Space-charge-limited, two-dimensional unmagnetized flow in a wedge geometry

This paper studies the space-charge-limited current in an infinite wedge geometry in two dimensions. This geometry permits a reduction of the problem to a set of easily solved ordinary differential equations. The system, though very simplified, exhibits features similar to those expected to occur in many realistic systems with inhomogeneous electric fields. We obtain, in particular, a universal form for the particle trajectories and a nonmonotone charge distribution with accumulation at both the cathode and the anode. The explicit solution of the model can be useful for testing numerical schemes. The case of a very low density current is also considered. Relaxation of the geometrical limitations of the model are studied using conformal mapping techniques. Possible applications to realistic systems, which can be tested by simple experiments, are presented