Aberrations of the cylindrical mirror time‐of‐flight mass spectrometers with oblique incidence

Abstract

Aberrations of the cylindrical mirror time-of-flight mass spectrometers with oblique incidence † Classical reflectron time-of-flight mass spectrometers create ion packets and focus them in time by plane grid electrodes. 1 There are no focusing forces to act on ions directing them back to the packet axis. A substantial sensitivity increase can be expected by focusing the ion packets laterally. An ion source from three cylindrical electrodes can be combined with a cylindrical reflectron, with all the electrode surfaces having a common symmetry axis. 2 The idealized calculations assume the ion source and detector as being coincident (or at least collinear) for this geometry as well as for plane electrode reflectrons. Except linear reflectrons, 3 the real-world reflectron time-of-flight mass spectrometers are so assembled that ion paths before the mirror do not interfere with those after reflection. This is achieved by the oblique incidence of ion packet with respect to the mirror entry limit. The effect of the oblique incidence has often been neglected, as the angle of incidence is usually less than a few degrees. For a quadratic field ion mirror, the oblique incidence, in a specific case, induced flight time changes of the order of ppm. 4 Oblique-incidence effect for homogeneous, electric reflectron time-of-flight mass spectrometers can be determined with the formulas derived by Ioanoviciu et al. 5 We determined the time of flight through the cylindrical mirror of an obliquely incident ion (Fig. 1). We used the Euler-Lagrange equations in cylindrical coordinates r, ϕ, and z to derive t mirror :The following symbols were used: r 0 is the radius of the cylindrical earthed electrode, v ref is the velocity of the reference ion, D ln r max /r 0 where r max is the r-coordinate of the farthest point on the reference ion trajectory,  is the incidence angle. For the double, longitudinal (time) and lateral focusing case, r max /r 0 D 1.339.The ion entering the mirror at ϕ i leaves it at ϕ f :We accounted also for the changes of the ion coordinate on entry into and exit from the mirror due to the angular spread of the packet as well as to the effect of the field-free spaces. 6 Finally, the ion packet is lengthened because of the oblique incidence, initial width and angular spread by t packet :Here x i and˛i are the ion distance to and angle with the packet axis, at the ion source longitudinal focus, while  0 is the packet-axis incidence angle. As the ion packets have the coordinates distributed between x i and Cx i and between angles ˛i and C˛i, the real resolution R cyl expressed by R normal , the ideal resolution, is: classical, homogeneous electric field, two-stage reflectrons, R class , for selected normal-incidence resolution values, R normal .As a comparison, the Á angle of Fig From the above results, we conclude that the double-focusing, cylindrical reflectron time-of-flight mass spectrometers are more sensitive to the incidence angle than the homogeneous electric field reflectrons. This fact is easy to explain as ...