A numerical technique has been developed to analyse the dynamics of a linear, magnetically confined plasma column and its associated fusion-produced alpha-particles in a self consistent manner. The thermonuclear background plasma is considered as a radially non-uniform, axially symmetric magnetofluid in pressure equilibrium with the surrounding axial magnetic field. A multi-group technique is utilized to examine the alphas as a collection of particles distributed among a continuous spectrum of confined orbits. The technique is shown to be an effective one for observing the interaction between super-thermal particles with large orbit sizes and a stable plasma of comparable size. The use of a distribution function in an adiabatic invariant representation results in an enormous increase in the time scale which can be treated. This enables analysis of the entire duty cycle of a laser solenoid plasma in reasonable computation times. An analysis of a fast solenoid plasma is described, where the initial plasma radius and temperature are varied parametrically. A plasma column of radius 7 mm, temperature 6 keV, and β = 0.95 will reach an ion temperature of 10 keV, corresponding to a fusion energy gain of 8, after 3 ms. A range of maximum gain occurs for initial temperatures of 5 to 7 keV, with larger radius plasmas more favoured by the cooler limits. The effect of increasing the alpha particle-electron energy transfer rate by a moderate amount to account for anomalous effects is to increase the plasma temperature at longer times, as long as this energy transfer is well-coupled to the electron-ion energy transfer. Increasing the rate at which plasma transport processes occur ("anomalous transport") always results in lower fusion yield, because of rapid plasma diffusion.