## 1 Introduction
In the context of the [PERSON]'s original idea [2] and assuming a two-dimensional heliocentric scenario, the in-flight control of the transverse direction of the thrust vector occurs by simply changing the electrical voltage applied to the panels, that is, by using a single (binary) scalar control term. This specific control technique was employed 2 years ago by the author [32] to investigate the performance of a Sun-facing electro-optically controlled diffractive sailcraft in a classical circle-to-circle orbit transfer. The results illustrated in [32], which also proposes an implicit and compact form of the optimal control law to design the heliocentric transfer trajectory, demonstrate the effectiveness of a solution that combines the concept of a diffractive sailcraft with that of electro-optically controlled panels. Furthermore, [PERSON]. [32] also discussed an analytical model of the thrust vector as a function of the binary control parameter, which is general and can be used to describe the heliocentric dynamics of the diffractive sailcraft in a wide range of mission applications. The latter analytical thrust model is used in this work to study the performance of a diffractive sailcraft with a Sun-facing attitude in a heliocentric mission scenario different from the one analyzed in [32]. More precisely, the aim of this paper is to investigate the performance of such an advanced propulsion system in a mission scenario involving the orbital repositioning of a diffractive sailcraft along an elliptical heliocentric orbit of assigned characteristics, that is, in a mission scenario that is consistent with a heliocentric phasing maneuver, as described in the textbook of [PERSON] [33]. Such a scenario is of scientific interest and has already been investigated in the literature, because it allows, for example, for moving spacecraft on the same heliocentric orbit of the Earth in a different angular position with respect to that of the planet, in such a way as to observe the Sun simultaneously from different observation points. This concept of phasing along the Earth's heliocentric orbit was used, for example, in NASA's STEREO mission [34] launched in 2006 to obtain a stereoscopic image of the Sun [35] through two space probes moving ahead of and behind our planet with a phase angle increasing with time, thanks also to a suitable succession of lunar gravity assist maneuvers. On the other hand, a phasing maneuver along the Earth's heliocentric orbit can be used in a preliminary mission design to approximate the transfer performance towards the Sun-Earth triangular Lagrange points [36] that are located approximately 60 deg ahead or behind the planet. For this reason, the author has already studied the performance of a spacecraft propelled by a propellantless propulsion system [37; 38] or a CubeSat equipped with a solar electric thruster [39] in a scenario that includes the azimuthal repositioning of a deep space probe along a circular orbit of radius equal to one astronomical unit. The latter, in fact, approximates the actual heliocentric orbit of the Earth and allows for simplifying the mathematical model for the study of the phasing maneuver. In this paper, instead, the performances of a Sun-facing diffractive sailcraft, equipped with electro-optically controlled panels, are studied, considering a generic heliocentric elliptical orbit, so that the mathematical model presented in Section 2 is general and can be applied to a closed (heliocentric) Keplerian orbit of assigned semimajor axis and eccentricity. In particular, following the usual approach in the preliminary design of missions involving propellantless thrusters [40], the method presented in the next section determines the transfer performance of the diffractive sailcraft in an optimization framework that allows for minimizing the total flight time [41].