Curvature of electric field around center of a quadrupole

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Main Question or Discussion Point

Hello all. I am working on a research project involving the Stark effect and its application in molecular guides and came across a bit of math in a paper that I don't understand. In this paper http://arxiv.org/abs/physics/0310046 there is an equation in the introduction concerning the electric field around the center of a quadrupole (4 rods with applied voltages). It says "... the field can be expanded harmonically, E = E 0 + H(t) β(x^2 − y ^2 )..."
where E0 is the electric field at the center, H(t) is either 1 or -1 depending on the time, and β is half the curvature of the field.

That last part is what I've been having issues with. What exactly is the "curvature" of the field? Is this just a term that comes from the expansion of the field using spherical harmonics? Any help or directions would be great.
 

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