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Cited article:

Approximate Expressions for the Magnetic Potential and Fields of 2-D, Asymmetrical Magnetic Recording Heads

Mustafa M. Aziz, Ammar I. Edress and C. David Wright
IEEE Transactions on Magnetics 52 (2) 1 (2016)
https://doi.org/10.1109/TMAG.2015.2492947

Gap-null free spectral response of asymmetric ring heads for longitudinal and perpendicular recording

Chia Shen Wang and Huei Li Huang
IEEE Transactions on Magnetics 26 (5) 2403 (1990)
https://doi.org/10.1109/20.104745