A system for generating a magnetic field orientable in three dimensions configured to be integrated in a test vessel in which an ultra-high vacuum medium reigns, the system for generating a vector magnetic field being including superconducting coils, a cooling system making it possible to cool the superconducting coils to a superconducting temperature; a leaktight case, leaktight to the ultra-high vacuum and compatible with the ultra-high vacuum, the leaktight case enclosing the superconducting coils and being cooled by the cooling system; a heat shield compatible with the ultra-high vacuum surrounding the leaktight case.