| Ultra-intense laser driven ion acceleration turned out to be an extremely interesting phenomenon, capable to produce ion beams which could potentially fit well for many applications as hadron therapy or dense matter diagnostic. The dominant accelerating mechanism so far, that is the Target Normal Sheath Acceleration (TNSA), has been widely studied experimentally as well as theoretically, and a variety of simplified models have been proposed to give reliable predictions on the acceleration features. In the present work we consider a quasi-static approach to describe TNSA, and focus on its improvements. We study the boundary conditions of the electro-static problem, in particular those related on the hot electron population density. To evaluate this parameter a simplified analytical model for the hot electron transport is proposed, starting from geometrical and physical observations such as the typical divergence and the reflux dynamics. Through this path we are able to introduce further properties of the physical system into the quasi-static model, thus enriching its physical content. The proposed approach makes possible to predict the dependence of the ion maximum energy on the thickness and transverse size of the target. The model predictions are compared to some recently published experimental results, often showing a satisfactory agreement. |
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