Radiating electron in a magnetic field

Abstract

The paper considers the application of Dirac's classical theory of radiating electrons to examine the motion of an electron in a uniform magnetic field. The non-relativistic equations of motion are solved exactly. It is shown that for the particular case when the motion is confined to a plane, the physical motion is such that the electron describes an equiangular spiral with velocity which steadily decreases asexp {negative constant × t};and in the non-physical motion the electron spirals outwards with velocity which steadily increases asexp {positive constant × t},and ultimately the electron escapes to infinity. The relativistic equations of motion are solved approximately as a series in ascending powers of the field. It is shown that in the physical motion the velocity begins to decrease, and hence after a time the motion is given correctly by the non-relativistic solution.I take this opportunity to express my deepest gratitude to Prof. Dirac, who suggested this problem, for his patient guidance and supervision.