Figure 4:

Simulated final magnetization $m_z^{\text{final}}$, after a sweep through resonance, plotted versus the unitless sweep rate ${\alpha }_1$. The Bloch equations were numerically integrated at (a) low intensity ($B_1=6.3\mu \text{T}$, $T_2=0.45\mu \text{s}$, and variable $d\Delta B_0/dt$) and at (b-d) high intensity ($d\Delta B_0/dt=0.70\text{mT}\mu {\text{s}}^{-1}$, variable $B_1$, and $T_2$ equal to (b) $0.45\mu \text{s}$, (c) $2.25\mu \text{s}$, and (d) $13.5\mu \text{s}$). In the top plots we graph the varied parameter, $d\Delta B_0/dt$ in (a) and $B_1$ in (b-d), versus ${\alpha }_1$, while on the bottom plots we graph the final magnetization. Open circles are the numerically computed magnetization. In (a), the solid line is eq. 25. In (b-d), the solid line is eq. 63 while the dotted line is the magnetization computed using the first-order Magnus expansion in eq. 56 taken in the $2\beta {\tau }_0\ll 1$, $a_0\to \infty$ limit.