hp finite elements for the simulation of coupled acoustic-magneto-mechanical systems with application to MRI coil design
Scott Bagwell  1, *@  , Ledger Paul  1@  , Antonio Gil  1@  
1 : Zienkiewicz Centre for Computational Engineering  (ZC2E)
College of Engineering, Swansea University Bay Campus, Crymlyn Burrows, Swansea SA1 8EN -  United Kingdom
* : Corresponding author

Recently Magnetic Resonance Imaging (MRI) has become an important tool in the medical industry. The non-intrusive imaging capability and high resolution makes it desirable for identifying a range of medical ailments, such as tumours, damaged cartilage and internal bleeding. The scanners utilise pulsed field gradients generated through resistive gradient coils to generate an image. Despite the application of active shielding, the gradient fields give rise to Lorentz forces in the conducting components of the magnet, which can cause them to deform and vibrate. The vibrations cause perturbations of the surrounding air, which in turn produces an acoustic pressure field. These phenomena can have undesired effects causing imaging artefacts (ghosting), decreased component life and can give rise to high noise levels, causing patient discomfort.

The aim of this work is to develop a computational analysis tool to aid in the magnet design by providing a better understanding of the induced vibrations and acoustic behaviour. These phenomena are described through the coupled set of Maxwell and linear elasticity equations. In the air the linear elasticity equations reduce to a scalar Helmholtz equation for the acoustic pressure, which is coupled to the magneto-mechanical problem through the air-conductor interface. The magneto-mechanical coupling arises in the conductor due to the Lorentz current terms and through body forces in terms of Maxwell stresses.

In this paper, we focus on the generation of a strongly coupled monolithic system to describe the interaction of the multiple physics. We linearise the resulting nonlinear equations and consider both temporal and frequency dependant axisymmetric formulations of the full three dimensional problem. We also utilise a stress tensor approach for the electromagnetic forces. This formulation allows the use of H1 conforming hp finite elements, which combined with hp refinement results in the possibility of accurate solutions. The fully discretised scheme is solved by a Newton-Raphson procedure. The results of our formulation are benchmarked against a series of numerical examples including an application to a realistic magnet geometry shown in Figure 1. 

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