Computing Lorentz forces generated by gradient coils in an open MRI system

Magnetic Resonance Imaging requires the use of gradient coils to perturb the main homogeneous static magnetic field. Sequential perturbations in each of the orthogonal cartesian directions results in the magnetic field becoming spatially encoded. The fast switching of the gradient coils produces large Lorentz forces which act on the coils. These unwanted forces dissipate as acoustic noise at sound pressure levels upward of 130dB. We present a method for designing open magnetic resonance imaging coils that produce reduced Lorentz forces whilst still producing highly accurate gradient fields. We show that when gradient fields of approximately 1% are considered, a linearised regularisation solves for the Fourier series coefficients.