Radiation damping relaxation from

In Ref. 13, we have proved that the A transformation constructed is invertible for the classical model discussed in the previous section. Here, using the same system discussed in the previous section, we demonstrate the invertiblity of our transformation by a numerical calculation of the time evolution of the action variable J (f) for an initial condition where all the field actions are zero [20]. Due to radiation damping, J t) follows an approximately exponential decay. However, there are deviations from exponential in the exact evolution both at short and long time scales as compared with the relaxation time scale. In Fig. 1, we present numerical results. 

As is evident from Eq. (1), the radiation damping effect is particularly severe for large solvent peaks and can make the solvent return to equilibrium many times faster than the intrinsic longitudinal relaxation time (see Fig. 2). Thus, the effects of radiation damping are a major source of difficulties in manipulating solvent magnetization and need to be considered in the... 

Pig, 4. An RF pulse initially rotates the magnetization away from the z-axis (i.e. thermal equilibrium) by, in this example, an angle of about 170°. In the absence of radiation damping effects the magnetization follows the normal relaxation pathway (—) back to the thermal equilibrium. However, in the presence of radiation damping, the magnetization retains its coherence and returns to the equilibrium position on the surface of the Bloch sphere (---). (After Mao et al )... 

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