Interaction of High-Pressure Arc Plasmas with Thermionic Cathodes

THERMCAT - On-Line Tool for Simulation of Current Transfer to Thermionic Cathodes of High-Pressure Arc Discharges

What is this code destined for?
The objective of this code is two-fold. The first one is to provide a fast and robust tool for simulation of diffuse and axially symmetric spot modes of current transfer from high-pressure plasmas to cylindrical thermionic cathodes in a wide range of arc currents, cathode materials and dimensions, and plasma compositions. The second objective is methodological. Nowadays, it is universally understood that different modes of current transfer to thermionic cathodes are described by multiple solutions that must exist under certain discharge conditions in an adequate theoretical model. Unfortunately, the concept of multiple solutions, while being quite common in many areas of theoretical physics, is not equally widespread in applied physics. Therefore, we tried to offer to applied physicists and engineers working in the field a tutorial that would help them to make themselves comfortable with multiple solutions describing different modes of current transfer to thermionic cathodes. Is should be stressed that the experience gained with this tutorial will facilitate work with other solvers, including commercial software like COMSOL Multiphysics or ANSYS: difficulties encountered in finding multiple solutions by means of any efficient solver are the same.

The code is based on the model of nonlinear surface heating [see, e.g., review M. S. Benilov, Understanding and modelling plasma–electrode interaction in high-pressure arc discharges: a review, J. Phys. D: Appl. Phys. 41, No. 14, pp. 144001-1-30 (2008) and references therein] and consists of three modules. The first module provides a solution describing the near-cathode plasma layer. The second module provides a solution of the heat conduction equation in the cathode body under the assumption of axial symmetry. The third module is dedicated to calculation of bifurcation points positioned on the axially symmetric modes, in particular, of the limit of stability of the diffuse mode.

The code is written in Fortran and is quite fast and robust. The database includes a large variety of plasma-producing gases (in particular, He, Ne, Na, Ar, Cu, Kr, Xe, Cs, Hg, air, mixture Na-Hg, mixture Cs-Hg, plasmas of mercury with addition of metal halides, plasmas of xenon with addition of metal halides) and of cathode materials (in particular, W, Mo, Fe, Nb, and Zr).
Current-voltage characteristics of different steady-state modes and typical distributions of the temperature of the cathode surface associated with each mode. Circles: bifurcation points. W cathode, R = 2mm, h = 10mm, Tc = 300K, Ar plasma, p = 1bar.

An example of current-voltage characteristics (CVCs) of different steady-state modes is shown in the figure. For U exceeding approximately 14V, nine different steady state are possible. Five of these states (those with spots at the edge of the front surface of the cathode) are 3D. The code is destined for finding the four states are axially symmetric:

and also for finding bifurcation points at which 3D modes branch off from the axially symmetric modes (note that one of these points represents the limit of stability of the diffuse mode).

To whom is this code destined?
The code is destined to applied physicists and engineers and can be used

Conditions of use
The code is free for non-commercial personal use only. Simulation results must not be transferred to third parties, however they may be used for producing scientific publications, provided that the references are made to the paper M. S. Benilov, M. D. Cunha, and G. V. Naidis, Modelling interaction of multispecies plasmas with thermionic cathodes, Plasma Sources Sci. Technol. 14, No. 3, pp. 517-524 (2005) and to this site (

The code is made available "AS IS" without warranty of any kind. The entire risk as to the results and the performance of the code is assumed by the user, and in no event will the authors be liable for any consequential, incidental or direct damages suffered in the course of using the code.

The modelling tool
You will need to perform three steps. The first one is definition of control parameters for simulations. The second step is generation of a starting-point solution. The third and final step is execution of simulations in a wide range of arc currents.

During the second and third steps, no intermediate information appears on the screen - you will be on hold until after the current run has been completed. Furthermore, there is no way to interrupt the current run until it has been completed. Therefore, the time of each run is limited to approximately 10 minutes. This means that each run must be not too long; for example, if you wish to calculate the current-voltage characteristic from the near-cathode voltage U=10V to U=100V with a very fine step, you may need to perform a number of separate runs, for example from 10V to 40V, from 40V to 70V, and from 70V to 100V.

You can leave the tool at any moment (provided that the code is not running right now) by clicking the button.

You may find it convenient to use the Text Zoom option, which is available in most popular browsers as "Cntrl +" or "Cntrl -" .

There are two alternative interfaces, you can use any one. (The engine is the same, just the interfaces are different.) The interface 1 allows only one user at a time and the maximum duration of a session with this interface is 60 minutes. There are no restrictions on session duration or number of users in the Interface 2.

Open Interface 1 Attention If this link does not work, there are two probable reasons:
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Changes made to the code after the release of the 3rd version (2009-04-30)  

Please report problems to Sergej Benilov