The Pierce-diode approximation to the single-emitter plasma diode

The possibility of modeling fast processes in the collisionless single-emitter plasma diode (Knudsen diode with surface ionization, KDSI) by means of the Pierce-diode is studied. The KDSI is of practical importance in that it is an almost exact model of thermionic energy converters (TICs) in the collisionless regime and can also be used to model low-density Q-machines. At high temperatures, the Knudsen TIC comes close to the efficiency of the Carnot cycle and hence is the most promising converter of thermal to electric energy. TICs can be applied as component parts in high-temperature electronics. It is shown that normalizations must be chosen appropriately in order to compare the plasma characteristics of the two models: the KDSI and the Pierce-diode. A linear eigenmode theory of the KDSI is developed. For both nonlinear time-independent states and linear eigenmodes without electron reflection, excellent agreement is found between the analytical potential distributions for the Pierce-diode and the corresponding numerical ones for the KDSI. For the states with electron reflection, the agreement is satisfactory in a qualitative sense. A full classification of states of both diodes for the regimes with and without electron reflection is presented. The effect of the thermal spread in electron velocities on the potential distributions and the (ε,η) diagrams is analyzed. Generally speaking, the methodology developed is usefully applicable to a variety of systems in which the electrons have beam-like distributions