Limits of validity of the one-dimensional wall theory for bubble materials

It is shown that the one-dimensional studies of the wall surrounding a bubble domain do not violate some necessary self-consistency requirements. Moreover, it is shown that the ratio of the magnetostatic self energy (which is neglected in these studies) to the total one-dimensional wall energy is
T/Q
, where
T
is of the order of 1 for typical film thickness of a typical bubble material. This justifies the use of the one-dimensional wall for these materials, as long as the quality factor
Q = K/(2\piM\min{s}\max{2})
is large.