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We have developed a finite-element micromagnetics model to investigate the dynamics of write heads for perpendicular recording at high density and high data-rates. The model includes the entire head geometry, with the large return pole and the soft underlayer. The response of the head to the coil current is determined by the current waveform shape and duration, Gilbert damping constant, and presence of soft underlayer and shields. Large damping leads to a large phase shift between the coil current and the head field while small damping causes strong gyromagnetic precession. We find that an intermediate value of the damping constant gives the fastest head field rise time. The intrinsic reversal time decreases from 540 to 250 ps by reducing coil-turns from two to one and shortening the yoke length. Thus, an intermediate value of the damping constant, short yoke length, and fast current rise time are needed for maximum data rate.