By Peter W. Hawkes (Ed.)
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Extra info for Advances in Electronics and Electron Physics, Vol. 76
One can easily see from Eq. (34) that the field of a round lens is characterized by the function 4(z) only. In conventional quadrupoles, possessing both symmetry and antisymmetry planes, the potential expansion contains only the . In symmetric octupoles, the . ,. &,,+ 4 ( z ) Similar expansions of the scalar potential may also be written for the vicinity of the magnetic lens axis. In the case of superposition of deflecting fields, or of some kind of mechanical defects in the lenses, expansions (33) and (34) will have additional terms containing odd-power transverse coordinates.
In order to find x2 or y,, it is necessary to multiply each term of the upper matrix row by the column (:) or by (::> and then add the products; to find xi or y; one should perform a similar operation with the bottom row. The determinant of each matrix (65) is equal to the Wronskian W of the respective differential equation. From the initial values of the independent solutions (61) we find the initial Wronskian to be equal to unity (W, = 1). Then, it follows from Eq. (44)that W2 = W, = 1. This result can be used to verify the matrices and to determine the fourth matrix element if three others are known.
38); A,, . . ,A , are arbitrary constants that can be unambigously defined by the coordinates and slopes of the trajectory in an appropriate reference 38 L. A. BARANOVA A N D S. YA. 7. A trajectory given by the coordinates of its intersection with the object and aperture planes. plane. In Section 111, in finding the solutions of x u , xg and y,, y p , the reference plane was the object plane. It is also possible to use two reference planes, the coordinates or the slopes of which are specified.
Advances in Electronics and Electron Physics, Vol. 76 by Peter W. Hawkes (Ed.)