Application of the multicriterion optimization techniques and hierarchy of computational models to the research of ion acceleration due to laser-plasma interaction

In this paper we discuss how a particles-in-cell computation code can be combined with methods of multicriterion optimization (in particular the Pareto optimal solutions of the multicriterion optimization problem) and a hierarchy of computational models approach to create an efficient tool for solving a wide array of problems related to the laser-plasma interaction. In case of the computational experiment the multicriterion optimization can be applied as follows: the researcher defines the objectives of the experiment - some computable scalar values (i.e. high kinetic energy of the ions leaving the domain, least possible number of electrons leaving domain in the given direction, etc). After that the parameters of the experiment which can be varied to achieve these objectives and the constrains on these parameters are chosen (e.g. amplitude and wave-length of the laser radiation, dimensions of the plasma slab(s)). The Pareto optimality of the vector of the parameters can be seen as this: x0 is Pareto optimal if there exists no vector which would improve some criterion without causing a simultaneous degradation in at least one other criterion. These efficient set of parameter and constrains can be selected based on the preliminary calculations in the simplified models (one or two-dimensional) either analytical or numerical. The multistage computation of the Pareto set radically reduces the number of variants which are to be evaluated to achieve the given accuracy. During the final stage we further improve the results by recomputing some of the optimal variants on the finer grids, with more particles and/or in the frame of a more detailed model. As an example we have considered the ion acceleration caused by interaction of very intense and ultra-short laser pulses with plasmas and have calculated the optimal set of experiment parameters for optimizing number and average energy of high energy ions leaving the domain in the given direction and minimizing the expulsion of electrons.