ANGLE, ENERGY, AND TIME-OF-FLIGHT FOCUSING WITH POLOIDAL TOROID ELECTROSTATIC ANALYZERS

A semiempirical approach for obtaining a "linearized" ion optical theory for the poloidal motion of charged particles in toroidal electrostatic analyzers is presented. Starting with the standard first order theory for equatorial motion, correction terms are introduced that modify the individual transfer matrix elements. These functions are evaluated by numerical computer ray tracing at the grid points of the two-dimensional scaling parameter space and as a function of deflection angle. Analytical expressions are then derived for the conditions of angle, energy, and time-of-flight focusing for a system consisting of two serially combined poloidal toroids. Solutions are obtained by iterative numerical methods with the added constraints of rotational symmetry. The resultant poloidal toroid geometry can be exploited for achieving angle imaging over a 360° field of view. © 1990.