# Magnetic Recording Head Fields

Visualizing the magnetic fields associated with digital recording heads and media has been a matter
of continued interest since the very beginning of the earliest drives. The earliest attempts to approximate them were
limited to 2D plots along the centerline of a track.

Increasingly sophisticated graphics have improved the plots to any accuracy desired. In this page, we provide a few
examples of fields computed by a method disclosed by Dennis Lindholm and examples using a custom Laplace/Poisson solver.
The plots are best displayed in a rectangular coordinate system where the 'x' direction is along the track, the 'z'
direction is across the track and the 'y' direction is perpendicular to the media.

## Lindholm 3D Surface Plots

**Lindholm's Equations** use superposition to
create a head model which simplifies the geometry to that of a finite track width, but semi-infinite
poles. We will show example surface plots using the directional terminology chosen by Lindholm.
The axes are labelled by grid points in the 'x' and 'z' direction.

**Downtrack Head Field**

The plot represents a single recorded transition in the media and, like all plots on this page,
shows the gradient in the media as seen by the chosen head geometry.

### Perpendicular Head Field

This plot shows the field at right angles to the media.

### Crosstrack Head Field

Here is a plot of the field across the track.

## Laplace/Poisson 3D Surface Plots

Unlike the Linfholm limitation of semi-infinite poles, these plots allow control over the pole length.
Note the presence of *undershoots* on either side of the main pulse.

**Downtrack Head Field**

**Perpendicular Head Field**

**Crosstrack Head Field**