[en] During the most recent funding period the authors obtained results important for helical confinement systems and in the use of modern computational methods for modeling of fusion systems. The most recent results include showing that the set of magnetic field functions that are omnigenous (i.e., the bounce-average drift lies within the flux surface) and, therefore, have good transport properties, is much larger than the set of quasihelical systems. This is important as quasihelical systems exist only for large aspect ratio. The authors have also carried out extensive earlier work on developing integrable three-dimensional magnetic fields, on trajectories in three-dimensional configurations, and on the existence of three-dimensional MHD equilibria close to vacuum integrable fields. At the same time they have been investigating the use of object oriented methods for scientific computing