Design considerations for a cycloidal mass analyzer using a focal plane array detector

With the advent of technologies such as ion array detectors and high energy permanent magnet materials, there is renewed interest in the unique focusing properties of the cycloidal mass analyzer and its ability to enable small, high-resolution, and high-sensitivity instruments. However, most literature dealing with the design of cycloidal mass analyzers assumes a single channel detector because at the time of those publications, compatible multichannel detectors were not available. This manuscript introduces and discusses considerations and a procedure for designing cycloidal mass analyzers coupled with focal plane ion array detectors. To arrive at a set of relevant design considerations, we first review the unique focusing properties of the cycloidal mass analyzer and then present calculations detailing how the dimensions and position of the focal plane array detector relative to the ion source determine the possible mass ranges and resolutions of a cycloidal mass analyzer. We present derivations and calculations used to determine the volume of homogeneous electric and magnetic fields needed to contain the ion trajectories and explore the relationship between electric and magnetic field homogeneity on resolving power using finite element analysis (FEA) simulations. A set of equations relating the electric field homogeneity to the geometry of the electric sector electrodes was developed by fitting homogeneity values from 78 different FEA models. Finally, a sequence of steps is suggested for designing a cycloidal mass analyzer employing an array detector.