Erhard Hantzsche

Mysteries of the arc cathode spot: A retrospective glance

The properties and the behavior of arc spots on cathodes, especially in vacuum arcs-the purest form of electrical discharges-are most surprising and very difficult to comprehend and to disclose at first glance. Their experimental exploration and theoretical interpretation took several decades and the task is not yet completed, in spite of many efforts and much progress. It remains an exciting problem and a challenge for future physical investigations, mainly due to the highly complex nature of arc spot operation, which calls for joint endeavors of several disciplines of physics, mathematics, chemistry, and material science. The effort is justified also by the technical applications and their requirements. I point out as a personal view some of these characteristic problems in the understanding of arc spots without claim to completeness. The main issues discussed are the cathode as the decisive electrode for the existence of electrical discharges, comparison with the anode, the strange properties of vacuum arc spots, their relation to glow cathodes and high pressure arc cathodes, the necessarily limited parameter range of arc spots, the astonishing, and the miraculous interplay of very different processes in arc spots cooperating in such a way to implement all the conditions to enable vacuum arcs, the conditions within the expanding cathodic plasma cloud (only briefly discussed) and, finally, arc spots as complex thermodynamic systems and self-organizing dissipative structures.

A hydrodynamic model of vacuum arc plasmas

The properties of plasmas expanding from cathode spots of vacuum arcs are calculated with a one-dimensional two-fluid model. The system of simplified hydrodynamic equations can be solved under stationary conditions using asymptotic power series. Although necessarily only an approximation, such analytical solutions prove to be advantageous compared with numerical integrations. All the plasma parameters are functions of (I/r)/sup 2/5/ (current, I: distance, r). The three forces accelerating the ions to high kinetic energies are quantitatively calculable: the electric field, the ion pressure gradient, and the electron-ion friction. The potential is decreasing towards the anode, and the residence of the plasma is negative. The ion temperature reaches only about 35% of the electron temperature. Although only asymptotic, the solution is suited to describe the arc plasma in a sufficient manner all over the expansion region. >

Consequences of balance equations applied to the diffuse plasma of vacuum arcs

By means of balance equations, the partial currents in vacuum arcs are represented by some simple coefficients, and it is shown that the surprising properties of the expanding diffuse arc plasma can easily be explained if the plasma temperature near the cathode is 4.5+or-0.5 eV (in the case of Cu), i.e., by a factor three times higher than that measured and presumed in most studies. Evidence for this high temperature comes from both the plasma energy balance and the Saha equation. >

Why vacuum arc cathode spots can appear larger than they are

The visual appearance of arc cathode spots in vacuum is studied experimentally and theoretically. Emission photographs of the spots taken with line radiation have a broad light profile with a rather flat slope (proportional to r/sup -/spl beta// with /spl beta//spl ap/2, r being the distance from the spot center), while photographs taken in absorption are small, having a sharp edge with a steep slope of the profile (/spl beta//spl ges/4). Emission photographs from the continuum are similar to absorption photographs. Theoretical analysis shows that the emitted line radiation cannot stem from the locus of excitation. As a consequence, the particles are excited at the edge of the dense spot core, but they radiate at a greater distance due to the finite lifetime of the excited levels and the plasma expansion. Thus, emission photographs from line radiation indicate a greater spot size (about 100 /spl mu/m) than corresponding to the active spot radius which amounts to /spl les/10 /spl mu/m. This statement holds for discharge durations from 10 ns up to at least 100 /spl mu/s. The spots exist not only at ignition but during the whole time of the discharge, the location varying due to the spot movement. Absorption photographs show a small size of 10-20 /spl mu/m still 200 /spl mu/s after ignition. >

Validity conditions for complete and partial local thermodynamic equilibrium of nonhydrogenic level systems and their application to copper vapor arcs in vacuum

Validity conditions for complete and partial local thermodynamic equilibrium (CLTE and PLTE) of homogeneous, time-dependent, and optically thin plasmas are derived. For Cu I, electron densities of n/sub e/>or=(5*10/sup 22/-5*10/sup 23/) m/sup -3/ are required for the establishment of CLTE. For Cu I and Cu II, n/sub e/>or=(5*10/sup 21/-5*10/sup 21/-5*10/sup 22/) m/sup -3/ is necessary for PLTE (for electron temperatures of 1-2 eV). Application to low-current copper vapor arcs in vacuum shows that CLTE can be expected for r >

A revised theoretical model of vacuum arc spot plasmas

The quasi-stationary hemispherical expansion of the cathodic plasma in vacuum arcs can be modeled with hydrodynamic two-fluid equations. In any case, the state of the plasma is determined by the only variable (I/r)/sup 2/5/ (with current I, distance r). In order to avoid some deficiencies of the model (as published) and to investigate more carefully the dependence of the plasma parameters on the arc current, the known analytic solution to the problem is improved by taking into consideration the variability of the Coulomb logarithm and the dependence of the boundary conditions on I. These effects are treated separately. Examples are used to illustrate the new results, with particular emphasis on ion acceleration. The influence of the above factors turns out to be rather unimportant. Quantitatively, they cause some shifts, but no qualitative change of the basic behavior of the plasma is seen. >

Arcing through a thick B/sub 4/C layer

The traces of strong erosion found on solid components covered with thick (0.17 mm) B/sub 4/C-layers facing the edge of a fusion plasma are identified as relicts of arcing. Spots of light observed on the surface seem to exist during the whole lifetime of the fusion plasma (4...5s) and stay motionless despite the strong external magnetic field (B=2.3 T). The related big craters are single cylindrical holes reaching through the B/sub 4/C-layer down to the Cu-substrate. In subsequent discharges the re-ignition of a new arc at the location of an old crater was found to be very probable. The interesting peculiarities of ignition and burning of arcs on B/sub 4/C-layers have been confirmed in laboratory experiments (B=0.4 T) revealing that the arc current has remarkably low noise. Theoretical investigations show that a thermal runaway does not exist because of the rise of the conductivity of the semiconducting B/sub 4/C with temperature. Long living arcs influence strongly the stability of the imbedding fusion plasma and the final erosion of the substrate material at the bottom of the crater holes reduces the suitability of B/sub 4/C as coverage material.

On the appearance of vacuum arc cathode spots imaged by the emitted light

The present paper discusses the appearance of arc cathode spots observed in emission. Photographs yield a size of about 100 micrometers when using line radiation, whereas imaging by absorption techniques or emission pictures with continuum radiation result in values of about 10 micrometers , comparable to the crater traces left at the surface. Besides the size, the slope of the spot profiles is considered. Experimentally, it is found that the light intensity decreases with the distance r from the spot center proportional to r-2. This slope is much less than the expected dependence proportional to r-(beta), (beta) > 4, i.e. the observed spot edge is much less sharp than expected. The behavior of the radiation is theoretically studied by modeling the radial dependence of particle densities and temperature. It is shown that the line radiation stems from a region which is greatly influenced by the plasma expansion in competition with the finite transition probability of excited levels. It is concluded that emission pictures of cathode spot yield considerably higher spot diameters than corresponding to the spot core.

Approaches to two-dimensional models of expanding vacuum-arc plasma

Multifluid equations describing the plasma of vacuum arcs expanding anisotropically from a cathode spot are given and discussed. Some first and preliminary results from an approximate analytical integration of such a system of equations are presented. Though the dependence of the plasma parameters on the direction is weak, the inclusion of angular terms and angular equations changes some results significantly, compared with the experiences from usual 1D models.