A Three-Dimensional Singular Model of a Magnetic Perpendicular Recording Head with Applications to Inter-Track Interference
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Two-dimensional models of the read head are not suitable for simulating the replay of the extremely high density data that is expected to be achieved in hard drives using perpendicular recording. By matching a singular function approximation to the Fourier solution at the air-bearing surface (ABS), a three-dimensional analytic model of a shielded giant magnetoresistive head, with side shields, for perpendicular replay is derived in this thesis. An explicit expression for the potential in the ABS is presented and parameters in that expression are accurately estimated for a range of practical head dimensions. Using only a few terms of this singular potential model, the vertical field is accurate to within 2% of the sensor potential in the region of the medium for the majority of head dimensions suitable for magnetic recording. The expected increase in areal density in hard drives using perpendicular technology will require very narrow t racks which normally suffer from large inter-track interference (ITI) or crosstalk. This interference can corrupt the read data and reduce t he signal strength. Here, the effects of ITI across three tracks in a three-head system are modelled by applying the three-dimensional singular function model of the head field. The magnetisation patterns which cause the worst ITI are identified so that these codes can be prohibited. A coding constraints scheme, in which ITI is exploited to read from tracks which have widths that are just 70% of the width of the head, is presented.
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