Child Langmuir law

One of the simplest sheath models is that of a DC high voltage ( T ) sheath that contains no electrons and in which ion flow is collisionless (space-charge limited current). The resulting sheath equation is called the Child-Langmuir law [165]. 

The maximum density j of the extracted current from a plasma is given by the Child-Langmuir law ... 

More commonly one uses the Child Langmuir law. It was observed that the current density scales with the inverse square of the dark space sheath width and other parameters as ... 

The fundamental thermionic diode has been illustrated in Fig. 5.2, and Fig. 5.4 illustrates the representation of a vacuum diode that has an oxide cathode. The plate current (Ip) vsplate-to-cathode voltage (Vp) description of diode operation is provided by the Langmuir-Child law that states that the plate current is proportional to the plate voltage raised to the three-halves power. 

Historically, the triode shown in Fig. 5.6(a) was the first vacuum tube used for signal amphfication. As noted in the introductory section (Fig. 5.1), the voltage applied between the grid (G) and the cathode (K) can be used to control the electron flow and, hence, the plate current. The dynamic operation of a triode is defined approximately by a modified form of the Langmuir-Child law as follows... 

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