Ekkehard Schade

Numerical simulation of high-current vacuum arcs with an external axial magnetic field

Numerical simulations are presented for physical behavior and heat flux to the anode of high-current diffuse of arcs as found in vacuum interrupters. The magnetohydrodynamic approach is applied. Of importance is the consideration of energy balance. Heat flux densities to the anode are predicted in the right order of magnitude and essential physical details of the high-current vacuum arc are disclosed. Only at low or no axial magnetic field superimposed externally and low-arc currents, the anode-directed flow of plasma of diffuse arcs reveals supersonic conditions. Otherwise, subsonic conditions exist. In supersonic diffuse arcs, the anode-directed plasma flow is decelerated and highest pressures appear in front of the anode. At subsonic conditions the highest pressure prevails in the cathode region and the pressure gradient drives the flow to the anode. The transition from diffuse to diffuse columnar arc seems to occur when the evaporation rate of metal vapor from the contact surfaces approaches the emission rate of plasma from the body of cathode spots. Diffuse columnar arcs have moderate pressure variations from cathode to anode. With rising plasma density, the energy loss from the emission of electromagnetic radiation increases and can no longer be neglected.

Vacuum arcs driven by cross-magnetic fields (RMF)

The principle of controlling a high-current vacuum arc by radial magnetic fields (RMF) forcing the constricted arc to move has been utilized for long time in the design of vacuum interrupters. Detailed electrical and optical measurements in conjunction with finite-element method (FEM)-calculations have provided a better physical understanding of the function of RMF contacts. By balancing the processes of surface heating and momentum gain in the moving arc column, an expression for the speed of the arc and arc voltage is obtained. The speed varies as the 5/6 power of the short-circuit current. This result is then used to describe the number of rotations of the arc on the contact and to explain the linear scaling law of contact diameter with current. The investigations are mainly concentrated on spiral-type contact designs.

Dielectric Recovery of Vacuum Arcs after Strong Anode Spot Activity

Recovery of dielectric strength and post-arc currents after diffuse and constricted vacuum arcs were measured for filat OFHC-Cu contacts (D = 25 mm, d = 7.5 mm) enclosed in a bakable UHV chamber. The arc current pulse had a trapezoidal shape of 5.5-ms duration with peak values up to 11 kA. In comparison with the fast recovery of diffuse arcs, the recovery of constricted arcs with gross melting is considerably retarded. Post-arc currents are simulated using the Andrews-Varey model extended to include the effects of secondary electron emission due to ion bombardment of the cathode and loss of the plasma due to thermal motion. The flow of charge carriers to the anode and the shield, which is at the anodes potential, are registered separately. The amount and decay of the residual plasma is evaluated from the measurements of post-arc current. The decay times of a few tens of a microsecond give evidence of ions with energies below 1 eV. The origin and effect of slow ions on recovery is discussed.

Measurement of Particles and Vapor Density after High-Current Vacuum Arcs by Laser Techniques

A laser-shadow technique of high time resolution was applied to study the erosion of high-current Cu vacuum arcs in situ. Cathodic processes lead to emission of high-velocity droplets shortly before and after current-zero. Increasing movements of the anodic melt produce large droplets several milliseconds after the arc. The many particles generated are responsible for the slow decay of vapor measured by laser-induced fluorescence (LIF). Densities greater than 1012 cm-3 were obtained near current-zero for the diffuse mode. Because of the optical thickness of the vapor to resonance radiation, radiative transfer had to be considered.

Electrical and pyrometric measurements of the decay of the anode temperature after interruption of high-current vacuum arcs and comparison with computations

Vacuum arcs of up to 20-kA peak current were investigated. The surface temperature of the anode area melted during the anode spot mode was determined by pyrometry and the evaluation of thermionic currents. The measurements confirm the computations of heating and cooling of the anode, taking into account heat conduction melting/solidification, and evaporation. Pyrometrically obtained temperatures agree well with theory. This gives confidence in the heat conduction model and also shows that the boiling temperature was reached during arcing. Another method evaluates currents of a milliampere value after arcs of several kiloamperes and postarc currents of amperes. Experimental observation (e.g., loading of the shield surrounding the contacts) and theoretical analysis of the interfering effects support the idea that the currents measured are due to thermionic emission. >

Numerical Simulation of a Moving High-Current Vacuum Arc Driven by a Transverse Magnetic Field (TMF)

This paper deals with the numerical simulation of the constricted high-current vacuum arc (>15 kA), driven by a transverse magnetic field (TMF), as found in vacuum circuit breakers applying the TMF arc control. The magnetohydrodynamic approach, together with the detailed heat transfer and evaporation equations for the electrodes, is used to describe the arc behavior self-consistently, restricted to 2-D. A newly developed model describes the cathode attachment of the constricted arc, as a large laterally extended foot points, instead of regular cathode spots. The arc maintains itself when the electrode temperatures are higher than 3400 K on the cathode and 2900 K on the anode. This model leads to the characterization of the physical quantities of the arc plasma and describes the arc motion. A stepwise movement of the arc results due to different instantaneous velocities of the current attachment areas at the cathode and anode.

Optical investigations of dynamic vacuum arc mode changes with different axial magnetic field contacts

By using a high-speed charge-coupled device (CCD) video technique, three different axial magnetic field contact systems (i.e., unipolar, bipolar, and quadrupolar systems) are investigated at an arc current of 10 kA. Video recordings were compared to computer simulations of light emission emitted at the side-on of diffuse and diffuse columnar arcs. The computer images reproduced typical trends, such as stronger light intensities in front of the cathode caused by higher-plasma densities in this region. A low-current dc vacuum arc was initiated by contact separation before the high current was injected at a fixed contact distance of 10 mm. Videos were taken from two directions perpendicular to each other to localize the vacuum arc properly. From these investigations, the transient development of vacuum arc under different axial magnetic field profiles can be visualized. The results were interpreted with respect to the behavior of the vacuum arc in the second half cycle after an eventual reignition.

Simulation of a High Current Vacuum Arc in a Transverse Magnetic Field

This paper presents the results of simulations using a model that describes constricted high current (>15 kA) vacuum arcs driven by a transverse magnetic field in a 2-D configuration (parallel rail electrodes). The simulations investigate a number of cases of practical interest for the use of vacuum interrupters. The influence of the electrode gap distance on the arc motion is discussed. It is found that faster arc velocities are obtained for larger gaps. For large gaps (ges5 mm), the Lorentz forces and pressure gradients acting on the plasma jets originating from the hot electrodes strongly affect the arc structure. The arc tends to expand on a longer distance and can efficiently preheat the next area of current attachment. The model also describes the jump of the arc over an electrically nonconductive part of an electrode (slit). This is possible due to the ability of the arc column to expand in the direction of motion and to prepare current attachment at a point beyond the slit. The characteristics of the jump depend on a function of the slit width, electrode gap, and current. Finally, the thermal effect on the electrode surface and the electrode bulk for an arc returning several times to the same position is investigated for a fixed DC current. The results show that the minimum surface temperature increases the first few times the arc returns, before stabilizing at a temperature given by the balance between the arc heat flow and the cooling by metal evaporation and conduction into the electrode.

Numerical simulation of a moving high-current vacuum arc driven by a transverse magnetic field(TMF)

This paper deals with the numerical simulation of the constricted high-current vacuum arc (>15 kA), driven by a transverse magnetic field (TMF), as found in vacuum circuit breakers applying the TMF arc control. The magnetohydrodynamic approach, together with the detailed heat transfer and evaporation equations for the electrodes, is used to describe the arc behavior self-consistently, restricted to 2-D. A newly developed model describes the cathode attachment of the constricted arc, as a large laterally extended foot points, instead of regular cathode spots. The arc maintains itself when the electrode temperatures are higher than 3400 K on the cathode and 2900 K on the anode. This model leads to the characterization of the physical quantities of the arc plasma and describes the arc motion. A stepwise movement of the arc results due to different instantaneous velocities of the current attachment areas at the cathode and anode.

Kinetic Numerical Simulation of the Cathode Attachment Zone of Constricted High-Current Vacuum Arcs

This paper is devoted to numerical simulation of the cathode attachment zone of constricted high-current vacuum arcs driven by a transverse magnetic field. With help of particle-in-cell and direct simulation Monte Carlo methods, a 1-D model of the attachment zone was developed, and the stationary-cathode-spot mode was investigated. The states of the charged particles and atoms in the Knudsen layer, the ionization layer, and the plasma sheath are determined in detail. The results support the adaptation of simplified cathode attachment models to be able to reduce the computational effort needed for self-consistent numerical simulations of magnetically driven constricted high-current vacuum arcs.