The aim of this work is to investigate the dynamics of collisions between ions and Rydberg atoms by using the Classical Trajectory Monte Carlo (CTMC) method. The study is started by collisions with oriented elliptical Rydberg atom, is then continued to collisions involving hydrogen Rydberg target in an external magnetic field in the l-mixing regime, and later arrives at antihydrogen formation in an external magnetic field where Rydberg positronium is taken as target.

The CTMC method has been applied in the study. For different targets, the CTMC method had to be adjusted and reconstructed to properly create the initial target state for the quasi-separable one-body initial system (hydrogen target) and the two-body initial system (positronium target). Charge exchange and ionization cross sections are calculated under special consideration of different initial target states.

The velocity matching phenomenon and Thomas capture which appears in the upstream-downstream asymmetry are found in ion-oriented elliptical Rydberg atom collisions, reflecting the important roles of the initial electron spatial and momentum distributions. By increasing the projectile charge, the distortion of the initial states caused by the strong perturbation of approaching projectile induces pronounced changes in the momentum distribution.

In the collisions involving hydrogen Rydberg atoms in a magnetic field, a cross section reduction in case of an increasing magnetic field is found for multiply charged projectiles. The structure effect due to the influence of the magnetic field on the initial state distribution results in different capture cross sections for two characterized, kmax and kmin, states. The velocity matching phenomenon as well as the effect of multiply charged projectile ion are observed in the collisions.

Furthermore, antihydrogen formation in a magnetic field has been studied. Rydberg positroniums are assumed to be the target atoms, colliding with antiprotons. The initial target positronium state is carefully constructed by means of a newly introduced conserved operator, the pseudomomentum K. Similar properties as in the previous hydrogen target atom case were investigated. It is found that the existence of the magnetic field changes the spatial distribution of positronium to irregular motion. By increasing the magnetic field, it induces a decrease of the resulting capture cross sections (i.e. the antihydrogen formation). Thomas capture which happens in the collision plane in the field-free case is foiled. A smaller positronium binding energy and a larger geometrical extension of the target positronium atom yield a larger capture cross section.