An improved system for generating graphene involves producing a plurality of ionized carbon atoms in a plasma generation chamber and providing the plurality of ionized carbon atoms to a graphene generation chamber having a magnetic structure that includes a two-dimensional array of alternating polarity magnetic sources that produce a magnetic field having a gradient sufficient to float graphene over the magnetic structure. The graphene generation chamber generates graphene from said plurality of ionized carbon atoms over said magnetic structure such that said graphene floats over said magnetic structure due to said graphene being diamagnetic. The rate at which the plurality of ionized carbon atoms is produced is controlled to control the rate of graphene generation. The magnetic field of the magnetic structure can be controlled to control the rate at which the generated graphene moves through the graphene generation chamber until it exits as a recovered graphene product.