I. V. Uimanov

Hydrodynamics of the Molten Metal During the Crater Formation on the Cathode Surface in a Vacuum Arc

2-D axially symmetric hydrodynamic model has been developed to describe the formation of a crater and liquid-metal jets on a vacuum arc cathode using Navier-Stokes equations for an incompressible viscous fluid with a free surface and a heat conduction equation taking convective heat transfer into account. The formation of an elemental crater on a copper cathode during the operation of a cathode spot cell has been numerically simulated by varying the heat flux and the pressure produced by the cathode spot plasma. Based on the simulation results, we can distinguish three different modes of the crater formation process: 1) no splashing; 2) inertial splashing; and 3) active splashing. It has been shown that a crater with metal jets forced away can be formed within 30 ns of plasma action if the heat flux density is above 1012 W/m2 and the pressure is above 108 Pa.

The mechanism of liquid metal jet formation in the cathode spot of vacuum arc discharge

We have theoretically studied the dynamics of molten metal during crater formation in the cathode spot of vacuum arc discharge. At the initial stage, a liquid-metal ridge is formed around the crater. This process has been numerically simulated in the framework of the two-dimensional axisymmetric heat and mass transfer problem in the approximation of viscous incompressible liquid. At a more developed stage, the motion of liquid metal loses axial symmetry, which corresponds to a tendency toward jet formation. The development of azimuthal instabilities of the ridge is analyzed in terms of dispersion relations for surface waves. It is shown that maximum increments correspond to instability of the Rayleigh–Plateau type. Estimations of the time of formation of liquid metal jets and their probable number are obtained.

Hybrid Computational Model of High-Current Vacuum Arcs With External Axial Magnetic Field

This paper deals with the computer modeling of a high-current (total current ≥10 kA) vacuum arc with an external axial magnetic field. This arc is typical for certain kind of vacuum interrupters. The described hybrid model treats electrons as a massless fluid and ions as macroparticles. The macroparticle dynamics are calculated with the use of the particle-in-cell method. Ion-ion Coulomb collision is considered with the use of the Monte Carlo method. The model can simulate high-current vacuum arcs as a whole including separate cathode plasma jets, mixing zone, and common plasma column. The hybrid model is able to calculate V-shape volt-tesla characteristics, which correlate well with experimental results.

Kinetic Modeling of Heating of Metal Microdroplet by Surrounding Plasma

A kinetic 1-D spherically symmetric model of heating of metal microdroplet (with a radius of 1–2

Generation of hydrogen isotope ions in a vacuum arc discharge with a composite zirconium deuteride cathode

\mu \hbox{m}

Pre-Explosion Phenomena Beneath the Plasma of a Vacuum Arc Cathode Spot

) by surrounding plasma was developed. The kinetic model is a model of 1D3V particle-in-cell/direct simulation Monte Carlo type. The model describes thermo-field electron emission and evaporation from the droplet surface and correspondent plasma creation. The droplet heating is self-consistently modeled, taking into account the influence of the plasma generated during the process. The calculations have shown that, beginning from the certain surface temperature, the droplet is heated mostly by electron flux from the plasma. A certain kind of thermal instability takes place in the developed model. Beginning from the certain value, the droplet surface temperature hyperbolically grows and reaches the critical temperature; after that, the calculation is stopped because of model restrictions.

On the limiting density of field emission current from metal

The mass and charge composition of the plasma of a vacuum arc with thick and film-type zirconium cathodes containing deuterium and hydrogen is investigated experimentally and theoretically. For a thick cathode, it is shown that such a system ensures effective generation of deuterium ions with an integral fraction per arc current pulse of approximately 60%; the maximal concentration of deuterium is observed at the initial stage of the arc operation. In the case of the film cathode, such a concentration of hydrogen isotopes can be attained for currents exceeding 400 A and for an arc duration at a level of a few tens of microseconds. Occlusion of deuterium in the cathode leads to additional energy expenditures for its ionization and, as a consequence, a decrease in the average charge of ions of the cathode material in the arc plasma. Deuterium in the cathode spot is ionized completely, and the drift velocity of its ions almost coincides with the velocity of ions of the cathode material due to the high frequency of ion-ion collisions in the cathode region. The interaction of a dense (∼1020 cm−3) cathode-spot plasma with microinhomogeneities of the cathode surface leads to the development of thermal instability in them over time intervals that do not exceed tens of nanoseconds.

Time-dependent modelling of electrohydrodynamic effects on the surface of a liquid metal

A 2-D hydrodynamic model has been developed that describes the pre-explosion processes in a microprotrusion of a vacuum arc cathode based on a self-consistent calculation of the electric potential drop in the near-cathode region. The model includes a calculation of the cathode temperature in view of the surface heat fluxes carried by electrons and ions during the interaction of the cathode surface with the cathode spot plasma and the Joule heating of the cathode. The near-cathode space charge sheath is considered in the 1-D local Bohm approximation. It has been shown that the heat flux from a cathode plasma having parameters characteristic of low-current vacuum arcs can induce thermal instability (thermal runaway) in a cathode microprotrusion and heat it to a critical temperature within some tens of nanoseconds. Comparative analysis of the volumetric Joule mechanism and the surface electron-plasma mechanism underlying the development of thermal instabilities in a cathode has been performed in one numerical experiment. It has been shown that the instability induced by the surface mechanism can arise at lower densities of the cathode spot plasma and its growth rate is lower compared with the instability induced by the Joule mechanism.

Features of the Energy Parameters and the Composition of the Ion Flow From the Plasma at the Spark Stage of Vacuum Discharge

The present work considers the problem of the field emission characteristics of metals for the range of external electric fields 10R-109 V/cm. It has been shown that the fields at which tbe height of the potential barrier decreases due to the Schottky effect is greater than the work function of the emitter are ultrahigh electric fields for FE. In this case. the penetration of the external electric field into the metal emitter results in a substantial increase in electron density near the emission boundary. It has also been shown that the Fowler-Nordheim relation that describes the electric field dependence of the current density does not hold at ultrahigh fields. Analytical expressions for this dependence have been obtained taking into account the perturbation of the electronic structure of the emitter by the external electric field both in the WKB and in the Miller-Good approximation in the low-temperature limit. Based on the results obtained, it has been shown that the saturation of the FE current density does not happen, as supposed earlier, and the current density practically linearly increases with electric field.

High speed and spectroscopic investigation of 300 kV pulsed vacuum spark in centimeter gap

Results of time-dependent modelling of electrohydrodynamic effects on the surface of a liquid metallic conductor are reported for a regime where no electron, ion or particle emission occurs. The Navier-Stokes equations, with free liquid boundaries subject to Maxwell field stress, surface-tension stress and viscous action, have been solved by a method that uses transformation of the interfaces into a rectangle; this overcomes a problem of surface oscillations that appeared using the Marker-and-Cell technique. The situation geometry is a deep unbounded surface with axial symmetry. With time, an almost flat surface evolves into a cone-like shape, which is in good agreement with experimental observations of this process. The calculations have also shown that, when the protrusion is formed, the time dependences of the surface radius of curvature, the electric field value at the protrusion apex, and the axial velocity of the liquid metal, exhibit a runaway behaviour: the physical values become very large for a short time. As a cusp evolves on a surface, the Maxwell stress acting outwards becomes very large and overtake the growth of both the surface tension and viscous stress acting inwards. The development of numerical methods using transformation of the interfaces appears very useful for the treatment of problems in which the cathode or the anode significantly change shape. This situation occurs, for example, when a liquid surface is covered by a metal plasma and evolution of the surface occurs in the context of a Langmuir shield.