Charged Particles in Near-Earth Space

In this chapter we discuss the concepts that govern the motion of charged particles in the geomagnetic field and the principles how they stay trapped in the radiation belts. The basic particle orbit theory can be found in most plasma physics textbooks. We partly follow the presentation in Koskinen (Physics of space storms, from solar surface to the earth. Springer-Praxis, Heidelberg, 2011). A more detailed discussion can be found in Roederer and Zhang (Dynamics of magnetically trapped particles. Springer, Heidelberg, 2014). A classic treatment of adiabatic motion of charged particles is Northrop (The adiabatic motion of charged particles. Interscience Publishers, Wiley, New York, 1963).

Adiabatic motion and statistical mechanics via mass-zero constrained dynamics

A symplectic, time-reversible algorithm for adiabatically separated systems that exactly samples the Born–Oppenheimer probability distribution is presented and its numerical efficiency is demonstrated on an orbital-free DFT simulation of solid Na.

Electronic non-adiabatic dynamics in enhanced ionization of isotopologues of hydrogen molecular ions from the exact factorization perspective

An exact-factorization perspective of enhanced ionization in isotopologues of H2+ demonstrates the concept of the exact potential driving the electrons in non-adiabatic motion of molecules in strong fields, and sets a new platform for introducing various approximations.

Entropy Production Within a Pulsed Bose–Einstein Condensate

We suggest to subject anharmonically trapped Bose–Einstein condensates to sinusoidal forcing with a smooth, slowly changing envelope, and to measure the coherence of the system after such pulses. In a series of measurements with successively increased maximum forcing strength, one then expects an adiabatic return of the condensate to its initial state as long as the pulses remain sufficiently weak. In contrast, once the maximum driving amplitude exceeds a certain critical value there should be a drastic loss of coherence, reflecting significant heating induced by the pulse. This predicted experimental signature is traced to the loss of an effective adiabatic invariant, and to the ensuing breakdown of adiabatic motion of the system’s Floquet state when the many-body dynamics become chaotic. Our scenario is illustrated with the help of a two-site model of a forced bosonic Josephson junction, but should also hold for other, experimentally accessible configurations.

Nonlinear interactions between relativistic radiation belt electrons and oblique whistler mode waves

Resonant interactions between relativistic charged particles and oblique whistler mode waves are explored in this work, and it is shown that nonlinear phase trapping could happen in a gyrophase averaged sense, consistent with previous studies of interactions between nonrelativistic electrons and oblique whistler mode waves. A dimensionless parameter χ is derived to represent the ratio of wave-induced motion to the adiabatic motion of the particle. We show that phase trapping is likely to occur when the wave-induced motion dominates the adiabatic motion, which is caused mainly by the background fields. A mapping of probable regions of nonlinear interactions is shown based on the parameter χ. We show that the nonlinear interactions might be important near the equatorial plane for even moderate wave amplitude, and the latitudinal range for nonlinear interactions to occur is largest for electrons with local pitch angles around 50 degrees, consistent with previous findings. The results are important for understanding the nonlinear dynamics of relativistic radiation belt electrons and the generation of chorus waves.