Abstract
The vacuum field flux tube ellipticity dependence on radius for quadrupolar mirror machines has been investigated. A third order expression in the paraxial approximation has been derived for the vacuum field ellipticity. The dependence of ellipticity on midplane radius has been examined in the SFLM Hybrid and the outermost plasma flux tube is 3.5 cm wider than predicted by the first order paraxial approximation, which is within boundaries set by the first wall. The third order approximation has a high accuracy for the ellipticity for long-thin mirrors such as the SFLM Hybrid, and even the first order approximation that is independent of radius is sufficient in many applications. The ellipticity dependence on midplane radius for mirrors with more strongly localized quadrupolar fields than the SFLM Hybrid is also shown to be minor.
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