Characterization of curved cathode guns by the generalized trajectory method: upgrade of G-optk programme for applications to non-planar objects.

A mathematical scheme has been proposed to extend the applicability of the generalized trajectory method to deal with curved cathodes such as cold field emitters and thermionic point cathodes. A connecting space is introduced between the cathode surface and the first reference plane, and the actual ray condition on the cathode is transformed into the trajectory condition at the reference plane: the generalized trajectory calculation is commenced from the reference plane. The electron acceleration due to the cathode surface field, which results in the increase of the transverse momentum p(x) at the reference plane, has been found to significantly influence the estimate of the spherical aberration coefficient. The new mathematical formulation has been incorporated into the upgraded G-optk programme and enabled it to carry out precise characterization of curved cathode guns.