Microtips and resistive sheet: a theoretical description of the emissive properties of this system

The purpose of this conference is to present a model which describes completely in a very simple way the physics of field effect emission for an ensemble of tips located on a 2-dimensional lateral resistive sheet. Given the well known a and b parameters of each tips, the geometry of the mesh and the square resistance of the resistive sheet, we have determined exactly the voltage on each tip as a function of its position in the mesh and then calculated each current effectively emitted. Thanks to this theory some simple questions, as the following, will be answered: What is the "equivalent" resistance of this ensemble? What is its exact meaning? When a specified number of tips is needed, and the mesh geometry fixed, where do we have to put the tips in order to get the most uniform emission or the maximum of current? When a tip has a short with the grid, how many tips are affected by the increase of potential in the region near the tip? Is that "better" to have some big meshes with a great number of tips or numerous small ones with a few tips? Is that "better" to have lines of tips or compact ensembles of tips distributed on a resistive sheet?.