Bifurcation points in the theory of axially symmetric arc cathodes

Abstract

Steady-state current transfer from arc plasmas to axially symmetric cathodes is treated in the framework of the model of nonlinear surface heating. An approach is developed to calculate the bifurcation points at which three-dimensional spot-mode solutions branch off from solutions describing the diffuse mode and axially symmetric spot modes. In particular, the first bifurcation point positioned on the diffuse-mode solution has been calculated, and thus its stability limit, i.e., the current below which the diffuse mode becomes unstable. Calculation results are given for the case of a tungsten cathode in the form of a circular cylinder in high-pressure plasmas. The effect produced on the stability limit by variations of control parameters (cathode dimensions, work function of the cathode material, plasma-producing gas, and its pressure) is studied and found to conform to trends observed experimentally. The stability limit is found to be much more sensitive to variations of control parameters than characteristics of the diffuse mode are, the strongest effect being produced by variations of cathode dimensions and of the work function of the cathode material. This finding conforms to the fact that the diffuse-spot transition is difficult to reproduce in the experiment.

Modelling interaction of multispecies plasmas with thermionic cathodes

“…The model of the near-cathode plasma [7,9,18], developed previously and validated by the experiment for the case of a single-species plasma-producing gas, has been generalized for the case of multiple ion and multiple neutral species and used for calculation of a diffuse mode of current transfer to tungsten cathodes in a mercury plasma with an addition of sodium. It is seen that the presence of 1% of sodium, while not strongly affecting the characteristics of the diffuse mode (such as the current-voltage characteristic of the near-cathode plasma region and the maximum temperature of the cathode surface), results in a considerable expansion of the range of stability of the diffuse mode.…”

“…In particular, one can determine functions q p (T w , U) and j (T w , U). A detailed presentation of the model can be found in [7,9,18].…”

“…In this paper, the model of the near-cathode plasma layer [7,9,18] is generalized to be applicable to a plasma composed of neutral particles and positive ions of several species, and electrons. The model thus obtained is employed for calculation of a diffuse discharge on tungsten cathodes in a mercury plasma with an addition of sodium.…”

Dissipative solitons

“…for the field distribution near the cathode [132]. From the point of view of 'Nonlinear Dynamics and Pattern Formation' a reasonably complete self-consistent description of the cathode spots in arc discharges can be developed only in special cases [133][134][135].…”

Understanding and modelling plasma–electrode interaction in high-pressure arc discharges: a review

“…Let us now consider recent models of the near-cathode layer on the whole. There are three models with a collisionless space-charge sheath: the model formulated in [37] and modified in [23,50] (a summary of equations of this model can be found in [51]), the model [52] and the model [53]. There is also a model [16], which is similar to [37] except that the ion motion across the space-charge sheath is treated as collision-dominated and the sheath is described by means of the solution [38].…”