The above suggests that dipolar field effects are effective in the magnetization dynamics of the experiments presented here and, therefore, the simple (3 + 1)-dimensional model of the BMP equations misses some of the observed features of the dynamics. Providing a detailed and effective model of the collective dynamics of a spin ensemble subject to the combination of radiation feedback from the probe, dipolar field effects and DNP is a complex task. However, one is only interested in the dynamics of a classical magnetization, so that the entire system can be described in terms of interacting classical moments. Nevertheless, even with such a drastic simplification, the complexity of this system requires further simplifications and hypotheses. In solids, dipole-dipole interactions provide an efficient mechanism for decoherence, leading to FIDs of a few hundreds of microseconds. This is particularly effective for near neighbor interactions, where dipolar coupling is strong. Alternatively, because the dipolar interactions fall off relatively fast as ∼ r 3 , these effects may assumed much weaker at long distances, where the interaction energies are smaller and the associated time scales accordingly longer. Therefore, we here assume that the environment of each spin i is decomposed as follows. A small region centerd on i, the dimensions of which are large with respect to the first neighbor distances but much smaller than the sample dimensions, is responsible for decoherence and the fast decay of the NMR signal. Alternatively, the long distance, and accordingly weaker, interactions with remote spins affect the magnetization dynamics only on time scales that are much longer than the typical inverse line width. Therefore, except for a contribution to the resonance frequency, this DDF is not expected to affect the magnetization dynamics. This may nevertheless be the case if phase coherence between spins is maintained long enough, as in the presence of a strong radiation feedback. These considerations lead us to envisage a simplistic model where all the spins in the system have a common T 2 relaxation time (and a γ 2 = T -1 2 rate) that represents the effect of the local dipolar interactions. Alternatively, the dipolar contribution from remote spins, an active ingredients of the magnetization dynamics in this context, is treated explicitly. In this model sample, the magnetic moments are sitting on a regularly spaced lattice and the local dipolar field at site i, B d (r i ), due to the long range dipole dipole interactions can be explicitly computed for all moments in the model sample as: