self-similarity of Rydberg hydrogen atom in parallel electric and magnetic fields

Abstract

Using the semi-classical methods, the self-similarity structure of Rydberg hydrogen atom in parallel electric and magnetic fields is analysed in this paper. Based on the Hamiltonian canonical equations, all the escape orbits are found, and the escape time and the initial launch angle of every escape orbit can be derived. The self-similarity structure of escape time plot is found by studying the relationship between the escape time and the initial launch angle of electron in parallel electric and magnetic fields. The relationship between the self-similarity structure and escape orbits is also established through the study of the escape orbits in the escape time plot. The regularity of escape orbits in self-similarity structure is found and the corresponding escape orbits in self-similarity structure plots meet the law of (-o)k. According to this rule, the self-similarity structure can be easily found, and the rule is applicable to other research system. Moreover, the influences of scaled energy and scaled magnetic field are analyzed in detail. It is presented that the dynamic behavior of the Rydberg hydrogen atom is sensitively controlled by scaled energy and scaled magnetic field. Different scaled energies or scaled magnetic fields can lead to different escape behaviors of electron. It is also found that the self-similarity structure is present not in all cases. When scaled energy or scaled magnetic field is small, the escape time plot is simple, and no self-similarity structure is observed. When scaled energy or scaled magnetic field increases, self-similarity structure appears accordingly and the system becomes complicated. When scaled energy or scaled magnetic field changes, the self-similarity region also changes. For a given scaled magnetic field, with the increase of scaled energy, self-similarity region shifts toward the bigger initial launch angle, while self-similarity region shifts toward the smaller initial launch angle with the increase of scaled magnetic field for a given scaled energy.