Beam dynamics in front ends of ion accelerators is often subject to strong space charge and significant transverse coupling due to magnetic fields in the source and the use of focusing solenoids in the beam line. This thesis starts with an overview and a brief primer on beam dynamics to frame two research themes: simulation and analytic studies on beam dynamics, and improvements on transverse beam diagnostics. Each theme is first developed in a general treatment, followed by applications to the front end of the Facility for Rare Isotope Beams (FRIB). The first research theme includes: (1) numerical modelling of accelerator front ends, and (2) analytic studies of coupled transverse beam dynamics. In (1), a set of readily adaptable simulation tools based on the PIC code Warp is constructed to model the transport and manipulation of intense multi-species beams with high levels of detail. The tools are applied to investigate beam evolution in the FRIB front end including the species separation process. In (2), general analytic results on beams with rotational symmetry and the formalism of eigen-emittances are derived to elucidate non-axisymmetric initial conditions at the ion source and beam states advantageous for solenoid transport. The results are employed to construct LEBT/MEBT (low/medium energy beam transport) tuning schemes currently adopted at FRIB for transverse matching of strongly magnetized beams into the RFQ and cryomodules respectively. The second research theme presents improvements on transverse beam diagnostics including: (1) corrections in the conventional data analysis model of high-resolution phase space measurements with Allison scanners, and (2) error minimization in beam matrix measurements and enhanced tomography capabilities using beam profile monitors. All techniques and algorithms under this theme have been verified using measurements at FRIB.
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