The limitations on the levitation height obtainable using permanent magnets are studied. We find that with mechanical transverse stabilization and optimal distribution of magnetization of the (infinite) base a maximum height of 12l/sub 0/ is achievable for ideal magnets. Here, l/sub 0/=M/sub 0//sup 2///spl rho/g where g is the free fall acceleration, /spl rho/ the mass density of the levitated magnet and M/sub 0/ is the magnetization of the supporting base plate and levitated magnet. For uniform magnetization this height is only 3.5l/sub 0/. With levitation based on spin transverse stabilization mechanism an additional constraint enters into the problem and we find that the maximum achievable height is only 4.7l/sub 0/. The value of l/sub 0/ for the best magnet known to us is about 1.5 meters. Note, however, that because real permanent magnets are not ideal the above results are only upper bounds on the levitation height by permanent magnets.
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机译：研究了使用永磁体可获得的悬浮高度的限制。我们发现，通过机械横向稳定和（无限）基极的最佳磁化分布，理想磁体的最大高度可以达到12l / sub 0 /。在这里，l / sub 0 / = M / sub 0 // sup 2 /// spl rho / g其中，g是自由落体加速度，/ spl rho /悬浮磁铁的质量密度，M / sub 0 /是支撑基板和悬浮磁铁的磁化。为了均匀磁化，该高度仅为3.5l / sub 0 /。在基于自旋横向稳定机制的悬浮作用下，一个额外的约束进入了这个问题，我们发现最大可达到的高度仅为4.7l / sub 0 /。对于我们所知的最佳磁体，l / sub 0 /的值约为1.5米。但是请注意，由于实际的永磁体不是理想的，因此上述结果只是永磁体在悬浮高度上的上限。
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