Hall thrusters are very efficient and competitive electric propulsion devices for satellites and are currently in use in a number of telecommunications and government spacecraft. Their power spans from 100 W to 20 kW, with thrust between a few mN and 1 N and specific impulse values between 1000 and 3000 s. The basic idea of Hall thrusters consists in generating a large local electric field in a plasma by using a transverse magnetic field to reduce the electron conductivity. This electric field can extract positive ions from the plasma and accelerate them to high velocity without extracting grids, providing the thrust. These principles are simple in appearance but the physics of Hall thrusters is very intricate and non-linear because of the complex electron transport across the magnetic field and its coupling with the electric field and the neutral atom density. This paper describes the basic physics of Hall thrusters and gives a (non-exhaustive) summary of the research efforts that have been devoted to th...

Tutorial: Physics and modeling of Hall thrusters

DOI: 10.2514/1.52476 This paper concerns the application of the homotopic approach, which solves the fuel-optimal problem of lowthrust trajectory by starting from the related and easier energy-optimal problem. To this end, some effective techniques are presented to reduce the computational time and increase the probability of finding the globally optimalsolution.First,theoptimalcontrolproblemismadehomogeneoustotheLagrangemultipliersbymultiplying the performance index by a positive unknown factor. Hence, normalization is applicable to restrict the unknown multipliersonaunithypersphere.Second,theswitchingfunction’s first-andsecond-orderderivativeswithrespectto time are derived to detect switching. The switching detection is embedded in the fourth-order Runge–Kutta algorithm with fixed step size to ensure integration accuracy for bang-bang control. Third, combined with the techniques of normalization and switching detection, the particle swarm optimization with well-chosen parameters considerably increases the probability of finding the approximate initial values of the globally optimal solution. Moreover, intermediate gravity assist, which brings complex inner constraints, is considered. To determine the approximate gravity assist date, analytical formulas are presented to evaluate the minimal maneuver impulse based on the results of Lambert problems. The first-order necessary conditions for gravity assist constraints are derived analytically.Theoptimalsolutioncanberapidlyobtainedbyapplyingthetechniquespresentedtosolvetheshooting function. The unknowns are far less than with direct methods, and the computational effort is also far lower. Two examples of fuel-optimal rendezvous problems from the Earth directly to Venus and from the Earth to Jupiter via Mars gravity assist are given to substantiate the perfect efficiency of these techniques.

Practical Techniques for Low-Thrust Trajectory Optimization with Homotopic Approach

1. The problem of spacecraft trajectory optimization Bruce A. Conway 2. Primer vector theory and application John E. Prussing 3. Spacecraft trajectory optimization using direct transcription and nonlinear programming Stephen W. Paris and Bruce A. Conway 4. Elements of a software system for spacecraft trajectory optimization Cesar Ocampo 5. Low-thrust trajectory optimization using orbital averaging and control parameterization Craig A. Kluever 6. Analytic representation of optimal low-thrust transfer in circular orbit Jean A. Kechichian 7. Global optimization and space pruning for spacecraft trajectory design Dario Izzo 8. Incremental techniques for global space trajectory design Massimiliano Vasile and Matteo Ceriotti 9. Optimal low-thrust trajectories using stable manifolds Christopher Martin and Bruce A. Conway.

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Spacecraft Trajectory Optimization

There are a number of pressing problems mankind is facing today that could, at least in part, be resolved by space systems. These include capabilities for fast and far-reaching telecommunication, surveying of resources and climate, and sustaining global information networks, to name but a few. Not surprisingly, increasing efforts are now devoted to building a strong near-Earth satellite infrastructure, with plans to extend the sphere of active life to orbital space and, later, to the Moon and Mars if not further. The realization of these aspirations demands novel and more efficient means of propulsion. At present, it is not only the heavy launch systems that are fully reliant on thermodynamic principles for propulsion. Satellites and spacecraft still widely use gas-based thrusters or chemical engines as their primary means of propulsion. Nonetheless, similar to other transportation systems where the use of electrical platforms has expanded rapidly, space propulsion technologies are also experiencing a shift toward electric thrusters that do not feature the many limitations intrinsic to the thermodynamic systems. Most importantly, electric and plasma thrusters have a theoretical capacity to deliver virtually any impulse, the latter being ultimately limited by the speed of light. Rapid progress in the field driven by consolidated efforts from industry and academia has brought all-electric space systems closer to reality, yet there are still obstacles that need addressing before we can take full advantage of this promising family of propulsion technologies. In this paper, we briefly outline the most recent successes in the development of plasma-based space propulsion systems and present our view of future trends, opportunities, and challenges in this rapidly growing field.

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Perspectives, frontiers, and new horizons for plasma-based space electric propulsion

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Low-Thrust Minimum-Fuel Optimization in the Circular Restricted Three-Body Problem

An indirect optimization method is used to find optimal trajectories that use solar electric propulsion. Missions that exploit variable specific impulse are compared to constant-specific-impulse trajectories, and the benefit, in terms of payload, is highlighted. The presence of limits on the attainable values of the specific impulse and the use of dual-mode thrusters, which operate only at two discrete values of specific impulse, are also considered. The analytical formulation of the problem is presented, and the necessary conditions for an optimal solution are discussed. Numerical examples deal with planet rendezvous missions; a Mercury mission would largely benefit from the management of the available power, which exhibits a tenfold variation caused by the vehicle's varying distance from the sun. The optimization method can also deal with planetary gravity assists; Mercury missions, which exploit Venus flybys, are optimized and their characteristics discussed. Results show that the dual-mode thrusters provide almost the same propellant savings as the more complex variable-specific-impulse thrusters.

Optimization of Variable-Specific-Impulse Interplanetary Trajectories

The theory of optimal control is used to find the best trajectories for the capture maneuver of an interplanetary probe, which employs electric propulsion. The thrust magnitude and direction are optimized to exploit the spacecraft continuous steering capabilities and maximize the spacecraft final mass. Strategies, which involve propelled and coast arcs, are analyzed. The influence on the optimal trajectories of some parameters, such as the thrust, the specific impulse, and the initial velocity, is also discussed

Indirect optimization of low-thrust capture trajectories

A nested direct/indirect method is used to find the optimal design of hybrid rockets for suborbital missions. The direct optimization of the parameters which affect the engine design is coupled with the trajectory indirect optimization. Different propellant combinations are analyzed. First, the simplest blowdown feed system is considered. A more complex pressurization system with an additional gas tank, which allows a phase with constant propellant tank pressure, is then analyzed. The optimization procedure provides the engine design and the trajectory, which maximize the mission performance index.

Optimal Design and Control of Hybrid Rockets for Access to Space

A hybrid rocket is considered as the third stage of a three-stage launcher. The propulsion system design and the trajectory are simultaneously optimized by means of a nested direct/indirect procedure. Direct optimization of the parameters that affect the motor design is coupled with indirect trajectory optimization to maximize the launcher payload for assigned conditions at the stage ignition and final orbit. A mission profile based on the Vega launcher is considered. The feed system exploits a pressurizing gas, namely helium, with hydrogen peroxide as the oxidizer and polyethylene as the fuel. The simplest blowdown design is compared with a more complex pressurizing system, which has an additional gas tank that allows for a phase with constant oxidizer tank pressure. The optimization provides the optimal values of the main engine design parameters (pressurizing gas mass, nozzle expansion ratio, and initial values of tank pressure, mixture ratio and thrust), the corresponding grain and engine geometry, and the control law (thrust direction during the ascent trajectory and engine switching times). Results show that a hybrid rocket may be a viable option for small launchers.

Optimal Design of Hybrid Rocket Motors for Launchers Upper Stages

The parameters that affect the design of a hybrid rocket for small satellites are highlighted, and the benefit of the oxidizer flow rate control is analyzed. A single-port circular-section polyethylene grain is considered; the oxidizer is 85% hydrogen peroxide. The engine design is optimized to search for the minimum engine mass when the initial satellite mass and the required velocity increment are assigned. First, the simplest blowdown feed system is considered. The analysis shows that the optimal design depends on a lower limit for the regression rate and sometimes on a further constraint, which is related to the occurrence of thermal choking. The initial values of the mixture ratio, the thrust level and the initial port area to the throat area ratio seem to be the most important parameters for an optimal design. As far as the oxidizer flow rate control is concerned, several control strategies, namely, constant mixture ratio, repressurization, constant combustion chamber pressure, and constant propellant tank pressure, are compared to the simplest blowdown system. The constant mixture ratio control is the worst case, as the mass and volume are similar to the blowdown case, while a large thrust variation occurs. Repressurization reduces the thrust variation. Constant pressure controls (both combustion chamber and tank pressures) guarantee a quasi-constant thrust and reduce engine dimensions, with a limited mass penalty.

Lorenzo Casalino

Papers

Optimization of Variable-Specific-Impulse Interplanetary Trajectories

Indirect optimization of low-thrust capture trajectories

Optimal Design and Control of Hybrid Rockets for Access to Space

Optimal Design of Hybrid Rocket Motors for Launchers Upper Stages

Oxidizer Control and Optimal Design of Hybrid Rockets for Small Satellites