Transaxial mirror with combined static electric and magnetic fields

Combined transaxial mirrors are studied. In the areas of motion of charged particles, the fields of these mirrors are symmetric relative to the axis and mid-plane representing the plane of symmetry for the electric field and the plane of asymmetry for the magnetic one. An image equation is inferred and simple relationships between the linear and angular dispersions with respect to mass and energy are obtained. Aberration properties of the mirrors in the directions parallel to the mid-plane are considered. Expressions for the coefficients of the third-order geometric aberration corresponding to the beam divergence angle in the mid-plane are obtained. These expressions are especially simple when both object and image are located in the principal planes of the mirror. The aforementioned coefficients are expressed via parameters characterizing the mirror under the first-order approximation.