Application of the Matrix Method to a Browne-Buechner Spectrograph

Abstract

The motion of a group of ions (with respect to the trajectory of one of the ions) in a magnetic field of the form B∼rⁿ may be described by linear second‐order differential equations when the displacement, slope, and momentum spread of the ions are small. The general solution may then be written as a matrix operating on the initial conditions. A procedure is described herein for interpreting the paraxial properties of a spectrometer system in terms of the matrix elements. Then it is shown that a similar treatment is applicable when the momentum spread is not small, as in the case of the Brown‐Buechner spectrometer. The matrices for the Browne‐Buechner spectrometer are derived and interpreted for a more general case than has heretofore been considered.