Arbitrary emittance partitioning between any two dimensions for electron beams

The flat-beam transform (FBT) for round symmetric beams can be extended using the concept of eigenemittances. By tailoring the initial beam conditions at the cathode, including adding arbitrary correlations between any two dimensions, this extension can be used to provide greater freedom in controlling the beam's final emittances. In principle, this technique can be used to generate extraordinarily transversely bright electron beams. Examples are provided where an equivalent FBT is established between the horizontal and the longitudinal beam dimensions.