The truncated Levy-flight process: Application to the random spin phase change in non-linear magnetic fields

In NMR experiments, self-diffusion of water molecules leads to a random spin phase distribution which is Gaussian in linear magnetic fields. The rate of convergence of the random phase distribution to the Gaussian distribution is very slow. Moreover, a small departure from linear magnetic fields results in significant changes in the spin phase distribution, especially in the central part, and the distribution can be described by Levy-flight process. However, the far-tails of the Levy-like distribution conserve information about the Gaussian prehistory and can validate the degree of non-linearity of the magnetic field. In this paper, the rate, α, of convergence to the Gaussian distribution is calculated for the case of the variation of the power of non-linearity of the magnetic field p   and it is shown that α(p)∈(0,0.66]α(p)∈(0,0.66] when p∈[1,∞)p∈[1,∞).