A burning Deuterium-Tritium plasma is one which depends upon fusion-produced alpha particles for self-heating. Whether a plasma can reach a burning state requires knowledge of the transport of alpha particles, and turbulence is one such source of transport. The alpha particle distribution in collisional equilibrium forms a non-Maxwellian tail which spans orders of magnitude in energy, and it is this tail that is responsible for heating the plasma. Newly-born high-energy alpha particles are not expected to respond to turbulence as strongly as alpha particles that have slowed down to the bulk plasma temperature. This dissertation presents a low-collisionality derivation of gyrokinetics relevant for alpha particles and describes the upgrades made to the GS2 flux-tube code to handle general non-Maxwellian energy distributions. With the ability to run self-consistent simulations with a population of alpha particles, we can examine certain assumptions commonly made about alpha particles in the context of microturbulence. It is found that microturbulence can compete with collisional slowing-down, altering the distribution further. One assumption that holds well in electrostatic turbulence is the trace approximation, which is built upon to develop a model for efficiently calculating the coupled radial-energy turbulent transport of a non-Maxwellian species. A new code was written for this purpose and corrections to the global alpha particle heating profile due to microturbulence in an ITER-like scenario are presented along with sensitivity studies.