A test particle approach is used to study two distinct plasma physics situations. In the first case, the collisionless response of protons to cold plasma fast Alfven waves propagating in a non-uniform magnetic field configuration (specifically, a two-dimensional X-point field) is studied. The field perturbations associated with the waves, which are assumed to be azimuthally-symmetric and invariant in the direction orthogonal to the X-point plane, are exact solutions of the linearized ideal magnetohydrodynamic (MHD) equations. The protons are initially Maxwellian, at temperatures that are consistent with the cold plasma approximation. Two kinds of wave solution are invoked: global perturbations, with inward- and outward-propagating components; and purely inward-propagating waves, localised in distance from the X-point null, the wave electric field E having a preferred direction. In both cases the protons are effectively heated in the direction parallel to the magnetic field, although the parallel velocity distribution is generally non-Maxwellian and some protons are accelerated to highly suprathermal energies. This heating and acceleration can be attributed to the fact that protons undergoing E x B drifts due to the presence of the wave are subject to an effective force in the direction parallel to B. The localised wave solution produces more effective proton heating than the global solution, and successive wave pulses have a synergistic effect. This process, which could play a role in both solar coronal heating and late-phase heating in solar flares, is effective for all ion species, but has a negligible direct effect on electrons. However, both electrons and heavy ions would be expected to acquire a temperature similar to that of the protons on collisional timescales. In the second case the same approach is used to study the collisional transport of impurity ions (carbon, mainly, although tungsten ions are also simulated) in spherical tokamak (ST) plasmas with transonic and subsonic toroidal flows. The efficacy of this approach is demonstrated by reproduscing the results of classical transport theory in the large aspect ratio limit. The equilibrium parameters used in the ST modelling are similar to those of plasmas in the MAST experiment. The effects on impurity ion confinement of both counter-current and co-current rotation are determined. Various majority ion density and temperature profiles, approximating measured profiles in rotating and non-rotating MAST plasmas, are used in the modelling. It is shown that transonic rotation (both counter-current and co-current) has the effect of reducing substantially the confinement time of the impurity ions. This effect arises primarily because the impurity ions, displaced by the centrifugal force to the low-field region of the tokamak, are subject to a collisional diffusivity that is greater than the flux surface-averaged value of this quantity. for a given set of plasma profiles, the carbon ions are found to be significantly less well-confined in co-rotating plasmas than in counter-rotating plasmas, although the difference in confinement time between co- and counter-rotation lessens as the mass of the impurity increases. In the case of carbon ions the poloidal distribution of losses exhibits a pronounced up/down asymmetry that is consistent with the direction of the net vertical drift of the impurity ions. Increasing the mass of the impurity ion is also found to significantly decrease the confinement time in the rotating cases, though the confinement time for the case of a stationary plasma is increased. Such studies of impurity transport within tokamaks are important because it is desirable to expel impurity ions from the plasma to avoid both dilution of the fuel ions and unacceptable radiation losses from the plasma.