Hello and thanks for taking a look I'm an undergrad student that is trying to design and make a ion thruster for my research project. I know, I should of started with something simpler. The first part of this project is creating an electron source to provide the electron beam to ionize the Argon gas. My design is basically a jerry-rigged Crook's Tube with an Aluminum Foil Membrane at one end. I'm Using steel sowing needles that are grouped in arrays of 1, 3, 5, 10, 20 and 25. I've looked for material with lower work functions but I'm working of a budget of a taste more then zero. I've built a Full wave rectifier power box to convert a 15kV AV to DC with 24kV, .3μF capacitance smoother caps in parallel with the Anode needle array, and cathode membrane. what I'm trying to find is a way or method to calculate the electric field/potential on the surface of a the needles, or for simpler modeling features, a metal cone. Cone Dimensions are Cylinder length 30mm, height of cone from cylinder to tip 2.5mm, radius of cylinder is 0.35mm. I've worked with finding and calculating electric potential on the surface of cylinder's and spheres witch is pretty straight forward but with a cone I've hit the wall. I've tried using several methods with different answers to all. I know that as curvature increases that potential field increases and that is what makes it difficult to calculate. any suggestions or advice would be greatly appreciated, excpecially any reading material on this type problem. Thanks Again.