Electrostatic and magnetostatic electron spectrographs based on euler’ homogeneous potentials with non-integer orders

Electron energy analyzers which are capable of simultaneous spectral acquisition over a wide energy range are of great interest and of great importance. From optical point of view the systems with good spectrographic properties are strongly different from the systems with good spectrometric properties. The task to create such a system results to quite different optical problems and quite different methods of its solution. A useful instrument here is the usage of the fields which are homogeneous in Euler’ terminology, i.e., electrostatic fields which satisfy the condition E( lx, ly, lz ) = l n E( x, y, z ) and magnetostatic fields which satisfy the contition B( lx, ly, lz ) = = l n B( x, y, z ) for some fixed order n and an arbitrary value l. While the fields with the integer orders n are well investigated the possibilities of the fields with non-integer orders are not considered to necessary extend yet. The paper outlines briefly the spectrographic properties of two-dimensional electrostatic and magnetostatic fields which are homogeneous in Euler’s terminology and have non-integer orders of homogeneity and demonstrates that the usage of non-integer orders enlarges greatly the flexibility of the designing of spectrographic energy analyzing systems.