Reinterpretation of Hoffmann's Ripple Theory

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Abstract
Hoffmann's linear theory of ripple in films has the advantage of an analytically simple Green's function; in the rigorous theory, only the Fourier transform is simple. Unfortunately, Hoffmann's treatment of the magnetostatic interaction rests on dubious approximations. It is proposed here that his formula be regarded merely as an empirical modification of the known Green's function for the case of no magnetostatic interactions, and his cy as a parameter to be adjusted for ``best fit,'' in some sense, to the rigorous formula; such an adjustment is possible if the fit criterion is an integrated quantity that can be evaluated from Fourier transforms by Parseval's theorem. Values of cv based on several such criteria agree fairly well with each other and with Hoffmann's value and give a fair fit as judged by the criterion. But the correct spatial variation of the first‐order correction for magnetostatic interaction, which can be expressed in terms of tabulated functions, shows little resemblance to Hoffmann's; in particular, at large distances it behaves like a dipole field instead of decaying exponentially.

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