Magnet coils designed to optimise fields

Complex mathematics, which were developed to improve the accuracy of magnetic resonance imaging scanners, could lead to a new way of designing electrical machines. Researchers at Nottingham University have used a novel boundary element method to predict the magnetic field that is produced by a particular spacing of electromagnet coils. While the development was aimed at producing coils that conform more closely to the human body shape – and producing better scanner images – it could be applied to the development of any electrical machine. This work on MRI scanners was carried out at the University of Nottingham, where “Sir Peter Mansfield pretty well invented them”, according to research team member Arthur Jones. Mansfield shared a Nobel Prize for their development in 2003. Dr Jones presented a paper on the research – co-authored with Liviu Marin – at a recent Institute of Physics conference. The conventional way of designing electromagnets is to produce a coil, see what field is produced and then adjust the coil design. The seven-strong Nottingham team, which includes engineers, physicists and a mathematician, has inverted the process. The team’s novel version of the boundary element method is applied to the problem of specifying the desired field gradient and the surface that the conductors are to be placed on – and uses it to work out exactly where the conductors need to be to achieve the necessary current densities and field configuration. “it can calculate the current densities needed to provide a uniform gradient of magnetic field in a specified direction – within the constraints of what is physically possible,” he said. The mathematics are extremely complex, and produce a system of linear algebraic equations that cannot be solved by direct methods. Instead, it approximates an answer using a function called the Tikhonov regularisation, with help from Matlab from Mathworks. Using these methods, it is possible to come up with coil configurations that achieve their goal -- when placed on the surface of a cylinder, or even a hemisphere. Conductors are placed in a particular way, with variable spacings between them, and in irregular patterns – made possible using modern CNC machinery. Since most electrical machines depend on coils of wire producing magnetic fields, the method constitutes a major breakthrough in electrical design. As well as optimising electromagnetic coils to achieve best torque and efficiencies, it would mean that motor casings need not be cylindrical and symmetrical. In future, it would be possible to design an electric motor that fits into any space – allowing huge design freedom. Email Dr Liviu Marin Pointers * Conductor paths can be generated on a surface to produce a specified magnetic field configuration * The method has been developed to improve the design and function of gradient coils in MRI scanners * It has so far been applied to conductors on cylindrical and hemispherical surfaces