Coil shape of a two-fold symmetric perfect superconducting quadrupole for use in common-coil twin magnets

A four-fold symmetric superconducting quadrupole with a coil shape generated by two perpendicular intersecting ellipses, produces the perfect quadrupole field. We have shown that a two-fold symmetric coil generated by two perpendicular ellipses of dissimilar sizes also can produce ideal quadrupole field. Two non-intersecting elliptic current distributions (one inside the other) also can generate quadrupole field. Such coil geometries can find application in common-coil twin quadrupole magnets.