• cathodes
• chemical model
• dispenser cathodes
• lifetime
• plasma model
• S-type
• thermal model
• thermionic

A self-consistent model is proposed to study the time-varying properties of a dispenser hollow cathode, addressing the plasma, thermal and chemical aspects of operation, and including an evaluation of the expected lifetime. A review of the available technical literature is provided, highlighting the main lumped-parameter plasma models, the principal heat exchange processes and the various approaches to describe the barium depletion from the insert and the formation of low-work function layers on its surface. A system of equations for the plasma was derived, featuring a number of closed-form solutions and leaving a few parameters to be solved iteratively. A dedicated model to study the temperature distribution along the cathode is presented, detailing the view factor computation with and without optical obstruction. Moreover, an updated model to describe barium evaporation is described, considering ternary diagrams for the BaO-CaO-Al2O3 system available in the more recent literature, along with a geometric approach to derive molar fractions from the diagram itself. Updated barium diffusion and layer deposition equations are implemented in the model, including simplifying assumptions to estimate the density variation due to evaporation. The problem is solved by considering at each time the nonlinear set of equations describing plasma and thermal properties, whereas the time-varying chemical processes allow to describe the evolution of the cathode parameters. MATLAB’s fsolve routine has been employed to obtain cathode properties at a given, instant, whereas the numerical integration of the differential equations describing barium oxide deposition on the insert surface and its depletion from the porous matrix is carried out to update said parameters.
The results obtained through the use of a MATLAB code are shown and compared to the available experimental data, showing good agreement between theoretical and experimental results and thus providing a fast and useful tool to carry out preliminary numerical simulations of dispenser hollow cathodes.