Two-Dimensional Short-Pulse Child-Langmuir Law

Summary form only given. Advances in laser-driven electron photo-injectors have pushed the operation of the photocathode from the normally source-limited regime to the space-charge limited regime. As the pulse length of the photo-injector is usually shorter than the transit time of the electrons across the vacuum gap, the classical Child-Langmuir (CL) law is expected to be exceeded as shown in previous experiments. Agust et al. has extended the classical 1D CL law to include the influence of a finite pulse length. However, in practical situations, the area and shape of the photocathode emitter are also important parameters to be considered. In this paper, we will present a simple theory of 2D or 3D short-pulse CL law for various emitting patches such as an infinitely long strip of width W, and a circular emitting patch of radius R. Our results are then compared with 2D or 3D PIC simulation, which show good agreements. Multi-pulse effects will also be discussed