Point-to-point focusing equation for double toroidal analyzer

Toroidal analyzer (TA) has high detection efficiency due to the parallel measurement of the energies and the angles of charged particles in wide range. Compared to a normal TA, double toroidal analyzer (DTA) has the advantages of flat focal plane and normal incidence angles of particles onto the detector surface. However, no analytical formula is available to describe the point-to-point focusing in its radial plane. In the present work, a simple equation for the point-to-point focusing is obtained. The calculated deflection angles using this equation are in good agreement with the trajectory simulations. This indicates the equation could be quite useful for the future analytical design of DTA.