On Projective Connection of Optically Conjugate Points of Static Mass Analyzers
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Dedicated to Prof. Lidiya Gall’ on her 85th birthday
On Projective Connection of Optically Conjugate Points of Static Mass Analyzers V. D. Sachenkoa, * a
Institute for Analytical Instrumentation, Russian Academy of Sciences, St. Petersburg, 198103 Russia *e-mail: [email protected] Received August 30, 2019; revised November 24, 2019
Abstract—The Barber rule, known in the theory of sector static mass analyzers and connecting geometrically the axial point of an object and its electron-optical image (Gaussian points) in the case of a uniform field of a magnetic sector with a normal incidence, is generalized to the case of arbitrary geometries and fields of magnetic and electrostatic sectors. It is proved that the Gaussian points of the optical axis of the mass analyzer are connected by a bipolar projection through two points – the poles of this projection, located on the straight lines passing through the optical foci of the mass analyzer parallel to the input and output arms of the optical axis. The distances of these poles from the foci adjacent to them are subject to the well-known optical invariant of Newton. Keywords: mass-analyzer, curvilinear optical axis, Gaussian points, optical poles, optical foci DOI: 10.1134/S1061934820140130
INTRODUCTION Eighty-five years ago, Barber [1] and, independently of him, Stephens [2], when studying the focusing properties of sector uniform magnetic fields in the median plane, found that, under conditions of orthogonal input into a magnetic field and output from it the ion beam, being emitted from one point, after passing the magnetic field being focused to a point in free space, the position of which is geometrically connected with the beam emission point (these points in light optics are called Gaussian points) by a straight line passing through the center of rotation of optical axis center (Fig. 1). This result is known in the theory of sector static mass analyzers as “Barber’s rule.” With the development of the general theory of ion focusing in magnetic fields, it became clear that Barber’s rule is violated for magnetic sectors with an inclined input or output of the ion beam [3]. In order to determine the location of the Gaussian pairs in such deflectors, Cartan [4, 5] has proposed a modification of Barber’s rule with the use of additional graphical constructions (Fig. 2). Similar methods for determining the positions of the Gaussian pairs in sector mass analyzers with a uniform field were used in the works of Tarantin and Wollnik [7, 8]. Judd [6] pointed out a possibility of using Barber’s rule in determining the
positions of the Gaussian pairs in sector static analyzers with a radially inhomogeneous field H(r) = H0(r0/r)ν. Judd’s method could be used in the case orthogonal modes of input and output of an ion beam, both for magnetic and electrostatic fields of the sector. We note that a similar method was shown earlier by Stephens [2] as applied to a cylindrical electrostatic capacitor. In Judd’s method, the actual geometry of the mass analyzer is compared with its
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