. The combustor uses the same heat engine as the nuclear fusion engine uses for power generation. The D2-O2 Auxiliary Power Unit (APU) will therefore be used to generate heat through the combustion of deuterium. This heat will be transported via the gaseous water (steam) outflow from the reaction. The steam will be passed through a heat exchanger in order to transfer the heat to the helium-xenon working fluid in the Brayton cycle. This heat will then reach its final destination, where the Brayton cycle will convert it to useful energy via a generator. This startup process is shown in Figure 10. When actuated valves are opened electrically from the battery supply, oxygen and deuterium will flow through an injector plate and into the combustion chamber. They will be electrically ignited and combust to form hot steam. This steam will flow through a heat exchanger and transfer its heat to the helium-xenon working fluid. The heat will then be converted to electricity in the Brayton Heat Engine for use in energizing the coils, powering the RF Heater, and charging the battery. Meanwhile, the cooled steam will pass through a condenser to change back to its liquid state so that it can be electrolyzed and fed into the deuterium and oxygen tanks for recycling. We estimate that the startup system should provide about 20% of the full engine power for 1000 seconds. For a 10 MW engine, this is 2 MW for 100 s, or 200 MJ. This will require 13.5 kg oxygen and 3.4 kg deuterium. For extremely long duration missions, the D2O can be electrolyzed once the engine has restarted. This provides oxygen for future restarts. On spacecraft with a crew there is likely to be sufficient O2 for this purpose without the needed for the added mass of an electrolysis unit. The electrolysis unit is sized based on the rate of electrolysis, or how quickly the oxygen needs to be recovered. The ISS unit has a mass of 446 kg and can produce 5 kg of oxygen per day. If we scale down from this system, we might have a unit that is 100 kg if we want to produce 1.5 kg per day or 15 kg if we want to produce 0.135 kg per day, which would require 100 days to regenerate the 13.5 kg oxygen consumed. Table 3. Startup System Component Mass Estimates - Combustion Chamber: 15 kg - Condenser: 5 kg - Heat Exchanger: 10 kg - Additional Piping and Valves: 10 kg - Oxygen Tank: 15 kg - SUBTOTAL – NO ELECTROLYSIS: 55 kg - Electrolysis Unit: 15 – 35 kg - SUBTOTAL – WITH ELECTROLYSIS: 70-85 kg 3.1.3 RF Subsystem Our reactor is RF heated, and efficiency in this subsystem will be crucial. Currently, a (linear) series of tube RF amplifiers takes a digitally synthesized waveform and amplifies it. The output is passed through a 90-degree hybrid splitter, a narrow band device that also provides phase control and isolation from load changes. The splitter is tunable over a limited but sufficient range to accommodate changes in plasma impedance. Reflected power is diverted to a dummy load. The source is able to keep the forward power constant despite loading changes. The matching network transforms the impedance of the plasma and RMF coils, a few tenths of an Ohm, to 50 Ohms and survive high voltages and currents. A critical reactor issue is the efficiency of the RF amplification stage. We propose adopting a new RF drive system using Class E amplifiers based on solid-state switches. Such Class-E amplifiers have achieved over 90% efficiency. The RF drive architecture is shown in Figure 11. It consists of a series of Class-E RF switching amplifiers that feed RF to the antennas via coaxial cables. One set is driven by a square wave, the other by a square wave that is 90 degrees out of phase. This produces the desired sine/cosine drive for the two antenna pairs required for RMF heating and current drive. The waveforms are measured and feedback from these measurements is used to adjust the phasing of the pulse trains that drive the amplifiers. Feedback can also correct for temperature drift of components in the high power stage. This design has the potential to be much more efficient than the linear design described above. Note that the tank (LC) circuit may be common for each antenna. Work on sizing the RF system is ongoing. No equipment like this has previously been design for space. Terrestrial systems of 200 kW run about 2000 kg, much of this weight being in cabinets and structures as well as the heavy linear amplifiers. The Class E amplifiers now on the market, which can handle roughly 200 kW, are exceedingly small – 12 x 25 x 40 mm package, literally about the size of a hockey puck. A full RF circuit analysis is required, which we have begun, and hope to continue in our Phase II or potentially a NASA STTR. 3.1.4 Radiators Current space-qualified radiators will be too heavy but there are upcoming radiator materials that will make the radiators mass a small fraction of the engine total. NASA is currently supporting research in this area, such as the work on carbon-carbon radiators performed by the University of Massachusetts with the support of the MSFC Center Innovation Fund. (R.W. Hyers 2012) The goal is reduce the areal mass of radiators from about 10 kg/m2 currently to 2 kg/m2 or less. Our proposal and Phase I work assumes carbon-carbon radiators with an areal mass of 2.75 kg/m2 and an average temperature of 625 K. As a point example, for a 1.1 MW engine assume 400 kW are going to the heat engine and 700 kW out the nozzle, of which 160 kW are going directly to the radiators and 240 kW is useful electric power. Assume the spacecraft has two such engines so the total load on the radiators is 320 kW. Recall that the power emitted by a black body per unit area is proportional to the fourth power of the body temperature T. The total power emitted is then obtained by multiplying by the radiator emissivity and surface area. We assume that both surfaces of the radiator emit so there is an additional factor of 2 in calculating the radiator size. Equation 1. Black Body Radiation. Power emitted per unit area is equal to the Stefan-Boltzman constant σ times the fourth power of the temperature T. Multiply by the area A and the emissivity ε to calculate the total power Q: Q = A ε σ T^4 Assume the radiator emissivity is 1, then the total area required to radiate 320 kW at 625 K is 37 m2, or taking into account both the front and back radiator surfaces, a total radiator size of 18.5 m2. If there are two wings then each might be 2 m by 4.6 m. With an areal mass of 2.75 kg/m2 then both wings together would have a mass of 50.8 kg. For comparison, consider a traditional system with an emissivity of 0.8, areal mass of 10 kg/m2, and a maximum temperature of 400 K. The total area would now be 138 m2 and the mass 1378 kg! Higher radiator temperature means lower cycle efficiency, so cycle efficiency and mass must be traded in the design. 3.1.5 Superconducting Coils Initially, we believed that the mass of the coils would be dominated by the structural mass, and we utilized a virial energy method to estimate the mass. However, when we actually computed the mass of superconducting wire needed using field strength and published properties for wire, we discovered that the wire mass itself could dominate the engine. This raises the question of whether it will be more mass-efficient to use the high-temperature wire that is in the current experimental machine, or use low-temperature wire with the necessary additional cooling. The high temperature wires are superconducting at liquid nitrogen temperatures, around 77 K, while the low temperature conductors require liquid helium cooling to achieve close to 4 K. This is a subsystem where the space and terrestrial engines may look very different. In the space engine, we will need to taper the coils with the plasma ellipsoid to save mass, while in a terrestrial engine it may save money to have all the coils the same diameter. Table 4 shows a very simple mass comparison for a HTS and a LTS, just counting turns of the wire at a single radius to produce 3 MA (3e6 A) and parameters from current data sheets. This would produce about a 7 T field at a 0.5 m radius. This does not take into account any packing factor or the reduction in field contribution for the wire that is at a higher radius, but represents an absolute minimum amount of conductor needed. It is important to note that, in most commercial Hi-T superconducting tape, 95% of the mass is in the 5-mil thick stainless steel or copper cladding (on both sides) that encapsulates the 10-µ thick Hi-T material. Companies are now promoting tapes with about ½ the cladding thickness. Table 4. Superconducting Wire Mass Comparison for a Single 0.5 m Radius Coil - NbTi 0.7 mm: Linear Density = 0.0372 g/cm, Temp = 4.2 K, Current = 350 A, Turns = 8572, Mass = 76.7 kg - NbTi 1.04 mm: Linear Density = 0.063 g/cm, Temp = 4.2 K, Current = 700 A, Turns = 4286, Mass = 84.6 kg - Amperium 12 mm: Linear Density = 0.2 g/cm, Temp = 30 K, Current = 700 A, Turns = 4286, Mass = 289.5 kg - Amperium 12 mm: Linear Density = 0.2 g/cm, Temp = 77 K, Current = 350 A, Turns = 8572, Mass = 579 kg The baseline coil design for the engine has 8 coils distributed evenly over the linear extent of the fusing plasma, on the order of 2 to 8 m. The coil radii follow an elliptical geometry with a maximum radius in the center and minimum at the ends. This is shown in Figure 12. Table 5. Coil Currents (MA) for Baseline Coil Geometry with Varying Minimum Radius for a Central Magnetic Field of 7 T - Coil 1: min radius 0.3m -> 2.66 MA; 0.35m -> 2.98 MA; 0.4m -> 3.31 MA; 0.45m -> 3.64 MA; 0.5m -> 3.99 MA - Coil 2: min radius 0.3m -> 3.14 MA; 0.35m -> 3.03 MA; 0.4m -> 2.94 MA; 0.45m -> 2.84 MA; 0.5m -> 2.75 MA - Coil 3: min radius 0.3m -> 2.92 MA; 0.35m -> 2.93 MA; 0.4m -> 2.94 MA; 0.45m -> 2.92 MA; 0.5m -> 2.91 MA - Coil 4: min radius 0.3m -> 3.01 MA; 0.35m -> 2.97 MA; 0.4m -> 2.93 MA; 0.45m -> 2.88 MA; 0.5m -> 2.83 MA - Coil 5: min radius 0.3m -> 3.01 MA; 0.35m -> 2.97 MA; 0.4m -> 2.93 MA; 0.45m -> 2.88 MA; 0.5m -> 2.83 MA - Coil 6: min radius 0.3m -> 2.92 MA; 0.35m -> 2.93 MA; 0.4m -> 2.94 MA; 0.45m -> 2.92 MA; 0.5m -> 2.91 MA - Coil 7: min radius 0.3m -> 3.14 MA; 0.35m -> 3.03 MA; 0.4m -> 2.94 MA; 0.45m -> 2.84 MA; 0.5m -> 2.75 MA - Coil 8: min radius 0.3m -> 2.66 MA; 0.35m -> 2.98 MA; 0.4m -> 3.31 MA; 0.45m -> 3.64 MA; 0.5m -> 3.99 MA The minimum coil current is seen to be 2.66 MA and the maximum about 4 MA for the different coil radius schemes. If we taper the outer coils enough, the current they require also decreases, but if we maintain the radius of 0.5 m across the length and require the full field strength at the ends then the outer coils would require even more turns than the inner coils. For a final radius of 0.35 m, the current in each coil is nearly constant at 3 MA. If the decreasing radii are taken into account, then the total conductor mass for 8 coils using 1.04 mm of NbTi carrying 700 A, using the simple turns calculation above, would be 596 kg. Our prior work on shielding was presented at the 2015 International Astronautical Congress (S. A. Cohen 2015). The neutron flux on the walls of the PFRC is orders of magnitude less than for a tokamak reactor, or other D-3He concepts, but is not zero; for long engine lifetimes or human presence some shielding will still be required. As neutron absorption cross-sections are many orders of magnitude smaller than their scattering cross-sections, the neutrons must be slowed significantly for attenuation to occur. Findings from Project Prometheus (Lewis 2006, A. Bushman 2004) showed that the best materials for neutron attenuation and absorption were low-Z (low atomic number) materials such as hydrogen (possibly in water), lithium, beryllium, and boron, particularly the 10B isotope of boron. Liquid water is an excellent material for neutron shielding, but difficult to handle in low pressure and low temperature environments. For space applications, solid materials are preferable. Solid low-Z material may also serve as liners for the reactor chamber as low-Z elements cause less problematic plasma contamination. These liners must be able to handle the extreme environment of space and also the internal thermal, electrical, and structural conditions in the reactor. 10B strongly attenuates neutron energy and, unlike lithium hydride (LiH) and Be, is also a neutron absorber and therefore reduces the total flux behind the shield. As 10B4C it is a very strong, stable solid over a very large range of temperatures. 10B4C is readily available in nature, safe to manufacture, inexpensive, and it does not exhibit any obvious structural deformities when irradiated. Since it is transparent to x-rays, bremsstrahlung radiation can pass through it to a thermal power conversion system. X-ray shielding is also required. Many materials absorb X-rays. Tungsten is one of the best attenuators on a per mass basis (Lewis 2006) and meets many of the material requirements for shielding including availability, manufacturability, and high temperature capabilities. The shielding can use thin tungsten sheets. This initial shielding analysis has focused on limiting the flux at the superconducting coils to a desired lifetime fluence. For ITER, this is 1e22 neutrons/m2, and for DEMO 3-5e22. The HTS YBCO has an unirradiated critical temperature of about 90 K. In order to maintain this temperature well above liquid nitrogen temperatures of 77 K, a conservative value for the fluence is 6e21 m-2. If the HTS are operated at a much lower temperature, 50 K or 40 K or even less, a much higher fluence can be tolerated. The reduction in critical temperature may be accompanied by a decrease or increase in critical current (M. Eisterer 2009), depending on the operating temperature and local magnetic field strength, making an optimal coil and shielding design a very complex problem. The required shielding was evaluated using the ATTILA code (S. A. Cohen 2015). ATTILA uses Chebyshev-Legendre quadrature to solve a particle (neutron) transport problem in space, angle, and energy. The model geometry, including material prescriptions, is given to the program and divided into a finite element mesh. ATTILA has a library of energy-dependent neutron cross-sections for over 100 different materials, prepared for the ITER project. The displacements-per-atom reaction rate, activation products, helium production, and heat deposition rates are unique to each material. Meshes were set up for several rocket engine models, one shown in Figure 15. The ATTILA simulations assumed that 1% of the fusion power would be in 2.45 MeV neutrons, a highly conservative value. Our calculations show this number could be reduced another order of magnitude to 0.1%; confirmation of whether the RMF heating method can achieve this requires self-consistent calculations and experimental tests. Hence the amount of shielding is an overestimate. Note that we assumed (enriched) B4C shielding. A further 20% reduction would accrue if pure B were used. The most sensitive element of the rocket structure is the HTS superconducting material. For these, too, we assumed a very conservative value of the tolerable damage (10^-3 displacements per atom, dpa), a factor of 10 lower than assumed by designers of tokamak reactors. This conservative stance was chosen because of the paucity of the available data, which should be remedied in efforts to refine our estimates. For comparison, structural materials, like steel, can tolerate up to 75 dpa. Figure 16 shows results for the DPA versus shield thickness for a 1% neutron power, which is about 3 kW/m2 for a 1-10 MW PFRC. The ATTILA results indicate that 20 cm of enriched, 10B4C shielding would protect the coils of a 1 MW/m FRC for one year of continuous operation to a dose of 6e21 n/m2. A 30 year lifespan would require 33 cm of enriched shielding or 39 cm of natural B4C shielding. The tungsten layers required to absorb the bremsstrahlung radiation x-rays, on the order of magnitude of 0.5 to 1 cm thick, reduces the fluence by another 7 to 14%. ATTILA showed the neutron losses through the axial ports to be small, around 0.5% of the total flux. The energy distribution of these neutrons is relatively mild, so the shielding requirements at the end caps is only half that of the center. If we assume optimistic instead of conservative conditions, we can first extend the lifetime afforded by the shielding ten times if the neutron fluence is ten times less. So if we are able to achieve a 0.1% neutron power through differential RMF heating of the two fusion fuels (deuterium and helium-3), the 20 cm of boron carbide would be sufficient for 10 years of operation. If we run the HTS at a low temperature such that they can absorb an order of magnitude higher fluence, 6e22 /m2, we can reduce the shielding further, likely by another factor of 2. Therefore, we use about 10 cm of 10B4C shielding in our current engine models. The thickness of the shielding is a driving factor in the DFD mass, not just because of the shielding mass itself, but because it needs to be internal to the magnetic coils; increasing the radius of the coils increases the currents required to produce the central field, and hence the coil mass. Table 6 gives masses for the shielding at different thickness. One column gives a simple cylinder while one gives the mass if the shielding is tapered. The plasma radius is 25 cm, so allowing for the scape-off-layer, the shielding starts at a radius of 32 cm. In the case of a tapered shield, the inner diameter tapers to 20 cm at the ends. We approximate this with a stepped cylinder, ½ at the largest diameter and ½ at the smallest diameter. Boron carbide has a density of 2520 g/cm³, lithium hydride 820 kg/m³. Table 6. Shielding Mass Calculations for a 3 m long FRC - B4C (10 cm): Cylinder (ID 32 cm) = 1757.5 kg, Stepped (ID 20 to 32 cm) = 1472.5 kg - B4C (20 cm): Cylinder (ID 32 cm) = 3990.1 kg, Stepped (ID 20 to 32 cm) = 3420.1 kg - Tungsten (0.5 cm): Cylinder (ID 32 cm) = 585.1 kg, Stepped (ID 20 to 32 cm) = 476.25 kg - Tungsten (1 cm): Cylinder (ID 32 cm) = 1179.3 kg, Stepped (ID 20 to 32 cm) = 961.56 kg Student interns at PPPL over the summer and performed 2D simulations using UEDGE, and we were able to utilize this data to produce a functional model of the thrust and specific impulse of the engine as a function of input power and gas flow rate. Figure 17 shows the latest data. The power levels in the legend are for power into the scrape-off-layer, which is only a portion of the total fusion power. The small dots mark the operating range of interest. For each power level there is a fairly narrow range of flow rates which can absorb the power and provide the maximum thrust. We have modeled these regions as linear, with the slope and intercept as a function of input power. This has resulted in the model shown in Figure 18. Our overall conclusion is that a feasible performance space is 5 to 10 N of thrust per 1 MW of thrust power, with a specific impulse of about 10,000 s. This translates to 2.5 to 5 N of thrust per megawatt of fusion power. Figure 19 shows the thrust model for a 1 MW power input. The specific impulse ranges from 8600 to 9200 seconds. Figure 20 shows a 4 MW power input. The specific impulse now ranges from 10,000 to 12,000 seconds. The efficiency increases both as the flow rate increases, at any given power level, and for higher power levels. Figure 21 shows the efficiency calculated from the model for 1 MW, 2 MW, and 4 MW power levels. Figure 22 shows the velocity model against the UEDGE data, where the bulk exhaust velocity is calculated from the thrust divided by the flow rate. The trend of higher specific impulse for higher power level is clear. The model allows us to generate contour plots for expected performance as a function of input power and flow rate. Figure 23 and Figure 24 shows contours for thrust and exhaust velocity, respectively. We used several approaches to further analyze potential trajectories to Pluto and determine if they are feasible with a 1-2 MW engine. Our initial analysis used a Lambert impulsive burn approach; burns on the order of 100 days with thrusts of 50 N could reach Pluto in 4 or 5 years. We next analyzed straight-line trajectories, with a constant thrust and a switch time between acceleration and deceleration phases. We separately studied both Pluto insertion spirals and Earth departure spirals. Finally, we did a simple optimization of a planar trajectory, which takes into account the initial motion of the Earth. The power relationship for an electric thruster is shown in Equation 2: Equation 2. Power is equal to one-half the thrust T times the exhaust velocity v, divided by the efficiency N: P = (1/2) * (T * v) / N In the case of DFD, efficiency N is a function of thrust. Therefore the trade between thrust and exhaust velocity is more complex. As an approximation we always start with an assumed constant efficiency in the range of 0.25 to 0.5. 3.4.1 Lambert Impulsive Trajectory For our NIAC Phase I proposal, we initially calculated an impulsive trajectory to Pluto using Lambert's law. Lambert's law is used for an array of start dates and time of flights, and a minimum delta-V is found. For instance, a 4 year trajectory with a start date in the next 40 years was found to require between 60 and 80 km/s delta-V. We then calculated the mission mass based on an estimate of specific power, thrust efficiency, and a target payload of 1000 kg. This requires an iteration on the thrust and fuel mass given a burn duration, for instance a 15% burn duration of the 4 year time of flight is 220 days. A delta-V of 70 km/s can be achieved with a thrust of 20 N and a specific impulse of 10,000 s in the allotted 220 days, with a total mission mass of less than 8000 kg, indicating initial feasibility. Table 7. Lambert Analysis Example Mission Inputs - Launch Date: March 21, 2036 - Payload Mass: 1000 kg - Flight Time: 4 years - Total Reactor Power: 2 MW - Engine Specific Power: 0.71 kW/kg - Thrust Efficiency: 0.5 - Tank Structural Fraction: 0.02 - Burn Fraction: 0.15 Table 8. Lambert Analysis Example Mission Results - Lambert Delta-V: 65.7 km/s - Burn Duration: 219.2 days - Thrust: 20.1 N - Specific Impulse: 10141.6 s - Engine Mass: 2816.9 kg - Fuel Mass: 3695.2 kg - Total Mission Mass: 7586.0 kg - Deuterium Volume (liquid): 22.6 m3 - Helium 3 Mass: 0.4 kg 3.4.2 Straight Line Trajectory We derived a formulation of a minimum mass optimization for a straight-line trajectory. This is interesting because it finds a value for a constant thrust that will be applied for the entire mission, with a switch in direction at a point somewhat more than halfway to the destination. This is probably a better model for how the fusion engine can operate than two short burns of higher thrust at the beginning and end of the trajectory. The inputs to the optimization are: • Straight line distance traveled • Payload mass (kg) • Duration (s) • Exhaust velocity (km/s) • Fuel structural fraction • Specific power (W/kg) • Thrust efficiency The outputs are the switch time, thrust, and resultant masses for the engine and fuel. A small change in the exhaust velocity results in a big change in the fuel mass required. Figure 25 gives an example result, arriving at Pluto in three years using 4.19 N thrust and 0.4 MW. The payload is seen to be 1000 kg and the total wet mass as 6998 kg. This is for a specific power of 700 W/kg, a thrust efficiency (conversion of output power to thrust) of 0.5 and an exhaust velocity of 100 km/s (specific impulse of 10,000 s). The fuel structural fraction is 0.02. Table 9 Straight Line Example Mission Inputs - Distance: 28.6 AU - Payload Mass: 1000 kg - Flight Time: 4 years - Engine Specific Power: 0.7 kW/kg - Thrust Efficiency: 0.5 - Tank Structural Fraction: 0.02 - Exhaust Velocity: 100 km/s Table 10 Straight Line Example Mission Results - Parameter (Duration 4 years / Duration 3.5 years): - Delta-V: 141.16 km/s / 163.5 km/s - Switch Time: 2.68 years / 2.43 years - Thrust: 4.19 N / 9.75 N - Power: 0.42 MW / 0.97 MW - Engine Mass: 598 kg / 1392.4 kg - Fuel Mass: 5287 kg / 10765.5 kg - Total Mass: 6991 kg / 13373.3 kg - Fuel Flow Rate: 0.04 g/s / 0.1 g/s Table 11. Straight Line Trajectory Results (Specific power 1000 W/kg, Exhaust vel 100 km/s, Thrust efficiency 0.4): - Payload 2000 kg, Duration 4 yrs, Thrust 7.8 N, Power 0.97 MW, Mass 13009 kg - Payload 1000 kg, Duration 4 yrs, Thrust 3.9 N, Power 0.49 MW, Mass 6504 kg - Payload 1000 kg, Duration 3.5 yrs, Thrust 8.3 N, Power 1.04 MW, Mass 11391 kg - Payload 1500 kg, Duration 3.5 yrs, Thrust 12.45 N, Power 1.56 MW, Mass 17086 kg - Payload 250 kg, Duration 3 yrs, Thrust 18.68 N, Power 2.33 MW, Mass 20623 kg 3.4.3 Pluto Insertion We wrote a 2D optimization to study the Pluto insertion from a hyperbolic approach with a fixed thrust and mass. The question to answer is, will it be possible to insert into orbit using the relatively low thrust of 5-10 N, and how much time and delta-V should be allocated. Our study has indicated that insertion will require less than 1 km/s delta-V, which is a small portion of the mission total. It is easily accomplished in about one day with 20-40 N thrust and in 2-3 days with 10 N thrust. (Figure 29 shows fixed mass, minimum fuel optimal insertion with thrust of 10 N, mass of 2500 kg, duration 2.8 days, delta-V of 977 m/s). 3.4.4 Earth departure The original concept in our NIAC proposal was to insert the Pluto spacecraft directly into heliocentric orbit. This required a Delta IV Heavy class booster. Analysis shows that an Earth departure from LEO uses very little fuel and takes between 25 and 60 days depending on engine parameters and vehicle mass. This allows a launch by almost any launch vehicle, dramatically reducing launch and overall mission costs. It also allows checkout and testing in low Earth orbit. A sample departure spiral is shown in Figure 30 for a thrust of 20 N, exhaust velocity of 120 km/s, and initial mass of 6500 kg. The red disk is the inner Van Allen belt. The total time in the belt for this case is 6.25 days. Table 12. Departure Spiral Results (Initial altitude 386 km, delta-V ~7 km/s): - Mass 6500 kg, Ve 120 km/s, Thrust 20 N: Spiral Time 24.92 days, Fuel Used 358.91 kg, Time in Belts 6.25 days - Mass 6500 kg, Ve 120 km/s, Thrust 10 N: Spiral Time 50.82 days, Fuel Used 365.89 kg, Time in Belts 12.49 days - Mass 6500 kg, Ve 100 km/s, Thrust 10 N: Spiral Time 50.51 days, Fuel Used 436.44 kg, Time in Belts 12.47 days - Mass 8500 kg, Ve 100 km/s, Thrust 10 N: Spiral Time 66.49 days, Fuel Used 574.45 kg, Time in Belts 16.30 days The DFD solenoid interacts with the Earth’s magnetic field and produces a substantial disturbance torque during the Earth spiral (magnitude 500-550 Nm). Compensating methods include correction coils, magnetic shielding (Hyperco-50), reaction wheels/CMGs, magnetic plume steering, and reaction control systems. 3.4.5 Planar Optimal Trajectories We wrote a direct method optimization to reach a planar target in a fixed amount of time, with constant thrust and minimum mass using MATLAB's fmincon. Table 13 Planar Optimization Example Mission Inputs - Distance: 29.6 AU - Payload Mass: 1000 kg - Flight Time: 4 years - Engine Specific Power: 0.7 kW/kg - Thrust Efficiency: 0.5 - Tank Structural Fraction: 0.02 - Exhaust Velocity: 100 km/s Table 14 Planar Line Example Mission Results - Delta-V: 143.81 km/s - Thrust: 4.45 N - Power: 0.44 MW - Engine Mass: 635.5 kg - Fuel Mass: 5615 kg - Total Mass: 7363 kg - Fuel Flow Rate: 0.04 g/s 3.5.1 Engine Modeling We have a MATLAB model of the PFRC reactor based on density and temperature of fusion reactants and engine size. Table 15. Nominal engine plasma parameters - Beta: 0.88 - Scrape off layer thickness: 0.05 m - Plasma radius: 0.3 m - Plasma length: 3.5 m - Deuterium number density: 1.4e+20 /m3 - Deuterium temperature: 100 keV - Helium-3 number density: 2.8e+20 /m3 - Helium-3 temperature: 100 keV - Electron temperature: 30 keV - f-T (factor for Tritium side reactions): 0 - f-D (factor for Deuterium side reactions): 1 Table 16. Nominal engine power parameters - Gas box power fraction: 0.1 - RMF heating power fraction: 0.11 - RMF drive efficiency: 0.9 - RMF plasma heating factor: 0.5 - Synchrotron wall reflection: 0 Table 17. Nominal engine subsystem parameters - Specific mass of the RMF heating: 0.001 - Specific mass of the power generation: 0.0007 - Specific mass of the refrigeration: 1e-4 - Efficiency of the power conversion: 0.6 - Shielding thickness factor: 50 m/(MW/m2) - Structural factor: 0.1 - Radiator areal mass: 2.1 kg/m2 - Radiator temperature: 625 K - Radiator emissivity: 1 Listing 1. 1 MW Engine Design Report - Total Engine Mass: 1528.09 kg - Total Fusion Power: 1.13 MW - Thrust Specific Power: 0.339518 kW/kg - Engine Specific Power: 0.498120 kW/kg - Fusion Specific Power: 0.739414 kW/kg - Subsystem Masses: Shielding Thickness: 10.27 cm, Shielding: 495.30 kg, Magnets: 471.04 kg, Coil Cooling: 24.44 kg, RMF System: 124.29 kg, Power Generation: 244.43 kg, Radiators: 29.67 kg, Overall Structure: 138.92 kg - Powers: 0.11 MW Gas Box, 3.48 kW Neutrons, 2.57 kW/m2 Neutron wall load, 0.27 MW Synchrotron Radiation, 0.23 MW Bremsstrahlung Radiation, 0.52 MW Thrust Input Power, Total Thermal Power: 0.61 MW, Conversion efficiency: 0.60, Bus Power: 0.24 MW, RMF Power: 0.12 MW, Radiated Power: 0.24 MW. 3.5.2 Engine Layout Cooling channels for the Brayton engine wrap around the engine embedded in shielding to allow modular, scalable discrete sections. 3.5.3 Vehicle Design The vehicle nominally has two 1 MW engines at one end with the main bus and lander attached to the other. Radiator wings reject 840 kW total (50 m2 total area at 625 K). Table 18 Orbiter Mass Budget - Engine (Qty 2): 1357 kg - Radiators (Qty 2): 66.75 kg - Magnetic Nozzles (Qty 2): 71.43 kg - D2 Tank (full) (Qty 1): 3432 kg - He3 Tank (Qty 1): 0.22 kg - Insulating Shell (Qty 1): 200 kg - Optical Truss (Qty 2): 10 kg - Gimbals (Qty 2): 3.75 kg - Laser Communication Unit (Qty 2): 2 kg - Orbiter Payload (Qty 1): 270 kg - Lander (Qty 1): 230 kg - TOTAL: 7154 kg Table 19. Launch Vehicle Performance (LEO / ISS / Escape in kg) - Atlas 401: 9800 / 8910 / N/A - Atlas 411: 12030 / 10670 / N/A - Atlas 421: 13600 / 12060 / N/A - Atlas 431: 15260 / 13250 / N/A - Atlas 501: 8210 / 7540 / N/A - Atlas 511: 11000 / 10160 / N/A - Atlas 521: 13500 / 12510 / N/A - Atlas 531: 15530 / 14480 / N/A - Atlas 541: 17410 / 16290 / N/A - Atlas 551: 18850 / 17720 / N/A - Delta IV Medium: 9190 / 851 / N/A - Delta IV Medium+ (4.2): 12900 / 12000 / N/A - Delta IV Medium+ (5.2): 11060 / 10220 / N/A - Delta IV Medium+ (5.4): 13730 / 12820 / N/A - Delta IV Heavy: 28370 / 25980 / 8000 (MTO) - Falcon 9 Block 1: 9000 / 8500 / N/A - Falcon 9 1.1: 13150 / 12420 / N/A 3.5.4 Lander Design The lander features 4 m2 solar panels on a gimbaled truss tracking the orbiter's 1080 nm laser beam (30 to 50 kW beamed power, 2119.1 Wh/hr received). Landing uses a 400 N green propellant engine (Isp 285 s, consuming ~88 kg fuel during a 13-minute landing from 20 km altitude). Table 20 Lander Mass Budget - ACS Subsystem: 1.25 kg - Propulsion Subsystem: 90.9 kg (Thruster: 5 kg, Fuel Tanks: 6 kg, Fuel: 80 kg) - Telemetry and Command: 1 kg - Power Subsystem: 26.63 kg (Battery: 13.3 kg, Panels: 13.2 kg) - Structure: 23.69 kg - Payload: 86.55 kg - TOTAL: 230 kg Conclusions: Phase I engine modeling demonstrates that 2.5 to 5 N of thrust per MW of fusion power with an Isp around 10,000 seconds and ~200 kW electrical power can be achieved. LEO departure spiral trajectories widen the range of launch vehicles to medium-class rockets. Superconducting magnets and shielding drive mass; low-temperature operation and advanced high-temperature superconductors require further trade study in Phase II. Closed-loop He-Xe Brayton cycles and solid-state Class E RF switching amplifiers show high efficiency. Appendix A. PFRC Technical Description Overview: • D-3He fusion produces charged particles (He-4, protons) without primary neutrons. Side reactions (D-D) are suppressed by operating at a 3:1 He-3 to D fuel ratio and rapidly exhausting tritium ash. • Odd-parity Rotating Magnetic Field (RMF) enables compact 0.5 m diameter plasma confinement and efficient ion heating to >50-100 keV. • Scrape-off-layer (SOL) ionized gas absorbs energy from fusion products and exhausts via a magnetic nozzle, providing thrust augmentation. • Phased development plan: PFRC-1 (electron heating), PFRC-2 (1 keV ion heating, 1.2 kG), PFRC-3A (thermonuclear parameters, 5 keV, 10 kG), PFRC-3B (D-3He fusion demonstration, 50 keV, 60-80 kG), leading to full-scale PFRC-4.