Finite size bi-planar gradient coil for MRI

Finite size high performance magnetic field gradient coils have always been desirable for today´s ever demanding magnetic resonance imaging (MRI) applications, We present a Lagrange multiplier technique for designing a minimum inductance gradient coil under a finite size planar geometry constraint. Based on this minimization approach, we construct a functional F in terms of the stored magnetic energy and a set of field constraint points which are chosen over the desired imaging volume. Minimizing F, we obtain the continuous current density distribution for the finite size planar gradient coil. Applying the stream function technique to the resulting continuous current distribution, the discrete current pattern can be generated, Employing the Biot-Savart law for the discrete current loops, the gradient magnetic field has been re-evaluated In order to validate the theory, Using this approach, we have been able to design a finite size (1.0 m×1.0 m) bi-planar y-gradient coil which is capable of generating a gradient field of 40 mT/m with an inductance of 71 μH over a 30 cm diameter spherical volume @ 334 A