In a generalized beam-target model, the "Gyrating Particle Model" (GPM), the strong suprathermal fusion production of both dynamic phases of the plasma focus POSEIDON (W0 = 280 kJ, U0 = 60 kV, Mather type) is considered to be due to the fast accelerated deuterons gyrating in pinch structures. The results of this new model are compared with spectrally and spatially resolved measurements of fusion protons and accelerated deuterons, to give evidence of the validity of this generalized beam-target model for both phases. Statements are obtained on the number and distribution function of accelerated deuterons, necessary to explain the observed fusion yield.