Completely bound motion of a positive-energy electron in the coulomb field of a motionless nucleus and a uniform magnetic field
We show that the completely bound classical motion of a positive-energy electron is realized in the Coulomb field of a motionless nucleus and a uniform magnetic field. Such a motion exists due to conservation of the so-called invariant tori in the phase space of the system for not only the negative, but also for the positive energy of an electron. The completely bound trajectories occupy a much larger interval of the velocity directions compared with free trajectories for the same energy in a range of distances from the nucleus in which the typical time of the electron transit near the nucleus is larger than the cyclotron-gyration period, while the negative energy of Coulomb interaction is larger (in absolute value) than the total electron energy. The indicated range of distances is realized in the case of a low electron energy or a strong magnetic field when the Larmor radius of the electron is smaller than the characteristic impact parameter of the close Coulomb collisions in the absence of a magnetic field. The required conditions are realized in the photospheres of isolated magnetic white dwarfs and in the experiments on creation of antihydrogen.
KeywordsTurning Point Pitch Angle Rotation Number Transverse Velocity Electron Motion
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