Mean square displacement in small-scale nonlinear dynamos

The stretching property of an underlying fluid is studied in a simplified statistical model of small-scale nonlinear dynamos, via the evolution of the mean square displacement. The nonlinear effect of small-scale magnetic fields is consistently incorporated in the limit of low kinetic Reynolds number. The mean square displacement between two neighboring particles, as well as that of a single particle, is shown to be reduced due to the Lorentz force associated with small-scale magnetic fields. This reduction is suggested to lead to the suppression of stretching of magnetic field lines, and subsequently to the saturation of the growth of small-scale magnetic fields.