用于抑制导向中心运动中跃迁的等强磁场
Isodrastic Magnetic fields for suppressing transitions in guiding-centre motion
AI总结：
本文提出等强磁场概念以抑制导向中心运动类别间跃迁，建立基于纵向绝热不变量的弱表述和基于 Melnikov 函数的精确强表述，并构造非全向弱等强磁镜场证明其更具一般性。
摘要：
在磁场中，导向中心运动类别之间的跃迁可能导致跨场扩散和逃逸。如果导向中心在运动类别之间不发生跃迁，我们就称该磁场是等强的。因此，这是增强约束的一个重要理想。首先，我们基于纵向绝热不变量提出一种弱表述，对全向性进行推广。为了证明等强性严格比全向性更一般，我们构造了非全向的弱等强磁镜场。随后，我们提出一种对导向中心运动精确成立的强表述。我们通过 Melnikov 函数发展了强版本的一阶处理方法，并表明它可以恢复弱版本。该理论给出了对偏离等强性程度的量化，可作为优化设计中的目标函数。本文还通过若干简单示例对该理论进行了说明。
英文摘要：
In a magnetic field, transitions between classes of guiding-centre motion can lead to cross-field diffusion and escape. We say a magnetic field is isodrastic if guiding centres make no transitions between classes of motion. Therefore, this is an important ideal for enhancing confinement. First, we present a weak formulation, based on the longitudinal adiabatic invariant, generalising omnigenity. To demonstrate that isodrasticity is strictly more general than omnigenity, we construct weakly isodrastic mirror fields that are not omnigenous. Then we present a strong formulation that is exact for guiding-centre motion. We develop a first-order treatment of the strong version via a Melnikov function and show that it recovers the weak version. The theory provides quantification of deviations from isodrasticity that can be used as objective functions in optimal design. The theory is illustrated on some simple examples.
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