Solenoidal SMES (Superconducting Magnetic Energy Storage) usually suff
er form their remarkable stray field. A certain arrangement was devise
d that should reduce the extension of the far ranging stray field. Hen
ce, a second solenoid was placed outside the SMES device with a curren
t flowing in the opposite direction compared to the inner coil. Config
urations with both coils in a single plane were regarded only. As an i
mportant factor the minimum energy to be stored was given. In a first
step calculations methods have been found that reveal data for the min
imum geometrical dimensions of the SMES device in an analytical way. I
t was shown that the stray field, compared to a single coil arrangemen
t could be reduced remarkably. Evolution strategies and a conjugate gr
adient method were used to improve the quality of the above solution.