The Joint European Torus (JET) recently carried out an experimental campaign using a plasma consisting of both deuterium (D) and tritium (T). We observed a high-frequency mode using a reflectometer and an interferometer in a DT plasma heated with low power neutral beam injection, $P_{NBI} = 11.6$ $MW$. This mode were observed at a frequency $f = 156$ $kHz$, was located deep in the plasma, and exhibited frequency chirping. The observed mode was identified as a toroidal Alfvén eigenmode (TAE) using the linear MHD code, MISHKA. The stability of 21 modes that match experimental measurements was investigated. Beam ions and fusion-born alpha particles were modelled using the full orbit particle tracking code LOCUST. LOCUST exploits GPU hardware to follow $\\\\sim 10^7$ particles from birth to thermalisation, producing a smooth distribution function suitable for stability calculations without analytical fits or the use of moments. At least 6M beam markers were required to capture all of the crucial features of the distribution function in sufficient detail. We calculated the stability of the 21 candidate modes using the HALO code, which models the wave-particle interaction. These calculations revealed that beam ions can drive TAEs with toroidal mode numbers $n\\\\geq 8$ with linear growth rates $\\\\gamma_d /\\\\omega \\\\sim 1\\\\%$, while TAEs with $n<8$ are damped by the beam ion population. This finding was supported by a simple analytical model. Alpha particles drive modes with significantly smaller linear growth rates, $\\\\gamma_\\\\alpha/\\\\omega \\\\lesssim 0.1 \\\\%$ due to the low alpha power generated almost exclusively by beam-thermal fusion reactions. At least 4M beam ions and 1M alpha particles were required in HALO to represent the distribution function. Guiding centre calculations were found to significantly over-estimate growth rates compared to full orbit calculations for both beam ions and alpha particles. Non-ideal effects were calculated using complex resistivity in the CASTOR code, leading to an assessment of radiative, collisional, and continuum damping for all 21 candidate modes. Ion Landau damping was modelled using Maxwellian distribution functions for bulk D and T ions in HALO. Radiative damping, the dominant damping mechanism, suppresses modes with high toroidal mode numbers. Collisional damping was also significant, particularly for modes in the outer half of the plasma. Comparing the drive from energetic particles with damping from thermal particles, we find all but one of the candidate modes are damped. The single net-driven $n=9$ TAE with a net growth rate $\\\\gamma/\\\\omega = 0.02 \\\\%$ matches experimental observations with a lab frequency $f = 163 kHz$, location $R=3.31m$ and marginal instability. The TAE was driven by co-passing particles through the $v_\\\\parallel = v_A/5$ resonance, with additional sideband resonances contributing significant drive. A beam-driven mode is observed in our experiment due to low damping caused by the weak electron temperature and high magnetic field.