A new simple algorithm for space charge limited emission

Many high power electronic devices operate in a regime where the current they draw is limited by the self-fields of the particles. This space charge limited current poses particular challenges for numerical modeling where common techniques like over-emission or Gauss' Law are computationally inefficient or produce nonphysical effects. In this paper, we show an algorithm using the value of the electric field in front of the surface instead of attempting to zero the field at the surface, making the algorithm particularly well suited to both electromagnetic and parallel implementations of the particle-in-cell algorithm. We show how the algorithm is self-consistent within the framework of finite difference (for both electrostatics and electromagnetics). We show several 1D and 2D benchmarks against both theory and previous computational results. Finally, we show the application in 3D to high power microwave generation in a 13GHz magnetically insulated line oscillator.