Magnetic susceptibility contrast induced field gradients in porous media

Using a two-component composite theory, we compute the internal field gradient of a periodic porous medium induced by the magnetic susceptibility contrasts. The magnetization of such a system is computed by using the diffusion eigenstates in Fourier representation. We show that the volume averaged field gradient, when used in the formula for free diffusion, significantly overestimates the magnetization decay rate. We also establish bounds for such a periodic system within which the Gaussian approximation is valid for diffusion of spins in the pore space.