# Optimal Interplanetary Transfer of Solar Wind Ion Focusing Thruster-Based Spacecraft
## 1 Introduction  
Propellantless systems are the frontier of current and near-term technology for space propulsion and are likely to become the only viable way to realize new advanced mission concepts, such as reaching high-energy orbits of comets [1, 2] or Solar System small bodies [3, 4, 5], rectilinear trajectories [6, 7], displaced orbits [8, 9, 10, 11], or the creation and maintenance of artificial Lagrangian points [12, 13, 14] and hovering conditions over asteroids [15]. Solar sails and electric solar wind sails (E-sails) are currently the most promising types of propellantless systems. They are both able to gain energy from the Sun, although with different physical mechanisms. On one side, solar sails are propelled by the momentum transfer of solar photons impinging on a large, lightweight, and reflecting membrane [16, 17, 18, 19, 20]. Examples, instead, produce a propulsive thrust by extracting momentum from the solar wind ions, which are shielded by an electric field generated around a large grid of conducting tethers [21, 22]. Despite their different working principles, the common feature of solar sails and E-sails is that both require large surfaces to produce thrust and that those surfaces must be suitably oriented with respect to the Sun-spacecraft (that is, radial) direction to generate a thrust component capable of modifying the spacecraft orbital momentum [16, 23, 24]. Their other common feature is that the maximum thrust magnitude, for a given distance from the Sun, is obtained when the reference plane (either the reflecting membrane or the nominal plane containing the conducting tethers) is placed normal to the radial direction [25]. The need to reorient the reference plane for guidance and navigation purposes gives rise to a double issue. In the first place, the rotations of the plane may represent a complex task to carry out, especially when large reorientation angles are involved. However, evenmore important is the propulsive effect caused by the rotation, since, as the reference plane strays from a Sun-facing orientation, the solar wind ions and photons \"see\" a smaller surface to hit, with a consequent reduction of thrust magnitude. Alternative configurations have been proposed to mitigate these drawbacks. For example, in the case of photonic propulsion systems, the functions of collecting and directing the solar radiation may be separated by means of an arrangement that is called Solar Photon Thrustor (SPT), according to its original definition by [PERSON] [26]. In that system, the solar rays impinging on a collector (a large curved reflecting surface) are first directed on a small flat mirror, the reflector, which redirects them on a second steerable mirror, the director, used to suitably orient the force acting on the SPT. Since the collector is always oriented orthogonal to the Sun-pointing direction, it always produces the maximum allowable thrust magnitude for a given collector reflecting surface. Due to its special arrangement, a typical SPT configuration is, in principle, superior to a conventional solar sail, as it may be concluded from simulations of Earth escape trajectories [27] or interplanetary trajectories [28; 29]. Updated results, made on realistic SPT configurations, have however called into question the actual effectiveness of this advanced propulsion concept [30]. Returning to systems that extract momentum from the solar wind ions, the Solar Wind Ion Focusing Thruster (SWIFT) is a new propellantless device, which may be thought of as an evolution of the E-soil concept [31; 32; 33]. It essentially consists of a grid of conducting tethers, electrostatically charged at a positive electric potential, arranged in a conically-shaped mesh with a circular base that has a radius of some kilometers and is supported by a few auxiliary booms with stiffening purposes. The solar wind ions are filtered by the charged SWIFT cone and the collected positive ions are accelerated by an ion thruster and then ejected in a beam that can be suitably oriented to provide the desired thrust component.