The PALS high power iodine laser system in Prague (lambda = 1.315 mu m) was used to study non-linear processes in a laser-produced plasma at intense laser beam interactions with planar targets. The focus setting allows to alter the non-linear interaction of the main laser pulse with the ablated plasma produced by the front edge of a nanosecond laser pulse (300 ps FWHM). The arisen non-linear effects significantly influence the behavior of electrons, which accelerate fully striped or highly charged fast ions. Variations in time of the expanding plasma, recorded at the target surface by the use of Kentech low-magnification soft X-ray streak camera on similar to 2 ns time scale, are presented and discussed. Narrowing, arching and even splitting of expansion paths in the target-normal space-time diagram are shown. These phenomena are ascribed to the magnetic field, self-generated at high laser intensities, which may become strong enough to cause pinching of the expanding plasma. (C) 2012 Elsevier B.V. All rights reserved.