In the paper, we applied the paraxial region theory and Wentzel–-Kramers–-Brillouin approximation to study laser beam self-focusing in the interaction of laser and collisional plasma with periodical density ripple. The results have shown that, under the influence of collision nonlinear effect, laser presents stable self-focusing, self-defocusing, and oscillational self-focusing in the plasma. Besides, the parameters of plasma with periodical density ripple have a greater impact on the effect of self-defocusing and oscillational self-focusing than stable self-focusing. In certain conditions, beam self-defocusing and oscillational self-focusing would decline and even disappear, and stable self-focusing would further be strengthened. Hence, selecting a suitable periodic plasma system is advantageous for separating self-defocusing and oscillational self-focusing, and for the formation of a more stable collisional self-focusing.

The purpose of this paper is to calculate proton energy loss straggling using a full conserving dielectric function (FCDF) for plasmas at any degeneracy. This dielectric function takes into account plasma electron-electron collision considering density, momentum, and energy conservation. When only momentum conservation law is accomplished, the FCDF reproduces the well known Mermin dielectric function, when none of the conservations laws are obeyed, the random phase approximation (RPA) is recovered. Then, the FCDF is applied for the first time to the determination of the energy loss straggling. Differences among diverse dielectric functions to determine straggling follow the same behavior for all kind of plasmas then, they do not depend on the plasma degeneracy but essentially do on the value of the collision frequency. These discrepancies can rise up to 5% between FCDF values and the Mermin ones, and 2% between the FCDF ones and RPA ones for plasma with high enough collision frequency. The similarity between FCDF and RPA results is not surprising, as all conservation laws are also considered in RPA dielectric function. The fact that FCDF and RPA give similar results and the fact that FCDF considers electron-electron collisions and RPA does not, means that latter collisions are not significant for energy loss straggling calculations.

Dielectric functions of an electron plasma are calculated for an electron gas in which number, momentum, and energy are conserved during electron-electron collisions. They are compared with others in the literature, revealing that, in general, that imposition of the conservation laws tends to make the full conserving dielectric response more similar to the random phase approximation dielectric response than without it. This is due to the fact that in the random phase approximation model all the conservation laws are also enforced. Our model is checked for other plasma degeneracies; concretely we consider partially degenerate plasmas and classical plasmas. The behaviour of the dielectric functions of these plasmas is similar to the degenerate one. Differences among dielectric functions are more significant than for the degenerate case, but it is mainly due to low relaxation time values. The most relevant issue for these plasmas is the fact that the consideration of energy conservation in the dielectric function is more important in these cases, because plasma temperature is significant.