Space-charge-limited current in cylindrical diodes with finite-length emitter

In the present paper we extend to two dimensions the classical Langmuir–Blodgett law, which determines the maximum current ILB that can be accelerated by a given voltage across two infinitely long coaxial cylinders. Generalization of the ILB law is established by performing two-dimensional 2D particle-in-cell numerical experiments on a variety of cylindrical diode configurations with a finite-length emitter. It is found that the limiting current in two dimensions I2D follows a monotonically decreasing function of the emitter length-to-outer electrode radius ratio L/R as expressed by the fitting function I2D/ILB=1+0.1536/(L/R)+0.0183/(L/R)2 within 2.5% accuracy for simulation data in which the ratio of the outer to inner radii exceeds 3.