Thermodynamics of singly charged particles

Broadly speaking, this thesis treats some theoretical aspects of ultracold physics.; Chapters 2--5 relate to work directly in support of the effort to produce the first cold antihydrogen atoms. There, we investigate the equilibrium of cold (4 K) plasmas of anti-protons and anti-electrons cooled and trapped in a Penning trap. We show how, in addition to the temperature, there exists an extra parameter o that determines the equilibrium. After deriving the relevant theoretical equilibrium distributions, we describe the algorithms to numerically simulate them. Additionally, we develop methods to visualize the classical dynamics of the equilibrium. This shows that o is not always simply the rigid body spin of the plasma cloud.; Chapters 6 and 7 deal with far colder temperatures of nanoKelvin, where quantum reflection prevents the classically expected sticking of cold atoms on "warm" surfaces. We provide a general and non-perturbative theoretical basis for quantum reflection of an ultracold atom incident on a cold or warm surface. Sticking is identified with the formation of a long lived resonance, from which it emerges that the physical reason for not sticking is that the many internal degrees of freedom of the target serve to decohere the incident one body wavefunction, thereby upsetting the delicate interference process necessary to form a resonance. We then explore the transition to the post-threshold behavior, when sticking prevails at higher incident energies. Studying the WKB wavefunctions of the atom provides a quick understanding of our results even in the ultracold regime where WKB is not in fact applicable. Explicit examples are examined in detail and we predict the temperatures required to reach the various regimes.