Two-fluid plasma model for radial Langmuir probes as a converging nozzle with sonic choked flow, and sonic passage to supersonic flow

Using the Lambert function, Guittienne et al. [Phys. Plasmas 25, 093519 (2018)] derived two-fluid solutions for radial Langmuir probes in collisionless and isothermal plasma. In this Brief Communication, we point out the close analogy with classical compressible fluid dynamics, where the simultaneous flows of the ion and electron fluids experience opposite electrostatic body forces in the inward radial flow of the plasma, which behaves as a converging nozzle. Hence, the assumed boundary condition of sonic flow of the repelled species at the probe is explained as choked flow. The sonic passage from subsonic to supersonic flow of the attracted species at the sonic radius is also interpreted using classical fluid dynamics. Moreover, the Lambert function can provide a general solution for one-dimensional, isothermal compressible fluids, with several applications.