The recording physics of bit-patterned media is studied for areal densities of around 2 Tbits/inch2 . A model of the writing process, based on the head field gradient and switching field distribution, including various interference fields, is presented to extract the write-head and media parameters which are necessary to attain a wider write margin. Write head field distributions, calculated by the finite-element method, are presented for various head pole structures with side- and trailing-shields to improve head field gradient. Optimization of the pole configuration increased the gradient to over 500 Oe/nm for a head-to-soft magnetic under layer (SUL) spacing of 14 nm. Using the head field distribution, a recording performance analysis by micromagnetic simulation indicated that the write margin was improved. Position and size dispersions of the dots deteriorated the signal-to-noise ratio (SNR) and increased adjacent track erasure (ATE).