INVARIANTS IN THE MOTION OF A CHARGED PARTICLE IN A SPATIALLY MODULATED MAGNETIC FIELD.
INVARIANTS IN THE MOTION OF A CHARGED PARTICLE IN A SPATIALLY MODULATED MAGNETIC FIELD.
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DOI：
10.1063/1.1664514
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发表时间：
1968-11
期刊：
影响因子：
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通讯作者：
D. A. Dunnett;E. W. Laing;J. Taylor
中科院分区：
文献类型：
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作者：
D. A. Dunnett;E. W. Laing;J. Taylor
在本文中，我们研究了磁场中的空间调制对磁矩μ=V⊥2/B等不变量的影响。特别地，我们研究了当调制的波长与粒子的陀螺半径相当时是否仍然存在不变量。在轴对称磁场中，采用方波调制，轨道方程简化为便于数值研究的代数关系。我们从这些研究中发现轨道有两种类型：(a)产生不变量的规则轨道；(b)准遍历轨道。我们还用微扰理论计算了一个不变量，以场的调制深度作为一个小参数。为此，我们发展了一种修正形式的微扰理论，克服了在微扰和回旋周期之间共振时产生无穷大的困难。这个困难实际上对应于不变曲线拓扑结构的变化。由该理论计算出的不变量显示出很好的结果。
In this paper we study the effect of a spatial modulation in the magnetic field on invariants such as the magnetic moment μ=V⊥2/B. In particular, we investigate whether an invariant still exists when the wavelength of the modulation is comparable to the gyro radius of the particle. In an axially symmetric magnetic field, with a square‐wave modulation, the orbit equations reduce to algebraic relations convenient for numerical study. We find from such studies that orbits are of two types: (a) regular orbits which generate an invariant; (b) orbits which are quasi‐ergodic. We have also calculated an invariant by perturbation theory with the depth of modulation of the field as a small parameter. For this we developed a modified form of perturbation theory which overcomes the difficulty of infinities arising at resonance between the perturbation and the cyclotron period. This difficulty in fact corresponds to a change in topology of the invariant curves. The invariant calculated from this theory shows very good...