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Research Project
Cathode spots in high-pressure DC gas discharges: self-organization phenomena
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Multiple solutions in the theory of dc glow discharges
Publication . Almeida, P. G. C.; Benilov, M. S.; Faria, M. J.
Multiple steady-state solutions existing in the theory of dc glow discharges are computed for
the first time. The simulations are performed in 2D in the framework of the simplest
self-consistent model, which accounts for a single ion species and employs the drift–diffusion
approximation. Solutions describing up to nine different modes were found in the case where
losses of the ions and the electrons due to diffusion to the wall were neglected. One mode is
1D, exists at all values of the discharge current, and represents in essence the well-known
solution of von Engel and Steenbeck. The other eight modes are axially symmetric, exist in
limited ranges of the discharge current, and are associated with different patterns of current
spots on the cathode. The mode with a spot at the centre of the cathode exhibits a well
pronounced effect of normal current density. Account of diffusion losses affects the solutions
dramatically: the number of solutions is reduced, a mode appears that exists at all discharge
currents and comprises the Townsend, subnormal, normal and abnormal discharges. The
solutions that exist in limited current ranges describe patterns, and these patterns seem to
represent axially symmetric analogues of the 3D patterns observed in dc glow microdischarges
in xenon.
What is the mathematical meaning of Steenbeck's principle of minimum power in gas discharge physics?
Publication . Benilov, M. S.; Naidis, G. V.
It is shown that Steenbeck’s principle of minimum power, or voltage, for discharges with fixed
current is not a corollary of the principle of minimum entropy production, in contrast to what
is frequently assumed; besides, the latter principle itself does not provide a reasonable
approximation in gas discharge physics. Similarly, Steenbeck’s principle is not a corollary of
mathematical models of gas discharges. Hence, this principle contradicts the mathematical
models. A methodically correct evaluation of the error caused by the use of Steenbeck’s
principle requires a comparison of a solution obtained with the use of this principle with an
exact solution to the same problem, rather than with experimental results or results deemed
reasonable from the point of view of common sense. Such a comparison is performed for two
examples from the theory of a cylindrical arc column. The examples show that the error
incurred by the usage of Steenbeck’s principle is uncontrollable and may be unacceptably high.
Simulating different modes of current transfer to thermionic cathodes in a wide range of conditions
Publication . Benilov, M. S.; Cunha, M. D.; Faria, M. J.
Changes in the pattern of steady-state modes of current transfer to thermionic cathodes
induced by variations of the cathode geometry and temperature of the cooling fluid are studied
numerically. For some combinations of control parameters, only one stable mode in a wide
current range exists, which combines features of spot and diffuse modes. This mode, when
attached to an elongated protrusion on the cathode surface, may be identified with the
so-called super spot mode observed in experiments on low-current arcs. There is also
reasonable agreement between the modelling and the experiment on cathodes of high-current
arcs operating in the diffuse mode. The conclusions on existence under certain conditions of
only one stable mode in a wide current range and of a minimum of the dependence of the
temperature of the hottest point of the cathode on the arc current, manifested by this mode,
may have industrial importance and admit a straightforward experimental verification.
The double sheath on cathodes of discharges burning in cathode vapour
Publication . Benilov, M. S.; Benilova, L. G.
The model of a collisionless near-cathode space-charge sheath with ionization of atoms
emitted by the cathode surface is considered. Numerical calculations showed that the
mathematical problem is solvable and its solution is unique. In the framework of this model,
the sheath represents a double layer with a potential maximum, with the ions which are
produced before the maximum returning to the cathode surface and those produced after the
maximum escaping into the plasma. Numerical results are given in a form to be readily
applicable in analysis of discharges burning in cathode vapour, such as vacuum arcs. In
particular, the results indicate that the ion backflow coefficient in such discharges exceeds 0.5,
in agreement with values extracted from the experiment.
Three-dimensional modeling of self-organization in DC glow microdischarges
Publication . Almeida, P. G. C.; Benilov, M. S.; Faria, M. J.
Three-dimensional simulations of self-organization
in dc glow microdischarges are reported. The results describe a
mode with a normal spot and modes with patterns of multiple
spots, qualitatively similar to those observed in experiments with
microdischarges in xenon.
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Funding agency
Fundação para a Ciência e a Tecnologia
Funding programme
3599-PPCDT
Funding Award Number
PTDC/FIS/68609/2006