Positron Emission Tomography is a non-disruptive and high-sensitive digital imaging technique which allows to measure in-vivo and non invasively the changes of metabolic and transport mechanisms in plants. When it comes to the early assessment of stress-induced alterations of plant functions, plant PET has the potential of a major breakthrough. The development of dedicated plant PET systems faces a series of technological and experimental difficulties, which make conventional clinical and preclinical PET systems not fully suitable to agronomy. First, the functional and metabolic mechanisms of plants depend on environmental conditions, which can be controlled during the experiment if the scanner is transported into the growing chamber. Second, plants need to be imaged vertically, thus requiring a proper Field Of View. Third, the transverse Field of View needs to adapt to the different plant shapes, according to the species and the experimental protocols. In this paper, we perform a simulation study, proposing a novel design of dedicated plant PET scanners specifically conceived to address these agronomic issues. We estimate their expected sensitivity, count rate performance and spatial resolution, and we identify these specific features, which need to be investigated when realizing a plant PET scanner. Finally, we propose a novel approach to the measurement and verification of the performance of plant PET systems, including the design of dedicated plant phantoms, in order to provide a standard evaluation procedure for this emerging digital imaging agronomic technology.