The high orders of Stark effects on spectral line shapes are examined in the ion-static and electron-impact approximations. At first the distribution functions of the spatial derivative of the ion microfield in He + plasma are calculated for different plasma conditions when the coupling parameter is weak. We present new results about the spatial derivative ion microfield distributions and apply them to show the asymmetry of the Lyman-α(Ly-α) line in He + plasma. At the second stage we show that asymmetry is affected by the spatial derivative tensor of the local ion electric field. We have used the Monte-Carlo simulation (MCS) to compute the distribution functions for all tensor components and use them to solve the evolution equation of emitter whose solution serves to compute and therefore to show the line shape asymmetry. Good agreement of our distribution functions of ion microfield gradients and the line asymmetry with other results are obtained.

In this work the distribution function of spatial derivative of parallel component of quasistatic ion electric microfield in plasma is calculated. Some physical approximations are used in these calculations, where only interactions between charged emitter and perturber ions are taken into account, as first step. This approximation is known as the independent particles model. Some special functions and series are used in these calculations. It is deduced that the distribution function of spatial derivative of the ion microfield may be depend more on the probability of finding the microfield rather than the microfield value itself.

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By using some physical approximations, distribution functions of spatial derivatives of components of an electric ionic microfield in plasmas have been theoretically evaluated. The particles are considered quasistatic. Only interactions between charged emitter and perturber ions are taken into account. Our theoretical results have been compared with those found in the literature. The few differences found are discussed. Some properties of distribution functions of spatial derivatives have been deduced from curves.

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