The Child-Langmuir Law and the Physics of Diodes

The Child-Langmuir Law (CL), discovered a century ago, gives the maximum current that can be transported across a planar diode in the steady state. It is central to the studies of high current diodes and high power microwave sources, vacuum microelectronics, electron and ion sources, and high current drivers used in high energy density physics experiments. This paper highlights some of the advances beyond the classical CL law, including extensions of CL to multiple dimensions, to the quantum regime, and to transient and ultrafast processes [1]. Crossed-field diodes, crucial to magnetic insulation, will be addressed. Also featured is the recent partial resolution [2] of an outstanding puzzle on the shape of Miram curves for thermionic cathodes [3], which show an unexpectedly gradual transition of the anode current from temperature-limited regime to space-charge-limited regime, as the cathode temperature is raised. This is an important consideration for thermal stability and long-cathode life, since most thermionic cathodes are operated in the vicinity of this smooth transition.