最小最大电流密度线圈设计
Minimax Current Density Coil Design
摘要：
“线圈设计”是一个逆问题，其中导线的布置被设计成当用电流激励时产生规定的磁场。用于磁共振成像（MRI）的梯度和匀场线圈的设计是线圈设计的重要示例。通常要求这些线圈产生的磁场既强又准确。在设计过程中可以考虑线圈的其他电磁特性，例如电感，这成为优化问题。在这项工作中，最大电流密度是另外优化和所得线圈的性能和实用性进行了研究。发现具有最小最大电流密度的线圈表现出最大程度的扩展导线，并且可能有助于分散焦耳加热的局部区域。对于任何给定的表面和导线尺寸，它们还产生每单位电流可能的最高磁场强度。三种不同风格的边界元法，采用不同的基函数（三角形元素均匀电流，正弦电流的圆柱形元素和正弦均匀电流的圆锥截面元素）与这种方法来说明它的通用性。
英文摘要：
'Coil design' is an inverse problem in which arrangements of wire are designed to generate a prescribed magnetic field when energized with electric current. The design of gradient and shim coils for magnetic resonance imaging (MRI) are important examples of coil design. The magnetic fields that these coils generate are usually required to be both strong and accurate. Other electromagnetic properties of the coils, such as inductance, may be considered in the design process, which becomes an optimization problem. The maximum current density is additionally optimized in this work and the resultant coils are investigated for performance and practicality. Coils with minimax current density were found to exhibit maximally spread wires and may help disperse localized regions of Joule heating. They also produce the highest possible magnetic field strength per unit current for any given surface and wire size. Three different flavours of boundary element method that employ different basis functions (triangular elements with uniform current, cylindrical elements with sinusoidal current and conic section elements with sinusoidal-uniform current) were used with this approach to illustrate its generality.
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