I have a question regarding Child's Law with thermionic emission. I understand that due to space-charge effects, that the emission current from a cathode reaches a saturation current at a certain temperature, explained mathematically by Richardson's Law. Utilizing an accelerating positive potential will raise this emitted saturation current. What does Child's Law exactly say? I know it relates a current density to a voltage raised to the 3/2. I've been looking into it, and I can't seem to make it clear to myself whether it's one of these two distinctions. In terms of a emission current vs. anode plate voltage curve, does Child's Law just show the increasing emission current as a function of the plate voltage disregarding the saturation current? Or does it show the saturation current as a function of the voltage across the cathode emitting the electrons? Thank you for any clarification!