Mechanisms limiting the electron current from a surface through a plasma*

Understanding the maximum current of surface-emitted electrons through a plasma is a key basic plasma physics problem relevant to numerous plasma technologes with thermionic cathodes. It has been known since Langmuir's time [1] that as the emitted electron flux from a surface is increased, the net electron current may saturate due to electric field reversal at the cathode (the “space charge effect”). In this poster, we demonstrate a second mechanism [2] that can saturate the current even while the cathode sheath is classical.  When the "backflow saturation limit" is breached the cathode sheath collapses to a very weak voltage to allow some of the emitted electrons injected into the interior plasma to backflow to the cathode, thereby contributing no net current. We demonstrate the physics of backflow saturation versus virtual cathode saturation using continuum kinetic simulations of a full plasma diode. Conventional theoretical models and simulation studies of emitted electron current limitation could not capture backflow saturation because they only considered the cathode sheath and treated its voltage as a fixed input independent of the emission [3,4].  Our simulations show that the backflow saturation depends on a coupling between the emitted flux, cathode sheath voltage, anode sheath voltage, and interior plasma collisional resistance. In common plasma conditions, backflow saturation occurs before a virtual cathode or inverse sheath forms. This means that backflow, not space charge, sets the limit on the passable current. Backflow saturation also causes global changes to the potential distribution; in real plasma devices it will likely manifest not as a simple current saturation but as a mode transition with global changes to plasma properties.

[1] Langmuir, I. 'The Interaction of Electron and Positive Ion Space Charges in Cathode Sheaths' Phys. Rev. 33, 954 (1929).

[2] Campanell, M. D., et al. (in prep)

[3] Takamura, S., et al. 'Space-Charge Limited Current from Plasma-Facing Material Surface' Contrib. Plasma Phys. 44, 126 (2004).

[4] Komm, M. et al., “Space-charge limited thermionic sheaths in magnetized fusion plasmas,” NF 60, 054002 (2020).