Theory of Unsymmetric Magnetic-Deflection Coils

We have developed a formalism for calculating the deflection errors due to a slightly unsymmetric magnetic deflection coil. Explicit expressions for the errors have been derived using an aberration theory type approach, but including the even-order contributions and retaining terms up to fourth order. The solutions are analyzed to get a physical idea about the nature of the errors involved. The same formalism can also be applied to larger deflection angles provided one knows the solutions for the corresponding symmetric coil.