# Magnetic Field Calculation

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One of the more difficult problems in recording technology is the determination of the magnetic fields associated with heads, transducers and media. Among other things in this page you will find an interactive solver which is designed for quickly finding approximate solutions to typical problems.

## Lindholm's Equations

The image above is a 3D plot of the field near the gap of a thin film, pole trimmed, write head calculated by the C source module here. Plots of the field near the gap for a large class of head geometries can calculated with this module. By projecting the field into thin media of a given coercivity, a recording contour can be found. Hence, with the head gap, width, write current, and efficiency, along with the media coercivity and spacing, multiple contours can be calculated and, using 2D FFT for convolution, the ontrack and offtrack readback signal can be found. Note that the above image shows 'Hx', the field in the 'x' direction, although Lindholm's model also supports computing the fields in the 'y' and 'z' directions.

The calculations required to produce the above plot are executed so quickly that real-time animation is possible.

## Laplace/Poisson Solver

This application uses an advanced finite difference engine with 1D and 2D cubic interpolation algorithms. A screen shot appears below.

#### Simplified Model of Alternating, Displaced Media Transitions

Here's a solution for the surface magnetic field in the neighborhood of a group of idealized media transitions. The transitions are modeled as simple line charges in 2D space and the field is found using Laplace's equation. While this particular simplified transition model has limited practical value, more elaborate representations are easily constructed. The finite difference engine used solves the Laplace or Poisson equation and supports sources, sinks, permeable materials and various boundary conditions including, Dirichlet, Neumann and periodic. This type of solver allows the researcher to deal effectively with the wide class of head and media problems for which no analytic solution is available.

The solver operates on a problem descriptor file which can be generated by hand using a text editor or with an interactive program. It only takes 1 or 2 seconds to solve the above problem or any of the following ones on a typical Pentium. Some screen shots of miscellaneous field solutions can be viewed by clicking the thumbnails below.

Parallel Plates        Media Transition     Offtrack Transitions      Write Head          Offset Poles       Transitions

The above fields are potential fields, but the vector fields for field strength or flux density are also available. Contours can be applied at the click of a button. The fields in the neighborhood of a write head model and the simplified model with slightly offset poles, and media transitions are shown in the next thumbnails. The plots were obtained by taking the gradient along a line near the surface of the component.