  This paper presents a novel approach for the preliminary design of
Low-Thrust, many-revolution transfers. The main feature of the novel approach
is a considerable reduction in the control parameters and a consequent gain in
computational speed. Each spiral is built by using a predefined pattern for
thrust direction and switching structure. The pattern is then optimised to
minimise propellant consumption and transfer time. The variation of the orbital
elements due to the thrust is computed analytically from a first-order solution
of the perturbed Keplerian motion. The proposed approach allows for a realistic
estimation of {\Delta}V and time of flight required to transfer a spacecraft
between two arbitrary orbits. Eccentricity and plane changes are both accounted
for. The novel approach is applied here to the design of missions for the
removal of space debris by means of an Ion Beam Shepherd Spacecraft. In
particular, two slightly different variants of the proposed low-thrust control
model are used for the different phases of the mission. Thanks to their low
computational cost they can be included in a multiobjective optimisation
problem in which the sequence and timing of the removal of five pieces of
debris are optimised to minimise propellant consumption and mission duration.
