Vector Potential and Stored Energy of a Quadrupole Magnet Array

The vector potential, magnetic field and stored energy of a quadrupole magnet array are derived. Each magnet within the array is a current sheet with a current density proportional to the azimuthal angle 2{theta} and the longitudinal periodicity (2m-1){pi}/L. Individual quadrupoles within the array are oriented in a way that maximizes the field gradient The array does not have to be of equal spacing and can be of a finite size, however when the array is equally spaced and is of infinite size the solution can be simplified. We note that whereas, in a single quadrupole magnet with a current density proportional to cos2{theta} the gradient is pure, such purity is not preserved in a quadrupole array