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Recent advances in the suprathermal ion diagnostic in the basic plasma experiment TORPEX have inspired our comprehensive theoretical study of suprathermal ion transport. TORPEX, an example of a simple magnetized toroidal plasma (SMT), is equipped with a flexible fast ion source and detector capable of exploring fast ion dynamics in a wide range of positions and energies. We simulate an ensemble of ion tracer trajectories as specified by ideal interchange-mode turbulence imported from a validated numerical simulation based on the drift-reduced Braginskii model. Using the variance of displacements, , we find that depends strongly on suprathermal ion injection energy and the magnitude of turbulent fluctuations. When the beam interacts with the turbulence, we find the remarkable presence of three regimes of dispersion: superdiffusive, diffusive, and subdiffusive, depending on the energy of the suprathermal ions and the amplitude of the turbulent fluctuations. Results from the source on TORPEX are consistent with the theoretical predictions.