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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.

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.