Write-separation loss and phase functions in AC-bias recording

The wavelength dependences of loss and phase, as functions of write-head-to-medium separation, are calculated for an AC-biased recording model which assumes a longitudinal magnetization that increases linearly with depth. For a penetration distance ymand a write separationb, the read-voltage loss is(1 + kb) - (1 + kyₘ) e^{-k(yₘ-b)} /kyₘ, as compared with the usual thickness loss1 - e^{-k(yₘ-b)}. The phase function is found by calculating the mean longitudinal position at which recording occurs vs. depth, weighted by the exponential read-distance loss. The resulting integrals cannot be solved in closed form, but series approximations allow numerical evaluation. Calculated loss and phase curves are shown for various relative separations.