Butterworth Edward J, Gore John C
Vanderbilt University Institute of Imaging Sciences, CCC 1121 MCN, Nashville, TN 37232-2675, USA.
J Magn Reson. 2005 Jul;175(1):114-23. doi: 10.1016/j.jmr.2005.03.021.
We present an analytic solution for the B1 field produced in a gapped toroidal cavity resonator designed as a probe for high field MRI. This resonator supports standing TEM waves, so its electric and magnetic fields are identical to those produced by a stationary planar current source with the same (constant) cross-section multiplied by a complex exponential propagation factor. An explicit expression for the field may therefore be found by solving Laplace's equation for the static potential, which is accomplished with a two-dimensional logarithmic conformal transformation algorithm. The equipotential curves are also the contours of the field strength B, and the B (vector) field at any point is directed along the contour passing through that point. With this information, we construct the solution by computing the angle made by the equipotential curve with the horizontal axis at each point, using this angle to analyze the B field into its x and y components, and adding the contributions from the current sources to obtain the magnitude and direction of B at each point in the region of interest. Some proposed extensions of this algorithm are also discussed.
我们给出了一种解析解，用于计算在设计为高场磁共振成像（MRI）探头的带隙环形腔谐振器中产生的B1场。该谐振器支持驻波TEM波，因此其电场和磁场与由具有相同（恒定）横截面的静止平面电流源产生的电场和磁场相同，并乘以一个复指数传播因子。因此，可以通过求解静电势的拉普拉斯方程来找到场的显式表达式，这通过二维对数共形变换算法来实现。等势曲线也是场强B的等值线，并且任意点处的B（矢量）场沿着穿过该点的等值线方向。利用这些信息，我们通过计算等势曲线在每个点与水平轴所成的角度来构建解，使用该角度将B场分解为其x和y分量，并加上电流源的贡献以获得感兴趣区域中每个点处B的大小和方向。还讨论了该算法的一些提议扩展。
