A quadrupole or quadrapole is one of a sequence of configurations of—for example—electric charge or current, or gravitational mass that can exist in ideal form, but it is usually just part of a multipole expansion

Multipole expansion

A multipole expansion is a mathematical series representing a function that depends on angles — usually the two angles on a sphere. These series are useful because they can often be truncated, meaning that only the first few terms need to be retained for a good approximation to the original...

 of a more complex structure reflecting various orders of complexity.
The zero-trace quadrupole moment tensor of a system of charges (or masses, for example) is defined as
for a discrete system with individual charges , or
for a continuous system with charge density .