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In this paper a future laser ion accelerator_x1048577_ is discussed to make the laser-based ion accelerator compact and controllable. Especially a collimation device is focused in this paper. The future laser ion accelerator should have an ion source, ion collimators, ion_x1048577_ beam bunchers, and ion post acceleration devices [Laser Therapy 22, 103(2013)]: the ion particle energy and the ion energy spectrum are controlled to meet requirements for a future compact laser ion_x1048577_ accelerator for ion cancer therapy or for other purposes. The energy efficiency from the laser to ions is improved by using a_x1048577_ solid target with a fine sub-wavelength structure or_x1048577_ a near-critical density gas plasma. The ion beam_x1048577_ collimation is performed by holes behind the solid_x1048577_ target or a multi-layered solid target. The control _x1048577_ of the ion energy spectrum and the ion particle energy, and the ion beam bunching would be successfully_x1048577_ realized by a multistage laser-target interaction.

Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given dataset by a combination of a small number of basis vectors of an overcomplete basis is termed the {\em sparse approximation}. In this paper, we apply simulated annealing, a metaheuristic algorithm for general optimization problems, to sparse approximation in the situation where the given data have a planted sparse representation and noise is present. The result in the noiseless case shows that our simulated annealing works well in a reasonable parameter region: the planted solution is found fairly rapidly. This is true even in the case where a common relaxation of the sparse approximation problem, the $\ell_1$-relaxation, is ineffective. On the other hand, when the dimensionality of the data is close to the number of non-zero components, another metastable state emerges, and our algorithm fails to find the planted solution. This phenomenon is associated with a first-order phase transition. In the case of very strong noise, it is no longer meaningful to search for the planted solution. In this situation, our algorithm determines a solution with close-to-minimum distortion fairly quickly., Comment: 12 pages, 7 figures, a proceedings of HD^3-2015