Slugs: Which is more important - Diameter or Mass?

[Mike Sulzer]

You are correct, and a little more googling explained where I went wrong.
I forgot about Lenz's law and the eddy currents. The relative motion between the string and the magnetic pole generates eddy currents in the string that have magnetic fluxes that oppose the movement of the string. So, it has nothing to do with the shape of the magnetic poles, but only the field strength seen by the string.

http://www.coolmagnetman.com/magplum.htm

Eddy currents in the string might be a factor, I do not know. The diameter of the string is small and the currents have to circulate, and so there is not a very big loop for them to circulate around.

Consider the motion of the string along the pole piece axis (up and down with the pickup poles pointing up). The field changes significantly in this direction, and so the force on the string changes with position. The field changes less in the direction perpendicular to the axis of the pole piece. Thus the vibrations in the two directions are affected differently. Complicated vibration results if the field is strong, and I think this increases the losses (damping) in the vibration.

[Joe Gwinn]

Eddy currents in the string might be a factor, I do not know. The diameter of the string is small and the currents have to circulate, and so there is not a very big loop for them to circulate around.

The eddy current effect in a long thin cylindrical body varies as the square of diameter, and strings are far thinner than slug poles. Wire is even thinner.

[Mike Sulzer]

The eddy current effect in a long thin cylindrical body varies as the square of diameter, and strings are far thinner than slug poles. Wire is even thinner.

That's true, but if we want to compare the the effect of eddy currents in the string to that of in the slug poles, we also need to consider the relative strengths of the B fields in the two cases. For the string, the relevant field is some fraction of the field from the magnetized slug. For the slug, it is the much smaller field induced by the string motion. I suspect both are negligible for damping the string, but some analysis (computation or modeling) would be necessary.