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The work describes the maximization problem regarding the heating of an area on the surface of a thin plate within a given temperature range. The solution of the problem is applied to ion injectors. The given temperature range corresponds to the required pressure of a saturated gas comprising evaporated atoms of the plate material. In order to find the solution, a one-parameter optimization problem was formulated and implemented leading to the optimization of the plate specific geometry. It was shown that a heated area can be increased up to 23.5% in comparison with a regular rectangle form of a given plate configuration.