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In the Earth auroral zone, the electron acceleration by Alfv\'en waves issometimes a precursor of the non-propagating acceleration structures. In orderto investigate how Alfv\'en waves could generate non-propagating electricfields, a series of simulations of counter-propagating waves in a uniformplasma is presented. The waves (initially not configured to accelerateparticles) propagate along the ambient magnetic field direction. It is shownthat non propagating electric fields are generated at the locus of the Alfv\'enwaves crossing. These electric fields have a component orientated along thedirection of the ambient magnetic field, and they generate acceleration and asignificant perturbation of the plasma density. The non-linear interaction ofdown and up-going Alfv\'en waves might be a cause of plasma densityfluctuations (with gradients along the magnetic field) on a scale comparable tothose of the Alfv\'en wavelengths.

On the role of Alfv\'en waves as precursors of quasi-static acceleration processes in the Earth auroral zone