Analysis of Multigrid Extraction Plasma Meniscus Formation

Negative ion source for spallation sources or neutral beam injectors (NBI) for tokamaks requires carefully matched electric and magnetic fields in the beam formation area due to the presence of three species of particles: the collisional and fully magnetized electrons; the slightly magnetized positive ions; the negative ions, formed within few cm from plasma-beam interface (meniscus). As a step towards a collisional and magnetized theory for a charged fluid in a realistic 2D or 3D geometry, a 1D model based on a Vlasov equation with a collision operator is written and discussed in detail. A closed equation is obtained for the forward directed current; its solution in modes and formulas for density n are given.