Skin and proximity effects in the conductors of split gradient coils for a hybrid Linac-MRI scanner

In magnetic resonance imaging (MRI), rapidly changing gradient fields are applied to encode the magnetic resonance signal with spatial position; however eddy currents are induced in the surrounding conducting structures depending on the geometry of the conductor and the excitation waveform. These alternating fields change the spatial profile of the current density within the coil track with the applied frequencies of the input waveform and by their proximity to other conductors. In this paper, the impact of the conductor width and the excited frequency over the parameters that characterise the performance of split transverse and longitudinal gradient coils are studied. Thirty x-gradient coils were designed using a "free-surface" coil design method and the track width was varied from 1 mm to 30 mm with an increment value of 1 mm; a frequency sweep analysis in the range of 100 Hz to 10 kHz was performed using the multi-layer integral method (MIM) and parameters such as power loss produced by the coil and generated in the cryostat, inductance, coil efficiency (field strength/operating current), magnetic field profile produced by the coil and the eddy currents were studied. An experimental validation of the theoretical model was performed on an example coil. Coils with filamentary conductor segments were also studied to compare the simulated parameters with those produced by coils with a finite track. There was found to be a significant difference between the parameters calculated using filamentary coils and those obtained when the coil is simulated using finite size tracks. A wider track width produces coil with superior efficiency and low resistance; however, due to the skin effect, the power loss increases faster in wider tracks than in those generated in coils with narrow tracks. It was demonstrated that rapidly changing current paths must be avoided in order to mitigate the power loss and the spatial asymmetry in the current density profile. The decision of using narrow or wider tracks in split coils should be carefully investigated using a temperature analysis which includes skin and proximity effects.