UC Berkeley

The asymmetry between matter and antimatter in the universe and the incompatibility between the Standard Model and general relativity are some of the greatest unsolved questions in physics. The answer to both may possibly lie with the physics beyond the Standard Model, and comparing the properties of hydrogen and antihydrogen atoms provides one of the possible ways to exploring it. In 2010, the ALPHA collaboration demonstrated the first trapping of antihydrogen atoms, in an apparatus made of a Penning--Malmberg trap superimposed on a magnetic minimum trap. Its ultimate goal is to precisely measure the spectrum, gravitational mass and charge neutrality of the anti-atoms, and compare them with the hydrogen atom. These comparisons provide novel, direct and model--independent tests of the Standard Model and the weak equivalence principle. Before they can be achieved, however, the trapping rate of antihydrogen atoms needs to be improved.

This dissertation first describes the ALPHA apparatus, the experimental control sequence and the plasma manipulation techniques that realised antihydrogen trapping in 2010, and modified and improved upon thereafter. Experimental software, techniques and control sequences to which this research work has contributed are particularly focused on. In the second part of this dissertation, methods for improving the trapping efficiency of the ALPHA experiment are investigated. The trapping efficiency is currently hampered by a lack of understanding of the precise plasma conditions and dynamics in the antihydrogen production process, especially in the presence of shot--to--shot fluctuations. This resulted in an empirical development for many of the plasma manipulation techniques, taking up precious antiproton beam time and resulting in suboptimal performance. To remedy these deficiencies, this work proposes that simulations should be used to better understand and predict plasma behaviour, optimise the performance of existing techniques, allow new techniques to be explored efficiently, and derive more information from diagnostics.

A collection of numerical models for Penning--Malmberg trap plasmas are introduced, which are designed to simulate a major subset of the plasma manipulation techniques used in ALPHA, targeted at the plasma conditions available therein, and with near--real--time experimental usability in mind. The first of these is a zero--temperature plasma solver, which exploits the water bag model to compute the density and potential of a cold, stationary plasma with a given radial profile and electrode excitations. It is suited to analysing slow (or stationary) processes, where the variations applied are on a much slower time scale than the typical time between collisions in the plasma. The density and electric potential output by the solver inform the programming of the electrode voltages, which is of particular value when plasma bunches need to be weakly confined in shallow wells.

The second numerical model developed for this work is a radially--coupled Vlasov--Poisson solver, which evolves the axial phase space distribution of a plasma under the influence of (time-dependent) electrode excitations, from a given initial state. It takes into account the plasma self--field and the radial variations in potential and density, and assumes that radial transport is negligible. This model simulates processes where the dynamic behaviour of the plasma is critical to their outcome. It allows for tests of plasma manipulation techniques over a wide range of tunable parameters and plasma conditions prior to an actual experiment, potentially reducing the need for empirical tuning.

The third numerical model is an azimuthally averaged, energy--conserving Fokker--Planck solver for a discrete, non-regular grid distribution. It simulates the effects of weakly magnetised collisions on the bulk parallel and perpendicular velocity distributions of a plasma, as the particles collide among themselves. The collision coefficients are analytically calculated by azimuthally averaging the derivatives of the Rosenbluth potentials. This model is applicable to plasmas where self--collisions of antiprotons have a non-negligible effect, possible examples of which include the antiproton--positron mixture which exists during antihydrogen formation, and the antiproton cloud captured from the Antiproton Decelerator, the source of ALPHA's antiprotons.

The fourth numerical model is an azimuthally averaged Fokker--Planck model for intermediately magnetised collisions. It generalises the preceding model to study Fokker--Planck--type collisions of electrons, positrons and antiprotons in magnetic fields of arbitrary strength. Unlike the previous model, analytic solutions for collisions in arbitrarily strong magnetic fields are not known. The collision coefficients are therefore computed numerically via an adaptive Monte Carlo averaging of the colliding particles' changes in parallel and perpendicular velocities, over their impact parameter and their velocity phase angles. The collision process itself is simulated via a variable--time--stepping Boris particle pusher. This model is applicable to a wide range of processes involving cooling and thermalisation, which are critical to the ALPHA experiment.

The water bag and Vlasov models are employed to simulate the excitation of antiprotons during the antiproton--positron mixing process, which produces antihydrogen atoms and determines whether they can be confined by the magnetic minimum trap. The agreement between the simulation and experimental measurements, analytic predictions and other existing simulations is demonstrated. The simulation is then used to optimise the excitation under various plasma conditions, and novel excitation techniques are proposed and explored.

The models developed throughout this work lay the foundation for a systematic analysis of the plasma phenomena in the experiment. Future work includes extending the result of the mixing simulation to study collisional and recombination effects, as well as applying the models to other processes in the experiment. It is also of interest to apply the collisional formulations in this work to particle--in-cell (PIC) models and to explore three--dimensional plasma effects.