Numerical Analysis of Eddy Current Induced by z-Gradient Coil in a Superconducting MRI Magnet

In magnetic resonance imaging (MRI), pulsed magnetic gradient fields induce eddy currents in surrounding conducting components of the MRI scanner. These eddy currents distort MRI image and introduce thermal load in cryostat. Ohmic heating of superconducting magnet due to eddy currents changes the operating temperature of magnet, which can lead to system quench. Numerical simulation of these eddy current is important to compensate/control their adverse effects. In this paper, a coupled circuit network method is outlined to model eddy currents in a superconducting magnet that induced by z-gradient coil. According to the axial symmetry, the cylindrical cryostat vessels are divided into several concentric slices with a finite thickness. Each slice is modeled as a series circuit composed of a resistor and an inductor, and inductively coupled with other slices and gradient coil. To improve the calculation efficiency, the Eigen matrix technique is used to simplify the coupled differential matrix equation. The undesired eddy current effects including time-varying secondary magnetic field and power losses are analyzed. In addition, the eddy current behavior due to mechanical errors of gradient coil is discussed. Compared with the simulation results of ideal gradient coil design, the misalignment between primary and secondary layer of z-gradient coil can cause asymmetric secondary magnetic field along z-axis and further introduce $B_{0}$ -shift in imaging area.