Advances in Electronics and Electron Physics, Vol. 76 by Peter W. Hawkes (Ed.)

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Extra resources for Advances in Electronics and Electron Physics, Vol. 76

Example text

Minimization involves all the meshes attached to a given lattice node; as a result, one gets a set of algebraic equations solvable with a computer. The conclusion that follows from the comparison of analytical and numerical methods is that the latter possesses the advantage of being applicable to problems with any boundary conditions. As a rule, they provide the necessary calculation accuracy if the procedure lasts a sufficiently long time. The principal disadvantage of numerical techniques is that the solution must be repeated for each new combination of problem conditions.

YA. YAVOR In the cylindrical coordinate system, the potential expansion q(r, $, z ) may be written as follows: + [ 4 4 ( z )- . ] r4 cos 41,b + . . 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.

ABERRATIONS OF ELECTROSTATIC LENSES If the beams of charged particles do not satisfy the paraxial condition, that is, if particles travel too far from the optic axis and form large angles with it, the image they form is distorted due to geometrical aberrations. The aberrations may be reduced by introducing apertures, but this decreases the beam intensity and is not always acceptable. Moreover, small apertures give rise to additional image defects due to electron diffraction. The theory of geometrical aberrations allows us to find the distortions and to determine the dimensions of the apertures at which these distortions are within acceptable limits.

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