The phase factor ψ depends on the impedance of the {spins + coil} circuit and its expression depends on the electrical model of the setup. When the Larmor frequency of the spins exactly matches the probe natural frequency, ω 0 = ω lc , then ψ = -π/2, and the radiation feedback field lags the in-plane magnetization by 90 o . The last ingredient of the dynamical model is the DNP hyperpolarization process of the nuclear spins, which provides the magnetization build-up mechanism. In our experiments, performed at or below 4 K with TEMPOL radical concentrations above 50 mM, DNP is assumed to be in the thermal mixing regime, a process described by the Provotorov equations. In this thermal mixing description, electron-electron and electron-nuclear spin interactions are associated to several coupled energy reservoirs, each of which characterized by a spin temperature T i (or its inverse β i = 1/k b T i ). Thus, Nuclear Zeeman (NZ) and electron dipole-dipole, non Zeeman, (eeD) reservoirs are in thermal contact with each other, and when several nuclear species are present, each one constitutes a distinct reservoir coupled to the eeD reservoir, hence indirectly to one another, adding further complexity to the associated Provotorov rate equations.