A concept for a tunable soft x-ray free electron laser (FEL) photon source is presented and studied numerically. The concept is based on echo-enabled harmonic generation (EEHG), wherein two modulator-chicane sections impose high harmonic structure with much greater efficacy as compared to conventional high harmonic FELs that use only one modulator-chicane section. The idea proposed here is to replace the external laser power sources in the EEHG modulators with FEL oscillators, and to combine the bunching of the beam with the production of radiation. Tunability is accomplished by adjusting the magnetic chicanes while the two oscillators remain at a fixed frequency. This scheme eliminates the need to develop coherent sources with the requisite power, pulse length, and stability requirements by exploiting the MHz bunch repetition rates of FEL continuous wave (CW) sources driven by superconducting (SC) linacs. We present time-dependent GINGER simulation results for an EEHG scheme with an oscillator modulator at 43 nm employing 50percent reflective dielectric mirrors and a second modulator employing an external, 215-nm drive laser. Peak output of order 300 MW is obtained at 2.7 nm, corresponding to the 80th harmonic of 215 nm. An alternative single-cavity echo-oscillator scheme based on a 13.4 nm oscillator is investigated with time-independent simulations that a 180-MW peak power at final wavelength of 1.12 nm. Three alternate configurations that use separate bunches to produce the radiation for EEHG microbunching are also presented. Our results show that oscillator-based soft x-ray FELs driven by CWSC linacs are extremely attractive because of their potential to produce tunable radiation at high average power together with excellent longitudinal coherence and narrow spectral bandwidth.

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.

‘Cold pools’ are pools of air that have been cooled by rain evaporation, and which subsequently slump down and spread out across the Earth’s surface due to their negative buoyancy. Such cold pools, which typically arise from rain produced by convection, also feed back upon convection by kicking up new convection at their edges.

This thesis studies the interaction of cold pools and convection at two levels of detail: on one end, we study the dynamics and thermodynamics of a single, idealized cold pool, and on the other, we study the interplay between a steady-state ensemble of convection and the many cold pools that accompany it. A recurring notion is that of ‘effective buoyancy’, which is the net acceleration experienced by a density anomaly such as a cold pool, including the back-reaction of the environment (i.e. the ‘virtual mass effect’) which reduces the net acceleration from its Archimedean value. We derive analytical formulae for the effective buoyancy of cold pools and other roughly cylindrical density anomalies, and use the same framework to understand the forces at play when cold pools trigger new convection. We also analyze the sizes and lifetimes of cold pools, and examine the impact of cold pools on the organization (i.e. clustering) of convection.

This dissertation focuses on three ideas useful to the nonneutral plasma experiment at

UC Berkeley and the ALPHA experiment at CERN. While these may seem like disparate

ideas, in all cases, a careful mathematical treatment of the problems yield useful insights.

First, we present improvements to the analysis for diagnostics of temperature and den-

sity of plasmas in Penning-Malmberg trap experiments. Our new methods are faster and

more accurate than previously used methods of analysis. This allows us to conduct these

diagnostics in real-time without any input from a human.

We then theoretically consider the problem of enhanced cooling of an electron plasma

from a coupling of the plasma to cavity modes. We make more rigorous the previous analysis

that was done on the topic, and then extend these results to a longitudinally dynamic plasma.

We compare our theoretical results with experimental observations from the Berkeley plasma

trap and with simulations and find good agreement.

Finally, we consider analyses of ALPHA data to measure antihydrogen properties. We

place a statistically rigorous bound on the antihydrogen charge from ALPHA data. This

improves the previous bound on antihydrogen charge by a factor of 20, and assuming super-

position, improves the bound on the positron charge anomaly by a factor of 25. Finally, we

consider analyses for a future measurement of the gravitational mass of antihydrogen. We

find that with reasonable constraints, a measurement of the gravitational mass of antihydro-

gen with a precision of 1% should be feasible.

Parker Solar Probe (PSP), launched in late 2018, is a mission designed to sample the near-Sun environment and solar corona, and answer broad open questions concerning coronal energy flow and solar wind dynamics. The SPAN-Ion instrument is an on-board electrostatic analyzer responsible for measuring 3D ion velocity distribution functions (VDFs). In the first part of this thesis, we give an overview of SPAN-Ion, its intrinsic uncertainties, and discuss the effect of its finite field-of-view on moment measurements. We then move on to study magnetic switchbacks, rapid radial reversals of the magnetic field. While their role in young solar wind dynamics and precise generation mechanisms are still unclear, their ubiquity marks them out as an important early PSP observation. Using MHD invariants to probe their macroscale structure, we show that they are localised S-shaped folds in the magnetic field with internally backward propagating Alfvénic fluctuations, which has important implications for studies of small-scale turbulence using such invariants. Using fits to SPAN-Ion data, we then investigate alpha particle density, abundance, and velocity fluctuations inside and outside individual switchbacks, showing that there are no consistent compositional changes inside vs outside, but argue that these findings cannot yet be used to definitively rule in favour of one particular switchback generation mechanism (although they may be able to in the future). We also show that alpha particle speeds may be enhanced, decreased, or remain constant during a switchback, depending on the relative values of the alpha proton drift and the local wave phase speed, in contrast to the always positive proton velocity spikes. In the final part we study the alpha VDFs in more detail, focussing on characterising secondary alpha populations or alpha ``beams”. These have been essentially unstudied relative to their proton beam counterparts. We find they are generally more dense and slower moving than proton beams, and occur less frequently. We report time localised correlations between proton and alpha normalised heat flux, suggesting the existence of a common mechanism for producing beams in each species. We then perform a case study of an ion scale wave event, showing for the first time an active role being played by the alphas, specifically the alpha beam population, in driving solar wind plasma unstable and locally generating right-handed fast magnetosonic waves. The predicted wave frequencies, polarisations, and times of occurrence agree remarkably well with the observations. Such wave events are important for understanding the mechanisms of energy exchange between waves and particles that may be responsible for in-situ heating of the solar wind.

Free-Electron Lasers (FELs) with ultra-intense coherent beams have been widely used for a variety of research, such as interrogations of the inner structure of atoms, molecules, clusters, and tightly-spaced crystal structures. Unfortunately, X-ray light sources suffer from both a high cost and limited scientific beam time, due to their kilometer-scale accelerator. On the other hand, laser-plasma accelerators (LPAs), enabling the production of high-quality MeV to GeV electron beams, are compact, less expensive, and have the electron and secondary radiation beams synchronized with a femtosecond laser driver. Here we pursue the technology required for a compact LPA based FEL, which has the capability to deliver high intensity coherent radiation pulses. A state-of-the-art 100-TW-class laser system dedicated to demonstrating an LPA based FEL was constructed. As part of this system, a novel online, non-destructive laser diagnostic, capable of measuring the transverse position and pointing angle of the laser at focus was developed. The diagnostic is based on a unique double-surface-coated wedged-mirror design for the final steering optic in the laser beamline. It produces a witness beam highly correlated with the main beam. By propagating low-power kHz pulses to the focus, the spectra of the focal position and pointing angle fluctuations with their dominant frequencies below 70 Hz, were observed. This diagnostic was also used to characterize the excellent position and pointing angle correlation of the 1-Hz high-power laser pulses to this low-power kHz pulse train, opening a promising path to implementing fast non-perturbative feedback concepts, even on few-Hz-class high-power laser systems. Furthermore, new aspects of the design and physics of an LPA based FEL, which are unique to the electron beam generated by the LPA, were investigated. One method to achieve coherent radiation in an FEL driven by an LPA is to reduce the electron beam slice energy spread by stretching the beam in a chicane, producing a linear energy chirp. Seed radiation at the resonant wavelength propagating in an undulator with the energy chirped beam may then be coherently amplified. With such a linear-energy-chirped beam, it is observed in simulations using GENESIS that the peak frequency of the seeded FEL radiation redshifts linearly with the amount of electron beam chirp and the undulator propagation distance, and inversely with the undulator wavelength and electron energy. This observed FEL radiation redshifting is explained by the dispersion of the microbunching structures during propagation due to the energy chirp of the electron beam, and analyzed using the coupled Maxwell-Vlasov equations describing the FEL dynamics.