  This paper presents the design of a mission to Europa using solar electric
propulsion as main source of thrust. A direct transcription method based on
Finite Elements in Time was used for the design and optimisation of the entire
low-thrust gravity assist transfer from the Earth to Europa. Prior to that, a
global search algorithm was used to generate a set of suitable first guess
solutions for the transfer to Jupiter, and for the capture in the Jovian
system. In particular, a fast deterministic search algorithm was developed to
find the most promising set of swing-bys to reach Jupiter A second fast search
algorithm was developed to find the best sequence of swing-bys of the Jovian
moons. After introducing the global search algorithms and the direct
transcription through Finite Elements in Time, the paper presents a number of
first guess Solutions and a fully optimised transfer from the Earth to Europa.
