The Paths of Ions in the Cyclotron I. Orbits in the Magnetic Field
The Paths of Ions in the Cyclotron I. Orbits in the Magnetic Field
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回旋加速器中离子的路径 I. 磁场中的轨道
DOI：
10.1103/physrev.54.580
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发表时间：
1938
期刊：
影响因子：
--
通讯作者：
L. H. Thomas
中科院分区：
文献类型：
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作者：
L. H. Thomas
Bethe和Rose在最近的一封信和一篇论文中坚持认为，当考虑到质量与速度的相对论增加时，来自回旋加速器的光束的最大能量是由共振和聚焦条件的不相容所固定的。如下所示，虽然这一结果对于径向对称的磁场是成立的，但在一般情况下不一定是正确的；并且对于随极角变化的磁场，存在附加的聚焦效应。如果场随极角的相对变化是离子速度与光速之比的数量级，这种聚焦效应将补偿Bethe和Rose的散焦效应。进一步证明了，如果这个变分有周期π2，则存在一族稳定的周期轨道，它们是近同心圆。在第二篇文章中，将考虑由于磁场和加速电场的极角变化同时作用而产生的二阶效应。
Bethe and Rose maintain in a recent letter and paper that a maximum energy for the beam from a cyclotron is fixed by the incompatibility of the conditions for resonance and focusing when the relativity increase of mass with velocity is taken into account. It is shown below that, while this result holds for a radially symmetrical magnetic field, it is not necessarily true in general; and that for a field varying with polar angle there is an additional focusing effect. If the relative variation of the field with polar angle is of the order of the ratio of the velocity of the ion to the velocity of light, this focusing effect will compensate the defocusing effect of Bethe and Rose. It is shown further that if this variation has period π 2, a family of stable periodic orbits exists which are nearly concentric circles. The second order effects due to the simultaneous action of the variations with polar angle of the magnetic field and the accelerating electric field will be considered in a second paper.