The theoretical basis is presented that allows to compute the Stark broaden
ed line shapes of atomic ions up to the quadrupole terms in the interaction
potential between the radiator and the plasma electric microfields and the
ir gradients. The nature of the corrections due to the plasma polarization
effects associated with the electron distribution around ion perturbers are
carefully analyzed. The relevant universal plasma functions are evaluated
in a cluster expansion or by Monte Carlo simulations, and the line shape is
calculated with ion dynamic effects by the Model Microfield Method. The as
ymmetry of the Lyman alpha line of hydrogenic ions is then studied.